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

Abstract

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 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.

Coupling between skeletal muscle fiber size and capillarization is maintained during healthy aging

“…The co‐ordinates were imported into AnaTis to calculate the capillary domains, defined as the area of a muscle cross‐section surrounding an individual capillary delineated by equidistant boundaries from neighbouring capillaries ( Figure 2C). A capillary domain is a good estimate of the capillary oxygen supply area 23. This method not only provides overall indices of muscle capillarization, such as capillary density (number of capillaries per mm 2 ) and the capillary‐to‐fibre ratio but also allows to determine the capillary supply to individual fibres even when they lack direct capillary contact ( Figure 2D).…”

“…To investigate this, we calculated capillary domains as the areas surrounding a capillary delineated by equidistant boundaries from adjacent capillaries,22 which is an index of the oxygen supply area of a capillary, including in muscles with a heterogeneous fibre type composition 23. Quantitative succinate dehydrogenase (SDH) histochemistry was used to estimate the maximal oxygen consumption of a fibre,24 to determine (i) the relationship between the oxidative capacity and the capillary supply to a fibre and (ii) whether this relationship is different in older human muscle compared with young muscle.…”

Local capillary supply in muscle is not determined by local oxidative capacity

“…However, if the principle of symmorphosis, which states that structures are matched to functional demand, is valid, then local capillarisation in a muscle should be arranged so that maximal oxygen demand per capillary is tightly regulated. To explore whether local feedback results in each capillary serving a similar maximal demand for oxygen, we estimated the supply areas (domains) of individual capillaries (Al-Shammari et al, 2014). Capillary domains provide a good estimate of the tissue oxygenation capacity of a capillary, even in muscles containing a mixture of fibres with different metabolic demand (Al-Shammari et al, 2014), whereas the total volume of mitochondria, as reflected by succinate dehydrogenase activity, in a domain is a reflection of the maximal oxygen demand served by that capillary.…”

Image-based modelling of skeletal muscle oxygenation

“…In the perfect case, where the Voronoi polygons match the trapping regions (Al-Shammari's hypothesis), no streamlines would cross over the lines of the Voronoi polygons. Al-Shammari's hypothesis was further supported by examining the difference between Voronoi and trapping regions when taking fibre type, size, distribution and varying oxygen demand into account [141]. It was found that the difference in Voronoi and trapping regions was small in most pathological cases, thus making Voronoi tessellations the best and most easily computable representation of capillary oxygen supply regions.…”

“…P 50 is usually found to be 0.5-1.0 mmHg [130] and can be determined experimentally by methods described in [160]. For skeletal muscle, Al-Shammari and co-workers [141] took into account the fact that M 0 can differ between different muscle fibre types (I, IIa and IIb). The use of Michaelis-Menten kinetics is only an approximation of the occurring process, describing it more accurately than any other model [130].…”