Formulation and Realization of a Multicompartmental Model for O₂-CO₂ Coupled Transport in the Microcirculation

Abstract

A multicompartmental model for gas transport in the microcirculation (M.C.M) is a lumped form of the corresponding distributed models. This idea can be understood by the sketch shown in Fig.l. The microcirculation consists of a series of arteriole beds, capillary beds, venule beds and the surrounding tissue, with an oxygen partial pressure distribution and a carbon dioxide partial pressure distribution in both the radial and longitudinal directions. Distributed models, based on either the modified Krogh cylinder or a nonKroghian geometry, usually simulate the radial and axial distributions in one vessel segment or within a local region of the microcirculation. If every vessel group is lumped into a compartment with a unique oxygen partial pressure and a unique carbon dioxide partial pressure, and the tissue is also lumped into one compartment (or more compartments, cf. Ye and Silverton, 1994), then a multicompartmental model is constructed. The model’s block diagram in Fig.1 shows that axial convection of both blood flow and gas occurs along the sequential vessel compartments, and that simultaneous gas diffusions take place between the tissue compartment and every vessel compartment. Thus the global relationship of gas transport and blood supply is quite clear for a M.C.M. It is also easier for a M.C.M to be linked to a global multielement-lumped model for the whole cardiovascular system. Moreover, a compartmental model is described by algebraic equations (for steady-state) or by ordinary differential equations (for time-varying state), whereas a distributed model is described by ordinary differential equations (for one-dimension distributed, steady state) or by partial differential equations (otherwise).