Computer simulation as an aid to incorporating diffusion effects into multicompartment models of Na exchange in tissues

Abstract

Digital computer simulation is used to determine the effects on calculated transport rate constants and relative compartment sizes caused by incorporating mathematical expressions for diffusion out of the extracellular space into compartmental models of Na kinetics. Four typical records were selected from sets of Na tracer washouts (kidney cortex, papillary muscle, carotid artery-control, and aldosterone treated) illustrative of widely differing patterns of Na distribution. Each record was analyzed first using a strictly compartmental model and then using a diffusional-compartmental model. Only for the kidney cortex tissue did inclusion of the diffusion constraints permit the model to be reduced from three to two compartments. The effects of the diffusion constraints on the three compartment models for the carotid and papillary tissues were more pronounced in the carotid, which is characterized by a predominantly extracellular localization of Na, than in the papillary tissue, which has its Na more equally distributed between three compartments. Furthermore, differences between the control and the aldosterone treated carotid tissues detected using the strict three compartment model became more apparent using the diffusional compartment model. Since the incorporation of the diffusion constraints into compartmental models results in much longer solution times on the computer, it appears advisable to use the diffusional-compartmental models only for further analysis of selected records after significant features of interest have been detected using strictly compartmental models.