Modelling capillary oxygen supply capacity in mixed muscles: capillary domains revisited.

Developing effective therapeutic interventions for pathological conditions associated with abnormal oxygen transport to muscle fibres critically depends on the objective characterisation of capillarity. Local indices of capillary supply have the potential to identify the onset of fine-scale tissue pathologies and dysregulation. Detailed tissue geometry, such as muscle fibre size, has been incorporated into such measures by considering the distribution of Voronoi polygons (VP) generated from planar capillary locations as a representation of capillary supply regions. Previously, detailed simulations have predicted that this is generally accurate for muscle tissue with uniform oxygen uptake. Here we extend this modelling framework to heterogeneous muscle for the assessment of capillary supply capacity under maximal sustainable oxygen consumption. We demonstrate for muscle with heterogeneous fibre properties that VP theoretically provide a computationally simple but often accurate representation of trapping regions (TR), which are predicted from biophysical transport models to represent the areas of tissue supplied by individual capillaries. However, this use of VP may become less accurate around large fibres, and at the interface of fibres of largely different oxidative capacities. In such cases, TR may provide a more robust representation of capillary supply regions. Additionally, given VP can only approximate oxygen delivery by capillaries, we show that their generally close relationship to TR suggests that (1) fibre type distribution may be tightly regulated to avoid large fibres with high oxidative capacities, (2) the anatomical fibre distribution is also tightly regulated to prevent a large surface area of interaction between metabolically dissimilar fibres, and (3) in chronically hypoxic tissues capillary distribution is more important in determining oxygen supply than the spatial heterogeneity of fibre demand.