Balance studies on compartmental systems with stochastic inputs

Abstract

For a population of identical one compartment systems with daily inputs which are random samples from a stationary distribution the mean of the daily balance (balance = input minus excretion) taken over the population of compartments or over days for one compartment is linearly dependent on input with a slope which is independent of the distribution of the inputs and an intercept which depends only on the mean of the distribution of intakes. Analytical and simulation studies on a model with three daily inputs gives essentially similar results. Even if the inputs are not from a stationary distribution but the inputs to a population of compartments are all from the same distribution, one still obtains a linear regression of the mean of the daily balance over the population of compartments, on intake for any particular day but this no longer holds from day to day. This provides a theoretical basis for the interpretation of balance studies on populations of individuals when the daily intakes of an element under study cannot be kept constant.