(a) Spherical geometry: a cross section of a tumour spheroid of radius ro. Oxygen partial pressure at ro is po and oxygen partial pressure falls to 0 at rn, the radius of the anoxic region. (b) A cross section of a DLD-1 colorectal spheroid with same regions visible .
Comparisons of the approximation solution (solid line) with numerical solution (dashed line) for (a) a 500 μm spheroid ( and po= 100 mm Hg), (b) a vessel of radius ro=5 μm (, po= 100 mm Hg, typical arterial pressure) and (c) a vessel of radius ro=5 μm (, po=40 mm Hg, typical venous pressure). For examples here, a=5×10−7 m3 kg−1 s−1 and D= 2×10−9 m2 s−1.
Comparison of the variation of relative oxygen consumption with oxygen partial pressure for the hyperbolic (dashed line) form (P/(P+Km)) and the approximation (solid line) derived in this work, outlined in equation (3.5).
Comparing the constant and Michaelis–Menten consumption rate models for (a) spherical geometry (ro=500 μm) and (b) cylindrical geometry (ro=5 μm). In both cases, D=2×10−9 m2 s−1 and a=5×10−7 m3 kg−1 s−1. When Km=0 mm Hg, the hyperbolic model reduces to the constant consumption case. Increased values of Km result in longer oxygen diffusion distances and higher overall oxygen profiles.