Predicting Fraction Dose Absorbed in Humans Using a Macroscopic Mass Balance Approach

Abstract

A theoretical approach for estimating fraction dose absorbed in humans has been developed based on a macroscopic mass balance that incorporates membrane permeability and solubility considerations. The macroscopic mass balance approach (MMBA) is a flow model approach that utilizes fundamental mass transfer theory for estimating the extent of absorption for passively as well as nonpassively absorbed drugs. The mass balance on a tube with steady input and a wall flux of J w = P w C b results in the following expression for fraction dose absorbed, F : F = 2 An ∫ 0 1 C * b dz * where the absorption number, An = L/R · P w / v z >;, L and R are the intestinal length and radius, P w is the unbiased drug wall permeability, 〈 v z 〉 is the axial fluid velocity, C * b = C b /C o and is the dimension-less bulk or lumen drug concentration, C b and C o are the bulk and initial drug concentrations, respectively, and z * is the fractional intestinal length and is equal to z/L . Three theoretical cases are considered: (I) C o ≤ S , C m ≤ S , (II) C o > S , C m ≤ S , and (III) C o > S , C m > S , where S is the drug solubility and C m is the outlet drug concentration. Solving the general steady-state mass balance result for fraction dose absorbed using the mixing tank (MT) and complete radial mixing (CRM) models results in the expressions for the fraction dose absorbed in humans. Two previously published empirical correlations for estimating fraction dose absorbed in humans are discussed and shown to follow as special cases of this theoretical approach. The MMBA is also applied to amoxicillin, a commonly prescribed orally absorbed β-lactam antibiotic for several doses. The parameters used in the correlation were determined from in situ or in vitro experiments along with a calculated system scaling parameter. The fraction dose absorbed calculated using the MMBA is compared to human amoxicillin pharmacokinetic results from the literature with initial doses approximated to be both above and below its solubility. The results of the MMBA correlation are discussed with respect to the nonpassive absorption mechanism and solubility limitation of amoxicillin. The MMBA is shown to be a fundamental, theoretically based model for estimating fraction dose absorbed in humans from in situ and in vitro parameters from which previously published empirical correlations follow as special cases.