| In this dissertation I present three mathematical models of hepatic transport kinetics. For each model, the system of partial and ordinary differential equations that govern it is solved and an algorithm developed for estimating a 3-dimensional parameter vector. The desired parameters are the rate constants for hepatic uptake, efflux and removal. Two of the models, the two-compartment lumped model of Richards and the multiple indicator dilution (MID) model of Goresky have previously been proposed as useful accurate representations of hepatic transport kinetics. However, each of these methods for estimating the rate constants is subject to error. The errors are inherent in the simplifying assumptions of the models and have been documented by subjecting the models to computer simulation analysis. The lumped model underestimates all three rate constants, with the magnitude of the underestimates increasing exponentially as a function of the single pass extraction fraction. The MID model also fails to provide consistently reliable estimates of the rate constants with estimates of the removal constant especially likely to be wrong. For each of these models the fit of the simulated data to the model equation is virtually perfect, despite the errors in the rate constants. It is unlikely therefore, that errors in estimating the rate constants would be recognized in an animal experiment.;The third model, developed as part of this dissertation, is a hybrid of its forerunners. It involves distributed modeling of a rat liver perfusion system. The method depends on recording the disappearance of a solute from the reservoir of the perfusion system. The function describing the time course of solute removal is available only as its Laplace transformation. However, the asymptotic behavior of the function can be used to obtain initial estimates of all three rate constants. Refined estimates of these parameters are then obtained from a least squares fit of the disappearance curve to the model equation through numerical inversion of its Laplace transform. A computer simulation analysis of the method shows that is feasible to obtain accurate estimates of the rate constants with only approximate information about the extra-reservoir distribution function. Since an accurate description of this function is not available, this insensitivity is an important feature of the new method. The new approach represents an important advance that can substantially reduce the errors inherent in previous approaches to estimating the rate constants for hepatic transport. |
