A semiparametric approach to physiological flow models

Abstract

By regarding sampled tissues in a physiological model as linear subsystems, the usual advantages of flow models are preserved while mitigating two of their disadvantages, (i) the need for assumptions regarding intratissue kinetics, and (ii) the need to simultaneously fit data from several tissues. To apply the linear systems approach, both arterial blood and (interesting) tissue drug concentrations must be measured. The body is modeled as having an arterial compartment (A) distributing drug to different linear subsystems (tissues), connected in a specific way by blood flow. The response C_A,with dimensions of concentration) of A is measured. Tissues receive input from A (and optionally from other tissues), and send output to the outside or to other parts of the body. The response C_T,total amount of drug in the tissue (T) divided by the volume of T) from the T- th one, for example, of such tissues is also observed. From linear systems theory, C_T can be expressed as the convolution of C_A with a disposition function, F(t) (with dimensions 1/time). The function F(t)depends on the (unknown) structure of T, but has certain other constant properties: The integral F(t) dt is the steady state ratio of C_T to C_A,and the point F(0)is the clearance rate of drug from A to T divided by the volume of T. A formula for the clearance rate of drug from T to outside T can be derived. To estimate F(t)empirically, and thus mitigate disadvantage (i), we suggest that, first, a nonparametric (or parametric) function befitted to CA data yielding predicted values, Ĉ_A,and, second, the convolution integral of C_A with F(t)befitted to C_T data using a deconvolution method. By so doing, each tissue's data are analyzed separately,thus mitigating disadvantage (ii). A method for system simulation is also proposed. The results of applying the approach to simulated data and to real thiopental data are reported.