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. To advance this area, a model of blood-tissue O transport in skeletal muscle was recently developed which uses continuously distributed capillaries and includes O diffusion, convection, and consumption. The present work extends this model to two adjacent layers of skeletal muscle with different blood flow rates and applies it to study steady-state O transport when flow regulation is stimulated using an O exchange chamber. To generate a model which may be validated through in vivo experiments, an overlying O permeable membrane is included. The model is solved using traditional methods including separation of variables and Fourier decomposition, and to ensure smooth profiles at the muscle-muscle and muscle-membrane interfaces, matching conditions are developed. The study presents qualitative verification for the model, using visualizations of tissue O pressure (PO) distributions for varying capillary density (CD), and presents capillary velocity response values in the near layer for varying chamber PO under the assumption that outlet capillary O saturation (SO) is equalized between adjacent layers. These compensatory velocity profiles, along with effective 'no-flux' chamber PO values, are presented for varying CD and tissue O consumption values. Insights gained from the two-layer model provide guidance for interpreting and planning future in vivo experiments, and also provide motivation for further development of the model to improve understanding of the interaction between O transport and blood flow regulation.