Metabolic system dynamics: lumped and distributed models

A quantitative understanding of the complexity of cellular metabolism integrated with tissue, organ, and whole-body processes requires sophisticated mathematical models, computer simulations, and validation with experimental data. Physiologically based models incorporate cellular metabolic reactions and transport processes of a large number of chemical species. In general, these dynamic models of spatially lumped and/or distributed systems involve highly nonlinear phenomena. Such models allow quantitative evaluation of metabolic pathways and regulatory mechanisms under normal and abnormal conditions. Furthermore, modeling can help quantify mechanisms and predict responses that cannot be directly measured. Consequently, these models can provide a basis for simulating the integrated effects of altering enzyme activities or substrate concentrations with pharmacological agents. For this complex biomedical systems research, we have started a Center for Modeling Integrated Metabolic Systems (MIMS). The thrust of the MIMS Center is mathematical modeling and computer simulation of metabolic systems and their changes with exercise, diet, and disease. We are developing a general integrative whole-body model that relates cellular intermediate metabolism with responses of four major tissue-organ systems: skeletal muscle, heart, liver, and brain. In each of these tissue-organ systems, it is essential to determine the effect of spatial distribution related to blood perfusion and capillary-tissue transport. As an example, we consider possible effects of spatial distribution of perfusion in skeletal muscle. In this model, blood perfusion occurs along one spatial coordinate while cellular metabolic processes are spatially lumped. In the dimensionless perfusion model, two key dimensionless parameter ratios characterize transport: axial dispersion to perfusion and capillarytissue transport to perfusion. These have a significant effect on the behavior of the system output and the quantitative evaluation of the metabolic processes. The simulated outputs of the 1-D perfusion model are compared with those of a compartment model in which tissue is perfused isotropically.