THE 'UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING A MATHEMATICAL MODEL DESCRIBING THE INSULIN SECRETORY RESPONSE OF THE PANCREAS IN THE DOG John A, Campbell A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Bioengineering Program 1967 December, 196'7 IP-80O

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ACKNOWLEDGEMENTS The helpful guidance and assistance of several faculty members and organizations has made this investigation possible. A sincere thank you is extended to the following: Assistant Professor Peter Ho Abbrecht, Chairman Doctoral Committee, for his helpful suggestions and stimulating discussions throughout this projecto Associate Professor John C. Floyd, Jr., and the Metabolism Research Unit of the Department of Internal Medicine for their assistance in providing equipment, insulin-I-131, and consultation on the insulin immunoassayo The doctoral committee for their suggestions, directions, and assistance in this investigationo The Department of Physiology for allowing this investigation to be conducted in its laboratories. Eli Lilly and Company for a grant-in-aid providing research supplies National Institutes of Health for support received through the Bioengineering Training Grant and predoctoral fellowships. The Industry Program in the College of Engineering for assistance in the preparation of this manuscript. ii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS.....................................o ii LIST OF ILLUSTRATIONS..o.........o..................... v LIST OF TABLES........ o o.............................. vi NOMENCLATURE.....................ii I INTRODUCTION...o. o.. e.. o.................................... II LITERATURE SURVEY.................................... 4 Mathematical Models................a.................. Insulin Secretion........................................ 11 Pancreatic Tissue Experiments...,.................... 12 Perfused Organ Experiments............................ 14 In Vivo Experiments, Intravenous Glucose Administrationo....................................... 15 In Vivo Experiments' Oral Glucose Administration...... 18 Effects of Other Stimuli........................... 19 III PHYSIOLOGICAL EXPERIMENTAL PROCEDURES.................... 25 Surgical Preparation................................... 25 Collection of Blood Samples............................. 26 Glucose Infusion....................................... 26 Experimental Protocol................................... 27 IV APPARATUS AND ANALYTICAL PROCEDURES..................... 29 Glucose Analysis..................................... 29 Insulin Analysis........................................ 35 Reagents for Insulin Analysis...................... 37 Analytical Procedure................................ 39 V MATHEMATICAL METHODS................................. 43 VI RESULTS................................................. 52 Experimental Results.................................. 52 Mathematical Model.................................... 52 Multivariate Statistical Analysis....................... 73 iii

TABLE OF CONTENTS (CONT'D) Page VII DISCUSSION................................... 75 Experimental Results.................................... 75 Mathematical Model...................................... 76 Multivariate Statistical Analysis.......................79 Spectral Analysis...................................79 Conclusions..................................... 80 APPENDIX A EXPERIMENTAL DATA AND PREDICTED PANCREATIC VENOUS INSULIN CONCENTRATIONS FOR ALL THE EXPERIMENTS................... 82 B THE COMPUTER PROGRAM FOR CORRELATING THE BLOOD GLUCOSE AND THE PANCREATIC VENOUS PLASMA INSULIN CONCENTRATIONS.. 106 C THE COMPUTER PROGRAM FOR THE INSULIN ASSAY CALCULATIONS.. 121 BIBLIOGRAPHY..................................... 129 iv

LIST OF ILLUSTRATIONS Illustration Page 1 Experiment in Progress......................... 28 2 Flow Chart for On-line Glucose Analysis........... 30 3 Standard Curve for On-line Glucose Analysis.......... 3 4 Standard Curve for the Insulin Assay................ 42 5 Intervals used in Hotelling's T Test............... 49 6-19 The Insulin Secretory Response of the Pancreas for all the Experiments Showing Measured and Predicted Pancreatic Venous Insulin Concentrations and the Arterial Blood Glucose Concentration e............... 53-66 20 Time Lags for the Model Represented by Equation (5.1) for all the Experiments....... o................. 68 21 Coefficients for the Model Represented by Equation (5.1) for all the Experiments...................... 69 v

LIST OF TABLES Table Page 1 Proportioning Pump Tube Sizes.......................... 31 2 Comparison of On-line and Manual Glucose Measurements for Whole Blood...........oo o...................... 36 3 Glucose Content of Whole Blood, Plasma and Red Cells.... 36 4 Preparation of the Insulin Assay Tubes for the First Incubation.oooooooooooo.................. ooo.ooooooo... 40 5 Time Lags and Coefficients for the Model Represented by Equation (5,1) for all the Experiments.................. 67 6 The Normalized Integral of the Square of the Error for the Models Represented by Equations (5.1 - 5.7)........ 71 7 The Effect of Variations in the Pancreatic Venous Blood Flow Rate.. eoo...,, o..........ooo........... o.......... 71 8 The Normalized Integral of the Square of the Error for Models Represented by Equations (5o8, 5.9, 5.10)....... 73 9 Comparison of Different Models using Hotelling's T2 Test.................................................... 74 10-23 Experimental Data and Correlations for all the Experiments..... o...............oooo...oo.oo........... 82 -105 24 Symbols used in the Computer Program for Correlating the Blood Glucose and the Pancreatic Venous Plasma Insulin Concentrations...o..ooooo oo.oo...,.,oooo..oo... 108 25 Symbols used in the Computer Program for the Insulin Assay Calculations....oo..o........ ooo...o..eo...o.oooo. 122 vi

NOMENCLATURE Symbol Meaning Units BZERO Quantity of Trace Insulin bound by the Antibody in the absence of unlabelled insulin counts/min CPM Radioactivity, insulin assay samples counts/min ERROR(N) I(N) - INS(N) MU/ml F F Statistic FVI Plasma Insulin Concentration, Femoral Vein [U/ml G Blood Glucose Concentration, Femoral Artery mg/100 ml I Calculated Insulin Concentration, Pancreatic Vein U//ml INS Measured Insulin Concentration, Pancreatic Vein pU/ml K1 Coefficient, blood glucose term (iU/min)(mg/100 ml)1 K2 Coefficient, derivative term (iU/min)(mg/100 ml) min K3 Coefficient, peripheral insulin term ([iU/min) (kU/ml)peripheral K4 Coefficient, constant term tU/min N Time index min N Number of Experiments (in equation(59.12)) p Number of groups into which each expeiment is divided PBZ Fraction of Trace Insulin bound by the Antibody in the presence of unlabelled insulin t Time min T HotellingTs T Statistic T Integration Limit (in equation (59)9) min vii

NOMENCLATURE (CONT'D) Symbol Meaning Units T Time Lag min V Pancreatic Venous Catheter Blood Flow Rate ml/min X1 Index, Experiment Number X2 Index, Model Number X1MAX Total Number of Experiments Y Mean Vector [U/ml Subscripts Cc Control C x Unknown Plasma Sample viii

I. INTRODUCTION The objective of this research was to study the dynamic response of the pancreas to regulated changes in arterial blood glucose and to develop a mathematical model describing this response. Knowledge concerning the regulation of insulin secretion is of importance both in obtaining a better understanding of the physiology of the pancreas and in improving the methods used for treating diabetes. There have been many studies of the factors which effect insulin (36) secretion. In 1937 London and Kotschneff(3 administered glucose orally to dogs and demonstrated increased amounts of substances having a blood sugar lowering property in pancreatic venous blood. In 1947 Anderson and Long(3), using a perfused rat pancreas, demonstrated that the administration of glucose was a stimulus which evoked increased levels of insulin-like activity in blood as detected by an in vivo bioassay using adrenodemedullated, alloxan-diabetic, hypophysectomised rats. Other investigators measured insulin-like activity or immunoreactive insulin in pancreatic venous blood at several intervals following the administration of glucose, but their results were not extensive enough to describe fully the insulin secretory response of the pancreas(l0, 14, 32, 39, and 56) The formulation of a quantitative expression describing the response of the pancreas requires the precise measurement of both the stimuli to, and the response of the organ over a sufficiently long period of time. The development of immunological techniques for the measurement of insulin in small volumes of plasma and the development -1 -

-2 -of equipment for the monitoring of blood glucose has facilitated the study of the dynamics of insulin secretion. With time histories of the glucose input and the insulin response obtained by utilizing these techniques it should be possible to apply the methods of engineering systems theory to the analysis of pancreatic endocrine function. Although the pancreas is not a precisely linear system, a linear model can be used to estimate its response over a limited range of operating conditions. In engineering systems theory systematic methods of mathematical analysis have been developed to study the response characteristics of dynamic systems. In this present work these methods have been utilized in the study of the dynamics of insulin secretion by the pancreas in response to the stimulus, glucose. The development of mathematical models describing biological systems has enabled investigators to state more clearly the relationships between given variables in a particular system. Having postulated certain relationships between experimental variables, it is possible to design experiments which will test the proposed model. Experimenting with the model can often result in new insights into the real system. The information obtained from working with a model for several hours might take months to obtain from the real system. After having studied a mathematical model it should be possible to conduct the most critical experiments on the real system. In this study mathematical models have been developed to describe the insulin secretory response of the pancreas to stimulation with glucose The models predict the insulin concentration in the pancreatic vein from the time history of the arterial blood glucose

-3 -concentration and the femoral venous insulin concentration. After studying a number of models which have been used to describe similar biological and physical systems, several models have been proposed for the pancreas. Using experimental data the parameters of these models were determined by a least squares procedure. The various models were tested against the experimental data using statistical methods. The possibility of applying power spectral analysis to obtain a transfer function for the insulin secretory response of the pancreas was also investigated.

IIo LITERATURE SURVEY Mathematical Models Several investigators have developed mathematical models to describe different endocrine control systems. Models describing the regulation of hormone secretion from the thyroid, parathyroid, and adrenal glands will be reviewed. A more extensive discussion of models describing the relationships between blood glucose and insulin secretion will then be made. These models will be reviewed in the chronological order of their development Roston(53) has applied mathematical analysis to a series of endocrine systems. He described the regulation of thyroid function by two simultaneous differential equations. One equation represents the rate of change of the thyroxine concentration outside of the thyroid gland and the other, the rate of change of the thyroid stimulating hormone outside the pituitary gland. Parathyroid function was analyzed using a system of three differential equations to describe the relationships between parathyroid hormone, calcium ion, and phosphate ion concentrations in extracellular fluid. The regulation of water and electrolyte balance was also described mathematically. A system of four differential equations was written to describe the relationships existing between the extracellular fluid volume, antidiuretic hormone, sodium ion, and aldosterone concentrations The differential equations describing these endocrine systems were solved by using Laplace transformso In these models only proportional relationships between the controlling and the controlled variables -4 -

-5 -were used, the effects of time lags between stimulus and response were not included, and the theoretical equations presented were not tested with experimental data. ([5) Norwich and Reiter(5) developed a mathematical model describing the relationship between the plasma concentrations of the thyroxine and thyroid stimulating hormone, TSH. In their model they assumed that the release of thyroxine from the thyroid is proportional to the plasma TSH concentration, and that thyroxine is degraded at a rate proportional to its own concentration. Other assumptions were that TSH is released by the anterior pituitary at a constant rate, that it is destroyed at a rate proportional to its own concentration, and also the thyroxine concentration. The constants appearing in the solutions of these equations could not be determined, since the necessary data were not available. Yates and Urquhart(6) studied the control of plasma concentrations of cortisol and corticosterone. They described the regulation of the adrenal cortical system by a closed-loop feedback control system with a variable set point. The set point and feedback effect were observed for corticoids but not for adrenocorticotropi'c~ hormone. Adrenal secretion was observed to be independent of adrenal blood flow. The rate of removal of corticoids followed a first order process and was delayed when hepatic blood flow was reduced. The total concentration of plasma corticoids showed diurnal variations within a subject. Different subjects at the same time of day exhibited different plasma corticoid concentrations and the same subject, observed at the same time of day showed day-to-day variations.

-6 -The negative feedback system controlling adrenal corticoid secretion was represented by a system equation, (2.1), giving the concentration of corticoids in the plasma, and a controller equation, (2o2), giving the secretion rate. dC c - =V d (2.1) ci= max -K Cp (2.2) where: ci = Manipulatedvariable-inflow rate, corticoid secretion Co = Load = Corticoid removal rate = k C cmax = Maximum secretion rate Cp = Controlled variable = Plasma corticoid concentration K = Proportional controller gain constant k = Rate constant V = Volume for corticoid distribution This model of the adrenal cortical system which incorporates the concepts of a load and a variable set point describes diurnal variations and rapid changes in plasma corticoid concentration which have been observed in healthy subjects. Previous models of this system were not adequate to describe diurnal variations and rapid changes in hormone concentration. Models for the Regulation of Glucose Metabolism and Insulin Secretion A mathematical model describing the time varying changes in blood insulin and glucose concentrations occurring during intravenous glucose and insulin tolerance tests was presented by Bolie(7 in 1960. The model consisted of four ordinary differential equations representing

-7 -changes in the quantities of insulin and glucose in the extracellular and the intracellular spaces. Seventeen independent parameters were required to describe the regulation of blood glucose and insulin. The rate of pancreatic insulin production was described by equation (2.3). I1(G) = Il(G%) + (G - Go) K1 (2,3) where: Ii = Rate of pancreatic insulin production G = Intravascular glucose concentration Go = Mean physiological value of G K1 = a I G = G An analog computer was used to simulate the results of glucose and insulin tolerance tests on subjects. Numerical values of physiological parameters were determined from the computer potentiometer settings that most closely reproduced the normal response curves. Seed and co-workers(5) have presented a model describing the changes in glucose concentration occurring during glucose metabolism. Their model consisted of a four compartment system described by four differential equations. The four compartments used in their analysis were: 1) the plasma volume, 2) a "fast" compartment, in which the glucose concentration may change rapidly, 3) a "slow" compartment in which only gradual changes in glucose concentration can occur, and 4) the red blood cells. The model fitted data obtained from the first 65 minutes of a glucose tolerance test. The model has not included the effect of insulin on the transport of glucose, however the model includes an arbitrary substance, Z, which increases and decreases in the "fast" compartment with corresponding changes in glucose concentration.

-8 -When the concentration of Z falls below a critical value, Z is defined as having the function of stimulating hepatic glucose release. The authors believed that Z is not the same as insulin, since insulin is released too slowly and has too long a half-life to account for rapid oscillations in the blood glucose concentration. On analyzing several sets of experimental data, the authors found the set of parameters giving the best fit for one experiment did not describe the other experiments adequately and the set of parameters best describing one experiment did not correspond to the physiologically most probable values. Ackerman and co-workers) developed a mathematical model describing the oral glucose tolerance test. The model considers the various sources and fates of glucose and insulin in the subject. The rates of change of the blood insulin and the blood glucose concentrations are given by equations (2.4 and 2.5), respectively. dI klI + k2 + k3G (2.4) dt ~ t k4G+ k5-kI+A (2.5) where: G = Blood glucose concentration I = Blood insulin concentration A(t) = Rate of increase of blood glucose due to absorption from intestines. kl = Rate constant for the degradation of insulin. k2 = Rate of secretion of insulin, independent of glucose k3 = Rate constant for the secretion of insulin due to glucose k4 = Rate constant for the removal of glucose independent of insulin.

k5 = Average rate of release of glucose into blood. k6 = Rate constant for the removal of glucose dependent upon insulin. In Equation (2.4) the rate of degradation of insulin is proportional to the plasma insulin concentration and the rate of secretion of insulin is controlled by a glucose independent term, k2, and by a term which is proportional to the blood glucose concentration, k3G. A similar equation, (2.5), was written to describe the time varying plasma glucose concentration. These two first order differential equations were combined to form one second order equation which was integrated to give equation (2.6). -at G= GF + A e sin 0t (2.6) where: G = Blood glucose concentration GF = Fasting blood glucose concentration A = Undamped amplitude of the glucose curve a = Damping coefficient = ~(kl + k4) 2 2~ = (Wo -a ) = frequency 0o = (klk4 + k3k6)2 = resonant or natural frequency, k's have been defined with equations (2.4) and (2.5) The natural frequency of this system is related to the rates of glucose removal and insulin release and removal. The damping coefficient is related only to the rates of removal of insulin and glucose. Data from normal and diabetic glucose tolerance curves were fitted with this equation. The following parameters characterize the glucose tolerance test: fasting blood sugar, undamped amplitude of blood

-10 -glucose curve, damping factor, damped frequency, and resonant or natural frequency. Of these only the resonant frequency appears to be an adequate criterion for distinguishing diabetic from non-diabetic subjects. (2) In a later paper Ackerman reported studies on the effects of various oral glucose loads and intestinal absorption rate on simulated glucose tolerance tests. The model could be fitted using five or six points on the glucose and immunoreactive insulin response curves in most cases, but in certain cases many more points on the curves would be needed to fit the models and make satisfactory interpretations. Janes and Osburn(31) used analog computer techniques to simulate glucose absorption and the blood glucose concentration in the rat and rabbit following oral glucose administration. Their model consisted of two differential equations expressing the time varying glucose and insulin concentrations. The insulin equation stated that the rate of change of the plasma insulin concentration was directly proportional to the blood glucose concentration and that insulin was destroyed at a rate proportional to its concentration. The parameters in the model were adjusted to fit experimental blood glucose data. No insulin measurements were made. The model predicted the maximum glucose concentration in the peripheral blood following the administration of glucose orally. It should be noted that this report assumed values for glucose released by the liver and did not consider glucose uptake by the liver which may occur following a glucose feeding in a fasted animal. A mathematical description of the peripheral venous blood

-11 -glucose concentration during an intravenous infusion of a hypertonic (9) glucose solution was developed by Brodan o Differential equations were written to relate the infusion rate to the plasma glucose concentration, the renal excretion rate and the metabolic rateo The effect of the blood glucose concentration on the pancreas and the subsequent effect of insulin on glucose transport were not included in this model. Methods for obtaining the parameters of the equations were outlined, but values were not given'-nor was the model tested with experimental data. Cerasi(3) recently described a mathematical model of the blood glucose and plasma-insulin system. He represented the increase in the plasma insulin concentration following an intravenous glucose load as the sum of two terms, one representing preformed insulin that was released immediately upon the intravenous administration of glucose as a function of the blood glucose concentration and another representing insulin that was synthesized and released after a glucose load was given. Using this model it was possible to simulate the peripheral venous blood glucose and plasma immunoreactive insulin responses during intravenous glucose tolerance tests in many subjects. Insulin Secretion Recently several investigators have studied the effects of various stimuli on the rate of insulin secretion. The stimuli include glucose, other sugars, metallic ions, sulfonylureas, and hormones. The insulin secretory response of the pancreas has been studied using pancreatic tissue, perfused organs, and intact animals. In most of

-12 -the experiments the number of samples of plasma analyzed. for insulin was not sufficient to establish a quantitative relationship between the stimulus and the response. Pancreatic Tissue Experiments (18) Creutzfeldt and co-workers studied the effect of varying the concentrations of glucose and other monosaccharides in the incubation medium on the release of insulin-like activity (ILA) from rat pancreatic islets incubated in vitro. The ILA of the incubation media (52) was measured by the rat fat pad method(5 after 30 minutes of incubation and then at intervals of one hour for five hours of incubation of the pancreatic tissue. The ILA in the medium increased when the incubation time or the glucose concentration or both were increased. After three hours a maximal level of ILA was attained. Pancreatic tissue was transferred successively between incubation media containing alternately high and low glucose concentrations. The observed secretion rate of insulin was higher when the glucose concentration was higher, and lower when the glucose concentration was lowero Other monosaccharides tested failed to produce an increase in ILAo Since incubation for 120 minutes in 20 mM glucose resulted in the secretion of only five to ten percent of the extractable insulin, the authors felt that only dissolved insulin was released and no true secretion occurred under these conditions. Coore and Randle(67) have studied the regulation of insulin. secretion using in vitro preparations of pieces of rabbit pancreas. An immunoassay was used to measure the insulin concentration in the incubation mediae The rate of pancreatic insulin output was measured

-13 -in the absence of glucose and at glucose concentrations ranging from 0.35 mg/ml to 20.0 mg/ml. There was some insulin output.even in the absence of glucoseo The rate of insulin release observed at a glucose. concentration of 0.70 mg/ml was double that observed in the absence of glucose. The.rate of insulin release was observed to increase with increasing glucose concentrations in the media, however the response tended to plateau at the high glucose concentration. The effect of various monosaccharides on the rate of insulin secretion was investigatedo Of the sugars.-tes-ted'd-glucose and d-mannose produced the greatest responses. The. effects of growth hormone, epinephrine, adrenal cortical trophic hormone, glucagon, and thyroxine were also studied. The only hormones which distinctly 'affected insulin secretion were glucagon, growth hormone and epinephrine. Addition of glucagon to media containing glucose and pancreatic tissue resulted in augmented insulin secretion. Addition of growth hormone or epinephrine to media containing glucose and pancreatic tissue inhibited insulin secretion. It should be noted. that this in vitro effect of growth hormone on pancreatic tissue is different from its systemic effecto Parry and Taylor(^4 have shown that glucose increases the rate of incorporation of leucine into the insulin molecule in slices of ox pancreas.. The rate of incorporation of tritiated leucine was considered to be.a measure of the rate of insulin synthesis. Increasing the concentration of either glucose or mannose in the media augmented insulin synthesis while galactose had no effecto (37) Malaisse and co-workers studied the effects of glucose, insulin and anti-insulin serum on insulin secretion using isolated

-14 -islets of rat pancreas. An immunological method was used to measure insulin concentrations in the media. Insulin secretion increased with increasing concentrations of glucose in the media. Secretion was not affected by the presence of anti-insulin serum or rat insulin. Perfused Organ Experiments Using an isolated perfused rat pancreas Anderson and Long(3) studied the relationship between the glucose concentration in the perfusing solution and the amount of insulin secreted. They measured the insulin concentration in the perfusate by observing the blood sugar lowering effect of the perfusate when it was injected into adrenaldemedulated diabetic hypophysectomized rats. An observation of blood sugar lowering was interpreted as evidence of the presence of insulin in the perfusate. Their results showed that a high glucose concentration (141-569 mg/100 ml) stimulated the secretion of insulin, and that a low glucose concentration (35-84 mg/100 il) did not result in the secretion of a detectable amount of insulin. Grodsky and associates(26) studied the insulin secretory response of the isolated perfused rat pancreas to the pulse administration of glucose and glucagon. The stimulating substance was rapidly injected into the arterial cannula and the total effluent from the pancreas was collected at 30 second intervals for the subsequent 4-5 minutes. Immunoassay of the effluent showed that the insulin concentration in the perfusate increased within 30 seconds indicating a prompt response. The insulin levels followed the rise and fall of the glucose concentration in the arterial cannula. Insulin secretion was significantly reduced

-15 -30 seconds after terminating the stimulus showing there was no pancreatic memory In Vivo Experiments, Intrayenous Glucose Administration Brown and co-workers(0) showed that infusion of glucose into a portion of the pancreas resulted in systemic hypoglycemia and in histologic changes in the islands of Langerhans, including hyperplasia and hydropic degeneration in that portion of the pancreas o In these dogs a 5-17% glucose- solution was infused into a pancreatic artery via a hepatic artery at a rate of 4.5 mg/kg/min for up to 18 days. Increased insulin release was infered from the peripheral hypoglycemia that occurred during the glucose infusions. If the same glucose infusion was given through the portal vein, no change in peripheral blood glucosewas detected. One of the first reports of pancreatic insulin secretion estimated from the quantity of insulin present in pancreatic venous blood was presented by Metz(39) in 1960. Pancreatic venous blood was collected from seven dogs during controlled infusions of glucose into a femoral vein. The insulin concentration in the plasma was determined using the rat diaphragm method( 0) The plasma insulin concentration in pancreatic venous blood varied from 100 - 9700 p[U/ml with peripheral blood glucose concentrations from 37 - 655 mg/100 mlo Since only one to five insulin measurements were made on each dog, it was not possible to establish whether there was a quantitative relationship between blood glucose concentration and insulin output for a given experiment When the data from all seven dogs were analyzed together, insulin

-16 -output could be related to blood glucose concentration by the following equation (2.8). log I = - 3.14 + 1.64 log G (2.8) where: I = Insulin output (mU/min) G = Blood glucose concentration (mg/100 ml) These data were not adequate to determine whether there were any time lags in the response of the pancreas to changes in blood glucose or to determine any dependence upon the rate of change of blood glucose. The author believed that this may have accounted for the departure of some of the data points from the curves describing the response. The possibility that the pancreas functioned in a negative feedback loop controlling blood sugar was suggested. Seltzer(56) investigated the "insulinogenic" effects of glucose and those of several hypoglycemia-inducing substances. The test substance was injected into a femoral vein during a two to five minute period and the entire effluent from the pancreatic vein was collected during three successive ten minute periods beginning at the start of the infusion. A pancreatic sample was collected before starting the infusion to establish a base line. The insulin content of the plasma was measured by determining the glucose uptake of a piece of rat diaphragm incubated with the unknown plasma. Glucose stimulation induced elevations in the plasma insulin level which were greater and more sustained than those induced by sulfonylureas suggesting that glucose is a more potent stimulus for insulin secretion. Salicylate and indole-3-acetic acid did not produce an insulin secretory response. This was one of the first

-17 -studies of the comparative insulin secretory effects of various hypoglycemia-inducing substances. (32) Kanazawa and colleagues(32) used a radio-immunological assay to measure the insulin concentration in femoral, hepatic, and pancreatic venous blood during and after glucose infusions into a femoral veino Glucose administration produced increased insulin concentrations in femoral, hepatic, and pancreatic venous blood.o This implied that the increased peripheral insulin concentrations resulted from pancreatic insulin secretion. Comparison of the peripheral and pancreatic insulin response curves showed a small secondary peak in the insulin concentration in the pancreatic vein only. The authors suggested that the secondary peak may have been caused by surgical stress or changes in the concentrations of epinephrine and growth hormone resulting from stresso The absence of a secondary peak in the peripheral curves may have been due to changes in pancreatic venous blood flow, changes in hepatic insulin clearance. dilution of secreted insulin in the blood volumne of the dog, or absorption or release of insulin by some peripheral tissue. (23) Gjedde(3) studied the effect of glucose-on the ILA in the pancreaticoduodenal vein and in the femoral artery of dogs. He found that the ILA measured by the rat fat pad method was significantly greater in the pancreaticoduodenal vein compared to the femoral artery and that the pancreatic vein ILA rose immediately following intravenous glucose administration whereas the femoral arterial ILA required ten to 15 minutes to riseo The fasting insulin output of the dog pancreas was estimated to be 300 aTU/kg/mino Insulin was shown to be distributed in 18 + 4% of the body weight (mean + SEM). The half-life of insulin

-18 -was estimated to be 23 + 5 minutes (mean + SEM) from femoral arterial blood samples collected immediately following a pancreatectomy. The blood flow rate in the pancreaticoduocenal vein was 1.95 + o.o68 ml/kg/min (mean + SD). This flow rate was over five times greater than those reported by Metz(39) and Seltzer(56) and was probably due in part to the method used to catheterize the vessels. (27) Hausberger and Ramsay(7) studied the effects of glucose alone, and of glucose together with insulin on the degranulation of beta cells in the guinea pig. They found that glucose alone produced considerable or complete degranulation of the beta cells and that glucose with insulin produced no degranulation or at most very little degranulation. Since degranulation of the beta cells usually represents insulin secretion, they concluded that insulin as well as glucose affected the insulin secretory response of the beta cells. In Vivo Experiments, Oral Glucose Administration Oral and intravenous routes of glucose administration to humans were studied by Elrick and co-workers(20) Rate constants for the disappearance of glucose administered by both routes were determined. Peripheral plasma insulin levels were measured using an immunoassay. Oral glucose resulted in greater and more sustained increases in plasma insulin concentration than did the same amount of glucose administered intravenously. The maximum blood glucose concentration in a typical subject in this study was 135 mg/100 ml and the mean blood glucose difference between the two routes of glucose administration was 4.1 mg/100 ml. Glucose administered intravenously resulted in the higher concentration. The rate constant for the disappearance of glucose was

-19 -independent of the route of administrationo The greater increase in insulin concentration associated with the oral administration of glucose suggested to the authors that ingested glucose stimulated the release of a humoral gastrointestinal factor from the stomach or the upper small intestine or stimulated the release of a factor from the liver, which in some way facilitated insulin secretion. Effects of. Other Stimuli Factors effecting the synthesis, storage release9 transport9 (34) and antagonism of insulin were reviewed by Lazarow ) and by Grodsky and Froshamn25) In a study of the dynamics of insulin secretion, the effects of hormonal and non-hormonal factors on insulin secretion should be consideredo Growth hormone, cortisone9 adrenocorticotropic hormone, glucagon, epinephrine, and insulin itself affect insulin secretion. Growth hormone acts as an insulin antagonist. Excessive levels of growth hormone can cause diabetes and in some cases a diabetic can be improved by hypophysectomyo Growth hormone has been shown to increase plasma insulin-like activity by both a direct effect on the pancreas and indirectly by increasing the blood glucose concentration o Cortisone administration produces hyperglycemia and thus results in increased insulin secretion, and beta cell overactivity and proliferationo Adrenocorticotropic hormone can stimulate the secretion of insulin in adrenalectomized animals. Glucagon administration results in increased insulin secretion when it is injected into animals in which the glucose concentration is maintained constant. In vitro studies have shown that glucagon stimulates insulin secretion directly(51) Unger( ) found glucagon Unger found~~~~~~~~~~~~~~~~~~~~

-20 -that insulin induced hypoglycemia in dogs resulted in elevated plasma glucagon levels. Campbell and Rastogi( studied the effects of glucagon and epinephrine on insulin secretion in dogs. They found that glucagon given intravenously resulted in a three-to-four fold increase in immunoreactive insulin in the pancreatic vein 15-30 minutes following injection. Epinephrine injections resulted in hyperglycemia without any increase in insulin secretion. They believe glucagon caused a transient increase in the rate of insulin secretion. Kris and co-workers (33) studied the effects of epinephrine on insulin secretion in rhesus monkeys. Portal vein insulin levels measured during epinephrine induced hyperglycemia showed no increased insulin secretion. When the epinephrine infusion was accompanied with a glucose infusion, the resulting hyperglycemia did not produce increased insulin secretion either. Epinephrine did not cause any changes in the insulin levels resulting from controlled injections in in vivo or in vitro experiments. Infusion of epinephrine into a carotid artery has shown that its site of action on insulin secretion is not in the brain. Porte and co-workers(49) studied the effect of epinephrine and glucagon on immunoreactive insulin levels in humans. Intravenous administration of epinephrine resulted in hyperglycemia without any increase in immunoreactive insulin levels during the infusion. Within 15 minutes after the end of an epinephrine infusion the peripheral immunoreactive insulin level increased from 12 pU/ml to 41 iU/ml in a typical subject. Intravenous administration of glucagon resulted in hyperglycemia and increased insulin secretion. The insulin levels attained during glucagon induced hyperglycemia were higher than those

-21 -produced during glucose infusions resulting in the same blood glucose level. When glucagon and epinephrine were administered together the insulin secretory response was less than that produced by glucagon aloneo One hour after the combined infusion was stopped the insulin level was higher than the level observed-one hour after the end of an infusion containing only glucagon. These experiments have shown that epinephrine inhibits insulin secretion-and that glucagon administration produces a greater response than would. result from hyperglycemia alone. The authors suggested that the mechanism of action of epinephrine on insulin secretion may be due tp an effect of epinephrine on the microcirculation of the pancreas, the production of a substance by epinephrine which in turn inhibits insulin secretion, or the accelerated degradation of insulin. Logothetopoulos and co-workers(35) investigated the effects of hyperglycemia and prolonged treatment with insulin on the pancreatic inSulih content in rats. Hyperglycemia was'produced in the rats by the infusion of a 20 percent glucos:e solution into a jugular vein. Three different infusion schedules were.followedo The pancreatic insulin content was measured in terms;of beta cell granulation, zinc content, and extractable insulino All three quantities decreased' progressively and simultaneously With increasing blood glucose concentrations and increasing periods of,hyperglycemia. The effect of prolonged insulin treatment on insulin content of the pancreas was studied by administering increasing doses of insulin to rats until a dose of 7-9 U/day was reachedo This dose was then given for 4 - 6 weeks, The amount of extractable insulin measured in two groups of treated rats was 4 percent of that measured in control rats.:demonstrating that high peripheral

-22 -insulin concentrations tend to inhibit insulin production. Floyd and associates(65) showed that some essential amino acids are stimuli for insulin release. They measured the levels of immunoreactive insulin in peripheral plasma in humans following protein meals, and after oral administration of leucine and intravenous doses of some individual essential amino acids and mixtures of essential amino acids. Of the ten individual amino acids tested L-arginine produced the strongest insulin secretory response and this response was equalled by that of the mixture of the ten essential amino acids. Leucine was intermediate in potency and valine was least potent. Histidine was unique in that it caused modest decreases in the levels (48) of plasma insulin. This effect was accentuated when dexamethasone was administered for three days prior to histidine infusions. Metallic ions have a significant effect on insulin secretion. Zinc complexes readily with insulin but is not required for insulin to be biologically active. Some workers have suggested that zinc is required for the release of stored insulin. Cobalt also combines with insulin readily, but there is little evidence that it is necessary for insulin synthesis or release. Calcium has been shown to be absolutely (24) necessary for insulin release. Grodsky(2) studied the perfused rat pancreas in a medium free of both calcium and magnesium and found that no insulin was secreted. Addition of 0.2 mM calcium ion restored insulin secretion. Seltzer and co-workers(57) studied the effects of prolonged sulfonylurea administration on the insulinogenic response of the dog pancreas to intravenous glucose. Pancreaticoduodenal venous blood was

-23 -collected during controlled glucose infusions and its insulin concentration was measured using an immunological method. Prolonged sulfonylurea administration did not alter the insulin secretory response of the pancreatic beta cells to infused glucose. The action of tolbutamide on the pancreas was studied by Colwell and Metz(l4) One gram of tolbutamide was administered to dogs over a period of five minutes. Pancreatic venous blood was collected prior to the start of the infusion and for four ten minute periods following the infusion. The plasma insulin activity was measured by the rat diaphragm method. The results showed the maximum insulin activity to occur during the first ten minutes after the beginning of the tolbutamide infusion. The range of the maximum insulin concentration following the administration of tolbutamide to the test dogs was from 70 to 175% of the base line insulin concentration. Saline infusions given to control dogs elicited no responses. This study showed that tolbutamide stimulates the release of insulin from the pancreas. Hormones, essential amino acids, sulfonylureas, and metallic ions have been shown to effect insulin secretion. In the work to be described it will not be possible to measure all of these factors. None of the dogs used had been treated with drugs prior to the experiment. Since all dogs were fed the same diet, no significant differences should exist which could be attributed to differences in plasma essential amino.acid or metallic ion concentration. Variations in glucagon, growth hormone, and epinephrine levels may vary from dog to dog due in part to stress and individual differences. These variations are not easily measured and may be the cause of some otherwise unexplained

-24 -variations in the insulin secretory response of the pancreas. After studying both the mathematical models and experimental data describing the dynamics of insulin secretion in response to glucose administration, it was apparent that none of the mathematical models gave an adequate description of the response of the pancreas to changes in blood glucose concentration and none of the data published is sufficient to derive a model which would describe this response fully. The model developed by Ackerman(2) provides a good description of the response of the subject to a glucose load but does not describe the action of the pancreas in detail. The model Bolie(7) postulated describes the glucose tolerance test response. Neither of these models includes a term relating the time derivative of the blood glucose concentration to the insulin secretory response of the pancreas. Tepperman(59) suggested that the system may contain such a derivative term and cited experiments by Anderson and Long(3 as support for this suggestion. None of these models considers the existence of lags between glucose stimulation and insulin secretiono Metz(39) in 1960 showed that pancreatic insulin secretion was a function of the arterial blood glucose concentration. His measurements were not made at time intervals short enough to determine the presence of derivative terms or time lags in the system More recently Seltzer(56) Kanazawa(32), and Colwell and Metz(14) have conducted a variety of experiments, previously discussed, in which pancreatic venous insulin concentrations were measured; but none of these reports contained data adequate to answer questions concerning the existence of derivative terms and time lags in the system, The experimental procedure to be discussed in Chapter III is designed to provide data which should enable these questions to be answered,

III. PHYSIOLOGICAL EXPERIMENTAL PROCEDURES To verify the proposed mathematical model describing the insulin secretory response of the pancreas a series of acute experiments was conducted in dogs. In this section the experimental procedure will be described. Description of the analytical methods for the determination of blood glucose and plasma insulin concentrations will be given in Chapter IV. Experiments were designed to measure pancreatic insulin secretion during controlled glucose infusions. Glucose was infused into a jugular vein while blood samples were collected from the pancreaticoduodenal and femoral veins for insulin analysis. Arterial blood glucose was continuously monitored using an on-line analysis system connected to a femoral artery. Surgical Preparation Female mongrel dogs, weighing 20 to 30 kilograms were fasted for at least 16 hours prior to the beginning of the experiment. The dogs were anesthetized with nembutal solution containing 60 mg/ml sodium pentobarbital, administered intravenously. The initial dose was 30 mg/kg and additional doses of 60 mg were given as required by observation of the pupillary reflexes. Immediately following the administration of the anesthesia a tracheostomy was performed to facilitate the animal's ventilation during the remainder of the experiment. The jugular and femoral veins were cannulated using No. 200 polyethylene tubing (ID 1.40 mm, OD 1.90 mm). A midline abdominal incision was made and the pancreas was exposed. A cautery was used in -25 -

-26 -the surgical procedures to minimize bleedingo The duodenum and the right lobe of the pancreas were brought to the incision. Blunt dissection was used to free a section of the pancreaticoduodenal vein from the pancreas. A silicone rubber catheter, ID 0.75 mm, OD 1.50 mm, was inserted into the vein retrograde to the direction of blood flow. The proximal end of the vein was tied off. Next, the femoral artery was cannulated with a No. 50 polyethylene tube, ID 0o580 mm, OD 0.965 mm, and this was connected to the blood sampling tube of the glucose analysis apparatus. Collection of Blood Samples Immediately before cannulation of the pancreaticoduodenal vein the dog was given 750 units of heparin per kilogram intravenously. Pancreatic venous blood was collected by allowing the blood to flow freely from the catheter into heparinized 10 x 75 mm soft glass test tubes held in a beaker of ice water. The pancreatic blood flow varied from 0.15 to 0.50 ml/min. Femoral venous samples were collected at intervals varying from ten to 15 minutes. Two ml samples were drawn from the femoral venous catheter using a syringe and were transferred to 10 x 75 mm test tubes which were stored in an ice water bath until the end of the experiment. Immediately following the experiment all the blood samples were centrifuged at 1100 g. for 20 minutes in a refrigerated centrifuge at 2~ C. Plasma was separated and stored in corked glass test tubes at -20 C. Glucose Infusion The glucose infusion contained 100 grams glucose and 4.5 grams

-27 -sodium chloride per liter. The infusion was given through a jugular vein using a Sigma Motor kinetic clamp infusion pump. Infusion speeds from 1.0 to 6.0 ml/min were used; this is equivalent to 100-600 mg glucose/minute. For a 20 kg dog this is equivalent to 5-30 mg/kg min or 300-1800 mg/kg hr. An infusion speed of 4 ml/min for one hour introduces 24.0 gm of glucose. If this amount of glucose remained in the blood volume (1.5 liters) a rise of 1600 mg% glucose would occur. If this glucose were distributed in the extracellular space (4 liters) also the rise would be 600 mg%. Experimental Protocol Following the surgical preparation of the dog, a ninety minute control period preceded the glucose infusions. During this control period pancreatic venous blood samples were collected for periods of from five to ten minutes depending on the blood flow rate. Femoral venous samples were collected at 15 minute intervals. During this period isotonic saline was infused into a jugular vein at 1-2 ml/min. A series of ramp changes in the dog's blood glucose concentration, i.e., blood glucose increasing or decreasing linearly with respect to time, was produced by varying the speed of the infusion pump in a step wise fashion. When the maximum desired glucose concentration was attained, as observed on the blood glucose concentration recorder, the infusion was changed from a glucose solution to isotonic saline. The saline infusion was continued until the blood glucose concentration had decreased to a constant level, usually about 100 mg percent. Two or three ramp changes in blood glucose concentration were made during an experiment depending on the condition of the

-28 -dog and the time required for each ramp. The rate of increase of blood glucose concentration was varied in order to study the effect of the rate of change of blood glucose concentration on insulin secretion. During these infusions pancreatic venous blood was collected continuously in 1 - 3 ml samples. The time required to collect each sample varied from two to ten minutes. Shorter collection periods were used when the blood glucose concentration was changing most rapidly. Femoral venous blood samples were obtained at approximately fifteen minute intervals. A typical experiment is shown in Fig. 1. Fig. 1 Experiment in Progress............. |~~~~~~~~~~~~~~~~.................. Si~~~~~~~~~s;S~~~~~~~~~~~~~....... 8 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... R~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......... -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~............ - v= S X - g W - - -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......... I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..............~~~~~~~~~ ~ ~ ~ ~ ~ ~ ~.... Fig. 1 Experiment in Progress~~........

IV. APPARATUS AND ANALYTICAL PROCEDURES This section describes the analytical methods and special apparatus used in this investigation. The glucose concentration in the arterial blood of the dog was continuously monitored using a modification of the method developed by Hoffman(28)> Plasma insulin concentrations were determined using the radio-immunological technique developed by Yalow and Berson(63) with the double antibody modification developed by Samols and Bilkus (54o Morgan and Lazarow have also modified the method developed by Yalow and Berson using a different buffer system(4) Glucose Analysis The basis of the Hoffman method for the determination of glucose is the reduction of potassium ferricyanide to potassium ferrocyanide with the concomitant oxidation of glucose to gluconic acid and Other prbducts. This method was adapted for on-line analysis by using a proportioning pump to continuously measure the reagents, a dialyzer to separate glucose from the Whole blood, a delay coil immersed.in a hot water bath to permit time for the oxidation-reduction reaction, a flow cell in a spectrophotometer to serve as a detector, and a recording potentiometer to make a continuous record of the data. The arrangement of the modules is shown ih Figo So (1) Proportioning Pump The proportioning pump is a device for delivering- measured quantities of solutions to a system continuously. It consists of a -29 -

-30 -FEMORAL ARTERY 0.05 ml./min. K3Fe (C N)6 0.25 gm./I. Na2 C 03 20.0 gm/ I. AIR Na Cl 9.0 gm./I. 1.2ml.//min. 2.9 mlJmin. KCN 5.0 gm./I. Na C19.0 gm./I. AIR 2.5 ml./min. 1.2ml/nin, PROPORTIONING PUMP |WASTE 10 ft.xmm. WASTE I 90 C. SPECTROPHOTOMETER 420. my l l 11 RECORDING POWER SUPPLY POTENTIOMETER 6 V. 8 A. Fig. 2 Flow Chart for On-line Glucose Analysis

-31 -manifold of Technicon precision bore Tygon tubes mounted below a roller assembly. Fluid is moved through the tubes by a series of rollers passing over the manifold. Different flow rates may be obtained by varying the tube diameter or the motor speed. The pump is driven by a 1/10 hp motor equipped with a Zero-Max Transmission giving an output shaft speed range from 0-400 rpm. The transmission was adjusted to produce a roller head speed of 13 revolutions per minute. The pump tube sizes used are listed below in Table 1. TABLE I PROPORTIONING PUMP TUBE SIZES Flow Stream Inside Flow Rate Diameter ml/min inches Blood 0.010 0.05 Potassium Cyanide 0.081 2.50 Air 0.056 1.20 Potassium Ferricyanide 0.090 2.90 Flow Cell 0.073 2.00 Debubbler 0.065 1.60 (2) Dialyzer The dialyzer was obtained from Technicon, Inc. It consists of two grooved plastic plates separated by a cellophane membrane, and is held in a stainless steel clamp. The total membrane surface area available for mass transfer is 34.5 cm2. The channel in each dialyzer plate is 2.3 meters long, 1.5 mm wide, and 1.0 mm deep.

-32 -Technicon Type C membranes were used in all experiments. The membrane was wetted with water and stretched tightly in a hoop before being placed between the dialyzer plates. The diatyzerwas operated in a battery jar filled with distilled water at room temperature. (3) Hot Water Bath The hot water bath was constructed from a 12 x 30 inch battery jar, 1000 watt immersion heater, and temperature regulator. The temperature regulator consisted of a mercury thermostat and an on-off relay. The delay coil consisted of three ten foot, 4 mm ID Pryex coils connected end-to-end with Tygon sleeves. (4) Spectrophotometer A Coleman Jr. Model 600 spectrophotometer set at awavelength of 420 mp. was used to measure the changes in the optical density of the analytical reagent. A flow cell was constructed from a piece of black Lucite with clear Lucite windows. The length of the light path was 2 lo90 cm and the area of the beam was 9.61 mm 2 The spectrophotometer power supply was a 6 volt, 8 amp direct current regulated power supply unit. A constant voltage transformer was connected between the laboratory power line and the DC power supply to further stabilize the voltage. (5) Recorder A Brown Electronik recording potentiometer was used to record the spectrophotometer output. The full scale voltage of the recorder was 1.0 mv and the response time for a full scale deflection was less

-33 -than 0.5 second. The recorder chart speed was 17.5 inches per hour. (6) Solutions Blood Diluent. The blood diluting solution contained 9.0 gm sodium chloride and 5.0 gm potassium cyanide per liter. It was prepared in 15 liter quantities. Alkaline potassium ferricyanide reagent. The alkaline potassium ferricyanide solution or dialyzing solution contained 0.25 gm potassium ferricyanide, 9.0 gm sodium chloride, and 20.0 gm sodium carbonate per liter. It was prepared in 15 liter quantities. Glucose standards. New standard glucose solutions were prepared at two month intervals and stored at 4~C. First a solution containing 100 mg/ml glucose was prepared by dissolving 10.00 gm glucose in 100 ml saturated benzoic acid solution. Standard solutions were then prepared to contain 50, 100, 150, 200, 250, 300, 350, 400, 450, and 500 mg glucose per 100 ml solution by diluting 05, 1.0, 1.5, 2.0, 2.5, 300, 3.5, 4o0, 4.5, and 5.1 ml of the initial standard glucose solution to 100 ml with distilled water in a volumeteric flask. Figure 3 shows a typical standard curve for the on-line glucose analysis. The response, measured in terms of peak height -in cm, is plotted against glucose concentration in milligrams percent. The peak height is related to the optical density of the reagent. Simultaneous measurements were made by the on-line method ('6) and by a modification of a manual method on blood samples obtained from one dog to check the accuracy of the procedure. Using the manual procedure glucose determinations were made on samples of whole blood,

-34 -16 14 12 I0 E I 8 -w w 6 0.^ ~/ 4 2 0 50 100 150 200 250 300 GLUCOSE ( mg/100 ml) Figure 3. Standard Curve for the On-line Glucose Analysis.

-35 -plasma, and red cells. Whole blood, plasma, and red cells were deproteinized using barium hydroxide and zinc sulfate solutions. The barium hydroxide solution was prepared by dissolving 45 grams Ba(OH)2 o 8H20 in 1.0 liter distilled water. The zinc sulfate solution was made by dissolving 50 grams ZnSO4 ~ 7H20 in loO liter distilled water. Equal volumes of thee' solutions must neutralize each other exactly. The neutrality'was checked by titration using phenophthalein as the indicator. The protein-free filtrate was prepared by adding 0'4 ml blood, plasma, or red cells to 4.8 ml barium hydroxide solution and mixing, followed by the addition of 4'8 ml zinc sulfate.,.solutiono The mixture stood for several minutes and was filtered -One ml of the filtrate was added to five ml alkaline potassium ferricyanide solution. The mixture was heated for five minutes at 90~C and cooled in tap water. The'-optical density of the -'sample was measured at 420 m. The results are presented inTables 2 and 3. The on-line method gave a glucose value approximately 10 mg percent lower than the manual determination. This error seemed to be constant throughout the operating range. As long as all data being analyzed are.measured by the same method this error should not be serious~ Insulin Analysis The radio-immunological insulin assay developed by Yalow and Berson(63) and as modified by Samols(5' was used. This method is based on the antigenic nature of insulin Insulin reacts with specific antibodies to form complexes. In a system in which suitable amounts of anti-insulin antibody and insulin are present some insulin will be

-36 -TABLE 2 COMPARISON OF ON-LINE AND MANUAL GLUCOSE MEASUREMENTS FOR WHOLE BLOOD Sample Manual Glucose On-Line Glucose mg/100 ml mg/100 ml 1 117 103 2 116 105 3 126 115 4 144 130 5 149 153 6 164 167 7 198 185 8 222 215 9 249 237 10 274 255 TABLE 3 GLUCOSE CONTENT OF WHOLE BLOOD, PLASMA, AND RED CELLS Sample Plasma Red Cells Hematocrit Total Whole Blood Glucose Glucose Plasma Glucose Content Content and Red Content Cells mg/100 ml mg/100 ml mg/100 ml mg/100 ml 1 172 43 0.48 117 117 5 260 52 0.45 166 149 15 530 94 0.33 384 382

-37 -bound to the antibody as an insulin-antibody complex and some insulin will not be bound, that is, it will be free. These complexes are separated from free insulin by addition of a second antibody which combines with the insulin-antibody complex to render it insolubleo The insoluble complex is separated by centrifugation. By adding the appropriate constant amount of insulin labelled with iodine-131 and antiinsulin antibody to a series of samples containing varying known amounts of unlabelled insulin, successively greater amounts of insulin-I-131 are displaced from anti-insulin antibody. Thus a standard response curve is obtained by plotting the percent insulin bound by the antibody vs the amount of unlabelled insulin added. Those standards containing the smallest amount of standard insulin have thehighest radioactivity in the bound fraction. The quantity of insulin in unknown plasma samples is measured by comparing the ability of the endogenous insulin in the plasma sample to displace insulin-I-131 from anti-insulin antibody with that of the set of standards. Reagents for Insulin Analysis (1) Barbital Buffer The barbital buffer was prepared by dissolving 3.68 gm barbituric acid and 20.6 gm sodium barbital in 1.0 liter deionized water. The pH of the buffer was 8.6. (2) Barbital Buffer with 0.25% Human Serum Albumin. Five ml 12.5% Human Serum Albumin were added to 500 ml of the barbital buffer solution (prepared above).

-38 -(3) Trace Insulin (Insulin-I-131) Pork insulin was iodinated using sodium iodine-131 in sodium hydroxide solution by the method of Hunter and Greenwood(30), After dialysis to remove unreacted sodium iodide and purification on a Sephadex column the trace insulin was diluted with barbital-albumin buffer solution to make a solution having an activity of 0o45 microcuries/ml on the day following iodination. (4) Anti-insulin Serum Anti-pork insulin guinea pig serum solution was prepared from guinea pig anti-insulin serum produced at the University of Michigan. To assay samples of peripheral plasma this serum was diluted 1:25,000 with barbital-albumin before addition to the assay tubes where the final concentration of anti-serum was 1o250,000. For pancreatic venous plasma this serum was diluted 1:2,500 before addition to the assay tubes where the final concentration was 1:25,000. (5) Carrier Protein The carrier protein solution was prepared by diluting normal nonimmune guinea pig serum 1:150 with barbital buffero (6) Rabbit-anti-guinea Pig Globulin Serum (RAGPS) RAGPS was obtained from Arnel Products. For use in the insulin assay, RAGPS was diluted with an equal part of barbital buffer. This amount was shown to be 100 percent in excess of the amount needed to precipitate all the bound insulin-I-131 in the presence and absence of plasma at a 1:1 dilution.

-39 -(7) Insulin Standards Crystalline pork insulin was obtained from Eli Lilly and Company, was diluted to 20,000 [U/ml in barbital albumin buffer and used in the preparation of the standard insulin solutions. For peripheral samples the standard insulin was diluted with barbital-albumin to make a standard solution containing 50 iU/ml. For pancreatic samples the standard insulin was diluted to make a solution containing 1000 PU/ml. These solutions were used to prepare the standard curves. Analytical Procedure The insulin assay tubes were prepared for the first incubation as shown in Table 4. The reagents were added in the following order: diluent; trace insulin; standard insulin or plasma; and anti-insulin serum. Two control tubes, Cc, were prepared using excess unlabelled insulin to determine the amount of labelled insulin that is precipitated when the antibody is combined with essentially only unlabelled insulin. The same information can be obtained by preparing a control containing no anti-insulin serum. Each tube was mixed gently on a vortex mixer and stored at 4~C. After 48 hours 100 p1 of carrier protein solution and 100 p1 of RAGPS solution were added to each assay tube. The second incubation period was 72 hours at 4~C. Following the second incubation the tubes were centrifuged at 1100 g. for 20 minutes at 4~C. in a refrigerated centrifuge. The supernatant was carefully decanted. The tubes were allowed to drain in an inverted position for 20 minutes. They were then counted to measure I gamma activity using a Nuclear Chicago automatic

-40 -TABLE 4 PREPARATION OF THE INSULIN ASSAY TUBES FOR THE FIRST INCUBATION Tube Number Volume of Volume of Volume of Volume of Diluent Trace Insulin Standard Insulin Anti-insulin or Plasma Serum Tr A 400 50 0 50 Tr B 400 50 0 50 Tr C 400 50 0 50 Tr D 400 50 0 50 1* 390 50 10 50 2 380 50 20 50 3 370 50 30 50 4 360 50 40 50 5 350 50 50 50 6 340 50 60 50 7 320 50 80 50 8 300 50 100 50 9 250 50 150 50 10 200 50 200 50 11 150 50 250 50 12 100 50 300 50 Cc 395 50 5** 50 Standard Plasma 350 50 50 50 Unknowns 350 50 50 50 * All tubes in the standard curve and all unknowns were prepared in duplicate. **The controlCc, is prepared using a concentrated insulin solution containing 1 mg/mli gamma counter. The samples were counted for five minutes or to obtain 10 000 counts. The concentration of insulin in each unknown was determined

-41 -from the fraction of insulin bound by the antibody, PBZ. CPMX - CPMc' PBZ = -. - BZERO (CPM Tr A + CPM Tr B + CPM Tr C + CPM Tr D) BZERO = - CPM Cc 4 A standard curve was plotted as PBZ vs amount of insulin, Figure 4. Unknowns were determined by observing the insulin concentration corresponding to a given PBZ. Diluent was measured using a 5 ml burette equipped with a reservoir. Trace insulin was measured using a 50 j1 reservoir pipette. Plasma and standard insulin solutions were measured using the appropriate sized lambda pipettes. Antiserum, carrier protein, and RAGPS solution were measured using 50 pl1 100 Fl and, 100 jl reservoir pipettes, respectively. An alternate technique for measuring diluent and plasma is that of using an automatic diluting pipette. Hamilton syringes can be used for measuring carrier protein, RAGPS solution, anti-insulin serum and trace insulin.

-42 -1.00 0.80 0.60 - 0 >D 4 0 z 0 0.40 - DQ 00 0.,I.I I 0 50 100 150 200 250 300 INSULIN (, U/m I) Figure 4. Standard Curve for the Insulin Assay.

V. MATHEMATICAL METHODS In this chapter the procedure used to develop the mathematical model describing the insulin secretory response of the pancreas will be discussed. Statistical methods used to test the differences between several proposed models will be discussed also. Development of the Model After reviewing models describing the insulin secretory response of the pancreas and other biological systems, analyzing the characteristics of physical control systems, and studying the physiology of insulin secretion, the model given in equation (5.1) was postulated. K1 G(t - T1)+ K2 dG(t - 2) + K3 FVI(t -T3) + K4 I(t) = dt (5.1) V(t)(l - H) where: I = Plasma insulin concentration, pancreatic vein pU/ml G = Blood glucose concentration, femoral artery mg/100 ml FVI = Plasma insulin concentration, femoral vein MU/ml H = Hematocrit percent K1 = Coefficient, blood glucose term (kU/min)(mg/100 ml)K2 = Coefficient, derivative term (iu/min)(mg/100 ml) min K = Coefficient, peripheral insulin term (pU/min)(iU/ml)-l -~~~3 ~~~~~~~~' - peripheral K4 = Coefficient, constant term [U/min t =-Time min T1 = Time lag, blood glucose term min 72 = Time lag, derivative term min T3 = Time lag, peripheral term min -43 -

-44 -Ta = Integration limit min Tb = Integration limit min Equation (5.1) indicates that the pancreatic venous insulin concentration is proportional to the arterial blood glucose concentration, the first time derivative of the arterial blood glucose concentration, and the femoral venous plasma insulin concentration. The derivatives term provides a more rapid response to large changes in blood glucose concentration and is included because this investigation showed that markedly different plasma insulin concentrations existed in a given dog at the same blood glucose concentration. Further inspection of this data showed that the glucose concentration was rising more rapidly at the time the higher insulin concentration was observed. This observation is explained by the presence of a derivative term in the model. The femoral venous insulin concentration term represents a possible negative feedback effect of insulin on the response of the pancreas. K3 will be a negative 3 number if this negative feedback can be detected. K4 represents a base-line insulin secretion independent of changes in blood glucose concentration. A time lag is associated with each of the first three terms. The sum of the four terms on the right side of equation (5.1) is divided by the product of the pancreatic blood flow rate and the hematocrit since the insulin measurements were made on plasma and the flow measurements on whole blood. Thus, if both sides of equation (5.1) are multiplied by the blood flow rate, the equation will represent the rate of insulin secretion into the cannulated vein. The values of the time lags and the constants must now be determined. The lag values are found using an iterative procedure.

-45 -For a given set of lag values the four coefficients were determined from the experimental data by applying the least squares method to equation (5.1)o The computer program for this procedure is given in Appendix B. The values of the coefficients and the time lags were substituted into equation (5.1) and the insulin concentrations were calculated at given time intervals. The error was defined to be the difference between the measured and the calculated pancreatic venous insulin concentrations at a given time. The criterion used to measure the goodness of the fit of the model to the experimental data was the integral of the square of the error. This is the same criterion that was used in the least squares procedure to determine the coefficients. A model having the smallest integral of the square of the error would be the "best". An iterative procedure was used to find the combination of lag values providing the "best" fit for the data from each experiment. A grid searching method was used to find the optimum combination of lags. Having determined the best set of lags for a given experiment, a series of modified models given by equations (5.2-5.7) were applied to the same data to study the effect of omitting various terms. K1 G(t - T1) + K2 d(t -2) + K3 FVI(t - T3) i(t) = ~~ (5.2) V(t)(l -H) K1 G(t - T1) + K2 G(t - 72) + K4 I(t) =d (53) V(t)(l - H) K1 G(t - T1) + K FVI(t - T) + K4 I(t) 1 (5 4) V(t)(l - H)

-46 -K1 G(t - T1) + K2 dG(t - T) I(t) dt (55) v(t)(1 - H) (t) K G(t - Tl) + K4 (5.6) I(t) (5.6) V(t)(l - H) K1 G(t - T1) I(t) =.. ~(5-7) V(t)(l - H) All the symbols are defined the same as in equation (5.1). The coefficients for each model were determined from the experimental data. Each model was then used to correlate the data and the integral of the square of the error was calculated. The contribution of a particular term to the response estimated by each model was estimated from the change in the integral of the square of the error that occurred when a given term was omitted. Three other equations were tested. They were models in which the insulin concentration in the pancreatic vein was dependent upon: 1) an integral of the blood glucose concentration, equation (5.8); 2) the logarithm of the blood glucose concentration, equation (5.9); and the reciprocal of the femoral venous insulin concentration, equation (5.10). K1 Log(G(t - T1)) + K2 dt - 2 + K3 FVI(t - 3) + K4 I(t) - dt (5.8) V(t)( - H) Ta K(t) K G(t)dt + K2 dt T2 + K3 FVI(t - T3) + K4 I~t) b Gdt- H) V(t)(l - H)

-47 -K1 G(t - ) + K2 dG(t - T2) + K3(1/FVI(t - T3)) + K4 1(t) =~"dt ~(5.10) V(t)(l - H) Multivariate Statistics Multivariate statistical methods were used to test for the existence of significant differences among the different models applied 2 to the experimental data. Hotelling's T test, a multivariate analog of the Student t test, was used to test for significant differences in the mean errors resulting from the use of different models(29'44) The models given in equations (5.1 - 5.7) were applied to the data obtained from twelve experiments. The record resulting from the application of each model to a given set of experimental data was divided into three sections and the mean error was determined for each section. The means for each section and for each model were then determined for the number of experiments being analyzed. The mean vector and the covariance matrix were determined according to the outline below. Hotelling's 2 2 T statistic is given by equation (5.11). The T statistic can be related to the F statistic by equation (5.12). T2 = Y S-1 Y (5.11) F = (N-p + 1 T2 (5.12) pN where: F = F statistic N = Number of experiments p = Number of groups into which each experiment was divided

-48 -S = Covariance Matrix T = Hotelling's T statistic Y = Mean vector Y' = Transpose of Y If the calculated value of the F statistic is less than the tabulated a level F percentile, for p and N-p + 1 degrees of freedom, then the probability of being wrong in concluding that the models are significantly different is less than a. 2 A computer program for determining Hotelling's T statistic and the F statistic is given in Appendix B. The computational procedure is outlined below, and the application to a set of experimental data is shown in Figure 5.

-49 -Mathematical Methods for Hotelling's T2 Test Insulin, [U/ml A /Measured / \ Calculated IA // \ by Model 1 Time (min) Experiment 1 correlated with Model 1, X1 = 1, X2 = 1. A I/ \ / Measured ERRORI / \ C\ C alculated // I `\V by Model 2 / ' // \\ 90 Time (min) 180 270 Experiment 1 correlated with Model 2, X1 = 1, X2 = 2. 2 Fig. 5 Intervals used in Hotelling's T Test Nomenclature: X1 - Index, identifies a given experiment X2 - Index, identifies a given model X1MAX - Total number of experiments being analyzed El -Mean error in the interval 0-90 E2 - Mean error in the interval 91-180 E3 - Mean error in the interval 181-270

-50 -Each experiment is divided into a given number of groups, where the number of groups is much less than the total number of experiments, X1MAXo Here the data for each experiment has been divided into three groups. The errors occurring between these groups are considered to have a multivariate normal distribution. The mean errors are determined for each model applied to all the experiments using equations (5.13 - 15). 90 El(Xl,X2) = ~ ERROR(N) (5-13) 90 N=O 180 E2(X1,X2) = Z ERROR(N) (5.14) 90 N=91 270 E3(Xl,X2) = ERROR(N) (5-15) 90 N=181 The mean error for each model was determined in each group using equations (5.16 - 18)o X1MAX Yl(X2) = El(Xl,X2) (5.16) X1MAX Xl=l X1MAX Y2(X2) Z - E2(Xl,X2) (5.17) X1MAX Xi=l XIMAX Y3(X2) -= 1 E E3(X1,X2) (5.18) X1MAX XI=l The differences between the errors resulting from the application of two different models to each dog were calculated. For arbitrary values of X2, e.g. X2a and X2b the differences are given by equations (5.19 - 21).

-51 -DIF1(X1) = E1(X1,X2a) — E1(X1,X2b) (5.19) DIF2(Xl) = E2(Xl,X2a) - E2(Xl,X2b) (5.20) DIF3(X1) = E3(X1,X2a) — E3(X1,X2b) (5.21) The variance-covariance matrix of the differences in the errors is given by equation (5.22). all a12 013 S= 22 23 I (5.22) a31 32 a33 The elements of S are calculated by equation (5.23). X1MAX X1MAX X1MAX an = l DIFm(Xl) DIFn(Xl) - IFm(XFm(X) Z DIFn(X)) (5.23) XI-I ^Xl~l _________~ i Xi=i1 X1MAX XlMAX - 1 Hotelling's T2 statistic can now be determined by using equation (5.11).

VI. RESULTS In this chapter the experimental results and the results of the mathematical methods are presented. Experimental Results The insulin secretory response of the pancreas was studied in 14 dogs. Twelve dogs received glucose infusions and two control dogs received saline infusions. The experimental data and the calculated results from each dog are presented in Appendix A. The measured values for the blood glucose concentration and the pancreatic venous plasma insulin concentration, and the values of the pancreatic venous plasma insulin concentration calculated from equation (5.1) are plotted for the various experiments in Figures 6 - 19o Figures 6 and 7 also show the peripheral venous plasma insulin concentration and the infusion pump speed. The pancreatic and peripheral insulin concentrations increased rapidly when glucose was administered. The pancreatic venous insulin concentration decreased rapidly when the blood glucose concentration decreased. The peripheral insulin concentration decreased more slowly than the pancreatic venous insulin concentrationo Variations in the pancreatic venous insulin concentration were in phase with changes in the blood glucose concentration and lagged by less than five minutes in most dogs studiedo Changes in the peripheral insulin concentration lagged the blood glucose concentration from 0 -15 minutes. Mathematical Model The mathematical model given in equation (5.1) was applied to -52 -

-53 -DOG M 60,000 DOG M 50,000 - Pancreatic 40,000 Venous Falculated Plasma 30,000 - Insulin tiUL/ml 20,000 - 10,000 - WMeasured 0 300 250 - Pancreatic 200 Venous Plasma 150 Glucose mg/OOmlI 100 50 - 0 Femoral 600 Venous Plasma 200 -Insulin yuL/ml 4 - iInfusion ml /minute Saline 2 ~ --- —- ~_ Glucose 0 60 120 180 240 300 Time (min) Fig. 6

-54 -DOG T 20,000 -Pancreatic 16,000 Venous 12 Plasma Insulin 8000 Measured 4'000 = uU/ml 4,000- Calculated 0 200 Arterial 150 Whole Blood 100 Glucose mg/lOOml 50 0 Femoral 200 Venous \ Plasma 100 - Insulin Alu/ml 0o ml/minute 2 ___ _- — J -Infusion mi/minuTe _ — Saline, Glucose 0 60 120 180 240 Time (min) Fig. 7

DOG D 600 _ Measured 400 3 c:./ ^Calculated 1 200 0 400 350 300 1250 200 aD 0 150 100 50 0 60 120 180 Time (min) Fig. 8

-56 -DOG E 4800..I.-.^~ ~Measured. E 5200 1 1600- i -- ~~Cao~lculated 0 300 250 200 E 150/ O 100 50 0 60 120 180 240 300 Time (min) Fig. 9

-57 -DOG F 1600 1 Calculated 1200- - E Measured 3 80oo0- / 400 300 250 / - / 200 0 0. 1500 0 60 120 Time (min) Fig. 10

-58 -DOG I 80001 Measured-b 6000 3 4000-.E Ic Calculated 2000 0 250 200 100 150-v 0 0 6 120 180 Time (min) Fig. 11

-59 -DOG J 24,000 18,000 3 12,000 Calculatfed Measured 6,000 0 300 250 E 200 150 3) 100 E 50 0 50 -0 60 120 180 240 Time (min) Fig. 12

-60 -DOG L 30,000 r Measured 24,000 18,000ooo E 12,000 - / = ^f UCalculated 6,000 0 300 250 o 150 (. 100 50 0 60 120 180 240 Time (min) Fig. 13

-61 -DOG N 10,000,, I '~' 8,000 - <Measured E 6,000 3= " 4,000 Calculated 2,000 700 600 - 500 - 400 - E 100 0 60 120 180 240 300 Time (min) Fig. 14

-62 -DOG S 40,000 I 32,000 Measured E 24,000 1 16,000 Calculated V - 8,000 0 20 0 e) Fig. 1 150 - E 0 100 - 0 60 120 180 240 300 Time (min) Fig. 15

-63 -DOG U 12,000 9,000 Measured —> E 6,000 3, Calculated C 3,000 - 0 250 200 ~ '150 - E 0 100 - 0 50O I 0 60 120 180 240 300 Time (min) Fig. 16

-64 -DOG V 9,000, I Measured 6,000 -E Calculated 250 - 200 -CL 1 150p -\ 0 300 50 J 0 60 120 180 240 300 Time (min) Fig. 17 Fig. 17

-65 -DOG 0 6,0001 4,000 3,200 2400 Calculated Measured 1,600 - 800 0 CD ) 100 ) 50 (9 0 60 120 180 240 Time (min) Fig. 18

-66 -DOG P 2000 I 1600 Measured 1 1200 - E 1200 ~__ ^ \'PCalculated 800 400 I100 CU n0 o 0 =3 0 60 120 180 240 300 Time (min) Fig. 19

-67 -the data from each experiment to determine the time lags and the values of the coefficients. These results are summarized in Table 5 and are shown in Figures20'and 21. TABLE 5 TIME LAGS AND COEFFICIENTS FOR THE MODEL REPRESENTED BY EQUATION (5.1) Experiment Lag 1 Lag 2 Lag 3 K1 K2 K3 K4 D 1 18 '38.07.001 -.70 17.5 E 0 4 45.41.74 1.04 83.6 F 0 0 49 31.o6 -1.5 19.5 I 2 5 65 2.2 16.8 2.58 -281. J 4 0 35 3.4 -34.2 -4.8 614. L 18 7 71 13.8 -58.4 -12.6 -612. M 0 4 0.34 51.5 2.0 119. N 4 11 55 -.37 -4.3 -8.9 838. S 26 9 47 25.8 99.3 7.25 -2276. T 0 1 50 12.9 16.9 6.0 -717. u 6 17 52 3.1 21. 85. -1410. V 0 6 13 3.3 5.4 34.1 -569. Control Dogs 0 8 6 23 -49.2 -41. -35.1 3002. P 0 29 47.04 -15.3 8.9 -94.2 The model describes the phasic nature of the data reasonably well. The correlations of data from dogs D, E I, J, M, N, S, and U show that the model does not fit the data as well at the maximum and minimum values of the pancreatic venous insulin concentration as it fits at the intermediate values, This result is to be expected since the least squares method was used to determine the coefficients.

-6B28 68 24 64 20 60 56 'l12 55 848 48, 36 32 28 28 24 24 20 20 'i 16 16 ~ 12 12 EH 8~- 8 ft~ i ~ ill a ~ Lag 2 Lag 3 Figure 20 Time Lags for the Model Represented by Equation (5.1) for all the experiments.

-69 -100 100 ~ 8o 80 60 - 60 40- 40 20 20 0 ' IT 1 0 -20 -20 --40 -40o -60 o -60 6_ Values of K1 Values of K2 100..I 3000 80 2000 60 4o 1000 20 - TrGlucose l ii on -20 g -1000 -40 f -60o -2000 -2.. Values of K3 Values of K4 Saline Infusion Glucose Infusion ~ Figure 21 Coefficients for the Model Represented by Equation (5.1) for all the Experiments.

-70 -The significance of the different terms in the model was studied by comparing the normalized integral of the square of the error obtained with different models related to the model of equation (5.1) but lacking certain terms. Table 6 shows the effects of removing various terms from the model given by equation (5.1). Equation (5.1) provided the best correlation of the experimental data in 11 of 12 dogs. The variation in the pancreatic venous blood flow rate was studied. Using data from nine dogs the predicted insulin concentration was corrected for changes in the pancreatic venous blood flow rate at the time each sample was collected. Equation (5.1) was used to describe the response for the variable blood flow case and for the same experiments assuming the pancreatic venous blood flow rate remained constant throughout the experiment. The normalized integrals of the square of the error for the variable blood flow calculations and for the constant blood flow calculations are given in Table 7. Since the normalized integral of the square of the error is larger for the The normalized integral of the square of the error is given by: 1 [Z(I(N) - INS(N)) /Nmax]2 ave where: I(N) = Predicted pancreatic venous insulin concentration at time N pU/ml INS(N) = Measured pancreatic venous insulin concentration at time N pU/ml INSa = Average measured pancreatic venous insulin concentration pMU/ml N = Time min Nmax = Length of experiment min

-71 -TABLE 6 THE NORMALIZED INTEGRAL OF THE SQUARE OF THE ERROR FOR THE MODEL OF EQUATION: Experiment 5.1 5.2 5.3 5.4 5.5 5.6 5.7 D 0.484 0.501 0.787 o.484 0.791 0.791 0.988 E 0.540 0.553 0.53 0.40.598 0.553 1.10 F 0.347 0.354 0.401 0.348 0. 447 0.402 1.11 I 0.568 0.613 0.759 0.583 0.819 0.768 1.23 J 0.442 0.447 0.455 0.443 0.455 0.455. 578 L 0.274 0.290 0.457 0.276 0.461 0.457 0.831 M 0.281 0.280 0.329 0.291 0.329 0.337 0.692 N 0.687 0.913 o.848 0.687 0.927 O.854 1.09 S 0.530 0.640 0.708 0.531 0.902 0.728 1.47 T 0.336 0.499 0.461 0.338 0.661 0.472 1.37 U 0.532 0.826 0.866 0.535 0.871 0.874 1.20 V 0.510 0.642 0.962 0.511 0.964 0.983 1.46 TABLE 7 EFFECT OF VARIATIONS IN THE PANCREATIC VENOUS BLOOD FLOW RATE Experiment No. Normalized Integral of the Square of the Error Variable Blood Flow Constant Blood Flow D O.480 0.484 E 0.536 0.540 F 0.843 0.347 M 0.357 0.281 N 0.781 0.687 S 0.627 0.529 T 0.426 0.336 U 0.548 0.532 V 0.907 0. 10

-72 -variable blood flow rate calculations in 7 of 9 experiments, variations in the pancreatic venous blood flow rate have not been included in the analysis of any other experiments. All coefficients and lags where calculated from constant blood flow rate data, Models in which the insulin concentration in the pancreatic vein was dependent upon: 1) an integral of the blood glucose concentration, equation (5o8); 2) the logarithm of the blood glucose concentration' equation (5.9); and 3) the reciprocal of the femoral venous insulin concentration, equation'(510) were applied to the experimental data. The integral of the square of the error occurring with each of these models was compared to the integral of the square of the error occurring with the model of equation (5.1) in Table 8. Since application of equations (5.8, 5.9, and 5.10) resulted in errors not significantly less than the error associated with equation (5.1), the model of equation (5.1) was used for the determination of the time lags and coefficients.

-73 -TABLE 8 THE NORMALIZED INTEGRAL OF THE SQUARE OF THE ERROR FOR THE MODEL REPRESENTED BY EQUATION: Experiment 5.1 5.8 5.9 5.10 D 0.484 o.474 0.510 o.o08 E 0.540 0.521 0.514 0.528 F 0.347 0.325 0.321 0.346 I o.568 0.535 0.602 0.709 J 0.442 0.421 o.460 0.455 L 0.274 0.289 0.210 0.349 M 0.281 0.273 0.281 0.324 N 0.687 0.694 0.702 0.706 S 0.529 0.542 0.595 o.470 T 0.336 0.307 0.555 0.432 U 0.532 0.523 0.559 0.539 V 0.510 0.500 0o593 0.733 Multivariate Statistical Analysis Hotelling's T2 test was used to test for the existence of significant differences in the different models applied to the experimental data from 12 dogs. The significance of the different terms in the model given by equation (5.1) was studied by using Hotelling's 2 T test to determine significant differences in the mean errors occurring when equation (5.1) was applied to the experimental data compared to the mean errors occurring when equations (5.2 - 5.7) were applied. The results are given in Table 9. The F statistic was calculated for N-p + 1 = 10 and p = 3 degrees of freedom. At a 0.90 confidence level F must be greater than 2.73 with N-p + 1 = 10

-74 -and p = 3 for a significant difference to be indicated between the models. Since all the models that were compared to equation (5.1) resulted in a value of F less than 2o73, the probability of being wrong in concluding that the models are significantly different from equation (5.1) is more than Oo10o TABLE 9 COMPARISON OF DIFFERENT MODELS USING HOTELLING'S T2 TEST Models Compared Equation Numbers F Statistic 5.1 and 502 0.10 5o1 5.3 0.53 5.1 504 0.07 5o1 5.5 0.14 5.1 5,6 o.40 5l1 5~7 0.27

VII. DISCUSSION In this chapter the results presented in Chapter VI will be discussed. The experimental results and the results of the mathematical procedures will be considered separately. Experimental Results The insulin secretory responses observed during and after glucose infusions were similar to those observed by other investigators (32,39,56) Administration of glucose resulted in increased insulin concentrations in pancreatic venous blood within five minutes. In dogs J, L, M, S, and T the pancreatic venous plasma insulin concentrations reported here are higher than those reported by other investigators (32,39,56) Analytical errors are not likely the cause of these high insulin levels, since several plasma samples were measured using both the double antibody and the paper electrophoresis immunoassays and the results were comparable. These high insulin levels may be related to the location at which the pancreaticoduodenal vein wascannulated or the responsitivity of the pancreas of a given dog. One inherent problem associated with the determination of a mathematical model of the insulin secretory response of the pancreas is the difficulty in obtaining representative measurements of the input and the output variables. Blood flows into the pancreas from many arteries and blood is drained from the pancreas by many veins making it difficult to obtain an accurate measurement of the pancreatic blood flow rate and the rate of insulin production. The glucose concentration in all the pancreatic arteries can be assumed to be the same without -75 -

-76 -introducing any significant erroro The beta cells, the insulin producing tissue of the pancreas,.are not uniformly distributed throughout the organ. Therefore, pancreatic venous blood collected from different veins cannot be expected to have the same insulin concentration. Some investigators have tried to overcome this problem by working with perfused organ or tissue preparations(l7 l8'24) These methods introduce many new problems, however. Inspection of the data in Appendix A showed different pancreatic venous insulin concentrations occurred in the same dog at the same blood glucose concentration at different times during the experiment, indicating the pancreas is responding to some stimulus other than the arterial blood glucose concentration. In some instances this observation could be explained by the derivative term in equation (5ol). Other factors including the effects of growth hormone, adrenal corticoids, epinephrine, glucagon, nembutal, and surgical stress may be causing variations in the response of the pancreas which are not described by the model. Mathematical Model Application of equation (51l) to the data of 14 dogs resulted in the time lags and coefficient values given in Table 5~ In 11 of 14 dogs studied Lag 1 was observed to be from 0-7 min and Lag 2 was observed to be from 0-11 min while Lag 3 ranged from 23-65 mino It should be noted that Lag 3 is associated with the response of the pancreas to changes in the peripheral insulin concentration and is not the lag between changes in arterial blood glucose concentration and peripheral

-77 -venous insulin concentration. The values determined for Lag 1 are in the same range as those values reported by Seltzer(57), 0-5min and Gjedde(23), 0-2 min. No values for Lag 2 or Lag 3 have been reported. The values of''the coefficients Kl, K2, and K3:represent the responsitivity of''the pancreas to changes in the blood glucose and insulin concehtrations. In'7 of 12 dogs the values of'K2 exceeded Klo Since the -magnitude of the time: derivative of the blood glucose' conieritration is generally smaller than the magnitude of the blood-glucose concentration' K2 must be larger than Kl if the derivative term is to have a significant effect 'on the response. K3 was observed to have positive as well as':negative valueso Positive values of K3 imply high peripheral' insulin concentrations result in more insulin secretiono This does not agree with the inhibitory effect of insulin on the pancreas suggested by Logothetopoulos(35) and by Hausberger(27). Another investigator has 'reported that insulin secretion was not effected by insulin itself(37)o The large variability in the values of the coefficients may be due to differences in: 1) the responsiveness to glucose of the dogs studied, 2) the location at which the pancreaticoduodenal vein was -cannulated and 3) the distribution of- beta cells within the pancreas. Variables which were not measured or included in the model, such as changes in the plasma epinephine or growth hormone concentrations, may also be partly responsible for the variatipns i the coefficients.and the errors between the measured and predicted pancreatic venous insulin concentrationso Inspection of the data in Table 6 shows that in 11 of 12 dogs equation (5.1) is the best representation of the 'insulin secretory

-78 -response of the pancreas. The contributions of the derivative and the negative feedback terms are small but generally reduce the integral of the square of the error. Therefore, for an individual dog the four term equation (5.1) is the "best" model. This model indicates the absolute level of the blood glucose concentration is the greatest factor in determining pancreatic insulin secretion. The derivative term functions to provide more rapid response to fast changes in blood glucose concentration and the peripheral or negative feedback term protects the animal from excess insulin secretion. A model containing the derivative of the input represents a system having infinite gain at high frequencies. Since the frequency range associated with the input to the pancreas is very low and is bounded, this is not a serious problem. The physiological mechanism for the derivative response is not known at this time. Recently Frohman and associates have shown that vagal stimulation results in augmented insulin secretion and vagotomy (21) in reduced insulin secretion(1) These effects were reported to be independent of the larger response of the pancreas to blood glucose. Since derivative control mechanisms have been shown to be present in neurological control systems, vagal control of part of the insulin secretory response of the pancreas may explain the mechanism for the derivative term. Additional experimentation will be necessary before any conclusion can be made. It may be noted that biological systems have been shown to respond to the rates of change of stimuli as well as to the absolute magnitude of the stimuli. One example of such a system is the carotid sinus baroreceptor which responds to the rate of change of blood pressure as well as to the absolute magnitude of the blood pressure (19).

-79 -Multivariate Statistical Analysis Utilization of statistical methods to determine significant differences between two models is difficult when the models have been applied to time series data. Univariate statistical tests are based on independence assumptions. Therefore, multivariate statistical procedures must be used to analyze time series. While it was possible to show that the addition of various terms to the model reduced the integral of the square of the error for a given dog, application of Hotelling's T2 test to determine significant differences in the mean errors resulting from the application of different models to the data from 12 dogs together showed no differences between the average performance for any of the models. Although large differences in mean errors occurred between the different models, the elements of the covariance matrix were much larger. This produced an inverse covariance matrix composed of very small numbers. Multiplication by this inverse covariance matrix produced small values for the F statistic. Spectral Analysis Spectral analysis provides a systematic method for determining the mathematical relationship which exists between the input and the out-.put of a linear system(5'6) Spectral analysis is applied to a set of experimental data by first determining the autocorrelation function of the input variable and the cross-correlation function between the input and the output variables. Second, the power spectral density function of the input and the cross-spectral density function between the input and the output variables are calculated. The power or cross-spectral

-80 -density function is the Fourier transform of the appropriate correlation functiono The transfer function can now be determined as the quotient of the cross-spectral density function divided by the power spectral density function of the input. Application of spectral analysis to the experimental data was inconclusive. The difficulty encountered may be due to the relatively short records available and the low frequency range of the data. The possibility of a computational error could not be totally eliminatedo Conclusions A model was developed which permitted reasonably accurate prediction of the pancreatic venous insulin concentration as a function of the time history of the arterial blood glucose concentration and the peripheral venous insulin concentration. A record of the pancreatic venous insulin concentration, peripheral venous insulin concentration, and arterial blood glucose concentration was used to determine the parameters of the model. Of the variables studied, the arterial blood glucose concentration is the most important factor in determining pancreatic insulin outputo This response is augmented by a response which is proportional to the time derivative of the blood glucose concentration. In some experiments a negative feedback effect of the peripheral insulin concentration on pancreatic venous insulin concentration was observed. In three-quarters of the dogs studied time lags from 0-6 min were associated with the response of the pancreas to changes in the blood glucose concentration, lags from 0-7 min were associated with the response to the derivative of the blood glucose concentration, and lags

-81 -from 15-55 min were associated with the response to changes in peripheral insulin. The values of the time lags and the coefficients of equation (5.1) varied greatly in the different experiments, consequently it was not possible to estimate a set of average time lags and coefficients which could be used to predict the response of the pancreas to changes in the blood glucose concentration in any normal dog. These variations may have been caused by the following: 1) differences in the responsiveness of the pancreas in different dogs, 2) variations in the location at which the pancreaticoduodenal vein was cannulated with respect to the distribution of the beta cells in the pancreas, and 3) changes in the levels of other hormones which effect the insulin secretory response of the pancreas. Multivariate statistics were applied to determine significant differences between different models. The variability of the data was so great that these techniques did not show any difference between the models tested. Spectral analysis was applied to estimate a transfer function describing the insulin secretory response of the pancreas. It was not possible to obtain a satisfactory transfer function by this method. The relatively short records available and the low frequency range of the data may be preventing an accurate determination of the transfer function.

APPEND IX A EXPERIMENTAL DATAAND PREDICTED PANCREATIC VENOUS INSULIN CONCENTRATIONS FOR ALL THE EXPERIMENTS -82 -

-83 -TABLE 10 EXPERIMENTAL DATA AND CORRELATION FOR DOG D MEASURED ESTIMATED PAhCRE- P~NCREFEMORAL BLgCD ~IIC ATIC PERCENT TIME GLUCOSE DG/OT INSULIN FLOW INSULIN INSULIN ERROR ERROR TERM 1 TERM 2 TERM 3 TERM 4 MIN MG PCT MU U/~L ML/MIN ~L/ML MU U/ML MU U/ML 1 35C.00 8.23 87 232 145 167 36 0 -42 239 4 230.00 11.23 194 391 1~7 101 194 0 -42 239? 236.00 lq.23 194 348 154 79 152 0 -42 239 1C 214.OC 17.25 160 336 176 110 139 0 -42 239 13 217.00 20.18 209 332 123 59 135 0 -42 239 16 22C. O0 23.18 209 334 125 60 137 0 -42 239 19 224 136.50 25.20 404 337.... -6i............... —1~....... 140 0 -42 239 22 22S -30.00 28.20 396 339 -57 -14 142 -0 -42 239 25 233 -6. CO 3C.20 396 342 -54 -14 145 -0 -42 239 28 237 -3.50 33.20 500 344 -156 -31 148 -0 -42 239 31 28C 1.00 36.20 500 347 -153 -31 150 0 -42 239 3q 333 1.50 39.20 500 409 -91 -18 212 0 -42 239 37 3~3 1. CO 41. 20 500 406 -94 -19 210 0 -42 239 4C 330 1. 50 44 ~ 20 500 392 -108 -22 207 0 -55 239 43 334 1.50 4? ~ 20 500 375 -125 -25 209 0 -73 239 46 339 1.50 50. 20 500 359 -141 -28 211 0 -91 239 45 344 50.00 52.20 500 344 -156 -31 214 0 -109 239 52 347 -1.50 55 ~ 20 500 334 -166 -33 217 -0 -121 239 55 34g -1.50 58.20 500 317 -183 -3? 218 -0 -140 239 58 35 I. O0 60. 26 260 300 40 16 219 0 -158 239 6! 353 1 ~ 50 63, 26 260 284 24 9 221 0 -176 239 64 356 1. 50 65.21 230 273 43 19 222 0 -188 239 67 356 1.50 66 ~ 21 230 256 26 11 224 0 -206 239 7C 360 ~ 50 64. 21 230 239 9 4 225 0 -225 239 73 343 ~ 50 63.23 181 215 34 19 219 0 -243 239?~ 324 1 ~ O0 61, 23 181 191 10 6 207 0 -255 239 79 30? 1 ~ O0 60 ~ 23 181 164 -17 -9 198 0 -273 239 82 2S4. 50 58. 23 181 134 -47 -26 186 0 -291 239 85 285. 75 57.20 144 116 -28 -19 180 0 -303 239 88 276 -2.00 55.20 144 92 -52 -36 175 -0 -322 239 gl 266 -6. 50 54.21 116 68 -48 -41 169 -0 -340 239 94 262 -6. CO 52.21 116 46 -70 -60 165 -0 -358 239 g7 256 -8. O0 51 ~ 21 1 16 30 -86 -74 162 -0 -370 239!OO 250 -3. gO 49 ~ 24 67 8 -59 -87 158 -0 -388 239 k03 242 -3. O0 48 ~ 24 67 -7 -74 -111 154 -0 -401 239 106 235 -3.00 46.22 59 -7 -66 -112 149 -0 -394 239 -09 227 -2.00 45.21 69 -5 — 74 -108 144 -0 -388 239!12 222 -2. CO 43 ~ 21 69 2 -67' -97 140 -0 -376 239!15 219 -2.00 43 ~ 21 69 7 -62 -90 138 -0 -370 239 118 216 -2.00 43.23 61 17 -44 -72 136 -0 -358 239 121 214 -3.00 43 ~ 23 61 21 -40 -66 134 -0 -352 239 124 214 -2.00 43.23 63 33 -30 -47 134 -0 -340 239 127 340 -3. O0 44. 27 79 68 -11 -14 163 -0 -334 239 13G 26C -1. O0 44. 27 61 105 44 73 188 -0 -322 239 133 271 -1. O0 45. 23 66 91 25 37 167 -0 -316 239 136 283 -1.00 46.20 67 110 43 65 175 -0 -303 239 139 295. O0 46 ~ 22 66 124 58 88 182 0 -297 239 142 303 ~ O0 47 ~ 22 66 142 76 116 189 0 -285 239 145 310 40. CO 47 ~ 25 68 153 85 125 193 0 -279 239 14~ 316 -18. 50 48 ~ 25 68 169 101 148!97 -0 -267 239 151 320 4. O0 49 ~ 25 83 179 96 115 201 0 -261 239 154 322 4. GO 49 ~ 25 83 179 96 116 201 0 -261 239 i 5? 324 %. CO 50. 25 81 180 99 123 202 0 -261 239 160 326 2. O0 50 ~ 25 81 182 101 124 204 0 -261 239 163 32 7 2 ~ O0 51. 2b 80 18 3 103 128 205 0 -261 239 166 329 2.00 52.26 80 177 97 122 206 0 -267 239 169 330 ~ 50 52. 26 62 172 110 178 206 0 -273 239 172 326. 50 52 ~ 26 62 172 110 177 206 0 -273 239 175 32~. 75 52 ~ 26 62 162 100 161 202 0 -279 239 LAG1 = LAG2 = 18, LAG3 = 38 K1 =.072068, K2 = 1.365341E-03, K3 = -.697925 K4 = 17.472030, SUM = 5.347178E+05, HGT =.500000 NMAX......................NC~'MER "=.......484175, AVGINS = 198. 310734 = 176,

-84 -TABLE 11 EXPERIMENTAL DATA AND CORRELATION FOR DOG E MEASURED ESTIMATED PANCRE- PANCREFENORAL BLOOD ATIC ATIC PERCENT TIME GLUCOSE DG/DT IkSULIN FLaW IISULIN INSULIN ERROR ERROR TERM 1 TERM 2' TERM 3 TERM 4 MID, MG PCT MU U/ML ML/MIN ML/ML MU U/ML MU U/ML 1 72. GO 10 ~ 22 100 122 5 1125 1125 271 0 94 860 4 72. O0 Ii. 22 IO0 I225 I125 II25 27i 0 94 860 7 76.00 13.22 100 1240 1140 1140 286 0 94 860 I0 84 2. O0 14 ~ 22 600 1274 674 112 316 3 94 860 13 92 2 ~ O0 15. 24 600 1304 704 117 346 ~ 94 860 16 101 2 ~ 50 17. 24 600 1338 738 123 380 4 94 860 19 lOS 2.50 18.24 600 1369 769 128 410 4 94 860 22 116 3.00 lg.26 850 1396 546 64 436 5 94 860 25 122 2.00 21.26 850 1417 567 67 459 3 94 860 26 127 1.50 22.21'~' 2150 1435 -715 -33 478 3 94 860 31 132 1.50 21.21 2150 1453 -697 -32 496 3 94 860 34 140 1.50 19.21 3050 1483 -1567 -51 526 3 94 860 31 151 3.00 17 '.22-...........3'-0-5'6...............I52'7..............-1523 -50 568 94 860 40 161 4.00 15.22 3050 1567 -1483 -49 605 94 860 43 171 3.50 13.22 3050 1603 -1447 -47 643 94 860 46 176 3.00 11.24 2300 1621 -679 -30 662 94 860 4~ 180 1.50 9.24 2300 1643 -657 -29 677 104 860 52 184 1.50 7.24 2300 1677 -623 -27 692 122 860 55 186 1 ~ O0 5. 24 2150 1693 -457 - 21 699 132 860 5 E I 88. 50 3. 24 2150 IT09 -441 -20 707 14I 860 6 1 192 ~ 50 3 ~ 24 2150 1743 -407 -i9 722 160 860 64 19~ I. 50 5 ~ 24 2150 I78I -369 -17 748 170 860 6 7 205 2 ~ 00 8. 24 24 O0 1814 -586 -24 771 179 860 70 212 2. O0 I1 ~ 24 2400 i859 -541 -23 797 IgB 860 73 218 2. 50 13.24 2400 1892 -508 -21 820 4 207 860 7a 224 2.00 16.23 2100 1904 -196 -9 842 3 198 860 79 228 2.00 18.23 2100 1900 -200 -10 857 3 179 860 82 232!. 50 21 ~ 23 2100 1895 -205 -10 872 3 160 860 85 232 1.50 24.23 2100 1877 -223 -11 872 3 141 860 88 232.00......27..........23..... 2.200.........!. 8_5.5_............ -345 -16 872 0 122 860 91 232. O0 29.23 2200 1836 -364 -17 872 0 104 860 94 218. O0 32.23 2200 1765 -435 -20 820 0 85 860 S7 190 -7.00 35.23 1300 1629 329 25 715 -12 66 860 i00 2CC -8. 00 38.23 1300 1646 346 27 752 -14 47 860!03 213 4. GO 41.23 1300 1696 396 30 801 7 28 860 106 222 4. 50.. 44.........,23......... 13.00..............~17.3!....... 431 33 835 8 28 860 109 23C 3 ~ CO 47 ~ 24 1100 1777 677 62 865 47 860 112 24C 2,50 50.24 1100 1842 742 67 903 75 860 115 246 3.50 53.24 1100!895 795 72 925 104 860 lib 252 2.00 56.I6 1550 1934 384 25 948 122 860!21 25E 2. O0 59. 16 1550 1985 435 28 970 151 860 124 264 2.00 62. 16 1550 2026 476 31 993 170 860 12 7 27 C 2. O0 65, 16 1T 50 2077 127 7 1015 3 198 860 13C 276 2. O0 68 ~ 16 1950 2128 178 9 1038 3 226 860 133 281 2.00 71 ~ 16 1950 2175 225 12 1057 3 254 860 136 284 1. 50 74. 16 1950 2204 254 13 1068 3 273 860 139 287 1.00 77 ~ 16 1950 2243 293 15 1079 2 301 860 142 29C 1 ~ O0 80 ~ 16 4550 2282 -2268 -50 1091 2 330 860 145 30C 1.00 83. I6 4550 2348 -2202 -48 1128 2 358 860 148 313 4. CO 86. 16 4550 2430 -2120 -47 1177 7 386 860 151 326 4.00 89. 16 4550 2507 -2043 -45 1226 7 414 860 154 333 4.50 92 ~ 25 3400 2563 -837 -25 1252 8 443 860 157 337 1 ~ 50 93 ~ 25 3400 2 601 -799 -23 1267 3 471 860

-85 -TABLE 11 (CONT'D) 16C 340 1.50 87.25 3400 2641 -759 -22 1279 3 499 860 163 273 1. 00 81.25 3150 2416 -734 -23 1027 2 528 860 166 243 -14.50 75.25 3150 2305 -845 -27 914 -24 556 860 169 215 -10.OC 69.25 3150 2236 -914 -29 809 -17 584 860 172 184 -10.00 63.22 2000 2148 148 7 692 -17 612 860 175 172 -10.50 57.22 2C00 2130 130 6 647 -18 641 860 178 162 -3.00 51.22 2000 2133 133 7 609 -5 669 860 181 154 -3.50 45.25 2850 2131 -719 -?5 579 -6 697 860 184 146 -3.00 39.25 2850 2130 -720 -25 549 -5 725 860 187 14C -2.00 36.25 2850 2137 -713 -25 526 -3 754 860 190 134 -2.00 33.24 1550 2143 593 38 504 -3 782 860 193 129 -2.CO 30.24 1550 2152 602 39 485 -3 810 860 196 126 -1.50 27.24 1550 2170 620 40 474 -3 838 860 199 123 - 1.CO 24-.24 '1550 2188 "638 - " 41 463 -2 867 860 202 120 -1.CO 21.25 - 800 2186 1386 173 451 -2 876 860 205 117 -1.00 18.25 800 2118 1318 165 440 -2 820 860 208 114 -1.00 15.25 800 2050 1250 156 429 -2 763 860 211 111 -1.CO 12.25 200 1982 1782 891 417 -2 706 860 214 109 -1.00 10.25 200 1918 1718 859 410 -2 650 860 217 10 -.5.25 2 5 8.50 -.2 -."6 829- 405 -1 593 860 220 1C7 -.40 12.20 2300 1797 -503 -22 401 -1 537 860 223 105 -.45 18.33 3850 1735 -2115 -55 395 -1 480 860 226 136 -.50 24.24 2900 1795 -1105 -38 511 -1 424 860 229 180 16.00 30.24 2900 1932 -968 -33 677 27 367 860 232 224 15.00 36.24 2900 2067 -833 -29 842 25 339 860 235 242 14.50 42 2 900 2106 -794 -2-7 - 910 24. 311. 860 238 255 5.00 48.24 2900 2110 -790 -27 959 8 283 860 241 27C 4.50 52.24 2900 2138 -762 -26 1015 8 254 860 244 285 5.00 55.24 2900 2167 -733 -25 1072 8 226 860 247 301 5.50 58.43 1425 2199 774 54 1132 9 198 860 250 317 5.50 61.28 900 2231 1331 148 1192 9 170 860 253 332 5.50 64.28 900 2259.- 1359 151 1249 9 141 860 256 344 5.00 67.12 1050 2275 1225 117 1294 8 113 860 259 356 4.00 7C.12 1050 2300 1250 119 1339 7 94 860 262 368 4.00 73.12 1050 2345 1295 123 1384 7 94 860 265 378 4.00 76.40 50 2402 2352 4703 1422 7 113 860 268 388 3.00 79.40 50 2494 2444 4888 1459 5 170 860 271 397 3.50 82.40 50 2585 2535 5070 1493 6 226 860 LAG1 = O, LAG2 = 4, LAG3 = 45 K1 =.413668, K2 =.743070, K3 = 1.036188 K4 = 83.626175, SUM = 9.982430E+07, HCT =.500000 NMAX = 272, NCPMER =.539604, AVGINS = 1951.739914

-86 TABLE 12 EXPERIMENTAL DATA AND CORRELATION FOR DOG F MEASUREO EST IMATEO F~NCRE- PANCREFEMORAL 8L0[}0 ATIC ATIC PERCENT TIME GLUCOSE DG/DT IKSULIN FLOW II~SULIN INSULIN ERROR ERROR TERM I TERM 2 TERM 3 TERM 4 MIN MG PCT MU U/lUL ML./M'IN... MLJ/ML.....MU U/ML....MU...U/M...L...................................................................................... ~ 1 130 22'50 34.15 50 216 166 331 524 16 -634 309 4 152 -2. CO 40.15 100 287 187 187 613 -1 -634 309 7 148 -1.50 46.15 260 271 11 4 597 -! -634 309 10 143.50 20.15 260 252 -8 -3 577 0 -634 309 13 149 2.50 20.07 260 278 18 7 601 2 -634 309 16 156 2. O0 20.07 260 306 46 18 629 1 -634 309 19 162 2. O0 2 0.05 520 330 -190 -37 653 I -634 309 22 166 1.00 21 ~ C5 520 345 -175 -34 670! -634 309 25 iTC 1.50 21.05 520 362 -158 -30 686 I -634 309 28 174 1.50 21.05 "; 520 378 -142 -27 702 1 -634 309 31 178 2 ~ O0 22 ~ 07 300 394 94 31 718 I -634 309 34 184 2. O0 22.07 300 419 119 40 742 1 -634 309 '3"~ 'i'gC..... 2"6-0............22.......'07............ 3'0'0....i.........44'3.................i) —i. 3 48 766 1 -634 309 40 196 -'1.00 23.07 300' 465 I65 55 791 -1 -634 309 43 187 -2.50 23,09 160 427 267 167 754 -2 -634 309 46 18o -2.50 23.09 160 399 239 lSO 726 -2 -634 309 49 172 -2.50 23.09 160 367 207 129 694 -2 -634 309 22 168 -1.00 23.09 210 233 23 ll 678 -t -753 309 ~5 165 -1. GO 23.08 210 102 -108 -51 666 -1 -872 309 58 162 -1.00 23.08 210 -29 -239 -114 653 -I -991 309 61 15c -1.00 23.07 270 554 284 105 641 -1 -397 309 64 156 -1.00 23.07 270 541 271 101 629 -! -397 309 67 153 -1.GO 23.C7 270 529 259 96 617 -1 -397 309 70!50 -1. O0 24.08 270 497 227 84 605 -1 -416 309 73 147 -1. O0 24. 08 320 485 165 52 593 -1 -416 309 7e 144 -1. O0 24.08 320 473 153 48 581 -1 -416 309 79 141 -1. O0 24 ~ 08 320 441 121 38 569 -1 -436 309 82, 14C. 00 24 ~ 10 860 438 -422 -49 565 0 -436 309 85 220 40. O0 24 ~ 10 860 790 -70 -8 887 29 -436 309 88 20G -10. O0 24. 09 280 673 -307 -31 807 -7 -436 309 g i 181 3.50 2 5. 09 980 586 -394 -40 730 3 -/*56 309 94 194 4.50 23 ~ 09 980 639 -341 -35 783 3 -456 309 q 7 2 C 7 4 ~ O0 2 0. C9 980 691 -289 -29 835 3 -456 309 i__OC 220 3. 50 15 ~ 10 1100 743 -357 -32 887 3 -456 309!03 229 3. O0 15 ~ 10 1 IO0 779 -321 -29 924 2 -456 309 [06 238 3. O0 15. 10 liO0 816 -284 -26 960 2 -456 309 109 247 3. O0 15.10 1100 852 -248 -23 996 2 -456 309!12 255 2.50 15.10 1100 884 -216 -20 1029 2 -456 309 i15 262 2.50 15.08 900 912 12 1 1057 2 -456 309!!~ 26c 2. 50 15.Od 900 940 40 4 1085 2 -456 309!21 276 2. O0 16.10 940 948 8! 1113 1 -476 309!24. 365.,2.50......... I6..........10....... 940. 1304................3._9_4 39 1472 -2 -476 309 127 350 -7. O0 16.10 1100 1240 140 13 1412 -5 -476 309 130 33C -1.50 16.10 1100 1164 6/* 6 1331 -1 -476 309 133' 338 2.50 16,10 lIO0 1199 99 g 1363 2 -476 309 136 3/,5 2.50 16.10 1220 1227 7 1 1392 2 -/*76 309 133 352 2.00 16,10 1220 1235 15 1 1420 1 -496 309 LAG1 = '....... O, -' LaG2"':..................O;...................... LAG3 = 49 K1:.302541, K2 =.218062, K3 = -1.487083 K4 = 19.457024, SUM = 2.046324E+06, HCT::500000 NMAX = _.........17!................. NO RMER=_._=_...............-__3_ 46_..7_4_8_.!.................'.....AV.GINS = 601.760559

-87 -TABLE 13 EXPERIMENTAL DATA AND CORRELATION FOR DOG I MEASURED ESTIMATED PANCRE- PANCREFEMORAL BLOOD ~TIC ATIC PERCENT TIME GLUCOSE DG/OT IhSULIN FLOW INSULIN INSULIN ERROR ERROR TERM 1 TERM 2 TERM 3 TERM 4 MIN MG PCT ML; U/I~L ML/MIN!~t'/ML MU U/ML MU U/ML I 66, O0 18. 25 175 -773 -948 -542 1008 0 289 -2070 4 S4.00 30.25 1625 -444 -2069 -127 1337 0 289 -2070 7 122 9.30 41. 25 1625 361 -1264 -78 1830 312 289 -2070 10 15G 9.30 50. 25 2525 855 -1670 -66 2324 312 289 -2070 13 15S 9.30 57.25 2525 1239 -1286 -51 2707 312 289 -2070 16 16S 3.10 60 ~ 25 1 595 1195 -400 -25 2872 104 289 -2070 1~ 178 3,10 63,25 2462 1359 -1103 -45 3036 104 289 -2070 22 183 3.10 66.25 2462 1524 -938 -38 3201 104 289 -2070 25 1~7 2.10 69.25 2462 1549 ' -913 -37 3259 70 289 -2070 28-' lgC 1.10 72.25 2850 1573 -1277 -45 3318 37 289 -2070 31 193 1.10 75.25 2850 1632 -1218 -43 3376 37 289 -2070.34!94!-!o.... 78.25.... 1~38.................l~p~............-!.69 -9 3413 37 289 -2070 37 196.50 81.25 1838 1675 -163 -9 3440 17 289 -2070 4(; 197.50 84.25 400 1702 1302 325 3466 17 289 -2070 43 20I.50 87.25 400 1742 1342 336 3507 17 289 -2070 46 205 1.30 92.25 1 162 1838 676 58 3576 44 289 -2070 4s 209 1.30 101.25 1425 1907 482 34 3645 46 289 -2070 52 214 1.30 110.25 1425 1976 551 39 3714 44 289 -2070 55 221 1.75 119.25 1300 2108 808 62 3830 59 289 -2070 58 228 2.20 128.25 13.00 2240 940 72 3947 74 289 -2070 61 232 2.20 137.25 2288 2357 69 3 4064 74 289 -2070 64 232 2.20 143.25 4600 2395 -2205 -48 4103 74 289 -2070,57 232. O0 149.25 4600 2487 -2113 -46 4103 0 455 -2070 7C 232. O0......155..........25.............._42_75.........2_735........._T. _154:.0............. -36 4103 0 703 -2070?~ 231.DO 161.25 4275 2933 -1342 -31 4094 0 909 -2070 76 229 —. 50 167 ~ 25 1788 3076 1288 72 4067 -17 1095 — 2070 79 22 8 - ~ 50 175.25 1788 3152 1364 76 4041 - 17 1 199 -2070 82 226 -. 50 184.25 1788 3188 1400 78 4014 -17 1261 -2070 85 224 -. 55 196 ~ 25 1437 3216 1779 124 3982 -18 1323 -2070 88 222 -.60 __.2.0..8_............:_25..................14._3_7.............. 3245..1.808 126 3951 -20 1385 -2070 91 212 -.60 214.25 3050 3275 225 7 3919 -20 1447 -2070 94 183 -. 60 216.25 3050 2990 -60 -2 3572 -20 1509 -2070 97 155 -9.50 217.25 1275 ' 2250 975 76 3068 -319 1571 -2070 100 126 -9,50 219.25 1737 1808 71 4 2564 -319 1633 -2070 103 11C -9,50 221.25 1737 1438 -299 -17 2133 -319 1695 -2070 ]06 cj4 -5.40 213...............2_5_......!_.4_3_7..............135!. _-86 -6 1846 -181 1757 -2070 i09 77 -5.40 186.25 1088 1127 39 ' 4 1560 -181 1819 -2070 '12 67 -5.40 159.25 1088 985 -103 -9 1273 -181 1963 -2070 115 60 -3.95 132.25 600 1087 487 81 1141 -133 2149 -2070 118 52 -2.50 108,25 600 1189 589 98 1008. -84 2335 -2070 i21 4c -2.50 92.25 637 1242 605 95 875 -84 2521 -2070 124.....53...... —.2.., 50.......9_4..........25 637 1441 804 126 888 -84 2707 -2070 127 58 1.05 96.25 950 1830 880 93 973 55 2873 -2070 130 63 1.60 98.25 863 2038 1175 136 1058 54.............299.7..... -2070 133 64 1.60 100.25 863 2225 1362 158 1121 54 3121 -2070 136 65.40 102.25 938 2330 1392 148 1142.......1_3............3245_..... —2070 13S 67.40 1C4.25 938 2475 1537 164 1164 13 3369 -2070 142 71 _,.4._0...........!Q7.....25............595_..............._2_(~._41............2046 344 1185 13 3514 -2070 145 76 1.10 108.25 1063 2926 1863 175 1280 37 3679 -2070 148 8/ 1.80 110.25 1063 3231 2168 204 1376. 60......... _3865 -2070 151 88 1.80 113.25 4075 3595 -480 -12 1471 60 4134 -2070 154 95 1.80 140.25 6125 3963 '-2162 -35 1592 60......43.82_ -2070 157 103 2.50 167.25 6125 4181 -1944 -32 1724 84 4444 -2070 16C 110 - 2.50 194.25 7800 4335 -3465 -44 1857 84 4464 -2070 163 113 2.50 221.25 7800 4482 -3318 -43 1963 84 4506 -2070 166 116 1. O0 23 8. 25 5 1 O0 452 6 -574 - 11 2 016 34 4547 -2070 16.S 119 1.00 238.25 5100 4620 -480 -9 2069 - 34 4588 -2070 172 122 1. O0 238. 25 5100 4301 -799 -16 2122 34 4216 -2070 175 125 1.00 239.25 /,150 3796 -354 -9 2175 34 3658 -2070 17~ 128 1.00 239.25 4150 3292 -858 -21 2228 34 3100 -2070 181 131 1.00 240 —;'2-5'................'2-75'0-...............2~8-'7 37 1 2281 34 2542 -2070 184 135 1.00 240.25 2750 2373 -377 -14 2343 34 2067 -2070 LAG1 = 2, LAG2 = 5, LAG3 = 65 K1 = 2.210507, K2 = 16.782595, K3: 2.583465 K4 = -280.676727, SUM = 1.062105E+08, HCT =.500000 _. NMAX: 184, NORMER:.567604, AVGINS = 2324.735107

-88 -TABLE 14 EXPERIMENTAL DATA AND CORRELATION FOR DOG J MEASURED ESTIMATED PANCRE- PANCREFEMORAL BLO]D ATIC ATIC PERCENT TIME GLUCOSE DG/DT IhSULIN FLOW IhSULIN INSULIN ERROR ERROR TERM 1. TERM 2 TERM 3 T ERMTER M 4 MIN MG PCT MU U/ML ML/MIN MfU/ML MU U/ML MU U/ML 1 73.00 23.30 9100 ~ 14299 5199 57 164.8 - -544 13195 4 114.00 41.30 91~: 00 15_199 6099 67 2548 -0 -544 13195 7 154 13.40 59.30 11700 15337 3637 31 3450 -764 -544 13195 10 194 13,40 77.30 12400 16242 3842 31 4355 -764 -544 13195 13 211 13.45 95..30 124o00 1...i6630.. 4230......34 4746.767 —..-'54' 4....i13i 95'16 229 5.80 110.30 13600 17457 3857 28 5136 -331 -544 13195 19 246 5.80 115. 30 13600 17847 4247 31 5527 -331 54 119 22 25S 5.80 115.30 13500 18139 4639 34 5819 -331 -544 13195 25 270 3.6O~ 115.30 13500~ 3jb0~~~ 1 8507 500~~~-~~~i O 67 37 -~~ ~~~ 6061 -2 ~ ~~;2 05 ~~ ~ ~ -~ —544 13195 28 281 3.60 116.30 13500 18750 5250 -3 63 -'2-)5 131.544.. 31 287 3.60 116.30 15700 18889 3189 20 6443 -205 -544 13195 34 284 1.30 116.30 15700 18953 3253 21 6376 -74 -544 13195 37 281 -1.00 116.30 15700 18633 2933 19 6308 57 -928 13195 40 278 -1.00 117.30 15700 17989 2289 15 6241 57 -1504 13195 43 278 'i.00..117.30.14800 17413 263 18 6-241-...57.-208..1 1.3195 46 278.00 117.30 14800 16780 1980 13 6241 -0 -2657 13195 4S 278.00 118.30 14800 16236 1436 20 19 52 265.O0 118.30 14800 15468 668 5 5954 -0 -3681 13195 55 246 -6.40 118.30 14800 15402 602 4 5523 365 -3681 13195 58 227 -6.40 119.30 15700 14971 -729 -5 5092 365 _3681 13195 61 217 -6;40 119.30 15700 14753 -947 -6 4874 365 -3681 13195 64" 226 -1.65 119.30 15700 14659 -1041. -7 5083 94 -3713 13195 67 236' 3.10' 120.30 16400 14597 -1803 -11 529 1 -177 -3713 13195 70 245 3.10 120.30 16400 14806 -1594 -10 5500 -177 -3713 13195 73 224 3.10 120.30 16400 14302 -2098 -13 5029 -177 -3745 13195 76 203 -7.00 120.30 18900 _14407... — 44_93........_-2_4_...____5__.....99.3745....... 13195 79 182 -7.00 120.30 18900 13936 -4964 -26 4086 399 -3745 13195 82 155 -7.00 120.,30 18900 13329 -5571 -29 3480 399 -3745 13195 85 125 -10.O0 120.30 18900 12795 -6105 -32 2806 570 88 95 -10.00 120.30 17000 12122 -4878 -29 2133 570 -3777 13195 91 74. -10.00 120.30 17000 11650 -5350 -31 1661 570 -3777 13195 94 71 -5.50 120.30 2537.2937 8757 345 1594 314 -3.809 13195 97 68 -1.00 113.30 2537 10970 8433 332 1527 57 -380 9 13195 100 65 -1.00 92.30 2537 10903 8366 330 1459 57 -3809 13195 103 61 -1.00 71.30 2537 10770 8233 325 1.358 57 -3841 13195 06 _ 56 -1.50 51.30 1075 10697 9622 895 1257 86 -3841 13195 109 52 -1.50 33.30 1075 10596 9521 886 1156 86 -3841 1319 112 5C -1.50 27.30 1075.10563 9488 883 1122 86 -38_4_1. 13.1_95 115 50.00 27.30 700 1047 7 9777 1397 1122 -0 -3841 131 95 I1e 50.00 27.30 700 104 77 9777 1397 1122 -0 -3841 13195 121 51.00 27.30 700 10490 9790 1399 1136 70 -3841 13195 124 52.30 34.30 700 10514 9814 1402 1176 -17 -3841 13195 _~~~~~~~~~~~~~~~~~~~~~~~17 -3841 13195 127 54.60 46.30 19100 10537 -8563 -45 1217 1303 56.60 58. 30 1911 00 ~ ~ __ ~~105 77 -8523_~-85~2~~~ _~~___ -45 1257 -34 -3841 13195 133 7C.60 70.30 19100 11342 -7758 -41 1574 -34 -3393 13195 136 84 4.70 82.30 21100.1_2097..... -43...90 -268 -2721..-13195_ 139 98 4.70 94.30 21100 13086 -8014 -38 2207 -268 -2048 13195 -1 4 7 70 106 30 21100 ' 13885 -7215 -34 2398 -268 -1440 13195 145 113 1.90 118.30 19800 14748 -5052 -26 2526 -108 -864 13195 148 118 1.90 130.30 19800 14876 -4924 -25 2654 -108 -864 13195 151 122 1.90 145.30 19800 14971 -4829 -24 2748 -108 -864 1319 154 124 1.15 160.30 19800 15040 -4760 -24........2775 -66 -864 13195. 157 125.40 175.30 17800 15110 -2690 -15 2802 -23 -864 13195 16C 126.40 190.30 17800 14785 2829 -23 -1216 13195 163 126.40 204.30 17800 14401 -3399 -19 2829 -23 -1600 13195 166 126.O0 216.30 16400 14040 -2360 -14 2829 -0 -1984 13195 2829 -0-94 13195 169 126..0 222.-'30.. 16400 13655 -2745.........-1..=...282-9.-r0-..... 172 128.00 228.30 16400 13307 -3093 -19 2865 -0 -2753 13195 175 130 ~~~~~~-.80 2..~ ~ 34.~,30 16000 ~~-~12931~ 1- - 3069 -19-3137 13195 178 132.80 238.30 16000 12601 -3399 -21 2972 -46 -3521 13195 ----- - ~~~ ~ ~~~~~~-23 3008 -46~ -3952 13195 181 134.80 240.30 16C 0 0 12253 -3747 184 134.40 242.30 16000 11860 -4140 r26 3008 -23 -4321 13195 187 134.00 244.30 17100 7L~d~' -~~~ ~1402 -5698 ----— 31~108- - — 0 —33 3008 -0 -4801 13195 190. 134..00 246.30 17100 10922 -6178 -36 3008 -0 -5281 13195 i93 131 6 248.36 -405 -5761 13195 196 136.40 249.30 18200 9993 -8207 -5 3062 -23 -6242 13195 19 _ 138.40 251.30 18200 9604 -8596 -47 3089 -23 -6658 13195 202 136.40 253.30 18200 9239 -8961 -49 3044 -23 -6978 13195 205 132 '1.20 255....... 30.....120'0..........9'i-05.......-'85.61- 195 208 128 -1.20 257. 30 1200 8785 7585 632 2883 68 -7362 13195 211 126 - 1.20 259...30.....1200.........8 539- -7339...........1- 2........2829-...-?-5'5-~.. —' 214 126 -.60 261.30 5600 8408 2808 50 2829 34 -7650 13195 217 126.00 263.30 5600 8310.2710 48 2829 0 7714 13195.1, A n 1~ 11. 'A A 1 12A An A9A/l 48A 294 -0 -7778 13195 '220 126.00 264..30......_8 e _-45~ __35_2?_~_~_~~-0~~__-7f 39 LAG! =......... L AG2__- =_______ 4,t___~_ L~_ AG3 = _ __ 3 5 K1 = 3.367422, K2 = _-34.227822, K =-.816 K4 = 614.3] 1539,......SUM. =..2, 53_1._'80E+09,.........................HCT.~~ ~_.=~ ~........,5~000.00..NMAX _=..........2.20,rr~........NR.MER __....,-_.........._44.2275.. _. '.......~ AVGIN S-.=...1_,.3_31.3_9...E+. 0_4.

-89 -TABLE 15 EXPERIMENTAL DATA AND CORRELATION FOR DOG L MEASURED ESTIMATED FANCRE- PANCREFEMORAL BLOOD ATIC ATIC PERCENT TIME GLUCOSE DG/OT INSULIN FLOW INSULIN INSULIN ERROR ERROR TERM 1 TERM 2 TERM 3 TERM 4 MIN MG PCT MU U/ML ML/MIN __ U/ML MU U/ML MU U/ML_ __ 1 89.00 20.25 4910 7528 2618 53 9528 -O -2017 16 4 98.00 21.25 4910 7528 2618 53 9528 -O -2017 16 7 106.00 21.25 4910 7528 2618 53 9528 -O -2017 16 10 115 2.90 22.25 4910 7189 2279 46 9528 -338 -2017 16 13 121 2.90 23.25 4910 7189 2279 46 9528 -338 -2017 16 16 127 _ 2.90 23.25 8530 7189 -1341 -16 9528 -338 -2017 16 19 133 2.00 24.25 8530 7616 -914 -11 9850 -233 -2017 16 22 13S 2.CO 25.25 14600 8580 -6020 -41 10814 -233 -2017 16 25 145 2.00 30.25 14600 9544 -5056 -35 11778 -233 -2017 16 28 151 2.00 34.25 1,4600 10508 -4092 -28 12742 -233 -2017 16 31 158 2.00 38.25 10500 11172 672 6 13406 -233 -2017 16 34 168 2.00 42.25 10500 11837 1337 13 14071 -233 -2017 16 37 178 2.65 48.25 12800 12426 -374 -3 14736 -309 -2017 16 4C 188 3.30 53.25 12800 13015 215 2 15401 -385 -2017 16 43 193 3.30 59.25 14600 13680 -920 -6 16065 -385 -2017 16 46 200 3.30 65.25 14600 14344 -256 -2 16730 -385 -2017 16 49 206 1.50 71.25 15800 15363 -437 -3 17539 -175 -2017 16 52 211 2.00 77.25 18200 16402 -1798 -10 18636 -233 -2017 16 55 216 2.00 83.25 18200 17499 -701 -4 19733 -233 -2017 16 58 220 1.50 89.25 14400 18654 4254 30 20830 -175 -2017 16 61 226 1.50 95.25 14400 19208 4808 33 21384 -175 -2017 16 64 233 1.50 101.25 17200 19984 2784 16 22159 -175 -2017 16 67 241 2.00 107.25 17200 20590 3390 20 22824 -233 -2017 16 7C 248 2.50 113.25 17200 21086 3886 _23 _ 23378 -292 -2017 16 73 249 2.50 119.25 17800 21584 3784 21 23877 -292 -2017 16 76 24S 2.50 125.25 17800 21982 4182 23 24375 -292 -2117 16 79 250.20 130.25 17800 22860 5060 28 24984 -23 -2117 16 82 25C.20 133.25 17800 23590 5790 33 25815 -23 -2218 16 85 250.20 136.25 17800 24320 6520 37 26646 -23 -2319 16 88 250.00 139.25 25600 25074 -526 -2 27477 _ -0 -2420 16 91 250.00 142.25 25600 25140 -460 -2 27544 -0 -2420 16 94 248.00 144.25 22300 24904 2604 12 27610 -0 -2722 16 97 247 -.20 141.25 21000 24591 3591 17 27677 23 -3126 16 100 246 -.40 138.25 21000 24233 3233 15 27699 47 -3529 16 103 246 -.40 136.25 25000 23829 -1171 -5 27699 47 -3932 16 106 246 -.40 134.25 25000 23325 -1675 __ -7_ 27_699 __ 47_ _-4436 16 109 246.00 133.25 25600 22730 -2870 -11 27655 -0 -4941 16 112 246.00 135.25 25700 21992 -3708 -14 27522 -0 -5546 16 115 246.00 136.25 25700 21254 -4446 -17 27389 -0 -6151 16 118 246.00 138.25 20700 20516 -184 -1 27256 -0 -6755 16 121 246.00 139.25 2C700 19911 -789 -4 27256 -0 -7360 16 124 246.00 _141.25_ 28300 19306 -8994 -32 27256 -0 -7965 _ 16 127 246.00 143.25 26700 18701 -7999 -30 27256 -0 -8570 16 130 246.00 148.25 26700 18096 -8604 -32 27256 -0 -9175 16 133 245.00 157.25 27700 17491 -10209 -37 27256 -0 -9780 16 136 245.00 167.25 27700 16887 -10813 -39 27256 -0 -10385 16 139 244 -.20 176.25 22700 16305 -6395 -28 27256 23 -10990 16 142 244 -.20 181.25 __ 198 100 15700 -4100 -21 27256 ___23 -11595 _ 16 145 243 -.20 184.25 19800 15095 -4705 -24 27256 23 -12200 16 148 242 -.20 187.25 13700 14490 790 6 27256 23 -12805 16 151 242 -.20 190.25 13700 14020 320 2 27189 23 -13208 16 154 241 -.20 185.25 15700 13651 -2049 -13 27123 23 -13511 16 157 241 -.20 170.25 13800 13282 -518 -4 27056 23 -13813 16

-90 -TABLE 15 (CONT'D) 16C 24C -.20 155.25 13800 __ 12913 -887 -E 26990 23 -14116 16 163 239 -.20 140.25 12300 12544 244 2 26923 23 -14418 16 166 237 -.20 125.25 12300 12579 279 2 26857 23 -14318 16 169 236 -.50 122.25 10900 12749 1849 17 26790 58 -14116 16 172 234 -.50 125.25 9900 12884 2984 30 26724 58 -13914 16 175 233 -.50 128.25 9900 13019 3119 32 26658 58 -13713 16 178 231 -.50 131.25 9800 13154 3354 34 26591 58 -13511 16 181 23C -.50 134.25 9800 12988 3188 33 26425 58 -13511 16 184 22E -.50 133.25 8900 12721 3821 43 26259 58 -13612 16 187 227 -.50 127.25 7700 12353 4653 60 26092 58 -13813 16 190 225 -.50 122.25 7700 12086 4386 57 25926 58 -13914 16 193 222 -.50 119.25 7800 11718 3918 50 25760 58 -14116 16 196 218 -.50 115.25 7800 11451 3651 47 25594 58 -14217 16 199 215 -1.10 111.25 6600 11053 4453 67 25428 128 -14519 16 202 212 -1.10 107.25 6000 10181 4181 70 25261 128 -15225 16 205 207 -1.10 103.25: 6000 9006 3006 50 25095 128 -16233 16 208 203 -1.10 99.25 5400 7933 2533 47 24929 128 -17141 16 211 1CE -1.60 94.25 5400 6819 1419 26 24563 187 -17947 16 214 190 -1.10 90.25 6800 5991 -809 -12 24198 128 -18351 16 217 183 -2.05 85.25 9100 5434 -3666 -40 23832 239 -18653 16 22C 175 -2.50 81.25 9100 4819 -4281 -47 23467 292 -18956 16 223 193 -2.50 78.25 6800 3984 -2816 -41 22935 292 -19258 16 226 211 -2.50 75.25 6800 4672 -2128 -31 22514 292 -18149 16 229 229 6.00 70.25 3100 4561 1461 47 21882 -700 -16637 16 232 24E 6.00 64.25 2800 5243 2443 87 21051 -700 -15124 16 235 268 6.CO 59.25 2800 592' 324 4 112 20220 -70-0 -13612 16 238 287 6.50 56.25 2800 6245 3445 123 19389 -759 -12402 16 LAG1 = 18, LAG2 = 7, LAG3 = 71 K1 = 13.849494, K2 = -58.359324, _ K3=_ -12.603527 K4 = -611.749435, SUM = 1.188603E+09, HCT =.500000 NMAX = 240, NCFMER =.274459, AVGINS = 1.404415E+04

-91 -T^B~ 16 EXPERIMENTAL DATA AND CORRELATION FOR DOG M MEASURED ESTIMATED F,~INCR E- PaNCREFENORAL BLOOD ATIC ATIC PERCENT TIME GLUCOSE DG/DT I!XSULIN FLOW IkSULIN INSULIN ERROR ERROR TERM i TERM 2 TERM 3 TERM 4 MIN MG PC'T MU U/ML ML/MIN Mb/ML MU U/ML MU U/ML 1 74 ~ O0 27. 10 16900 20869 3969 23 495 0 1094 19280 4 86 ~ GO 75 ~ 10 16900 22895 5995 35 575 0 3040 19280 7 98 4. O0 123 ~ 10 16900 25951 9051 54 656 1029 4986 19280 10 111 4. 10' 171 ~ 12 33100 28008 -5092 -15 742 1055 6932 19280 13 124 4.20 194 ~ 12 33100 29050 -4050 -12 826 1081 7864 19280 16 132 4.20 209 ~ 12 33100 29713 -3387 -10 881 1081 8472 19280 19 131 2.00 224 ~ 12 33100 29751 -3349 -10 877 515 9080 19280 22 131 -.20 239.13:33400 29789 -3611 -11 873 -51 9688 19280 25 130 -. 20 252 ~ 13 33400 30312 -3088 -9 869 -51 10215 19280 28 132 -.20 264 ~ 13 33400 30811 -2589 -8 881 -51 10701 19280 31 134,60 276 ~ 14 41400 31515 -9885 -24 893 154 11188 19280 34 135.60 281, 14 41400 31730 -9670 -23 905 154 11390 19280 37 139.60 283,14 41400 31833 -9567 -23 928 154 11471 19280 40 143 1.40 285 ~ 15 41100 32148 -8952 -22 956 360 11553 19280 43 147 1.40 287,15 41100 32257 -8843 -22 984 360 11634 19280 46 14~ 1,40 290 ~ 15 41100 32393 -8707 -21 998 360 11755 19280 49 147. 35 290, 15 41 100 32109 -8991 -22 984 90 11755 19280 52 145 -, 70 292 ~ 16 43700 31906 -11794 -27 970 -180 11836 19280 55 143 -,70 326 ~ 16 43700 33270 -10430 -24 956 -180 13215 19280 58 150 -, 70 377 ~ 16 43700 ~5381 -8319 -19 1000 -180 15282 19280 61 156 2.20 428, 14 45500 38239 -7261 -16 1044 566 17349 19280 64 163 2, 20 475 ~ 14 45500 40188.-5312 -12 1088 566 19254 19280 67 164 2.20 520 ~ 14 45500 42022 -3478 -8 1097 566 21078 19280 70 163 -,40 554,14 46200 42723 -3477 -8 1089 -103 22457 19280 73 162 -, 40 564 ~ 14 46200 43120 -3080 -7 1081 -103 22862 19280 76 160 -.40 563.14 46200 43068 -3132 -7 1069 -103 22821 19280 79 I63 -. 60 572 o i4 46200 43401 -2799 — 6 1089 -I54 23186 19280 82 166 1.00 580.i3 50600 44157 -6443 -I3 liIO 257 23510 I9280 85 16c. 1,00 586,13 50600 44420 -6180 -12 1130 257 23754 19280 88 179 1. O0 596 ~ 13 50600 44891 -5709 -11 1195 257 24159 19280 9I lg2 4.40 604 ~ I3 55C00 46178 -8822 -16 I283 1132 24483 19280 94 205 4.40 625.13 55000 47118 -7882 -14 1372 1132 25335 19280 97 214 4,40 670,13 55000 49003 -5997 -11 1432 1132 27159 19280 100 215 2,35 715 ~ 17 55C00 50305 -4695 -9 1438 605 28983 19280 103 216, 30 760 ~ 17 50000 51607 1607 3 1444 77 30807 19280!06 217, 25 805 ~ 17 50000 53423 3423 7 1448 64 32631 19280 109 219.20 850,17 50000 55247 5247 10 1460 51 34455 19280 112 223. 85 895.17 50000 57268 7268 15 1491 219 36279 19280 ii5 228 1.50 936 ~ 21 59700 59127 -573 -1 1521 386 37941 19280 118 232 1. 50 928.21 59700 58833 -867 -1 1551 386 37617 19280 121 23c 1,50 904 18 54800 57906 3106 6 1597 386 36644 19280 124 245 2.30 880.18.54800.. 5.7_!77...........23.77.........................4..............1_63_5_..............59..~......_3_5__67_1_......._~1_9_2_8.9.... 127 257 2.20 856.18 54800 56260 1460 3 1716 566 34698 19280 130 27C 4.40 832.19 56500 55942 -558 -1 1805 1132 33725 19280 133 283 4,40 808,19 56500 55057 -1443 -3 1893 1132 32753 19280 136 292 4.40 784.19 56500 54142 -2358 -4 1950 1132 31780 19280 139 291 2, 10 765.19 56500 52776 -3724 -7 1946 540 31010 19280 142 291 -, 20 750,19 51900 51572 -328 -1 1942 -51 30401 19280 145 290 -. 20 735, 19 51900 50960 -940 -2 1938 -51 29793 19280 148 292 -.20 720 ~ 19 51900 50366 -1534 -3 1952 -51 29185 19280 IS1 294. 70 705.21 56300 50004 -6296 -I1 I966 180 28577 19280 i54 296. 70 690,21 56300 49410 -6890 -12 1980 180 27969 19280 157 2S5.70 675,21 56300 48794 -7506 -13 1973 180 27361 19280

-92 -TABLE 16 (CONT'D) 160 293 -.93 630.20 50900 46540 -4360 -9 1955 -232 25537 19280 163 29C -.90 560.20 50900 43685 -7215 -14 1937 -232 22700 19280 166 275 -.90 500.20 50900 41154 -9746 -19 1838 -232 20268 19280 169 236 -6.95 440.20 50900 36904 -13996 -27 1577 -1788 17836 19280 172 197 -13.00 380.15 48800 32655 -16145 -33 1317 -3345 15403 19280 175 158 -13.00 320.15 48800 29962 -18838 -39 1056 -3345 12971 19280 178 139 -13.00 280.15 48800 28212 -20588 -42 928 -3345 11350 19280 181 120 -6.40 264.13 1(7C0 29134 9434 48 799 -1647 10701 19280 184 1CO -6.40 240.13 1S700 28033 8333 42 671 -1647 9728 19280 187 86 -6. 40 216.13 19700 26961 7261 37 572 -1647 8756 19280 190 75 -4.20 192.13 10700 26480 15780 147 498 -1081 7783 19280 193 64 -3.70 169.13 1C700 25609 14909 139 430 -952 6850 19280 196 70 -3.70 147.13 10700 24752 14052 131 465 -952 5959 19280 199 107 4.45 120.13 10700 26007 -15307 143 718 1145 '4864 19280 202 145 12.60 93.15, 54800 27262 -27538 -50 970 3242 3770 19280 205 183 12.60 161.15 54800 30271 -24529 -45 1223 3242 6526 19280 208 21C 12.60 230.15 54800 33248 -21552 -39 1404 3242 9323 19280 211 239 8.85 299.16 40000 35273 -4727 -12 1596 2277 12120 19280 214 267 9. 4 365.16 40000 38276 -1724 -4 1783 _ 2419 14795 19280 217 280 9.30 425.16 40000 40769 769 2 1869 2393 17228 19280 220 285 1.80 485.19 25700 41307 15607 61 1905 463 19660 19280 223 29C 1.80 542.19 25700 43654 17954 70 1941 463 21970 19280 226 292 1.80 518.19 25700 42689 16989 66 1949 463 20997 19280 229 284 -.30 494.19 25700 41128 15428 60 1901 -77 20024 19280 232 272 -2.40 470.18 22700 39532 16832 74 1818 -618 19052 19280 235 27C -5.00 446.18 22700 37877 15177 67 1805 -1287 18079 19280 23E 256 -2.40 422.18 22700 37478 14778 65 1710 -618 17106 19280 241 242 -4.70 398.15 22700 35820 13120 58 1616 -1209 16133 19280 244 228 -4.70 372.15 22700 34671 11971 53 1522 -1209 15079 19280 247 207 -4.70 345.15 22700 33436 10736 47 1381 -1209 13985 19280 250 182 -8.20 324.17 19900 31520 11620 58 1216 -2110 13133 19280 253 157 -8.20 303.17 19900 30504 10604 53 1052 — 2110 12282 19280 256 135 -8.20 282.17 19900 29502 9602 48 902 -2110 11431 19280 259 117 -7.15 271.17 19900 29204 9304 47 779 -1840 10985 19280 262 98 -6.10 250.16 9200 28501 19301 210 657 -1570 10134 19280 265 80 -6.10 220.16 9200 27163 17963 195 535 -1570 8918 19280 268 75 -6.10 191.16 9200 25951 16751 182 499 -1570 7742 19280 271 6c -1.80 164.13 6100 25927 19827 325 463 - -463 6648 19280 274 64 -1.80 137.13 61CO 24796 18696 306 426 -463 5553 19280 LAG1 = 0, LAG2 = 4, LAG3 = 0 KI =.334194,, K2_- __ 51.460q585,-__ K...3_- __2.0267_66 K4 = 118.9857409 SUM = 1.063288E+10, HCT =.500000 NMAX = 275, NGPMER =.281051, AVGINS = 3.846087E+04

-93 -TABLE 17 EXPERIMENTAL DATA AND CORRELATION FOR DOG N MEASURED ESTIMATED PAtCRE- PANCREFEMORAL BLOOD ATIC ATIC PERCENT TIME GLUCOSE DG/DT INSULIN FLOW INSULIN INSULIN ERROR ERROR TERM 1 TERM 2 TERM 3 TERM 4 MIN MG PCT MU U/ML ML/MIN Mb/ML M__U U/ML MU U/ML ____ 1 152.00 25.26 920 5303 4383 476 -422 -0 -1647 7372 4 167.00 29.26 5e75 5303 -572 -10 -422 -O -1647 7372 7 183.GO 30.26 5875 5260 -615 -10 -465 -0 -1647 7372 IC 200.00 29.26 2670 5215 2545 95 -510 -0 -1647 7372 13 217 5.00 29.26 2670 5124 2454 92 -559 -42 -1647 7372' 16 233 5.35 28.26 2670 5072 2402_ 90 -608 -45 -1647 7372 19 243 5.70 28.26 2670 5020 2350 88 -657 -48 -1647 7372 22 254 5.7C 30.26 4050 4989 939 23 -688 -48 -1647 7372 25 266 5.90 33.22 6350 4956 -1394 -22 -719 -50 -1647 7372 28 281 3.60 36.22 6350 4940 -1410 -22 -755 -30 -1647 7372 31 289 3.60 39.19 1480 4897 3417 231 -798 -30 -1647 7372 34 297 4.40 42.19 1480 _4866 3386 229 -822 -37 -1647 __ 7372 37 308 5.00 44.19 1480 4837 3357 227 -846 -42 -1647 7372 4G 320 2.80 45.19 5100 4829 -271 -5 -873 -24 -1647 7372 43 332 2.70 47.19 5100 4795 -305 -6 -907 -23 -1647 7372 46 343 3.35 48.19 5100 4755 -345 -7 -941 -28 -1647 7372 49 352 4.00 50.19 5100 4715 -385 -8 -976 -34 -1647 7372 52 361 4.00 49.20 5500 4690 -810 -15 -1002 -34 -1647 7372 55 37C 4.00 47.20 5500 4664 -836 -15 -1028 -34 -1647 7372 58 374 3.00 45.20 5500 4372 -1128 -21 -1053 -25 -1922 7372 61 37E 3.00 43.22 6400 4218 -2182 -34 -1070 -25 -2059 7372 64 383 3.00 41.22 6400 4206 -2194 -34 -1082 -25 -2059 7372 67 385 1.40 41.22 6400 4276 -2124 -33 -1094 -12 -1991 7372 70 386 1.40 43.22 8500 4335 -4165 -49 -1103 -12 -1922 7372 73 387 1.40 45.22 8500 4332 -4168 -49 -1107 -12 -1922 7372 76 409.90 47.22 8500 4264 -4236 -50 -1110 -8 -1991 7372 79 472.40 48.22 8500 4059 -4441 -52 -1114 -3 -2197 7372 82 535.40 55.20 6700 3672 -3028 -45 -1295 -3 -2402 7372 85 596.40 70.20 6700 3285 -3415 -51 -1475 -3 -2608 7372 88 575 21.00 79.20 6700 2728 -3972 -59 -1653 -177 _ -2814 7372 91 55E 21.00 88.23 4420 2576 -1844 -42 -1668 -177 -2952 7372 94 538 20.50 97.23 4420 2498 -1922 -43 -1613 -172 -3089 7372 97 544 -7.40 98.23 4420 2713 -1707 -39 -1564 62 -3158 7372 10 562 -6.40 93.25 1850 2587 737 40 -1544 54 -3295 7372 103 58C -6.40 88.25 1850 2467 617 33 -1596 54 -3363 7372 106 598 -.20 84.25 1850 2363 513 28 -1648 _ 2 -3363 7372 109 616 6.00 78.25 1850 2397 547 30 -1699 -50 -3226 7372 112 634 6.00 78.22 2510 2482 -28 -1 -1751 -50 -3089 7372 115 652 6.CO 81.22 2510 2568 58 2 -1803 -50 -2952 7372 118 634 6. CO 84.22 2510 2653 143 6 -1854 -50 -2814 7372 121 616 6.00 87.26 2360 2739 379 16 -1837 -50 -2746 7372 124 598 6.00 90.26 2360 2654 294 12 -1785 -50 -2883 7372 127 562 -6.00 90.26 2360 2669 309 13 -1734 50 -3020 7372 130 516 -6.00 89.22 800 2609 1809 226 -1656 50 -3158 7372 133 468 -6.00 87.22 800 2601 1801 225 -1527 50 -3295 7372 136 43C -10.50 86.22 800 2571 1771 221 -1389 88 -3501 7372 139 411 -15.00 85.22 800 1785 985 123 -1251 126 -4462 7372 142 393 -16.CO 83.22 610 1092 482 _79 -1198 135 -5217 7372 145 374 -16.00 78.22 610 528 -82 -13 -1145 135 -5835 7372 148 363 -6.20 73.22 610 -119 -729 -120 -1091 52 -6452 7372 151 352 -6.20 69.18 750 -424 -1174 -157 -1053 52 -6796 7372 154 342 -6.20 63.18 750 -50 -800 -107 -1022 52 -6452 7372 157 338 -3.60 59.18 750 234 -516 -69 -991 30 -6178 7372

-94 -TABLE 17 (CONT'D) 16C 338 -3.60 56.18 730 598 -132 -18 -970 30 -5835 7372 163 338 -3.60 55 ~.18 " 730 941 211 29 -970 30 -5491 7372 166 335 -1.80 52.18 730 1132 402 55 -970 15 -5285 7372 169 325.00 49.18 730 911 181 25 -970 -0 -5491 7372 172 315.00 46.15 840 733 -107 -13 -942 -0 -5697 7372 175 305.00 43.15 840 556 -284 -34 -913 -0 -5903 7372 178 299 -3. 30 40.15 840 406 -434 -52 -885 28 -6109 7372 181 293 -3.30 38.18 1020 290 -730 -72 -864 28 -6246 7372 184 287 -3.30 37.18 1020 444 -576 -56 -847 28 -6109 7372 187 28C -2.00 38.18 1020 519 -501 -49 -830 17 -6040 7372 190 273 -2.00 40.17 480 675 195 41 -811 17 -5903 7372 193 265 -2.00 41.17 480 765 285 59 -789 17 -5835 7372 196 258 -2.25 43.17 480 858 378 79 -768 19 -5766 7372 199 252 -2.50 4.17 824- 4 --- - 2 44 155 -746 21 -5423 7372 202 246 -2.50 46.15 1000 1585 585 58 -729 21 -5080 7372 205 240 -2. 50 47.15 1000 1877 877 88 -712 21 -4805 7372 208 239 -2. 00 49.15 1000 2233 1233 123 -695 17 -4462 7372 211 238 -2.00 50.17 5370 2584 -2786 -52 -687 17 -4119 7372 214 236 -2.00 51.17 5370 2794 -2576 -48 -683 17 -3913 7372 217 232 -.40 51.17 5370 2989 -2381 -44 -680 3 -3707 7372 22C 226 -.40 53.16 4590 3066 -1524 -33 -672 3 -3638 7372 223 22C -.40 54.16 4590 3289 -1301 -28 -654 3 -3432 7372 226 228 -1.20 56.16 4590 3519 -1071 -23 -637 10 -3226 7372 229 265 -2.00 57.16 4590 3749 -841 -18 -620 17 -3020 7372 232 301 -2.00 61.15 1480 3850 2370 160 -725 17 -2814 7372 235 338 -2. O 67.15 1480 3951 2471 167 -830 17 -2608 7372 23E 386 12.20 73.15 1480 3795 2315 156 -935 -103 -2540 7372 241 434 12.20 79.15 620 3599 2979 481 -1062 -103 -2608 7372 244 482 12.20 82.15 620 3393 2773 447 -1200 -103 -2677 7372 247 518 16.00 85.15 620 3086 2466 398 -1338 -135 -2814 7372 250 548 16.00 88.19 620 2897 2277 367 -1458 -135 -2883 7372 253 578 16.CO 91.9 650 2673 2023'6 — 311 -1544 -135 -3020 7372 256 601 13.00 94.19 650 2544 1894 291 -1630 -109 -3089 7372 255 612 10.00 97.19 650 2346 1696 261 -1716 -84 -3226 7372 262 622 10.00 100.19 210 2248 2038 970 -1746 -84 -3295 7372 265 632 10.00 104.19 210 2081 1871 891 -1775 -84 -3432 7372 268 569 3.40 109.19.2.10 2039 1829 871 -1804 -29 -3501 7372 271 506 3.40 1 114.17 45 2150 17 15 394 -1693 -29 -3501 7372 274 445 3.40 118.17 435 2262 1827 420 -1513 -29 -3569 7372 LAGI = 4, LAG2 = 11, LAG3 = 55 K1 = -.373144, K2 =_-4.374039, K3 = -8.923467 K4 = 838.814850, SUM = 3.383696E+08, HCT =.500000 NMAX = 275, NORMER =.686968, AVGINS = 2806.974609

-95 -TABLE 18 EXPERIMENTAL DATA AND CORRELATION FOR DOG S MEASURED ESTIMATED P6NCRE- PANCREFEMORAL BLOCD ATIC ATIC PERCENT TIME GLUCOSE DG/DT INSULIN FLOW INSULIN INSULIN ERROR ERROR TERM I TERM 2 TERM 3 TERM 4 MIN MG PCT Ml U/ML ML/MIN MU/ML MU U/ML MU U/ML______ 1 85.00 31.30 462 1397 935 202 146100 0 1498 -14711 4 85.00 30.30 462 1397 935 202 14610 0 1498 -14711 7 85.00 29.30 329 1397 1068 325 14610 0 1498 -14711 10 85.00 27.30 329 1397 1068 325 14610 0 1498 -14711 13 85.00 26.33 538 1397 859 160 14610 0 1498 -14711 16 85.00 25.22 412 1397 985 239 14610 0 1498 -14711 19 85.00 23.22:412 1397 985 239 14610 0 1498 -14711 22 85.00 22.30 205 1397 1192 582 14610 0 1498 -14711 25 85.00 23.30 134 1397 1263 943 14610 0 1498 -14711 28 85.00 24.27 134 1397 1263 943 14610 0 1498 -14711 31 85.00 25.27 134 1397 1263 943 14610 0 1498 -14711 34 85.00 26.30 110 1397 1287 1170 14610 0 1498 -14711 37 85.00 27.22 105 1397 1292 1231 14610 0 1498 -14711 40 85.00 27.22 105 1397 1292 1231 14610 0 1498 -14711 43 85.00 27.22 105 1397 1292 1231 14610 0 1498 -14711 46 85.00 27.30 115 1397 1282 1115 14610 0 1498 -14711 49 85.00 28.30 115 1397 1282 1115 14610 0 1498 -14711 52 85.00 28.22 109 1301 1192 1093 14610 0 1402 -14711 55 85.00 28.22 109 1252 1143 1049 14610 0 1353 -14711 5E 85.00 28.30 173 1204 1031 596 14610 0 1305 -14711 61 85.00 28.28 236 1156 920 390 14610 0 1257 -14711 64 85.00 27.28 236 1059 823 349 14610 0 1160 -14711 67 85.00 26.28 252 1011 759 301 14610 0 1112 -14711 7C 85.00 26.28 252 962 710 282 14610 0 1063 -14711 73 85.00 25.23 346 1059 713 206 14610 0 1160 -14711 76 85.00 24.23 346 1107 761 220 14610 0 1208 -14711 79 85.00 24.24 404 1156 752 186 14610 0 1257 -14711 82 85.00 24.28 548 1156 608 111 14610 0 1257 -14711 85 85.00 24.28 548 1204 656 120 14610 0 1305 -14711 88 85.00 25.22 543 1204 _ 661 122 14610 0 1305 -14711 91 85.00 25.28 808 1204 396 49 14610 0 1305 -14711 94 85.00 25.28 808 1252 444 55 14610 0 1353 -14711 97 85.00 28.23 1880 1252 -628 -33 14610 0 1353 -14711 10C 91.00 34.22 1725 1252 -473 -27 14610 0 1353 -14711 103 1CC.00 40.22 1725 1252 -473 -27 14610 0 1353 -14711 106 110.00 48.22 1220 1252 _ 32 3 14610 0 1353 -14711 109 119 3. C5 54.22 1220 1757 537 44 14610 505 1353 -14711 112 124 3.10 60.28 1314 1717 403 31 14610 513 1305 -14711 115 126 3.10 66.28 3350 1669 -1681 -50 14610 513 1257 -14711 118 128 3.10 72.28 3350 1620 -1730 -52 14610 513 1208 -14711 121 130.80 77.24 2975 1240 -1735 -58 14610 132 1208 -14711 124 13C.80 82.24 2975 1191 -1784 -60 14610 132 1160 -14711 127 130.80 81.30 1525 2755 1230 81 16174 132 1160 -14711 130 112.CO 68.30 1525 4222 2697 177 17773 0 1160 -14711 133 1C3.CO 55.28 718 5868 5150 717 19371 0 1208 -14711 136 95.00 40.32 638 7467 6829 1070 20970 0 1208 -14711 139 86 -5.95 40.32 638 6894 6256 981 21382 -985 1208 -14711 142 83 -2.90 39.30 608 7812 7204 1185 21795 -480 1208 -14711 145 83 -2.90 38.30 608 8466 7858 1292 22207 -480 1450 -14711 148 83 -2.90 37.30 598 8893 8295 1387 22345 -480 1740 -14711 151 83.00 37.30 1050 9664 8614 820 22345 0 2030 -14711 154 83.00 36.30 1050 10050 9000 857 22345 0 2416 -14711 157 83.00 42.30 2580 6748 4168 162 18752 0 2706 -14711

-96 -T~L~, 18 (CONT'D) 16C 88.00 62.30 2580 5542 2962 Ii5 17257 0 2996 -i4711 163 107.00 81....30.... 3935 4385. 450 1i 15762.......0........3335...... '14711 166 125. dO 98.32 3380 3132 -248 -7 14266 0 3576 -14711 162 144 4.60 116.32 3380 4135 755 22 14266 761 3818 -14711 172 154 6.20 130.30 4860 4593 -267 -5 14266 1026 4011 -14711 175 159 6.20 135.30 4860 4303 -557 -11 I4266 1026 3721 -14711 178 164 6.20 140.35 8040 3675 -4365 -54 14266 1026 3093 -14711 181 16E 1.80 145.36 12620 2270 -10350 -82 14266 "29'8......241'6 - -14711 184 168 1.80 151. 36 12620 1786 -10834 -86 14266 298 1933 -14711 187 168 1.80 158.36 8110 3663 -4447 -55 16191 298 1885 -14711 190 16C.00 165.36 8110 6562 -1548 -19 19388 0 1885 -14711 193 14E.00 174.34 10590 9711 -879 -8 22585 0 1837 -14711 196 12C.GO 175.32 13800 12860 -940 -7 25782 0 1788 -14711 199 100 -5.15 172 ~ 32 13800 12887 -913 -7 26711 " "852..........i'740 ' ' -14711 202 100 -6.70 162.34 13550 13558 8 0 27639 -1109 1740 -14711 205 100 -6.60 166.34 13550 15083 1533 11 28567 -1093 2320 -14711 208 100 -3.50 163.32 15450 16921 1471 10 28876 -579 3335 -14711 211 88.00 160.28 15950 18322 2372 15 28876 0 4156 -14711 214 87.00 156.28 15950 19191 3241 20 28876 0 5026 -14711 217 86.00 160.28 27300 17604 -9696 -36 2641'8 ' ' 0....5-i~-96 '14711 220 85 -.30 190.28 27300 14582 -12718 -47 22964 -50 6380 -14711 223 111 -.30 220 ~ 32 32700 11421 -21279 -65 19560 -50 6621 -14711 226 136 -.30 242.40 20000 9242 -10758 -54 17188 -50 6814 -14711 229 162 4. 10 248.40 20000 10260 -9740 -49 17188 679 7104 -14711 232 175 8.50 254.30 20550 11327 -9223 -45 17188 1407 7443 -14711 235 182 8.50 260.30 20550 11665 -8885 -43 17188 1407 7781 -14711 238 191 8.50 266.36 18050 9838 -8212 -45 15023 1407 8119 -14711 241 194 2.40 272.34 16200 9157 -7043 -43 14868 397 8603 -14711 244 194 3.40 276.34 16200 8974 -7226 -45 14713 563 8409 -14711 247 194 2.40 283.40 16200 10022 -6178 -38 16071 397 8264 -14711 250 194.00 292.40 16200 13862 -2338 -14 20454 0 8119 -14711 253 202.00 298.40 18350 18100 -250 -1 24837 0 7974 -14711 256 210.00 301.33 19250 22338 3088 16 29220 0 7829 -14711 359 180 1.30 304.33 19250 23646 4396 23 30458 215 ~ 7684 -14711 262 164 2.70 316.40 23400 25218 1818 8 32039 447 7443 -14711 265 155 -3.65 380.40 23400 26177 2777 12 33276 -604 8216 -14711 268 146 -10.00 460.26 27450 26645 -805 -3 33345 -1655 9666 -14711 271 138 -3."CO' 500 '.32 33650 29253 -4397 -13 33345 '497 11116 -14711 374 132 -3.C0 575.32 33650 29930 -3720 -11 33345 -497 11792 -14711.~77 126 -3.00 650.34 33050 30667 -2383 -7 33792 -497 12082 -14711 280 120 -2. CO 700 ~ 34 33050 32497 -553 -2 35167 -331 12372 -14711 283 114 -2 O0 722.26 29150 31997 2847 10 34377 -331 12662 -14711 286 108 -2. GO 741 ~ 34 23900 27130 3230 14 29220 -331 12952 -14711 289 102 -2. O0 762 '-34 23900 25777 1877 8 27673 '33-i.........i3i46- '14711 292 100 -2.00 775.15 19250 24520 5270 27 26126 -331 13436 -14711 295 100 -2. 00 775.15 19250 23359 4109 21 24579 -331 13822 -14711 298 100 -2. O0 775.15 19250 22639 3389 18 23376 -331 14306 -14711 301 9~. O0 775 ~ 15 19250 22084 2834 15 22345 0 14451 -14711 304 97.00 775.15 15050 21198 6148 41 21313 0 14596 -14711 307 94.00 775.15 15050 20457 5407 36..... 20282.....6.......1488'6...........Ji47'11 31C 92 -. 80 775.15 15050 19873 4823 32 19251 -132 15466 -14711 LAG1 = 26, LAG2 = LAG3 = 47 K1 = 25, 7823S6y K2 = 99.319598,........K3 =. 7_?2_4?457 K4 = -2275.961578, SUM = 2.373112E+09, HCT =.500000 NMAX = 310, ~CRMER =.52~478, AVG[NS = 9065.507935

-97 -TABLE 19 EXPERI~NTAL DATA AND CORRELATION FOR DOG T MEASURED ESTIMATED PANCRE- PANCREFEMORAL BLOOD ATIC ATIC PERCENT TIME GLUCOSE DG/DT IhSULIN FLOW IIxSULIN INSULIN ERROR ERROR TERM 1 TERM 2 TERM 3 TERM 4 MIN MG PCT ME U!.ML _ML/MIN... ~U/M.L. MU U/ML. MU U_/ML 1 5S. O0 9,20 336 1348 1012 301 7640 0 537 -6829 4 59.00 10,20 336 1348 1012 301 7640 0 537 -6829? 5~,00 10,20 469 134.8 879 187 7640 0 537 -6829 10 55.00 11.20 469 1348 879 187 7640 0 537 -6829 1] 55,00 12,20 469 1348 879 187 7640 O 537 -6829 le 5c. O0 13.19 422 1348 926 219 7640 0 537 -6829 19 5~. O0 14,19 422 1348 926 219 764.0 0 537 -6829 22 5~.00 13.19 422 1348 926 219 7640 0 537 -6829 e5 5~.so le.25 243 1348 ].105 455 7640 0 537 -6829 28 55,03 10,25 2%3 1348 1105 455 7640 0 537 -6829 31 55.00 9.25 243 1348 1105 455 7640 0 537 -6829 34 59, O0 7.25 243 1348 1105 455 7640 0 537 -6829 37 59.00 7.20.....889 i3'48 459...........5'2...................?-946.....................6...............55-7........-g~-29 — 40 59.00 8.20 889 1348 459 52 7640 0 537 -6829 4~ 5~.00 8.15 918 1348 430 47 7640 0 537 -6829 ~6 59. O0 9.20 868 1348 480 55 7640 0 537 -6829 4c 59 ~ O0 9 ~ 13 720 1348 628 87 7640 0 537 -6829 52 5c.00 9.13 720 1348 628 87 7640 0 537 -6829 55 5~. oo' 9.13 820 1408.........5-88....... 7'2......76'40............................................................................... 0 597 -6829 58 5c. O0 9 ~ 13 820 1467 647 79 7640 0 657 -6829 61 5 c o O0 9, 15 930 1467 537 58 7640 0 657 -6829 64 5 c. O0 10. 15 930 1527 597 64 764 0 0 716 -6829 67 5 9. O0 10. 18 778 1587 809 104 7640 0 776 -6829 7C 55. O0 11, 18 1470 1647 177 12 7640 0 836 -6829 73 5~.oo ll.15 147o 1587 ll? 8 7640 o 776 -6829 76 59.00 12.20 1350 1467 117 9 7640 0 657 -6829 75 5~,00 13,20 1350 14-08 58 4 764-0 0 597 -6829 82 68 4.50 17,18 4795 2643 -2152 -45 8805 190 478 -6829 ~q5 7G.50 23.20 3125 2609 -516 -16 8999 21 418 -6829 88 71 ~ 50 29.18 5750 2804 -2946 -51 9194 21 418 -6829 91 74, 1.40 35. 18 5750 3329 -2q. 21 ' -42....962i........... -5-79..............'47-~.......... —6829 ' 94 81 2,30 41.18 8405 4247 -4158 -49 10502 97 478 -6829 '97 88 2,30 46.20 7490 5200 -2290 -31 11395 9'7 53]' -6829 100 95 2. ~5 54.20 9410 6109 -3301 -35 12301 99 537 -682'9 103 102 2,30 60,18 ':3410 7000 -2410 -26 13195 97 537 -6829 1.06 109 2.30 66.23 10025 7894 -2131 -21 14088 97 537 -6829 109 116 2. 30 72 ~ 20 12150 8787 -3363 -28 14982 97 537 -6829 ii 2 122 2 ~ O0 70 ~ 20 9290 9650 360 4 1 5798 84 597 -6829 ii5 110 -4. O0 64.20 9290 7843 -1447 -16 14244 -169 597 -6829 118 ~8 -4. O0 58 ~ 20 9490 6289 -3201 -34 12690 -169 597 -6829 i21 88 -2.90 49. 18 1038 5126 4088 394 11421 -122 657 -6829 124 83 -1.80 40 ~ 18 4750 4533 -217 -5 10722 -76 716 -6829 127 77 -1.80 30.18 4750 3834 -916 -19 10022 -76 716 -6829 130 12 -1.80 24 ~ 18 3840 3194 -646 -17 9323 -76 776 -6829 133 69 -1.00 20.20 2300 3198 898 39 8935 -42 1134 -6829 136 66 -1.00 17.14 2300 3167 867 38 8546 -42 1492 -6829 139 63 -1. O0 14.14 2300 3137 837 36 8158 -42 1850 -6829 142 69 3.30 13.23 1795 4402 2607......!.45.............8..883................1_3_.9.............._2.2._0_9..............76_829. 145 79 3.30 13.20 5250 6101 811 15 10165 139 2626 -6829 148 88 3.30 30. ZO 5290 7741 2451 46 11447 139 2985 -6829 151 101 4.40 48.23 12250 9713 -2537 -21 13014 185 3343 -6829 154 117 5.50 66.Z3 15950 127..54 -3696 -23 15150 232 3701 -6829 157 134 5.50 82.23 15600 14749 -851 -5 17287 232 4059 -6829

-98 -TABLE 19 (CONT'D) 16C 150 5.50 97.23 15600 17243 1643 11 19423 232 4417 -6829 163 153 1.co 112.23 12600 17084 4484 36 19812 42 4059 -6829 166 156 1.00 127.23 19600 17114 -2486 -13 20200 42 3701 -6829 16S 159 1.00 148.30 12450 17145 4695 38 20589 42 3343 -6829 172 157 -1.60 147.23 12400 16153 3753 30 20304 -67 2746 -6829 175 152 -1.60 138.23 12400 14935 2535 20 19682 -67 2149 -6829 178 147 -1. b 129.20 12600 13836 1236 10 19061 -67 1671 -6829 181 136 -4.65 120.20 10250 1i-938 i688 16 17649 "-196 - 3113 -6829 -184 113 -7.70 111.23 7465 8639 1174 16 14658 -324 1134 -6829 187 90 -7.70 104.25 3735 5469 1734 46 11667 -324 955 -6829 190 67 -7.70 86.25 3735 2298 -1437 -38 8676 -324 776 -6829 193 64 -1.10 68.20 2040 2149 109 5 8248 -46 776 -6829 196 60 -1.10 50.20 1690 2020 330 20 7821 -46 1074 -6829 199 57 -1.10 33.25 2015 2667 - 652 32 7394 -46 2149 -6829 202 61 2.50 15.25 2015 4398 2383 118 7899 105 3223 -6829 205 69 2.50 14.20 ' 1540 9444 4904 318 8870 105 4298 -6829 2C8 76 2.50 43.25 4910 8311 3401 69 9841 105 5193 -6829 211 86 3.65 89.25 18400 10523 -7877 -43 11110 154 6088 -6829 214 100 4.80 134.25 18400 13332 -5068 -28 12975 202 6984 -6829 217 115 4.80 160.20 18400 16211 -2189 -12 14839 202 7999 -6829 220 12S 4.80 175.25 20600 19210 -1390 -7 16704 202 9133 -6829 223 137 2.50 190.23 20750 19547 -1203 -6 17675 105 8595 -6829 226 144 2.50 205.23 2C750 19981 -769 -4 18646 105 8058 -6829 229 152 2.50 218.20 18850 20415 1565 8 19618 105 7521 -6829 232 145 -4.40 223.20 17500 18771 1271 7 18802 -185 6984 -6829 235 132 -4.40 226.23 16900 16644 -256 -2 17093 -185 6566 -6829 238 119 -4.40 181.23 16900 14219 -2681 -16 15383 -185 5850 -6829 241 105 -4.60 13b.23 11600 11375 -225 -2 13622 -194 4775 -6829 244 91 -4.80 91.23 10500 8427 -2073 -20 11758 -202 3701 -6829 247 76 -4.80 7C.20 4225 5488 1263 30 9893 -202 2626 -6829 250 62 -4.80 58.20 4225 2609 -1616 -38 8028 -202 1612 -6829 253 56 -2.00 46.20 2630 1233 -1397 -53 7251 -84 895 -6829 256 50 -2.00 34.18 1910 337 -1573 -82 6474 -84 776 -6829 259 44 -2.00 22.18 1660 2246 586 35 5698 -84 3462 -6829 LAG1 = 0, LAG2 = 1, LAG3 = 50 K1 = 12.9489c1, K2 = 16.856740, K3 = 5.969039 K4 = -716.499863, SUM = 4.024684E+08, HCT =.500000 NMAX = 260, NCPMER =.335662, AVGINS = 6444.881226

-99 -TABLE 20 EXPERIMENTAL DATA AND CORRELATION FOR DOG U MEASURED ESTIMATED PANCPE- PANCREFEMORAL BLOOD ATIC ATIC PERCENT TIME GLUCOSE DG/DT INSULIN FLOW IhSULIN INSULIN ERROR ERROR TERM 1 TERM 2 TERM 3 TERM 4 MIN MG PCT ML U/ML ML/MIN MU/ML MU U/ML MU U/ML_ 1 6C.00 14.35 517 306 -211 -41 1046 0 6799 -7538 4 60.00 14.35 457 306 -151 -33 1046 0 6799 -7538 7 60.00 14.35 192 306 114 59 1046 0 6799 -7538 10 6C.00 14.35 202 306 104 52 1046 0 6799 -7538 13 6C -.00 14.35 275 306 31 11 1046 0 6799 -7538 16 6C.00 14.35 257 306 49 19 1046 0 6799 -7538 19 60.00 14.35 257 306 49 19 1046 0 6799 -7538 22 46.00 13.35 257 306 49 19 1046 0 6799 -7538 25 53.00 13.35 374 306 -68 -18 1046 0 6799 -7538 28 57.00 13.35 374 97 -277 -74 836 0 6799 -7538 31 6C.00 13.35 299 175 -124 -41 915 0 6799 -7538 34 60.00 13.35 226 254 28 12 _ _993 0 6799 -7538 37 60 -6.75 13.35 226 104 -122 -54 1046 -203 6799 -7538 40 60 1.50 13.35 226 351 125 55 1046 45 6799 -7538 43 64 1.50 14.35 226 351 125 55 1046 45 6799 -7538 46 67 1.50 14.35 226 351 125 55 1046 45 6799 -7538 49 71.00 14.35 226 369 143 63 1108 0 6799 -7538 52 7C.00 15.35 141 432 291 206 1171 0 6799 -7538 55 66.00 15.35 141 457 316 224 1234 0 6761 -7538 58 62 1.20 14.40 141 435 294 208 1213 36 6724 -7538 61 62 1.20 14.40 234 335 101 43 1150 36 6687 -7538 64 69 1.20 14.40 234 234 0 0 1087 36 6649 -7538 67 75.00 13.40 234 158 -76 -33 1084 0 6612 -7538 7C 82 -1.20 13.40 508 199 -309 _ -61 1199 -36 6575 -7538 73 84 -1.20 13.36 508 277 -231 -45 1314 -36 6537 -7538 76 87 -1.20 13.36 508 355 -153 -30 1429 -36 6500 -7538 79 89 2.20 12.34 460 461 1 0 1471 66 6463 -7538 82 92 2.20 12.34 460 466 6 1 1513 66 6425 -7538 85 95 2.20 12.34 460 470 10 2 1554 66 6388 -7538 88 98.80 13.34 460 439 -21 -4 _ 1603 24 6351 -7538 91 102.80 13.33 412 454 42 10 1655 24 6313 -7538 94 1G8.80 14.33 412 701 289 70 1708 24 6507 -7538 97 114.90 15.33 412 968 556 135 1777 27 6702 -7538 100 120 1.00 24.34 155 1270 1115 719 1882 30 6896 -7538 103 134 1.00 23.34 1011 1568 557 55 1987 30 7090 -7538 106 147 1.00 22.34 1641 1867 226 _____ 14 _ 2091 30 7284 -7538 109 161 2.00 22.35 1326 1938 612 46 2326 60 7090 -7538 112 17C 2.00 21.35 999 1979 980 98 2562 60 6896 -7538 115 179 2.00 20.35 703 2020 1317 187 2797 60 6702 -7538 118 187 4.50 19.35 1196 2074 878 73 2969 135 6507 -7538 121 192 4.50 18.40 1463 2020 557 38 3110 135 6313 -7538 124 192 4.50 16.40 1105 2064 _ 959 87 3252 135- 6216 -7538 127 152 3.60 14.40 1192 2034 842 71 3346 108 6119 -7538 130 176 2.70 13.40 999 1910 911 91 3346 81 6022 -7538 133 159 2.70 14.40 1028 1813 785 76 3346 81 5925 -7538 136 142 2.70 15.40 1498 1437 -61 -4 3067 81 5828 -7538 139 126.00 15.40 1498 1355 -143 -10 2774 0 6119 -7538 142 114.00 _ 16.40 1454 1353 -101 -7 2481 0 6410 -7538 145 104 -4.00 16.40 1454 1232 -222 -15 2189 -120 6702 -7538 148 94 -5.60 15,.40 1724 1268 -456 -26 1981 -168 6993 -7538 151 86 -5.60 16.40 1554 1390 -164 -11 1812 -168 7284 -7538 154 82 -5.60 17.40 1554 5338 3784 244 1645 -168 11400 -7538 157 77 -4.35 18.38 1216 4853 3637 299 1506 -131 11016 -7538

-100 -TABLE, 20 (CONT'D) 16C 72 -3. 25 1 9. 38 12 58 4419 3161 2 51 142 2 -98 10633 -7 538 166 1 12 - 3. 20 22.38 23 80 3486 1106 46 12 55 -96 9866 -7538 169 131 -1, 60 23.38 3450 3496 46 1 1600 -48 9483 -7538 17 2 141 -1. 60 23.43 3403 3294 -109 -3 1945 -48 8936 -7538 1 75 147. -1.,60 24.40 3 51 5 2 765 -750 -21 2290 -48 8061 -7538 178 1 52 6.60 24.40 4498 231 1 -21 87 -49 2464 -198 7187 -753 8 '18 1 1 5 7 6. 60 2 3 3 ' 0.. 3291 i 1........i'26.......... 184 162 6. 60 2 2.40 3719 1951 -1768 -48 2642 198 6649 -7538 1 87 168 4. 15 2 1.40 37 63 2304 -1459 -39 273 2 1 25 6986 -7 538 190 173 1.70 20.40 2665 2661 -4 -0 2826 51 7322 -7538 193 166 1.70 19.40 2885 3091 206 7 2921 5 1 7658 -7538 196 145 1.70 19.40 3642 3159 -483 -13 3015 5 1 7631 -7538 199 126 2 6.4o 542628 2832 20 202 116 1, 80 18.40 3989 2521 -1468 -37 2527 54 7479 -753 8 205 110 1.30 16.40 '~ 3618 2758 -860 -24 2196 39 8061 -7538 208 104.00 14,40 4575 312 7 -1448 -3 2 2021 0 8644 -7538 211 100 -7.00 13.40 3959 3395 -564 -14 1917 -210 9227 -7538 214 100 -6.50 15, 40 4006 3889 -117 -3 1812 -195 9810 -7538 220 1~0 -2.0O0 20.40 5529 5120 -409 -7 1743 -60 10975 -7538 223 ill -2.00 23.40 5728 5411 -317 -6 1743 -60 11267 -7538 226 12 2 -2.00 23.40 6521 5557.-964 -15 1743 -60 11412 -753 8 229 13 2. CO0 23.40 S,564 5950 -3614 -38 1931 0 11 558 -75 38 232 13c..00 2 3.40 9107 6062 -3045 -33 2119 0 11482 -7538 2 35 143 - 0).......4... 40 6'5 35 730-....-80......'1.. 2307.......0...10961 -'753 8 238 147 3.60 28. 40 5982 5429 -553 -9 2419 108 10441 -7538 241 151 3.60 31.40 5 555 4982 -573 -10 2492 108 9921 -7538 244 154 3.60 35.40 4643 4535 -108 '-2 2565 108 9400 -753 8 2 47 154 2.50 2 8.40 2.849 4534 1685 59 2631 75 9366 - 753 8 250 1 54 1,40 22.40 2650 4761 2111 80 2684 42 9574 -7538 253 150 1 4....18...,40.......2207....45ii 2364.....0........."'7........ 2 56 1 37 1.40 21.40 3028 3346 318 10 2684 42 8159 -7538 2 59 124 1.00 24, 40 4304 2093 -2211 -51 2609 30 6993 -7538 262 116.00 23.40 2463 673 -1790 -73 2384 0 5 82 8 -7538 265 110.0O 20.40 3636 1686 -1950 -54 2164 0 7060 -7538 268 104.00 19.40 3650 2776 -874 -24 ~ 2021 0 8293 -7538 271 99 ''-4,'30' 20......40.....4'833..... 3775 -1-058.....-2-2.......191'7 -129 9526 -753'8' 274 98 -4.20 21.40 4833 4907 74 2 1812 -126 10759 -7538 277 96 -3.10 22.40 3231 5271 2040 63 1733 -93 11169 -7538 LAG1 = 6, LAG2 = 17, LAG3 52 Ki = 3.04jo4cS3, K2 = 21.002S82, K3 = 84.985326?4 = -1409.673035, SUM = 1.285563E+08, HCT =.500000 NMAX = 279, NCSMER =.532178, AVGINS =2209.267853

-101 -TABLE 2! EXPERI~NTAL DATA A~D CORRELATION FOR DOG V MEASURED ESTIMATED FA~CRE- PANCREFEMORA. L BLOGD ATIC ATIC PERCENT TIME GLUCOSE DG/DT I~SULIN FLaW IKSULIN INSULIN ERROR ERROR TERM 1 TERM 2 TERM 3 TERM 4 MIN MG PCT...MU..U/~L__ M._L_/M!N........... ~_U../__M.L........._M..U.._.U.../_ML_.....M._.U U/_ML............... 1 8C. O0 6.42 82 -66 -148 -181 1272 0 1290 -2628 4 80.00 6.42 82 -66 -148 -181 1272 0 1290 -2628 7 80 ~ O0 6.42 82 -66 -148 -181 1272 0 1290 -2628 IO 8C.00 6.54 102 -66 -168 -165 1272 0 1290 -2628 13 8C ~ O0 6.54 ~!02 -66 -158 -165 1272 0 1290 -2628 16 8C.00 6.52 78 -66 -144 -185 1272 0 1290 -2628 19 80 ~ O0 6. 52 78 -66 -144 -185 1272 0 1290 -2628 22 8C ~ O0 6.62 117 -66 -183 -156 1272 0 1290 -2628 2 5 80. O0 6 ~ 62 117 -66 - 18 3 - 156 1272 0 1290 -2628 28 80 ~ O0 b ~ 52 151 -66 -217 -144 1272 0 1290 -2628 31 80 ~ O0 6 ~ 52 76 -69 -145 -191 1269 0 1290 -2628 34 79.00 6. 62 76 -79 -155 -204 1260 0 1290 -2628 37 79 -. 20 6.48 46 -90 -136 -295 1250 — 1 1290 -2628 40 78 -.20 6.48 46 -99 -145 -315 1241 -1 1290 -2628 43 77 -.20 6.55 36 -I13 -149 -415 1226 -1 1290 -2628 ':,6 76 -. 25 6.55 36 -128 -164 -456 1212 -2 1290 -2628 4s 75 -.30 o.60 19 -143 -162 -851 1198 -2 1290 -2628 52 75 -. 30 6.58 21 -147 -168 -802 1193 -2 1290 -2628 55 '7.5 -.3o........ 6.....06...............i6........... -14f........i=-i63........= i0-2.'~...............i].9~,................. —:~........ —i-r~_-g-6.......... —~.-62 8 -58 75.00 6.06 16 -146 -162 -1010 1193 0 1290 -2628 61 75.00 6.50 20 -146 -166 -828 1193 0 1290 -2628 64 75.00 5.50 20 -146 -166 -828 1193 0 1290 -2628 67 75.00 5.48 31 -146 -177 -570 1193 0 1290 -2628 70 75.00 5.48 31 -174 -205 -662 1193 0 1261 -2628 73 75.00 5.57 17 -217 -234 -1378 1193 0 1218 -2628 76 75 ~ O0 5. 55 22 -260 -282 -1283 1193 0 11 75 -2628 79 75.00 5.55 22 -303 -325 -1478 1193 0 1132 -2628 82 75. O0 4.50 24 -346 -370 -1542 1193 0 1089 -2628 85 75.00 4.38 24 -382 -406 -1692 1193 0 1053 -2628 88 75 ~ O0 4. 38 24 -414 -438 -1826 1193 0 1021 -2628 91 75.00 4.38 24 -446 -470 -1960 1193 0 989 -2628 94 75.00 5.38 24 -479 -503 -2095 1193 0 956 -2628 97 88 ~ O0 6.45 295 -301 -596 -202 1403 0 924 -2628 100 108.00 7.45 1020 -18 -1038 -102 1718 0 892 -2628 103 122 6. 60 7 ~ 45 109 212 103 94 193 7 43 860 -2628!06 136 5. 60 8 ~ 40 604 586 - 18 - 3 215 7 36 1021 -2628 109 149 4.60 8.50 1288 960 -328 -25 2376 30 1182 -2628 11 2 158 4.60 9.50 1328 1264 -64 -5 2520 30 1343 -2628 115 165 4.60 9.50 1623 1531 -92 -6 2625 30 1504 -2628 118 172 2.20 9.50 1136 1749 613 54 2729 14 1633 -2628 121 178 2.20 9.45 1961 1974 13 I 2826 14 1762 -2628 124_..... 177. 2_.20......l.__O............ -_b.O................_I_9..04 2097 193 10 2820 14 1891 -2628 127 166 1.67 11.65 2358 1960 -398 -17 2643 11 1934 -2628 130 155 -3.71 12.50 2090 1748 -342 -16 2465 -24 1934 -2628 133 143 -3. 7t 14.50 2313 1562 -751 -32 2279 -24 1934 -2628 136 132 -3.81 14.58 2222 1465 -757 -34 2093 -25 2024 -2628 139 12~ -3.90 14.65 2292 1546 -746 -33 1907 -25 2293 -2628 142 111 -3.90........!4.............50 1982 1677 -305 -15 1769 -25 2561 -2628 145 104 -3.90 '14.50 1405 1831 426 30 1654 -25 2830 -2628 148 97 -2.40 14.50 1184 1905 721 61 1540 -15 3009 -2628 151 90 -2.40 13.67 990 1795 805 81 1430 -15 3009 -2628 154 84 -2.40 12.52 864 1694 830 96 I328 -15 3009 -2628 157 77 -2. 13 12.70 303 1594 1291 426 1227 -14 3009 -2628

-102 -T^BL 21 (CON 'D) 160 75 -2.13 11.60 893 1515 622 70 1193 -14 2964 -2628 163 89 -2.13 10.45 1470 15'94 i24....... 8 1408 -14 2828 -2628 166 102 2.25 11, 60 2123 1701 -422 -20 1622 14 2692 -2628 169 116 4.50 12 ~ 50 2381 1795 -586 -25 1837 29 2557 -2628 172 123 4. 50 14.55 2989 1775 -1214 -41 1953 29 2421 -2628 175 127 4.50 16,60 2878 1706 -1172 -41 2020 29 2285 -2628 178 131 1.40 19. 60 2439 1617 -822 -34 2087 9 2149 -2628 181 135 1.40 22. 50 2676 2056 =6-2-0................. —23 —.........2-I39 - 9 2536 -2628 184 136 1.40 25.60 3765 2467 -1298 -34 2163 9 2923 -2628 187 138 ~ 50 28.55 3531 2872 -659 -19 2187 3 3310 -2628 19C 139 ~ 50 2 5. 67 3502 3455 -47 - 1 2211 3 3869 -2628 193 125.50 23. 53 3237 3871 634 20 1982 3 4513 -2628 196 110 -2.15 20. 55 1941 4269 2328 120 1753 -14 5158 -2628 199 96 -4. 80 ' i'8 55 1377 4668......3-2'9i.... 239 1524 -31 5803 -2628 202 89 -4.80 15.60 1163 4403 3240 279 1412 -31 5650 -2628 205 85 -4.80 13.47 1032 3798 2766 268 1360 -31 5097 -2628 208 82 -1. IO I2.57 1029 3225 2196 213 I307 -7 4553 -2628 211 78 -1. 10 10.56 260 2631 2371 912 1241 -7 4025 -2628 214 72 -1.10 9.65 352 2008 1656 470 1145 -7 3497 -2628 217 7C '2.00....... 7.60 332 1442........ 1110 -' 334 1113 -13 2970 -2628 220 7C -2.00 8.45 285 1068 783 275 1113 -13 2596 -2628 223 70. O0 10. 50 207 783 576 278 1113 0 2298 -2628 226 97 ~ O0 12. 35 596 910 314 53 153 8 0 2000 -2628 229 137.00 14.45 2524 1249 -1275 -51 2174 0 1703 -2628 ~32 163 13.33 16.50 2988 1680 -1308 -44 2586 86 1636 -2628 235 181 13.33 17.45 3721 '~23'7'5....... -1346............. -36 2887 86 2030 -2628 238 200 6.30 20. 30 3856 3024 -832 -22 3188 41 2424 -2628 241 217 6.-30 23. 45 4129 3676 -453 -11 3446 41 2818 -2628 244 228 6.30 27. 50 4105 4243 138 3 3619 41 3212 -2628 24'; 238 3.63 30; 65 3907 4793 886 23 3792 23 3606 -2628 250 248 3.63 32 ~ 65 5028 5443 415 8 3945 23 4103 -2628 253 218 3.63 33.60 4360 '5'66'9............1309 30.3468 23 4807 -2628 256 188 -3. 50 35.60 5337 5850 513 10 2990 -23 5510 -2628 259 162 -10. O0 37.45 5768 6090 322 6 2569 -64 6213 -2628 962 145 -10. O0 34. 50 8850 6308 -2542 -29 2302 -64 6699 -2628 265 129 -6. 50 32.45 7800 6463 -1337 -17 2058 -42 7075 -2628 268 114 -5. 13 29.40 8300 6603 -1697 -20 1813 -33 7451 -2628 P71 101 -5.13 26.40 7104 6766 -338 -5 1600 -33 7827 -2628 274 96 -5.56 23.40 7104 6440 -664 — 9 1533 -36 7570 -2628 277 93 -i.40 20.30 6403 5839 -564 -9 1479 -g 6997 -2628 28C 88 -1.40 18.40 7944 5187 -2757 -35 1400 -9 6424 -2628 283 85 -1.00 18.35 4042 4521 479 12 1352 -6 5803 -2628 286 82 -1.50 18.45 1853 3825 1972 106 1304 -10 5158 -2628 285 80 -1.00 18.45 1548 3151 1603 104 1272 -6 4513 -2628 ~92 77 -1.00 18.45 1008 2454 1446 143 1219 -6 3869 -2628 295 75 ~ O0 18.45 323 2434 2111 653 1193 0 3869 -2628 298 87 -1.67 19.30 274 2606 2332 851 1376 -11 3869 -2628 301 121. O0 19 ~ 30 270 3165 2895 1072 1925 0 3869 '2628 304 156 11. 50 19.50 4157 3822 -335 -8 2473 74 3903 -2628 307 190 11.50 19.50 5181 4405 -776 -15 3022 74 3937 -2628 310 218 1t. 50 22.60 5742 4884 -858 -15 3468 74 3970 -2628 313 30C 10. ze2 25.60 5418 6215 797 15 4772 67 4004 -2628 316 257 18. 33 28 ~ 70 4787 5608 821 17 4080 118 4038 -2628 319 221 6.42 31. 70 4269 4996 727 17 3510 41 4072 -2628 322 202 -14.50 34.65 4893 5005 112 2 3213 -93 4513 -2628 325 19C -10.67 36.43 5036 5484 448 9 3022 -69 5158 -2628 328 173 -4. CO 39.65 5101 5906 805 16 2757 -26 5803 -2628 331 151 -4. O0 37 ~ 50 7909 6181 -1728 -22 2406 -26 6428 -2628 334 137 -8.67 35.50 8817 6512 -2305 -26 2181 -56 7014 -2628 337 123 -4.71 34.42 1154 6899 5745 498 1956 -30 7601 -2628 340 130 -4.71 33.42 8559 7596 -963 -11 2068 -30 8187 -2628 343 121 -1.19 32.42 8559 7406 -1153 -13 1918 -8 8124 -2628 346 111 -.40 31.46 9578 6875 -2703 -28 1768 -3 7737 -2628 349 93 -3. 14 31.46 9578 6187 -3391 -35 1485 -20 7351 -2628 352 86 -3.14 29 ~ 34 7207 5769 -1438 -20 1368 -20 7050 -2628 355 86 -7. 33 28.42 7207 5613 -1594 -22 1368 -47 6921 -2628 358 86.00 27.42 7207 5532 -1675 -23 1368 6792 -2628 361 86 ~ O0 26. 42 7207 5403 -1804 -25 1368 0 6663 -2628 364 86. 00 25. 42 7207 5145 -2062 -29 1368 0 6405 -2628 LAG1 = O, LAG2 = 6, LAG3 = 13 KI = _........3._.3_4_.Q2. 8__8~.................K.2.-............5.4_1.__2__9_.06_~ K3 = 45.134725 K4 = -569.115639, SUM = 2.040092E+08, HCT =.500000 NMAX = 365, NORMER =.510262, AVGINS = 2544.713104

-103 -TABLE 22 EXPERIMENTAL DATA AND CORRELATION FOR DOG0 MEASURED ESTIMATED FA~CRE- PANCREFEMORAL BLOOD ATIC ATIC PERCENT TiME GLUCOSE DG/DT IIxSULIN FLOW IKSULIN INSULIN ERROR ERROR TERM 1 TERM 2-' TERM 3 TERM 4 MIN MG PCT MU U/~L ML/MIm ~L;/ML MU U/ML MU U/ML....... I' 5'2.'0'0.....i2 '.25.....i'7'4-'0 -" 1930 190 11 -20461 -0 -3366 25757 4 J2. O0 12.25 1740 1930 I90 1 1 -2046i -0 -3366 25757 7 52.00 12.25 1740 ig30 190 I1 -20461 -0 -3366 25757 10 52.00 12.25 1740 1930 190 11 -20461 -0 -3366 25757 13 52.00 11.25 1690 1930 240 14 -20461 -0 -3366 25757 16 52, O0 10,25 1690 1930 240 14 -20461 -0 -3366 25757 "19 ' 52."00.................. 9..... 25....I6'90-...............i-93'0-.................240...................1-4-......=2-0-:~-6-I -0 -3366 25757 22 52.00 8.25 1690 1930 240 14 -20461 -0 -3366 25757 25 52.00 7.25 1690 19.30 240 14 -20461 -0 -3366 25757 28 52. GO 6,25 1690 1930 240 14 -20461 -0 -3366 25757 31 52, O0 6.25 2970 1930 -1040 -35 -20461 -0 -3366 25757 34 52. O0 6.25 ~:29 70 1930 -1040 -35 -20461 -0 -3366 25757 37 52 ' O0...........7....,'25 297'0.........2211......:- '759..... -26 -20461 -0 -3086 25757 40 52,00 7.25 2970 2491 -479 -16 -20461 -0 -2805 25757 43 52. O0 8.25 2970 3052 82 3 -20461 -0 -2244 25757 46 52, dO 8 ~ 25 4250 3333 -917 -22 -20461 -0 -1964 25757 49 52. O0 8.25 4250 3613 -637 -15 -20461 -0 -1683 25757 52 52. gO 8 ~ 25 4250 3613 -637 -15 -20461 -0 -1683 25757 55 52 O0 ' ' 7 '.25 4250....3613 -637...."-'15......'-'20461 -0 -1683 25757 58 52. O0 7.25 4250 3613 -637 -15 -20461 -0 -1683 25757 6i 52. O0 7.25 4250 3333 -917 -22 -20461 -0 -1964 25757 ~ 54 52, O0 6.25 4250 3333 -917 -22 -20461 -0 -1964 25757 67 52. O0 6.25 4250 3052 -1198 -28 -20461 -0 -2244 25757 70 52. O0 6.25 4250 3052 -1198 -28 -20461 -0 -2244 25757 73 52 CO ' 6 25 ' 4250" ' 3052 -Iig~3............................................ ---0 --- 25757., - -28 -20461 -2244 76 52. O0 6.25 3420 3333 -87,3 -20461 -0 -1964 25757 79 52 ~ O0 5.25 3420 3333 -87 - 3 -20461 -0 -1964 25757 82 52.00 5.25 3420 3333 -87 -3 -20461 -0 -1964 25757 85 52 o O0 5.25 3420 3333 -87 -3 -20461 -0 -1964 25757 ~18 52. O0 4.25 3420 3613 193 6 -20461 -0 -1683 25757 91 52.00 4.25 1550 3613 20'6-3........1'3"3........-20461 -0 -1683 25757 ~ 94 52. O0 4.25 1550 3613 2063 133 -20461 -0 -1683 25757 ~ 97 52. O0 4.25 1550 3613 2063 133 -20461 -0 -1683 25757 100 52.00 4.25 1550 3894 2344 151 -20461 -0 -1403 25757 103 52, O0 4,25 1550 3894 2344 151 -20461 -0 -1403 25757 I06 52.00 4.25 2260 3894 1634 72 -20461 -0 -1403 25757 109 52 ~ O0 4 ~ 25 2260 3894 '- '].634...............7'2...... -20461 -0 -1403 25757 112 52. O0 4.25 2260 4174 1914 85 -20461 -0 -1122 25757 115 52.00 4.25 2260 4174 i914 85 -20461 -0 -1122 25757 118 52.00 4.25 2260 4174 1914 85 -20461 -0 -1122 25757 121 52.gO 4.25 6000 4174 -1826 -30 -20461 -0 -1122 25757 124 52. O0 5.25 6000 4174 -I826 -30 -20461 -0 -I122 25757 127 52.00 6.25 6000 '4i74' ' "i'826..... -30 -20461 -0 -1122 25757 1,30 52.00 7.25 6000 4174 -1826 -30 -20461 -0 -1122 25757 133 52. O0 7.25 6000 4174 -1826 -30 -20461 -0 -1122 25757 136 52, O0 8.25 5770 4174 -1596 -28 -20461 -0 -1122 25757 I~9 52.30 7 025 5770 4174 -I596 -28 -20461 -0 'I122 25757 142 53.05 7 ~ 25 5770 4170 -1600 -28 -20461 -4 -1 122 25757 145 53.1 0 7.25 5770 3846 -1924' -33 -20500 -8 -1403 25757 148 53.10 6.25 5770 3728 -2042 -35 -20618 -8 -1403 25757 151 53.10 6,25 2130 3369 1239 58 -20697 -8 -1683 25757 154 53.10 6.25 2130 3010 880 41 -20776 -8 -1964 25757 157 54.10 6.25 2130 265I 521 24 -20854 -8 -2244 25757 160 54.10 6.25 2130 2572....44~2..............21_ -20933 -8 -2244 25757 163 54. i0 6.25 2130 2774 644 30 -21012 -8 -1964 25757 166 54. IO 6, 25 2480 2695 215 9 -21090 -8 -1964 25757 I69 54. iO 6. 25 2480 2616 i36 5 -2II69 -8 -1964 25757 172 55.10 6.25 2480 2818 338 14 -21248 -8 -1683 25757 175 55 ~ 10 6. 25 2480 2740 260 10 -21326 — 8 -1683 25757 I78 55 ~ lO 7 ~ 25 2480 266I IS1 7 -21405 -8 -I683 25757 181 55.10 7.25 1810 2582 772 43 -21484 -8 -1683 25757 184 55. 10 7.25 1810 2503 693 38 -21563 -8 -1683 25757 187 56. iO 7,25 I8iO 2425 615 34 -21641 -8 -I683 25757 190 56.10 6.25 1810 2346 536 30 -21720 -8 -1683 25757 193 56.10 6.25 1810 2267 457 25 -21799 -8 -1683 25757 I96 56 ~ 10 6,25 I230 2189 959 78 -21877 -8 -I683 25757 199 56.10 6.25 1230 1829 599 49 -21956 -8 -1964 25757 202 57.10 7.25 1230 1751 521 42 -22035 -8 -1964 25757 205 57. I0 7.25 1230 1672 442 36 -22113 -8 -1964 25757 208 57.10 7,25 1230 1593 363 30 -22192 -8 -1964 25757 211 57.10 7.25 1330 I515 185 14 -22271 -8 -1964 25757 214 5e..lo......?.....25...........!330_.................!_7_! (:,_.........._38.a...... 29 -22350 -8 -1683 25757 217 60.10 6.25 1'330 1598 268 20 -22468 -8 -1683 25757 220 60 ~ 20 6.25 1330 1472 142 11 -22586 -16 -1683 25757 223 6C, O0 6,25 1330 1253 -77 -6 -22822 -0 -1683 25757 226 60.00 6.25 845 185 -660 -78 -23609 -0 -1964 25757 22~ 6C.00 7.25 845 185 -660 -78 -23609 '-0 -1964 25757 232 6C.00 8.25 845 185 -660 -78 -23609 -0 -1964 25757 235 63. O0 8. 25 845 185 -660 -78 -23609 -0 -1964 25757 238 67 ~ O0 9. 25 845 466 -379 -45 -23609 -0 -1683 25757 LAG1 = 8, LAG2 = 6, LAG3 = 2'3... K._I =..._4~_.!__846._~__4_~.............................K._2__ —......_-_41_____.0__32_ 6_4_7__t K3 = -35.067274 K4 = 3002,178925t SUM = 9.372513E+O7t HCT:.500000....... o~c~_ NF~MER =.39~032, AVGXNS = 2729.645813

-104 -TABLE 23 EXPERIMENTAL DATA AND CORRELATION FOR DOG P MEASURED ESTIMATED PANCRE- PANCREFEMORAL BLOOD AT IC ATIC PERCENT TIME GLUCOSE OG/DT IINSUL'IN FLOW INSULIN INSULIN ERROR ERROR TERM I 'TERM 2 TERM' 3- TERM 4 MIN MG PCT MU U/ML ML/MIN P.U/ML MU U/ML MU U/ML ' 1.. 7-5 -0-0-....i5....20.....380 822 442 116 27 -0 1339 -544 4 75.00 16.20 380 822 442 116 27 -0 1339 -544 7 75. O0 17. 20 380 911 531 140 2-7 -0 -1429 -544 1 0 75. O0 1 8. 20 380 iOO0 620 163 27 -0 151 8 -544 13 75. O0 18. 21 730 1090 360 49 2 7 -0 1607 -544' 16 75. O0 18 ~ 21 730 1090 360 49 27 -0 1607 -544 '19......75......00..... 8.21 730 1090 360 49 27 -0 1607 -544 22 75. O0 17.21 730 1000 270 37 27 -0 1518 -544 2 5 7 5. O0 1 7 ~ 2-! 730 1000 270 37 2 7 -0 1518 -544 28 7 5 ~ O0 T 7.21 1060 1000 -60 -6 27 -0 1518 -544 3 1 72 ~ CO 17. 21 1060 1000 -60 -6 26 -0 1518 -544 34 7C 0 ~0 17 ~ 21 1060 998 -62 -6 25 -0 1518 -544 37 65.0......... 17 ~ 21 1060 997 -6 3 -6 23 -0 1518 -544 40 64 ~ O0 17 ~ 21 1060 996 -64 -6 23 -0 1518 -544 43 64. O0 17.1l6 1435 996 -439 -31 23 -0 1518 -544 46 64 ~ O0 17 ~ 16 1435 996 -439 -31 23 -0 1 51 8 -544 49 64.00 17.16 1435 996 -439 -31 23 -0 1518 -544 52 64. O0 17.16 1435 996 -439 -31 23 -0 1518 -544 55 64 ' -,00.........1"7 -.....,16 1435 996 -439 -31 23 -0 1518 - 5A44 5 8 64 -1.00 17.17 1695 1034 -661 -39 2 3 38 1518 -544 61 64 -1.50 17.20 1695 1054 — 641 -38 23 5 7 1518 -544 64 64 -2.00 17.20 1695 1073 -622 -37 2 3 76 1518 -544 6 7 6 C -. 50 1 8.20 1695 1103 -592 -35 21 1 9 1607 -544?C 60.00 19.20 1695 1084 -611 -36 21 -0 1607 -544 73 6C. O0 19.15 1260 1173 -87 -7 21 -0 1697 -544 78 55. DO 18.15 1260 1172 -88 -7 20 -0 1697 -544 79 55. O0 18 ~ 15 1260 1082 -178 -14 20 -0 1607 -544 82 55. O0 18.15 1260 1082 -178 -14 19 -0 1607 -544 85 54 ~ O0 17 ~ 15 1260 993 -267 -21 19 -0 15 18 -544 88 54. O0 1 7 ~ 14 1105 993 -1 12 -10 19 -0 1518 -544 91 54 ~ O0 17. 14 1105 993 -1 12 -10 19 -0 1518 -544 94 54 -2.00 I8. 14 II05 II58 53 5 19 76 1607 -544 97 5 3. O0 18 1.14 1105 1082 -23 - 9- 67 -4 100 53. O0 19 ~ 14 1105 1171 66 6 19 -0 1697 -544 103 53 ~ O0 19. 13 870 1171 301 35 19 -0 1697 -544 lo06 5 2 ~ O0 1 8 ~ 13 870 1081 211 24 19 -0 1607 -544 109 52 -.~10 17 ~ 13 870 996 126 14 1 8 4 1518 -544 112 52 -. 10 16 ~ 13 870 996 126 14 18 4 1518 -544 115 51 -. 10 15 ~ 13 870 906 3 6 Z.....18 4 1 2 ' — 4!18 51 -. 10 15 ~ 13 640 817 177 28.18 4 1339 -544 121 51 -. 10 14.13 640 817 177 28 18 4..1339......54'4 124 51 -.10 14.13 640 728 88 14 18 4 1250 -544 -1-2'7.......51....10 ' 13 ' -.13......640 728 88 14 18 4 1250 -544 130 51 -.10 13.13 640 638 -2 -0 18 4 1161 -544 133 51 -. 10 13.15 65 0 638 -12 '2.....-8.......4 1161l......-4 136 5 1 -.10 1 2.15 650 638 -1 2 - -2 18 4 1161 - 7544- 1313 51 -.10 I11.15 650 549 ' "10.........16....................................... 1 42 51 -.1 O 11.15 650 460 -190 -29 18 4 982 -544 145 51 -. 10 10 ~ 15 650 460 -190 -29 18 4 982 -544 148 51 -. 05 '10. 16 660 369 -291 -44 ]~8 2 893 -544 151 51 ~ O0 11 ~ 16 660 367 -293 -44 18 -0 893 -544 154 50. O0 11 ~ 16 660 456 -204 -31 18 -0 982 -544 157 49 ~ O0 12 ~ 16 660 544 -1 16 -18 17..................

-105 - TABLE 23 (CONT'D) 160 48.00 13. 16 660 544 -116 -18 17 -0 1072 -544 163 47.00 13.18 570 633 63 11 17 -0 1161 -544 166 46.00 13.18 570 633 63 11 16 -0 1161 -544 169 45.00 13.18 570 633 63 11 16 -0 1161 -544 172 44.00 12.18 570 543 -27 -5 16 -0 1072 -544 175 44.00 12.18 570 543 -27 -5 15 -0 1072 -544 178 43.00 12.21 670 542 -128 -19 15 -0 1072 -544 181 42 -.30 13.21 670 553 -117 -17 15 11 1072 -544 184 42 -.30 13.21 670 643 -27 -4 15 11 1161 -544 187 42 -.30 13.21 670 643 -27 -4 15 11 1161 -544 190 42 -.30 14.21 670 643 -27 -4 15 11 1161 -544 193 42 -.30 14.22 475 732 257 54 15 11 1250 -544 196 42 -.30 13.22 475 732 257 54 15 11 1250 -544 199 42 -.30 12.21 488 643 155 32 15 11 1161 -544 202 42 -.30 11.21 488 553 65 13 15 11 1072 -544 205 42 -.30 10.21 488 464 -24 -5 15 11 982 -544 208 42 -.30 9.21 395 375 -20 -5 15 11 893 -544 211 42.00 10.21 395 363 -32 -8 15 -0 893 -544 214 42.00 11.21 395 _ 453 58 15 15 __ -0 982 -544 217 42.00 12.21 395 542 147 37 15 -0 1072 -544 22C 42.00 13.21 395 631 236 60 15 -0 1161 -544 223 42.00 14.23 490 721 231 47 15 -0 1250 -544 226 42.00 14.23 490 721 231 47 15 -0 1250 -544 229 42.00 14.23 490 721 231 47 15 -0 1250 -544 232 42.00 13.24 490 631 141 29 15 -0 __ 1161 -544 235 42.00 13.24 490 631 141 29 15 -0 1161 -544 238 42.00 13.24 535 631 96 18 15 -0 1161 -544 241 42.00 13.24 535 631 96 18 15 -0 1161 -544 244 42.00 13.24 535 631 96 18 15 -0 1161 -544 247 42.00 13.24 535 631 96 18 15 -0 1161 -544 250 42.00 13.24 535 631 96 18 15 -0 1161 -544 253 42.CO 13.27 725 631 -94 -13 15 -0 1161 -544 256 41.00 13.27 725 631 -94 -13 15 -0 1161 -544 259 41.00 13.27 725 631 -94 -13 15 -0 1161 -544 262 41.00 13.27 725 631 -94 -13 15 -0 1161 -544 265 41.00 13.27 725 631 -94 -13 15 -0 1161 -544 268 41.00 13.27 _ 535 631 96 18 15 -0 1161 -544 271 41.00 13.27 535 631 96 18 15 -0 1161 -544 LAG1 = 0, LAG2 = 29, LAG3 = 2 K1 =.035518, K2 = -15.253547, K3 = 8.929317 K4 = -92.439417, SUM = 5.878529E+06, HCT =.500000 NMAX = 271, NOPMER =.320221, AVGINS = 798.110291 **** ALL INPUT DATA HAVE BEEN FROCESSED. AT LOCATION 17040

APPENDIX B GLUCOSE AND INSULIN CORRELATION PROGRAM AND MULTIVARIATE STATISTICAL ANALYSIS This MAD(4) program predicts the insulin concentration in pancreatic venous plasma given continuous records of the arterial blood glucose concentration and the pancreatic venous plasma insulin concentration, and the femoral venous insulin concentration measured periodically. A mathematical model describing the response of the pancreas to changes in the blood glucose and insulin concentrations is given by equation (5.o)o Application of this model to a set of experimental data requires the determination of three time lags and four rate constants. This program determines the rate constants by using the least squares method to fit the model to the experimental data when the time lags are specified. An iterative procedure is used to determine the set of time lags giving the "best" fit of the model to the data. The smallest integral of the square of the error between the measured and the predicted insulin concentrations is the criterion for determining the "best" fit. Having determined the "best set of time lags the program can be used to study the modified models given by equations (5.2-5.7). For each model the program determines the appropriate rate constants and prints out the arterial glucose concentration, femoral venous plasma insulin concentration, pancreatic venous catheter blood flow rate, measured pancreatic venous insulin concentration, predicted pancreatic venous plasma insulin concentration, error, percent error, and the contribution of each of the four terms of the equation to the total -106 -

-107 -response at given times during the experiment. The blood glucose concentration, the measured and the predicted pancreatic venous insulin concentrations are plotted as functions of time using the library subroutines (40) When data from a series of similar experiments are processed together, the program is designed to use multivariate statistical techniques to test for the existance of significant differences between the different models applied to the experimental data. Hotelling's T test is used to test for differences in the mean errors obtained with the different models. This method was described in Chapter V. Modifications 1o The multivariate statistical analysis section of the program can be deleted by removing all those statements following the statement TRANSFER TO START up to the beginning of the internal function FILLIN. 2. To minimize computer time required for the iterative determination of the time lags, it is desirable to delete the six modified models, the table of results at given times, the plots of the results, and the multivariate statistical analysis, printing only the lags, constants and the integral of the square of the error for each iteration.

-108 -TABLE 24 SYMBOLS USED IN THE COMPUTER PROGRAM FOR CORRELATING THE BLOOD GLUCOSE AND THE PANCREATIC VENOUS PLASMA INSULIN CONCENTRATIONS MAD Name Mode Definition Units A2 1 Index for plotting INS A3 1 Index for plotting I AA Index for plotting GLUC ADDINS 0 Partial Sum AVGINS 0 Average pancreatic venous insulin concentrat ion [U/ml BASE 1 Index representing the model used as the references in Hotelling's T testo B 1 Index specifying a given model Dl 0 Number of data points in group 1 for Hotellingis T2 test D2 0 Number of data points in group 2 for Hotelling's T2 test D3 0 Number of data points in group 3 for Hotelling's T2 test DGDT 0 Time derivative of the blood glucose concentration mg/100 ml min DG 0 Glucose derivative term DIF1 0 Difference in mean errors for Hotellingis T2 test DIF2 0 Difference in mean errors for Hotellingvs T2 test DIF3 0 Difference in mean errors for Hotellingis T2 test DUMMY 0 Arguement of GJR. DY 0 Increment in Y El 0 Mean error in group 1 for Hotellings T2 test E2 0 Mean error in group 2 for Hotelling's T2 test E3 0 Mean error in group 3 for Hotelling's T2 test ERROR 0 Difference between measured and calculated insulin concentrations iU/ml

-109 -TABLE 24 (CONT'D) SYMBOLS USED IN THE COMPUTER PROGRAM FOR CORRELATING THE BLOOD GLUCOSE AND THE PANCREATIC VENOUS PLASMA INSULIN CONCENTRATIONS MAD Name Mode Definition Units EX 0 Exponent on the peripheral insulin term FA2 0 Dummy variable for A2 FA3 0 Dummy variable for A3 FA 0 Dummy variable for AA FI 1 Integer value of F F 0 Scale factor for plotting blood glucose concentration FSTAT 0 F statistic FVI 0 Femoral venous plasma insulin concentration [U/ml GLUC 0 Blood glucose concentration mg/100 ml G O Blood glucose term HCT 0 Hematocrit HOTELT 0 Hotelling's T2 statistic II 0 Pancreatic venous insulin term [U/ml IMAGE 0 Storage location used to dimension the graph INS 0 Measure pancreatic venous plasma insulin concentration kU/ml INVSSS 7 Inverse of SSS I 0 Calculated pancreatic venous insulin concentration pU/ml IX 1 Index JJJ 7 Copy of SSS J 1 Index JX 1 Index Kl... K44 0 Estimated values of K1, K2, K3, K4 K1 0 Coefficient, blood glucose term (iU/min)(mg/100 ml1 K2 0 Coefficient, derivative term (IU/min)(mg/100 ml)-lmin K3 0 Coefficient, peripheral term (iU/min)(kU/ml)-l peripheral

-110 -TABLE 24 (CONT'D) SYMBOLS USED IN THE COMPUTER PROGRAM FOR CORRELATING THE BLOOD GLUCOSE AND THE PANCREATIC VENOUS PLASMA INSULIN CONCENTRATIONS MAD Name Mode Definition Units K4 0 Coefficient, constant term (uU/min) KK 2 Boolean control symbol KX 0 Constant in the peripheral insulin term KY 0 Constant in the peripheral insulin term Ll oooL44 0 Estimated time lags min LABEL 1 Graph title LAG1 1 Time lag on the blood glucose term min LAG2 1 Time lag on the derivative term min LAG3 1 Time lag on the peripheral insulin term min M 0 Argument of SLE. N 1 Time min Nl 1 Time at start of experiment min N2 1 Time at end of experiment min NAME 0 Identification NAME1 0 Identification NAME2 0 Identification NCHAR 0 Argument of PLOT4., number of characters in LABEL NMAX 1 Total number of data points less one NMLAG1 1 N - LAG1 min NMLAG2 1 N — LAG2 min NMLAG3 1 N - LAG3 NORMER 0 Normalized Error iU/ml PCTERR 0 Percent error PR1 2 Printing control P 0 Peripheral insulin term kU/ml? RR 0 Argu~ment of SLEo RT 0 Least squares analysis, vector of right side SD 0 Standard deviation of the error SETS 1 Number of groups into which each experiment is divided in Hotelling's T2 test

-111 - TABLE 24 (CONT'D) SYMBOLS USED IN THE COMPUTER PROGRAM FOR CORRELATING THE BLOOD GLUCOSE AND THE PANCREATIC VENOUS PLASMA INSULIN CONCENTRATIONS MAD Name Mode Definition Units SIG 0 Element of the covariance matrix SKIP 1 Number of data points bypassed in printing results SSERR 0 Sum of the error SSS 7 Covariance matrix SUMERR 0 Sum of the absolute value of the error kU/ml SUMSQE 0 Sum of the square of the error iU/ml SX... 0 Partial sum SY... 0 Sum error for a given group of data TA 1 Time required to print summary TB 1 Time at given location in program TC 1 Time at given location in program TERM1 0 Response of pancreas proportional to glucose concentration TERM2 0 Response of pancreas proportional to the derivative of glucose concentration TERM3 0 Response of pancreas proportional to femoral TERM4 0 Response independent of insulin or glucose insulin concentration TL 0 Time left sec T 0 Storage for least squares calculations V1 0 Argument of SLE. V 0 Pancreatic venous blood flow rate ml/min W1 0 Partial sum of errors W2 0 Partial sum W3 0 Partial sum X1MAX 1 Number of experiments X1MAXL1 1 XlMAX - 1 X1 1 Index, Experiment number X2 1 Index, Model number XBAR 0 Mean error X 1 Index XX 0 Index

-112 -TABLE 24 (CONT'D) SYMBOLS USED IN THE COMPUTER PROGRAM FOR CORRELATING THE BLOOD GLUCOSE AMD THE PANCREATIC VENOUS PLASMA INSULIN CONCENTRATIONS MAD Name Mode Definition Units Y1 0 Mean error in group 1 for Hotelling's T test Y2 0 Mean error in group 2 for Hotelling's T test Y3 0 Mean error in group 3 for Hotelling's T2- test YF 0 Floating point equivalent for elements of YY YMAX 0 Maximum insulin value to be plotted YY 6 Mean error vector LIBRARY(40) SUBROUTINES CALLED BY PROGRAM MODE NUMBERS GJRo DAYTIM. 0 = Floating point PLOTlo ZEROo 1 = Integer PLOT2. SETERR. 2 = Boolean PLOT3. TIMLFT. 6 = Vector PLOT4o 7 = Matrix SLEo INCLUDE MATRIX PACKAGE

-113-.$COMPILE MAD, EXECUTE, DUMP, I/O DUMP, PRINT OBJECT $PUNCH OBJECT R READ INSULIN AND GLUCOSE DATA R' N INCLUDE VMATR I X PARAMETER Vv (6), MM(7) MODE NUIM BER M Ml, J J ( 1 '3':'3) MODE U M B E R M M, S SS ( 1 3,-3 ) 1iMODE NUIVIBER V M., YY( 1' 3) MODE NUMBER MM, INVSSS(1 i"3:- 3) EQUIVALENCE (SSS, SIG) EOUII\ALENCE (YY, YF) FTRA-P. BOOLEAN KK, PR1 INTEGER AA, A2, A3, B, BASE, E, FI, IX, J, J1, JX, K, LAG1, 1 LAG2, LA(-G3 MAX, N N1, N2, NMAX, NMLAG1, NM'LAG2, NMLAG3, 1 SKIP, X, X1, XllvXL1, X22 DIMENSION DGDT(400), DIFI(14), DIF2(14), DIF3(14)h. Ei(14*7), 1 E2(14*7), E3(14"7), ERR(400*7),.ERROR(400), FVI(400), 1 GLUC(400), I(400), INS(400), M(5), PCTERR400), RT(5), __ _ SIG(3*3), T(4"*4), V(400), Vi.(5), Yl(7), Y2(7), Y3(7), YF,3) READ FORMAT FIRST, X1MAX, BASE, SETS V'S FIRST = $ 3 I 10 *$ _ PRINT RESULTS X1MAX, BASE, SETS X1 = 1 START READ FORMAT PX, EX, KX, KY, TA, PR1 ___ V 'S PX = $ 3F100.,3I10$____ READ FORMAT DOG, AMAX E NAME AMEI1 NAME2, SKIP,LAG1,LAG2, 1 Ni, N2, YVMAX, KK, HCT VECTOR VALUES DOG = $ 13, S2, 3C6, S2, I3, S2, I3,S2, 13, 1 S2, I3, S2, I313,, F6.U, S5, I1, S5, F5.0*$ READ FORMAT DOG1, Kll, K12, K13, K14, K21, K22, K23, K24 1, K31, K32, K33, K34 -READ FORMIAT DOG1, Lll, L12, L13,, L14, L21, L22, L23, L24, 1 L31, L32, L33, L34 VECTOR VALUES DOG 1 = $13F6. 0$ READ FORMAT DATA G, GLUCC(O)...GLUC(XlNMAX) F I LL I i, (GLUC, tN MAX) _ _ READ FORMAT DATA I, INS (().. I NS ( XNMAAX) READ FORMAT DATA F, FVI(O)...FVI(NMAX) FI L L I IN. (F V, NMAX) REA[) FORMAT DATA V V ( O )...V( NMAX) VECTOR VALUES DATA G= $10F60.*$ VECTOR VALUES [)ATL I = $ 10 F 6.0 *$ V'S DATA F = $10F6.0*()$ \'S DATA V = $20F3.2*$ T'H AAA, FOR r',i=l 1, N.G. \IMViAX W'R V(N ).E. (0.0, V(N) = V(N-1) AAA W'R I S(N).E.O.O, INS(N) = INS(N-1) ADDINS = 0.0 T H AAAA, FOR N = 0,1, N.G. NMIAX AAAA ADDINS = ADDINS + INS(N) AVGINiS = ADDIN\S/(NMAX + 1 ) PRINT FORMAT TITLE, NAME, NAME1, NAME2, AVGINS VECTOR VALUES TITLE = $ 1Hi, 40HCORRELATION OF INSULIN AND GL 1 UCOSE FROM 3C6, F20.0'$ ____ TH DONE, FOR B = 1, 1, B.G. 7 R SELECT CONSTANTS Ki, K2, AND K3 ______ LAG1 = L 1________ LAG2 = L21

LAG3 = L31 W'R KK, T'O B1 ZERO.(T(1)...T(16), RT(1)...RT(4)) T'O A(B) A(1) THROUGH LOOPli FOR N = Ntl, 1, N.G.N2 II = (INS(N) V(N) - INS( 1) ': V ( 1)) ) (1.0 - HCT) NMLAG1 = N - LAG1 NMLAG2 = 1\ - LAG2 NI\MLAG3 = N1 - LAG3 W 'R NMLAG1.L. O, N\iiLAGI = 0 W'R NIlvLAG2.L. O NMiLAG2 = 0 I! R NliLLAG3. L 0, O NML AG3 = 0 G = GLUC(NMiLAGI) (G = (GLUC(NMLAG2+1)-GLUC(N MLlLAG2-1 ) ) O.5 P = ((KX (FVI (NivLAG3) ) ).P.EX) ':KY T(1,1) = T -(1,1) + G::-G T(1,2) = T(1,2) + G'DG__ T(1,3) = T(1,3) + G T(2,1) = T(l,2) T(2,2) = T(2,2) + DG*DG T(2,3) = T(2,3) + DG T(3l1) = T(1,3) T(3,2) = TI(2,3)__ __ T(3,3) = T(3,3) + 1.0 RT(2) = RT(2) + II*:UG RT(1) = RT(1) + GII LOOP RT(3) = RT(3) + II RR = SLE.(3,4,?T( 1l),i( 1),RKT( 1),VI(O),O) W'R PR1, P'S T(lil)....T(3,3), M(1)....iM(3), RT(1)...RT(3), RR K1 = M(1) K2 = M(2) K3 = 0.0 K4 = M(3) T'O B2 A(2) THROUGH LOOP2, FOR N = Ni, 1, N.G.N2 NfMILAG1 = N - LAG1 NI\MLAG2 = N - LAG2 \MNLAG3 = N - LAG3 W 'R NfILAG1. L 0, NiVLAG1 = 0 W'R NLA2 L MLAG2. LAG2 = 0 W'R NMLAG3.L. O, NI\ILAG3 = 0 II =(INS(N) V(N) - INS(1) V()) ( 1 0 - HCT) G = GLUC (N lLAG1) DG = (GLUC( iVNlLAG2+1)-GLUC(NlILAG2-1))o:'0.5 P = ((KX F ( FVI (NMLAG3) ) ).-E ) -=KY T(1,1) = 1 (1,1) + G*G T( 1,2) = r (1,2) + G':)G _ T(2,1) = T(1,2) T(2,2) = T(2,2) + DLG * DG RT(1) = RT(1) + II *: G LOOP2 RT(2) = RT(2) + II'*lDG RR = SLE. (2,4,T(1,1),M(1),RT(1),V1,O) W' R PRi, P'S T(1,1)...T(2t2) M(1)...(2), RT(1)..(2 R(1. (2) R K1 = M(1) K2 = M(2) K3 = 0.0 K4 = O.) T'O B2 A(3) THROUGH LOOP3, FOR N = N1, 1, N.G.N2 II =( INS(N) * V(N) - INS(1) * V( 1)) * (1.0 - HCT)

-115 -NMLAG1 = N - LAG1 NMLAG2 = N - LAG2 NMiLAG3 = N - LAG3 W'R NMLAG1.L. 0, NMLAG1 = 0 W'R NMLAG2.L. 0O NMLAG2 = 0 W'R NMLAG3.L. 0, NMLAG3 = 0 G = GLUC(NMLAG1) DG = (GLUC (NMLAG2+1)-GLUC(NNMLAG2-1) )O.5 P = ((KX * (FVI(NMLAG3))).P.EX)*KY T(1,l) = T (1,1) + G*G T(1,2) = T(1,2) + G T(2,1) = T(1,2) T(2,2) = T(2,2) + 1.0 RT(1) = RT(\1) + IIG LOOP3 RT(2) = RT( ) + II RR = SLE. (2,4, T(1,1), M(1), RRT(1), VI, 0) W'R PRI, P'S T(l,1),... T(2,2), M(1)...M(2), RT(1).. RT(2), RR K1 = MI1) K2 = 0.0 K3 = 0.0 K4 = M(2) T'0 B2 A(4) THROUGH LOOP4, FOR N = Nl, 1, N.G.N2 II =(INS(N) '' V(N) - INS () * V(1)) * (1.0- HCT) NMLAG1 = N - LAG1 NMLAG2 = N - LAG2 NMLAG3 = N - LAG3 W'RMLAG L NML.L. LAG' = 0 W'R NMLAG2.L. 0, NMLAG2 = 0 W'R NMLAG3.L. 0, NiMLAG3 = 0 G = GL UJC ( N MLAG 1) DG = (GLUC(NMiLAG2+1)-GLUC(NMLAG2-1))*O. 5 P = ((KX * (FVI (NMLAG3 ).P.EX ) *KY T(1,1) = T (1,1) + G'=G LOOP4 RT(1) =R T(1) + II __ KI = RT(1)/T(1,1) K2 = 0.0 K3 = 0.0 K4 = 0.0_ T'O 82 A(5) THR OUGH LOOP5, FUR N = N1, 1, N.G.N2 II =I S (NN) 4; V (N) - INS( 1) - V( 1 ) (1.0 HCT) NMLAG1 = N - LAGI NM L A G 2 = N - LAG 2 M_____LAG3 = N - LAG3 W'R NMLAG1.L. 0, NMLAG1 = 0 W'R _ R NMLAG2.L. 0, NMLAG2 = 0 W'R NMVLAG3.L. O, NMLAG3 = 0 G = GLUC (NMLAG1) DG = (GLUC(NM\LAG2+1)-GLUC(NMLAG2-1)) 0.5 P = ((KX: (FVI(N\MLAG3) )).P.EX)'KY' T(1,1) = T(1,1) + G G T(1,2) = T(1,2) + DG0 G T(1,3) = T(1,3) + P * G T(2,1) = T(1,2) T(2_2) = T(2,2) + DG*DG T(2,3) = T(2,3) + P * DG T(3,1) = T(1,3) T(,3,2) = T(2,3) T(3,3) = T(3,3) + P * P

RT(1) = RT(1) + II * G RT(2) = RT(2) + II * DG LOOP5 RT (3) = RT(3) + II * P RR = SLE. (3,4, T(1 ),M(1),RT(1) tV,O ) W'R PR1, P'S T(1,1)..T(3,3), M(1)..M.(3), RT(1)...RT(3), RR KI = M( ) K2 = M(2) K3 = M(3) K4 = 0.0 T'O B2 A(6) T'H LOOP6, FOR N= Ni, 1, N.G. N2 II = (INS(N)*V(N)-INS(1)*V(1)) * (1.0-HCT) NMLAGI = N - LAG1 NMLAG2 = N - LAG2 NMLAG3 = N - LAG3 W'R NMLAG1.L. 0, NMLAG1 = 0 W'R NMLAG2.L. O, NMLAG2 = 0 W'R NIMLAG3.L. 0, NMLAG3 = 0 G = GLUC(NMLAG1) DG= (GLUC(NMLAG2+1)-GLUC(NMLAG2-1))*'0.5 P = ((KX * (FVI(NMLAG3))).P.EX)*KY T(1,1) = T(1,1) + G*G T(1,2) = T(1,2) + G*P T(1,3) = ( 1,3) + G T(2,1) = T(1,2) T(2,2) = T(2,2) + P*P T(2,3) = T(2,3) + P T(3,1) = T(1,3) T(3,2) = T(2,3) T(3,3) = T(3,3) + 1.0 RT(1) = RT(1) + G*'II RT(2) = RT(2) + P*II LOOP6 RT(3) = RT(3) + II RR = SLE.(3,4,1(1,1),M(1),RT( ),VI(0),O) W'R PRi, PRINT RESULTS T(l,l)...T(3,3),M(1)...M(3),RT(l)...RT 1(3), RR K1 = A(1) K2 = 0.0 K3 = M(2) K4 = M(3) T'O B2 A(7) T'H LOOP7, FOR N N 1N, 1, N.G.N2 II =(INS(N) * V(N) - INS( ) * V(1)) * (1.0 - HCT) NIMLAG1 = N- LAGI NMLAG2 = N - LAG2 NMLAG3 = N - LAG3 W'R NMLAG1.L. 0, NMLAG1 = 0 W'R NMLAG2.L. 0, NMLAG2 = 0 W'R NMLAG3.L. O, NMLAG3 = 0 G = GLUC(NMLAG1) DG = (GLUC(NMLAG2+1)-GLUC(NMLAG2-1))*0.5 P = ((KX * (FVI(NMLAG3))).P.EX)*KY T(1,l) = T(1,1) + G * G T(l,2) = T(1,2) + DG* G T(1,3) T(1,3) + P * G T(1,4) = T(1,4) + G T (2,1) = T(1,2) T(2,2) = T(2,2) + DG* DG T(2,3) = T(2,3) + P * DG T(2,4) = T(2,4) + DG

-117 -T(3,1) = T(1,3) T(3,2) = T(2,3) T(3,3) = T(3,3) + P * P T(3,4) = T (3,4) + P T(4,1) = T(1,4) T(4,2) = T(2,4) T(4,3) = T(3,4) T(4,4) = T(4,4) + 1.0 RT(1) = RT(1) + II * G RT(2).= RT(2) + II *DG RT(3) = RT(3) + II * P LOOP7 RT(4) = RT(4) + II RR = SLE.(4,4,T(1,1),M( 1),RT(1),Vl(O),O) W'R PRI, P'S T(1,1)...T(4,4), M(1)...M(4), RT(1)...RT(4), RR Ki = M( 1) K2 = M(2) K3 = M (3) K4 = M(4) TRANSFER TO B2. Bl THROUGH DONE, FOR VALUES OF K1 = K K, K12 K13, K14 THROUGH DONE, FOR VALUES OF K2 = K21, K22, K23, K24 THROUGH DONE, FOR VALUES OF K3 = K31, K32, K33, K34 THROUGH DONE, FOR VALUES OF K4 = K41, K42, K43, K44 B2 PRI\IT COMMENT $ CONSTANTS AND PARAMETERS$ P'S K1, K2, K3, K4, LAG1, LAG2, LAG3, Nl, N2, SKIP, EX, KXKY P'S RR R PREDICT INSULIN 'CONCENTRATIONS PRINT FORMAT TOP, X1, NAME+ NAME1, NAME2 X1 = X1 + 1 PRINT COMMENT $0 FEMORAL BLOOD i PANCREATIC PANCREATIC$ PRINT COMMENT $ TIME GLUCOSE DG/DT INStJLIN FLOW M 1EAS. INSULIN CALC. INSULIN ERROR PERCENT ERROR TERMI TER 1M2 TERM3 TERM4$ PRINT COMMENT $ MPiII\I MG/100 ML MU U/LML ML/MIN I MU U U/ML MU U/ML MU U/ML $ SUMFSOE = 0.0 SUMSOE = 0.0 SSERR= 0.0 _ __ T'H TABLE, FOR N = 1, SKIP, N.G. NMAX NMVLAGI = N - LAG1 NMLAG2 = N - LAG2 NMiLAG3 = N - LAG3 W'R NMLAG1.L. 0, NMLAG1 = 0 W'R NMLAG2.L. 0,.NMLAG2 = 0 W'R NMLAG3.L. 0, NMLAG3 0 DGDT(N) = (GLUC(NMLAG2+1)-GLUC(NMLAG2-1) )*-0.50 TERM1 = K1*GLUC(NILAG1)/(V(1)*(1.-HCT)) TERM2=K2*( (GLUC(NMILAG2+1)-GLUC(NMLAG2-1) )0*.50)/V( 1)*('.-HCT) TERM3 = K3*((KX*(FVI(NMLAG3))).P.EX)*KY/(V(1)*(1.-HCT)) TERM4 - K4/(V(1)*(1.-HCT)) + INS(1)*V(1)/V(1) I(N\) = TERM 1 + TERM 2 + TERM 3 + TERM 4 ERROR(N) = I(N) - INS(N) PCTERR(N) = (I(N) - INlS(N))*100./INS(N) PRINT FORMAT RESULT, N., GLUC(N), DGDT(N), FVI(N), V(N), 1INS(N), I(N), ERROR(N), PCTERR(N), TERMI, TERM2, TERM3, 1 T ER Iv4 -SUMERR = SUMERR +.ABS. ERROR(N) SSER.R = SSERR + ERROR(N)____ SUMSOE = SUMSOE + ERROR(N)*ERROR(N)

-118 -TABLE CONTINUE XBAR = SSERR/(N2-N1) SD = ( ( SUMSOE/(N2-I\ ) )-XBAR':XBAR).P..50 NORMER = (SORT. (SUMSOE/(NMAX/SKIP)))/AVGINS PRINT RESULTS SUMERR, SU"MSSOE, XBAR, SSERR, SO, AVGINS, NORMER W1 = 0.0 W2 - 0.0 W3 = 0.0 T'H ALPHA, FOR I1 = 1, SKIP, N.G.90.(R. N.G. NMAX ALPHA W1 = W1 + ERROR(N) W'R N.GE. NMAX D1 = (N —)/SKIP O'E D1 = 90./SK-IP E'L E1(X1,X2) = W1/D1 T'H BETA, FOR N = 91, SKIP, N..G. 180.OR. '.G. NMAX BETA W2 = W2 + ERROR(N) W 'R N.GE. NMAX 02 = (N-91)/SKIP 0'E D2 - 90.0/SKIP E'L_ _ E2(X1,X2) = W2/D2 W'R E2(X1,X2).L. 1.0, E2(X1,X2) = E1(X1,X2) PTH GAMMA, FOR N = 181, SKIP, N.G. 270.OR. N.G. NMAX GAMMA W3 = W3 + ERROR(N) W 'R N.GE. N\MAX D3 = (N-181)/SKIP O'E D3 = 90.0/SKIP E I L E'L E3(X1,X2) = W3/D3 W'R E3(Xi,X2).L. 1.0-, E3(Xi,X2) = E2(XI,X2) P'S E1(X1,X2), E2(X1,X2), E3(X1,X2), D1, D2, D3, N PRINT FORMAT T1, NAME, NAME1, NAME2 PRINT COMMENT $0 * = MEAS. GLUCOSE IN MG PCT., + = MEAS. INS 1ULIN IN MU U/ML, X = CALC. INSULIN IN MU U/ML$ F = i10.0 * YMAX/300.0 FI = F/10 PRINT RESULTS FI PLOT1. (0, 5, 10, 10, 10) DIMENSION IMAGE (867) PLOT2. (IMAGE, 300., 0.0, YMAX, 0.0) T'H P1, FOR AA = 1, SKIP, AA.G. NMAX FA = AA 'P1 __ PLOT3. ($*$, FA, FI*'GLUC(AA), 1) THROUGH P2, FOR A2 = 1, SKIP A2.G. NMAX FA2 = A2 P2 PLOT3. ($+$, FA2, INS(A2), 1) THROUGH P3, FOR A3 = 1, SKIP, A3.G. NMAX FA3 = A3 P3 PLOT3. ($X$, FA3, I(A3), 1) NCHAR = 20 DONE PLOT4. (NCHAR, LABEL) W' R Xi.E. X1MAX, T'O OMEGA X1 = X1 + 1 T'O START OMEGA T'H SIGMA, FOR X2 = 1, 1, X2.G. 6 SY1 = 0.0

-119 -SY2 = 0.0 SY3 = 0.0 T'H CHI, FOR Xl 1, 1, X1.G. XVIMAX SY1 = SY1 + Ei(X1,X2) SY2 = SY2 + E2(Xl1X2) CHI SY3 = SY3 + E3(X1,X2) Y1 (X2) = SY1/XlMAX Y2 (X2) = SY2/X1MAX SIGMA Y3 (X2) = SY3/X1MAX PRINT RESULTS Yi(1)...YI(7) PRINT RESULTS Y2(1)...Y2(7) PRINT RESULTS Y3(1)...Y3(7) PRINT RESULTS E(l1,1)... El(14,7) PRINT RESULTS E2(ll)... E2(14,7) PRINT RESULTS E3(1,1)... E3(14,7) T'H Z4, FOR X2 = 1, 1, X2.G. 6 T'H Z4, FOR X22 = 1, 1, X22.G. 6 W'R X22.E. X2, X22 = X22 + 1 YF(1) = Y1(X2) - Y1(X22) YF(2) = Y2(X2) -Y2(X22) YF(3) = Y3(X2) -Y3(X22) T'H Z5, FOR X1 = 1, 1, Xl.G. X1MAX DIFI(X1) = E1(X1,X2) - E1(Xl,X22) DIF2(X1) = E2(X1,X2) - E2(XlX22) Z5 DIF3(X1) = E3(X1,X2) - E3(X1,X22) ZERO.(SX1, SX2, SX3, SX1,. SX22, SX33, SX12, SX13, SX23) T'H Z6, FOR X1 = 1, 1, X1.G. X1MAX SX 1 = SX 1 + DIF1(XI) SX 2 = SX 2 + DIF2(X1) SX 3 = SX 3 + DIF3(Xl)- SX11 = SX 11+ DIF1 (XI)* DIFl(Xl1) SX22 = SX22 + DIF2(X1) DIF2(XI) SX33 = SX33 + DIF3(X1) * DIF3(X1) SX12 = SX12 + DIFI(XI) * DIF2(X1) SXi3 = SX13 + DIF1(X1) * DIF3(X1) Z6 SX23 = SX23 + DIF2(X1) * DIF3(X1) X1MXLI = X1MAX - 1 SIG(1,1) = ((SX11 - (SXI*SX1/X1MAX))/X1MXL1) ___SIG(2,2) = ((SX22 - (SX2X2*SX2/XMAX))/XIMXL1) SIG(3,3) = ((SX33 - {SX3*SX3/XIMAX))/X1MXL1) SIG(1,2) = ((SX12 - (SX1*SX2/X1MAX))/X1MXL1) SIG(1,3) = ((SX13 - (SX1-SX3/XIMAX) )/X1MXL1) SIG(2,3) = ((SX23 - (SX2SX2 3/X1MAX))/XllMXL1) SIG(2,1) = SIG(1,2) SIG(3,1) = SIG(1,3) SIG(3,2) = SIG(2,3) JJJ = SSS_ ___ W'R GJR.(3,3,JJJ(1,1),DUMMY).NE. 1., T'O INVERR PRINT COMMENT $6 $ P'S X2, X22, X1MAX, SETS HOTELT = YY * (.INVERT. SSS) * YY FSTAT = ((1. * XIMAX - SETS + 1.)/(SETS * X1MAX)) * HOTELT INVSSS =.INVERT. SSS P'S SSS(l,1)...SSS(3,3), INVSSS(1,l)...INVSSS(3,3) P'S- HOTEL T, F'STAT T'O Z4 INVERRR PRINT COMMENT $ SINGULAR MATRIX $ Z4 CONTINUE V'S. LABEL = $ $ VECTOR VALUES RESULT = $IH, I10, F1O.0, F7.2, F9.0, F6.2, 2F

-120 -115.0, F7.0, F15.0, 4F7.0*$ V'S TOP = $IH1, 7HTABLE, 2,43H EXPERIMENTAL DATA AND 30 1RRELATION FOR 3C6'$ VECTOR VALUES Tl=$1H1,40HCORRELATION OF INSULIN AND GLUCOSE F 1ROM 3C 6*$ R THIS SUBROUTINE FILLS IN DATA SETS BY LINEAR INTERPOLATR ION. INTERNAL FUNCTION (Y,MAX) ENTRY TO FILLIN. IX= 0 ZO T'H ZO, FOR JX=IX+1, 1, Y(JX).NE.O. W'R JX-IX.E. 1 IX= IX+ 1 T'O Z3 E'L DY = (Y(JX)- Y(IX))/(JX-IX) T'H Z1, FOR IX=IX+l, 1, IX.E.JX Z1 Y(IX) = Y(IX-1) + DY Z3 W'R IX.L. MAX, T'O ZO F'N END OF FUNCTION E 'M R R CONTRACTRACTIONS USED IN THIS PROGRAM ARE... R E'L END OF CONDITIONAL _R, E 'M EN\'D OF PRO GRAM R E 'N ENlD OF FUNCTION R P'S PRINT RESULTS R P'T PRINT FORMIAT R T'HH THROUGH R -'O TRANSFER TO R V'S VECTOR VALUES R W'R WHENEVER _______ ____454 LINES PRINTED

APPENDIX C DOUBLE ANTIBODY INSULIN ASSAY PROGRAM This MAD program calculates the insulin concentration in plasma which has been assayed using the double antibody method. The fraction of insulin bound is calculated for each sample of standard insulin representing a point on a standard curve. The least squares method is used to determine the coefficients in a polynomial equation which represents the standard curve. The program is written to fit the standard curve using two equations of the same general form: 1 1 1 I = x q 1 q2 + x x3 4 5 (Ca) where: I = Plasma insulin concentration x = Percent of labelled insulin bound by the antibody q = An array of constants determined by least squares One array of constants is determined for samples having from 0-50 PiU/ml insulin and another array for samples having from 50-300 1U/ml insulin. After the constants are determined, the points on the standard curve are calculated and compared with the experimentally determined values. The standard curve is plotted including both the computed and the experimentally determined points. The insulin concentration of plasma samples is calculated using the equation given above with the appropriate set of constants. A provision is made to multiply the results by a dilution factor if the samples have been diluted. -121 -

-122 -TABLE 25 SYMBOLS USED IN THE COMPUTER PROGRAM FOR THE INSULIN ASSAY CALCULATIONS MAD Name Mode Definition Units ADD 0 Partial sum A 0 Coefficient matrix Bl 0 Bl(I-11) = INS(I) iU/ml BKGD 0 Background radioactivity counts/min BKPT 0 Breakpoint between the 1 st and 2 nd branches of the standard curve BR 1 Break switch B 0 B(J) = INS(J-1) pU/ml BZERO 0 Average specific activity of counts/min TrA, Tr B, Tr C, and.Tr'D CCC 0 Counts, control C counts CMAX 0 Maximum number of counts counts C 0 Counts in period TMAX counts Dl 0 Storage array DIL 0 Plasma dilution factor, DIL = 1.0 means no dilution D 0 Storage array ENDSC 2 Control - Indicates last test to be run with a given standard curve ENDT 2 Control -Indicates last data card of a given experiment FTY 0 The value of PCTBZ for standard samples containing 50 kU/ml insulin GRAPH 0 Storage location for plotting sub-.routines H 0 Storage array IDENT 1 Sample identification symbol IN 0 Insulin concentration in-unknown plasma kU/ml INS 0 Insulin concentration in standard curve lU/ml I 1 Index, 2 nd branch of standard curve J 1 Index, 1 st branch of standard curve K 1 Index used in plotting

-123 -TABLE 25 (CONT'D) SYMBOLS USED IN THE COMPUTER PROGRAMI FOR THE INSULIN ASSAY CALCULATIONS MAD Name Mode Definition Units LABEL 1 Vector name - Graph title M 1 Counting index, data cards N1 1 Number of points on the first branch of the standard curve N2 1 Number of points on the second branch of the standard curve NAME 1 Experiment identification - up to 30 characters NC 2 Control for reading data cards NN 1 Counting index N 1 Card number, standard curve P1i Format variable PBZ 0 Percent labelled insulin bound for unknown plasma PCTBZ 0 Percent labelled insulin bound for standard curve PR1 2 Printing control for table title PR2 2 Printing control for deviations PR3 2 Printing control for checking program Q 0 Coefficient matrix, X or X1 RRR 0 Result of SLE. RR 0 Result of SLEo R 1 Index for reading data cards RT 0 Vector of the right side of least squares equations TCC 0 Time, control C min TMAX 0 Maximum time a sample is counted min T 0 Time a given sample is counted min Ul 0 Deviation, below BKPT lU/ml U 0 Deviation, above BKPT.IU/ml U2 0 Arguement of CALC., U2 = PBZ V1 0 Arguement of SLE. V2 0 Arguement of SLE. W1 0 1.0/U2 W 1 Index

-12)4 -TABLE 25 (CONT'D) SYMBOLS USED IN THE COMPUTER PROGRAM FOR THE INSULIN ASSAY CALCUATIONS MAD Name Mode Definition Units WT 1 Vector name — weights, here equal-l X1 0 Array of constants for CALC. X 0 Array of constants for CALC. Y 1 Index Z 1 Index LIBRARY(40) SUBROUTINES CALLED BY:PROGRAM MODE PLOTlo 0 Floating point PLOT2. 1 Integer PLOT3 2 Boolean PLOT4o SLEo ZEROo INTERNAL FUNCTION CALC

-125 -$COMPILE MAD, PRINT OBJECT, EXECUTE, I/0 DUMP, DUMP R*.....PROGRAM FOR CALCULATION OF PLASMA INSULIN CONCENTRATION R USING THE DOUBLE ANTIBODY ASSAY. FTRAP. BOOLEAN ENDSC, ENDT, NC, PR1, PR2, PR3 FORMAT VARIABLE I, J, P1 INTEGER BR, I, IDENT, J, K, M, N, NAME, NN, R, TO INTEGER W, Y, Z, N1, N2 DIMENSION A(5')., B(20), Bl(30), BB(20), BB1(20), C(30), 1 D(O00,DIM ), Dl(100,DIMI1), H(5:5), IDENT(30), NAME(9), 1 PCTBZ(30), RT(5), T(30), U(20), Ul(20), Vl(5), V2(5), 1 X(30,DIM2), Xl(30,DIM2), W(30,DIM2) R......READ, TRANSFORM, AND STORE DATA FOR THE STANDARD CURVE. READ FORMAT R1, CMAX, TMAX, PR1, PR3, N1, N2 Al READ FORMAT R2, NAME(O)...NAME(4), BR, BKPT, DIL PRINT COMMENT $1 $ P'S CMAX, TMAX, PR1, PR3, BR, BKPT, N11, N2 PRINT FORMAT P4, NAME(O)...NAME(4), DIL W'R BR,E. 1, BKPT = 1.OE04 FTY = 0.0 PRINT FORMAT P2 NC = OB T'H A2, FOR NN= 0,1, NC READ FORMAT R3, NC, N, IDENT(N), C(N), T(N), INS(N), BKGD W'R C(N).E. O.0, C(N) = CMAX A2 W'R T(N).E. 0.0, T(N) - TMAX CCC = ( C(28) + C(29))/2.0 TCC = ( T(28) + T(29))/2.0 BKGD = (C(28)/T(28) + C(29)/T(29))/2.0 BZERO = ((C(O)/T(O) + C(1)/T(1) + C(2)/T(2) + C(3)/T(3))/4.0) Ig -- BKGD T'H A3, FOR N = 0O 1, N.G. 29 PCTBZ(N) = ((C(N)/T(N)) - BKGD)/BZERO A3 PRINT FORMAT P3, N, IDENT(N), C(N), T(N), C(N)/T(N), 1 BKGD,PCTBZ(N), INS(N) PRINT RESULTS BZERO NC = OB T'H A51, FOR I = 12, 1, I.G. 27 Di(1,I-11) = PCTBZ(I) Dl(2,I-11) = 1.O/PCTBZ(I) Di(3, -11) = Dl(2,-11 )*D1(2,I-11-) 1D(4,I-11) 2,-11) )*D(3,I-11) A51 Bl(I-11) = INS(I) THROUGH A52, FOR J = 1, 1, J.G. Ni PCTBZ(O) = 1.00 PCTBZ(I) = 1.00 PCTBZ(2) = 1.00 PCTBZ(3) = 1.00 D(1,J) = PCTBZ(J-1) D(2,J) = l.O/PCTBZ(J-1) D(3,.J) = D(2,J) * D(2,J) D(4,J) = D(2,J) D(3,J) A52 B(J) = INS(J-l) FTY = (PCTBZ(12) + PCTBZ(13))/2.0 I = I -1 J= J - 1 W 'R PR3, 1P'S D(1,1)...D(4,J), B(0)..B(J), WT, J W'R PR3, 1 P'S DI(1,i)...D1(4,I),B1(1)...BI(16),WT, I

-126 -R....FIND LEAST SOUARES ESTIMATES. ZERO. (A(1)...A(25)) T'H SUMvllB, FUR Y = 1, 1, Y.E. 5 T'H SUI.JM1, FOR Z = 1, 1, Z.E. 5 ADD = 0.0 T 'H SUMllB, FORW = 1,1, W.G. Ni ADD = ADD + D(YW), D( Z,W) SUMvi B A(YZ ) = AiD) THROUGH SUMlAFDR I = 1,1, I.G. N\l A(1,5) = A(1.5) + D (1,I) A(2.5) = A(2 5) + 0 (2 I) A(3,5) = A( 35) + D (3,I) A(4,5) = A(4,5) + l- (4,I) S UI 1 A A ( 5,5 ) = A(5,5) + 1.0 A(51,1) = A(1,5) _ __ A (5,1) _i i5 )_____ _ ____ _______A(5,2) = A(2,5) A(5,3) = A(3,5)_____________ A(5,4) = A(4,5) ZERO.(RT(1)...RT( 5) ) T'H SUM 2, FOR W = 1,1, W.G. N1 RT( ) = RT( 1) + D( 1,) ( B(l) R (2) = RT(2) + D(2,!;) ' B(W) T _ (3) = RT(3) + D (3,W) _ B( W) RT (4) = RT(4) + D(4,W) B(W) SUIM2 R-T(5) = RT(5) + B(W) W'R PR3, IP.S A(1,1)...A(5,5), R ( 1)...RT(5) RR =.SLE. (5,5, A(1,1),X(1),RT(1),V1(1), 0)........._. _........_. ______ _.. _, '__ __..._ _____ 1PRINiT RESULTS RR, X(1)...X(5) ZERO. (H(1)...H(25)) ZERO. (RT( )... RT (5)) T_'H SUM3,FOR Y = 1,1, Y.E. 5 T'H SUPi3SFOR Z = 1,1, Z.E. 5 ADD = 0.0 ___ T.'H S J13, FR W = 1,1, W.. 12 ADD = ADD +D1(YW) D) ( Z,W SUvi3 H ( Y Z) = ADD THROtlGH SUMi4, FOR I = 1,_, I.G._ N2 H(1,5) = H(1,5) + D( 1, ) H(2,5) = H(2,5) + D01(2,1)_ ____ H(3,5) = H(3,5) + D0(3,I) H(4,5) = H(4,5) + D1(4,1) SUliM4 H(5,5) = H(5,5) + 1.0,H ( 5, 1) -1 H( 1,.5) t _____....____ ---— ____ —_ — -— 'H(5,2) = H(2,5) H(5,3)= H(3,5) _____ __._ -.. H(5,4) = H(4,5) T'H SliMv 5, FOR W = 1,1, W.G. N2 RT(i) = RT(1) +DI(1,W) "BI(.W) RT ((2).= R.T ( 2 2) +Di (2,)'B(W)_________________ RT(3) = RT(3) +[1(3,W) "1,1(W) RT ( 3 ) = RT ( 3 ) +Dt1 ( 3, W ) B 1 ( ) RT(4) = () I(4,Nl) __1(W SUM5l5 RT 5) = RT () +B 1 (W) WR ' PR3, IP'S H(1,1)...H(5,5), RT(1)...RT(5).RRR = SLE. (5,5_. (1 1S)X(1), RT ( (1,1),Xi(1), RT2( ( 1), V ) W'R PR3, I P 'S A(ll)...A(55,5) R T( )...RT( 5) _ ____ W'R PR3,

-127 -1P'S H(1 1)...H(.5,5), RT( 1)..RT(5) W'R PR3, iP'S V1(1)...V1(5), V2(1)...V2(5) W'R PR3, IPRINT RESULTS RRR,XI(1)...Xl(5) R PRINT OUT LEAST SQUARES ESTIMATES AND DEVIATIONS FROM THE R STANDARD CURVE, AND THE LEAST SQUARES COEFFICIENTS. P1 =(1-BR)*6 P'T T31, '$BELOW$,BKPT SUM = 0.0 T'H A23, FOR K = 1, 1, K.G.J BB(K) = CALC.(X,D(1,K)) U(K) - B(K) - BB(K) A23 SUM = SUM + U(K) * U(KI PRINT FORMAT T3, (K=l,l,K.G.J,D(1,K),B(K),BB(K),U(K)) W'R.NOT. PR2,T'O A9 P'T T4, X(1)...X(5) P'S RR, RRR A9 P ' T 7, SUM T'O A21(BR) A21(0) P'T T31, $ABOVE$,BKPT SUM1 = 0.0 THROUGH A24, FOR K = 1, 1, K.G. N2 BB1(K) = CALC.(X1,D1(1,K)) U1(K) = B1(K) - BB1(K) A24 SUMI = SUMI + U1(K) * U1(K) PRINT FORMAT T3, (K=llltK.G.N2,DD(1,K),B1(K),BB1(K),UI(K)) W'R.NOT. PR2, T'O A22 P'T T4, X1(1)...X1(5) A22 P'T T7, SUMI A21(1) CONTINUE DIMENSION GRAPH (867) PLOT2. ( GRAPH,300.,,1.,0 ) T'H A91, FOR B=0.02,002, B.G.1.0 A91 PLOT3.($*$,CALC.(XtB),B,) _) T'O A95(BR) A95(0) T'H A92t FOR B=0.02,0.02, B.G,1.0 A92 PLOT3.($+$,CALC.(X1,B) B,1) A95(1) T'H A93, FOR K=,ll,K.G.N1 A93(0) PLOT3. ($0$,B(K),D(1,K), 1) T'O A96(BR) A96(0) T'H A94, FOR K=1,1,K.G.lN2 A94 PLOT3.($X$,B1(K),D1( 1,K),1) A96( 1) COI\T I NUE PRINT COIMMEN\T$1 ' - CALC. CURVE, 1ST BRANCH + - CALC. CURVE 12ND BRANCH 0 - OBS. CURVE, 1ST BRANCH ETC.$ K = T PLOT4. ( K, LABEL) PRINT COMMiENT $ TOTAL$ VECTOR VALUES LABEL = $ PERCENT BZERO$ R CALCULATE AND PRINT RESULTS FOR UIIKNI\OWN SAMPLES ENDSC = OB T'H B2, FOR M = 1, I, ENDSC READ FORMAT R4, NAME(0)...NAME(4), ENDSC, DIL PRINT FORMAT P4, NAME(0)...NAME(4), DIL PRINT FORMAT P6 ENDT = OB T'H B2,,OR R = O0 1, ENDT B11 READ FORMAT R3, ENDT, 0.0,.IDENT, C, T, 0.0, BKGD W'R C.E. 0.0, C = CMAX

-128 -W'R T.E. 0.0, T = TMAX W'R BKGD.E. 0.0, BKGD = CCC/TCC PBZ = ((C/T) -BKGD)/(BZERO) W'R PBZ.L. FTY IN = CALC. (X1, PBZ) OTHERWISE IN = CALC. (X, PBZ) END OF CONDITIONAL W'R DI 0, IL 0, IL= 1.0 W'R.ABS.(IN*DIL).G. 1.0E05 PRINT COMMENT $ ERROR$ PRINT RESULTS IDENT, PBZ, IN*DIL T'O B11 O'E B2 PRINT FORMAT P5, IDENT, C, T, C/T, BZERO, BKGD, PBZ, IN*DIL E'L TRANSFER TO Al INTERNAL FUNCTION (0,U2) ENTRY TO CALC. W1= 1.0/U2 FUNCTION RETURN U2 * 0(1) + 0(2) * WI+ 0(3) * W1*W1+ 0(4) * 1 W1.P.3 + 0(5) E'N_ V'S R1 = $S5, F5.0, S5, F5.0, S5, II, S5, 415*$ V'S R2 = $ S5, 5C6, S5, Ii, S5, F3.0, S5, F5.0*$ V'S R3 = $ S1, I1, S,- I2, S2, C4, S2, F5.0, S2, F5.2, S2, 1_ F5.0, S2, F5.2, 5F5.0*$ V'S R4= $ S5, 5C6, S5, II, SO1, F10.0*$ V'S P2 = $1HO,H+ NO. IDENT. COUN ITS TIME COUNTS/TINE BKG. PERCENT BZERO i INSULIN+/ 1 H+ 1 IIN. CTS./MIN. CTS./MIN. MU U / ML.+* $ V'S P3=$S20,13,S8,C5,S5,F6.O,S9,F6.2,S6,F6.0,S6,F7.2tS3,F9.4, 1 S5, F 10.2*$ V'S P4=$1H1,lH 5C6, H*THE DILUTION FACTOR FOR THE PLASMA IS 1*F3.0*$ __V'S P5 = $S15, C6,_ F13.0, F13.2, 3F13.0, F13.4, F13.2*$ V'S P6 = $1HO,H+ IDENT. COUNTS TIM 1E COUNTS/TIME BZERO BKGD. PERCENT BZERO I 1NSULIN+/ 1 H+ MI N. 1CTS./MIN. CTS./MIN. CTS./MIN. MU U/ML. VECTOR VALUES T3 = $S5, F5.3, S11, F6.2, S11,F6.2,S13,F7.2*$ VECTOR VALUES T31=$ 1H2,S10,C'P1',S10,F'P1',1/1HO,S5,3HB/F,S1 12,7HT(OBS.), 10,8HT(CALC.),S10,9HDEVIATION*$ VECTOR VALUES T4= $7HOCOEFF.,S8,5E18.4.*$ VECTOR VALUES T6= $H/O****** THERE ARE NO POINTS ON THE STAN 1DARD CURVE WITH T VALUES EXACTLY EQUAL TO/E18.4,/S5,H/THE PRO 1GRAM WILL USE FOR THE UNKNOWN SAMPLES THE COEFFICIENTS CALCUL _1ATED FOR T VALUES LESS THAN THE BREAKPOINT./*$ VECTOR VALUES T7= $25HORESIDUAL SUM OF SOUARES=,S2,E18.4*$ V'S DIM1 = 2,1,20 V'S DIM2 = 2,1,5 VECTOR VALUES WT = -1 VECTOR VALUES DATA (81 )=1.0,1.0,1.01.0,1.0,1.00,1. 0, 1.0, __ 11.0,1.0,1.0,1.0,1.0,1.1.1.0,1.0,1.01.01.0,1. VECTOR VALUES DATA1(81 )= 1.0,1.0,1.0,1.01. 01.0,1.0,1.0,1.0, 1111.,1. 0,1.0 1.01.0,..1.1.0 1. 0,1.0,1.0.- '' E'M R R CONTRACTRACTIONS USED IN THIS PROGRAM ARE... R E'L END OF CONDITIONAL R E'M END OF PROGRAM R E'N END OF FUNCTION R P'S PRINT RESULTS R P'T PRINT FORMAT R T'H THROUGH R T'O TRANSFER TO R V'S VECTOR VALUES R W'R WHENEVER 253 LINES PRINTED

BIBLIOGRAPHY 1. Ackerman, E., Rosevear, J. M., McGuckin, W. F., "A Model of the Glucose Tolerance Test," Physics in Medicine and Biology 9:203 (1964). 2. Ackerman, E., "Blood Glucose Regulation - Model Studies," Bull. Math. Biophysics 27:21 (Special Issue) (1965). 3. Anderson, E., Long, J. A., "The Effect of Hyperglycemia on Insulin Secretion as Determined with the Isolated Rat Pancreas in a Perfusion Apparatus," Endocrinology 40:92 (1947). 4. Arden, B., Galler, B., Graham, R., Michigan Algorithm Decorder, Computing Center University of Michigan, (1964). 5. Bendat, J. S., Piersol, A. G., Measurement and Analysis of Random Data, John Wiley, New York, (1966). 6o Blackman, R. B., Tukey, J. W., The Measurement of Power Spectra, Dover, New York, (1958). 7. Bolie, V. W., "An Analog Computer Model of the Glucose and Insulin Tolerance Tests," Proc. 3rd. International Conference on Medical Electronics P. 39 (1960). 8. Bouman, P. R., Bosboom, R. S., "Effects of Growth Hormone and of Hypophysectomy on the Release of Insulin from Rat Pancreas in Vitro," Acta Endocrinologia 50:202 (1965). 9. Brodan, V., "A Mathematical Expression of the Glucose Curve During Infusion of an Hypertonic Glucose Solution," Physiologia Bohemoslovaca 15:487 (1966). 10. Brown, E. M. et al., "The Effects of Prolonged Infusion of the Dog's Pancreas with Glucose," Endocrinology 50:644 (1952). 11. Campbell, James A., Rastogi, K. S., "Effects of Glucagon and Epinephrine on Serum Insulin and Insulin Secretion in Dogs," Endocrinology 79:830 (1966). 12. Campbell, J., Bower, E., Dwyer, S. J., Lago, G. V., "On The Sufficiency of Autocorrelation Functions as EEG Descriptors," IEEE Transactions of Bio-Medical Engineering 14:49 (1967). 13. Cerasi,. E., "An Analogue Computer Model for the Insulin Response to Glucose Infusion," Acta Endocrinology 55:163 (1967). -129 -

-130 -14. Colwell, A. R. Jr., Metz, Ro., "Secretion of an Insulin-Like Substance into the Pancreatic Vein," Diabetes 11:504 (1962). 15o Cole, Jo Wo Lo, Grizzle, J. E., "Application of Multivariate Analysis of Variance to Repeated Measurements Experiments," Biometrics 22:810 (1966). 16. Coore, H.G., Randle, P. J., "Insulin Secretion from Rabbit Pancreas in Vitro," In Brolin, S. E., Hellman, B., Knutson, Ho, The Structure and Metabolism of the Pancreatic Islets, MacMillan, New York, 1964, p. 295. 17, Coore, Ho G., Randle, P. Jo. "Regulation of Insulin Secretion Studied with Pieces of Rabbit Pancreas Incubated in Vitro," Biochemo J. 93:66 (1964)0 18, Creutzfeldt, W., Frerichs, H., Reich, U., "In Vitro Studies on Rat Islets," In Brolin, S E., Hellman, B., Knutson, H., The Structure and Metabolism of the Pancreatic Islets, MacMillan, New York, 1964, po 323. 19. Ead, H. W., Green, J. H., Neil, E., "A Comparison of the Effects of Pulsatile and Non-Pulsatile Blood Flow through the Carotid Sinus on the Reflexogenic Activity of the Sinus Baroceptors in the Cat," J. Physiol. 118:509 (1952). 20. Elrick, H., et al,, "Plasma Insulin Response to Oral and I. V. Glucose Administration," Jo Clino. Endocrin. 24:1076 (1964). 210 Frohman, L. A. Ezdinli, E. Zo, Javid, R., "Effect of Vagotomy and Vagal Stimulation on Insulin Secretion," Diabetes 16:443 (1967). 22, Frohman,.L.Ao, Mac Gillivray, M. H., Aceto, T., "Acute Effects of Human Growth Hormone on Insulin Secretion and Glucose Utilization in Normal and Growth Hormone Deficient Subjects," J. Clin, Endocr. 27:561 (1967)o 23, Gjedde, F., "Effect of Glucose on the Insulin-Like Activity of Serum from V. Pancreatico-Duodenalis and from A. Femoralis in Dogs," In Brolin, S..Eo, Heilman, B., Knutson, H., The Structure and Metabolism of the Pancreatic Islets, MacMillan, New York, 1964, p. 469 24. Grodsky, Go.Mo, Bennett, "Insulin Secretion from the Isolated Pancreas in the Absence of Insulinogenesis, Effect of Glucose," Proc. Sfoc. Experimental Biology and Medicine 114:769 (1963). 25. Grodsky, G. M., Forsham, P. H., "Insulin and the Pancreas," Annual Review of Physiology P. 347 (1966).

-131 -26. Grodsky, G.M.., Bennett, L. L., Smith, D. F., Schmid, F. G., "Effect of Pulse Administration of Glucose or Glucagon on Insulin Secretion in Vitro," Metabolism 16:222 (1967). 270 Hausberger, F. X., Ramsay, A. J., "The Influences of the Administration of Glucose, and of Glucose Together with Insulin on the Granulation of Beta Cells in Guinea Pigs," Anat. Record 112:341 (1952). 28. Hoffman, W. S., "A Rapid Photoelectric Method for the Determination of Glucose in Blood and Urine," J.Biolo Chem. 120:51 (1937). 29. Hotelling, H., t'The Generalization of Student's Ration," Annals of Mathematical Statistics 2:360 (1931). 30. Hunter, W. M., Greenwood, C. F., "Preparation of Iodine-131 -Labelled Human Growth Hormone of High Specific Activity," Nature 194:495 (1962). 31. Janes, R. G., Osburn, J. O., "The Analysis of Glucose Measurements by Computer Simulation," Jo Physiology 181:59 (1965). 32. Kanazawa, Y., Kuzuua, T., Ide, T., Kosaka, K., "Plasma Insulin Responses to Glucose in Femoral, Hepatic, and Pancreatic Veins in Dogs," Amer. Journal of Physiology 211:442 (1966). 33. Kris, A. 0., Miller, R. E., Wherry, F. E., Mason, J. W., "Inhibition of Insulin Secretion by Infused Epinphrine in Rhesus Monkeys," Endocrinology 78:87 (1966). 34. Lazarrow, A., "Insulin Synthesis, Storage, Release, Transport and Antagonism," Diabetes 15:281 (1966). 35. Logothetopoulos, J., Kaneko, M., Wrenshall, G., A., Best, Co, H., "Zinc, Granulation and Extractable Insulin of Islet Cells Following Hyperglycemia or Prolonged Treatment with Insulin," In Brolin, S. E., Hellman, B., Knutson, H., The Structure and Metabolism of the Pancreatic Islets, MacMillan, New York, 1964, P. 333. 36. London, E. S., Kotschneff, "Measurement of Insulin-Like Substance in the Pancreatic Vein Following Glucose," Ztschro Fo D. Ges. Exper. Med. 101:767 (1937). 37. Malaisse, W. J., Malaisse-Lagae, Fo, Lacy, P. E., Wright, P. Ho, "Insulin Secretion by Isolated Islets in Presence of Glucose, Insulin and Anti-insulin Serum," Proco Soc. Experimental Biology and Medicine 124:497 (1967). 38. Merimee, T. J., Burgess, J. A., Rabinowitz, D., "Influence of Growth Hormone on Insulin Secretion," Diabetes 16:478 (1967).

-132 -39~ Metz, Ro, "The Effect of Blood Glucose Concentration on Insulin Output," Diabetes 9~89 (1960). 40, Michigan, University of, University of Michigan Executive System for the IBM 7090 Computer, 1966 41i Morgan, C. R., Lazarow, A., "Immunoassay of Insulin Using a TwoAntibody System," Proc. Expt. Biology and Medicine, 110:92 (1962). 42, Morgan, C Ro., Lazarow, A., "Immunoassay of Insulin-Two Antibody System, Diabetes 12:115 (1963)o 43, Morgan, C. R., et al,, "Further Studies of an Inhibitor of the Two Antibody Immunoassay System," Diabetes 13:579 (1964). 44. Morrison, D. Fo, Multivariate Statistical Methods, McGraw-Hill, New York, 1967. 45~ Norwich, Ko. N, Reiter, Ro, "The Homeostatic Control of Thyroxin Concentration Expressed by a Set of Linear Differential Equations," Bullo Math. Biophysics 27:133 (1965). 46. Oser, B. L., Hawk's Physiological Chemistry, McGraw-Hill, New York, 1965, p 10547. 47, Parry, Do G., Taylor, Ko W., "The Effects of Sugars on Incorporation of Leucine-H3 into Insulin," Biochem. Jo 100:2C (1966). 48. Pek, S., Fajans, S S., Floyd, J..C., Jr., Thiffault, C. Ao, Knopf, R. Fo, Conn, JoW., "Effect of Dexamethasone on Amino Acid Induced Changes in Insulin Release in Man," Clinical Research 15:430 (1967). 49. Porte, Do, Graber, Ao.Lo, Kuzuya, T., Williams, Ro.Ho, "The Effect of Epinephrine on Immunoreative Insulin Levels in Man," J. Clin. Invest, 45:228 (1966). 50. Randle, Po J., "Assay of Plasma Insulin Activity by the Rat Diaphragm Method," Brit, Med. Jo, 1:1237 (1954). 51o R-Canswla, J. Lo, R-Candela, R., et al., In Perspectives in Biology, Cori, C. F., et al., EdSo, Elsevier, Amsterdam (1965) 52, Renold, A. Eo, Martin. Do B., Dagenais, Y. M, Steinke, Jo, Nickerson, Ro J., Sheps,.. M C., "Measurement of Small Quantities of Insulin-Like Activity Using Rat Adipose Tissueo I. A. Proposed Procedure,". J. Clino Investo 39:1487 (1960). 53. Roston, S., "Mathematical Representation of Some Endocrinological Systems," Bull Matho Biophysics 21:271 (1959) 54. Samols, E., Bilkus, Do, "A Comparison of Insulin Immunoassays," ProCo Soco. Experimental Biology and Medicine 115:79 (1964).

-133 -55. Seed, J., Acton, F. S., Stunkard, A. J., "A Model for the Appraisal of Glucose Metabolism," Clin. Phartn. Ther. 3:191 (1962). 56. Seltzer, H. S., "Quantitative Effects of Glucose, Sulfonylureas, Salicylate, and Indole-3-Acetic Acid on the Secretion of Insulin Activity into Pancreatic Venous Blood," J. Clin. Invest. 41:289, (1962). 57. Seltzer, H. S., et al., "Failure of Prolonged Sulfonylurea Administration to Enhance the Insulogenic Response to Glycemic Stimuli," Diabetes 14:392 (1965). 58. Soeldner, J. S., Slone, D., "Critical Variables in the Radioimmunoassay of Serum Insulin using the Double Antibody Technique," Diabetes 14:771 (1965). 59. Tepperman, J., Metabolic and Endocrine Physiology, Year Book Medical Publishers, New York, 1962. 60. Unger, R. H., Eisentraut, A. M., McCall, M. S., Madison, L. L., "Measurements of Endogenous Glucagon in Plasma and the Influence of Blood Glucose Concentration upon its Secretion," J. Clin. Invest. 41:682 (1962). 61. Unger, R. H., Eisentraut, A. M., "Studies of the Physiologic Role of Glucagon," Excerpta Medica International Congress No. 84, Fifth Congress of the International Diabetes Federation 1965. 62. Unger, R. H., Ketterer, H., Dupre, J., Eisentraut, A. M., "The Effects of Secretion, Pancreozymin, and Gastrin on Insulin and Glucagon Secretion in Anesthetized Dogs," J. Clin. Invest. 46:630 (1967). 63. Yalow, R. S., Berson, S. A., "Immunoassay of Endogenous Plasma Insulin in Man," J. Clin. Invest. 39:1157 (1960). 64. Yates, F. E., Urquart, J., "Control of Plasma Concentrations of Adrenalcortical Hormones," Physiological Reviews 42:359 (1962). 65. Floyd, J. C., Jr., Fajans, S.S., Conn, J. W., Knopf, R. F., Rull, J., "Stimulation of Insulin Secretion by Amino Acids," J. Clin. Invest. 45:1487 (1966).

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