Cut set analysis of compartmental models with applications to experiment design

Abstract

Conventional compartmental analysis typically involves equations derived from mass-rate balance considerations for each compartment (pool), with each equation associated with a single pool. However, alternative mathematical descriptions, which effectively group pools into various other configurations, facilitate model analysis in certain applications, e.g., for kinetic experiment design or analysis. Such equivalent models are usually obtained using (often) complex matrix operations. An alternative approach, cut set analysis, can be applied directly to the graph of the compartmental model to readily generate alternative mathematical descriptions in which the needed equivalence transformations are easily performed graphically. This graphical transformation is developed here for linear, time-invariant multicompartmental models in which particular parameter values are the experimental objective. The method potentially provides greater flexibility in analyzing complex compartmental models in theory and practice, and it is exemplified here by application to the design of steady-state kinetic endocrine system studies in experimental animals.