The ability to quantify capillary supply plays a key role in developing effective therapeutic interventions for numerous pathological conditions, e.g. chronic ischaemia in striated muscle, but is fraught with difficulties. Averaged measures – such as mean capillary density (CD) or mean intercapillary distance (ICD) – may characterise global tissue ischaemia [1], but cannot account for local dysfunction associated with the underlying capillary distribution. Detailed tissue geometry including muscle fibre size has been incorporated into indices of capillary supply, e.g. local capillary-to-fibre ratio (LCFR) and local capillary density (LCD), by considering the distribution of capillary domains. By identifying vessel locations in a plane perpendicular to muscle fibre orientation, each capillary domain represents the area of supply of its enclosed capillary [2]. Although such geometrical constructs have proven useful in describing oxygenation for homogeneous muscle tissue such as the myocardium [3], it is unclear how well they may capture capillary supply areas in the presence of structural and metabolic heterogeneities. Using a mathematical framework to assess the maximal capacity of capillary supply in uniform and mixed muscles [4], we theoretically demonstrate that under normal physiological conditions capillary domains can provide an accurate representation of the tissue region supplied by each capillary, or trapping region, based on oxygen flux lines. In contrast, reduced accuracy is found with increasing levels of pathological heterogeneities such as (a) local capillary rarefaction, (b) pathological variations in PO2 of neighbouring capillaries, and (c) substantial differences in O2 extraction capacities among different fibre types. For aerobic muscle, the correlation between capillary domain and diffusive supply areas suggests a sensitive local control of angiogenesis on the length scale of fibre diameter. In contrast, the effect of capillary loss becomes insignificant when localised to glycolytic fibres, suggesting that such rarefaction may be mitigated by reducing the oxygen extraction capacity per fibre volume. Moreover, in the presence of hypoxia, the decay and desaturation of mitochondrial oxygen extraction and myoglobin-O2 complex, respectively, is predicted to significantly improve the utility of capillary domains. Given that capillary domains are based solely on the spatial distribution of capillaries, this suggests that in chronically hypoxic tissues the oxygen supply of each capillary is predicted to be essentially determined by, and most sensitive to, the distribution of capillaries rather than fibre oxygen demand.