We expanded a prior model of whole-body O2 transport and utilization based on diffusive O2 exchange in the lungs and tissues to additionally allow for both lung ventilation-perfusion and tissue metabolism-perfusion heterogeneities, in order to estimate V̇O2 and mitochondrial PO2 (PmO2) during maximal exercise. Simulations were performed using data from (a) healthy fit subjects exercising at sea level and at altitudes up to the equivalent of Mount Everest and (b) patients with mild and severe chronic obstructive pulmonary disease (COPD) exercising at sea level. Heterogeneity in skeletal muscle may affect maximal O2 availability more than heterogeneity in lung, especially if mitochondrial metabolic capacity (V̇ MAX ) is only slightly higher than the potential to deliver O2 , but when V̇ MAX is substantially higher than O2 delivery, the effect of muscle heterogeneity is comparable to that of lung heterogeneity. Skeletal muscle heterogeneity may result in a wide range of potential mitochondrial PO 2 values, a range that becomes narrower as V̇ MAX increases; in regions with a low ratio of metabolic capacity to blood flow, PmO2 can exceed that of mixed muscle venous blood. The combined effects of lung and peripheral heterogeneities on the resistance to O2 flow in health decreases with altitude. Previous models of O2 transport and utilization in health considered diffusive exchange of O2 in lung and muscle, but, reasonably, neglected functional heterogeneities in these tissues. However, in disease, disregarding such heterogeneities would not be justified. Here, pulmonary ventilation-perfusion and skeletal muscle metabolism-perfusion mismatching were added to a prior model of only diffusive exchange. Previously ignored O2 exchange in non-exercising tissues was also included. We simulated maximal exercise in (a) healthy subjects at sea level and altitude, and (b) COPD patients at sea level, to assess the separate and combined effects of pulmonary and peripheral functional heterogeneities on overall muscle O2 uptake (V̇O2) and on mitochondrial PO2 (PmO2). In healthy subjects at maximal exercise, the combined effects of pulmonary and peripheral heterogeneities reduced arterial PO2 (PaO2) at sea level by 32mmHg, but muscle V̇O2 by only 122mlmin(-1) (-3.5%). At the altitude of Mt Everest, lung and tissue heterogeneity together reduced PaO2 by less than 1mmHg and V̇O2 by 32mlmin(-1) (-2.4%). Skeletal muscle heterogeneity led to a wide range of potential PmO2 among muscle regions, a range that becomes narrower asV̇ MAX increases, and in regions with a low ratio of metabolic capacity to blood flow, PmO2 can exceed that of mixed muscle venous blood. For patients with severe COPD, peak V̇O2 was insensitive to substantial changes in the mitochondrial characteristics for O2 consumption or the extent of muscle heterogeneity. This integrative computational model of O2 transport and utilization offers the potential for estimating profiles of PmO2 both in health and in diseases such as COPD if the extent for both lung ventilation-perfusion and tissue metabolism-perfusion heterogeneity is known.