A two-layer continuously distributed capillary O transport model applied to blood flow regulation in resting skeletal muscle.

The microcirculation is the site of direct oxygen (O) transfer from blood to tissue, and also of O delivery control via regulation of local blood flow. In addition, a number of diseases including type II diabetes mellitus (DMII) and sepsis are known to produce microcirculatory dysfunction in their early phases. Given the complexity of microvascular structure and physiology, and the difficulty of measuring tissue oxygenation at the micro-scale, mathematical modelling has been necessary for understanding the physiology and pathophysiology of O transport in the microcirculation and for interpreting in vivo experiments.

A two-compartment model of oxygen transport in skeletal muscle using continuously distributed capillaries.

For future application to studying regulation of microvascular oxygen delivery, a model is developed for O transport within an idealized volume of tissue, that is perfused by a continuous distribution of capillaries. Considering oxygen diffusion, convection, and consumption, an O-dependent transfer term between the capillaries and tissue is used to extend previous single-compartment approaches to include separate tissue and capillary compartments. The coupled tissue-capillary PDE system is considered for unidirectional capillary flow in z, as a simplified model of O transport in skeletal muscle, and steady-state 2D solutions are obtained using boundary conditions in x that are consistent with two experimental situations of interest.