Mathematical modeling of oxygen transport in skeletal muscle under conditions of high oxygen demand

Abstract

Maximal oxygen consumption rates in exercising skeletal muscle are studied using a Krogh-type cylinder model. Effects of the decline in oxygen content of blood flowing along capillaries, intravascular resistance to oxygen diffusion, and myoglobin-facilitated diffusion are included. Parameter values are based on human skeletal muscle. The model is used to predict oxygen consumption rates in exercising skeletal muscle, based on transport processes occurring at the microvascular level. The dependence of maximal oxygen consumption rates on oxygen demand, perfusion, and capillary density (defined as number of capillaries per unit cross-section area of muscle) is examined. When demand is high, model results show that capillary oxygen content declines rapidly with axial distance and radial oxygen transport is limited by diffusion resistance within the capillary and within the tissue. Under these conditions, much of the tissue is hypoxic and consumption is substantially less than demand. Predicted consumption rates are compared with experimentally observed maximal rates of oxygen consumption. Capillary densities in human skeletal muscle are estimated by using the model to determine the minimum number of straight, evenly spaced capillaries required to achieve experimentally observed oxygen consumption rates. Estimated capillary density values are generally higher than values obtained using either histochemical staining techniques or electron microscopy on quadriceps muscle biopsies from healthy subjects. This discrepancy is partly accounted for by the fact that capillary density decreases with muscle contraction, and muscle biopsy samples typically are strongly contracted. These results imply that estimates of maximal oxygen transport rates based on capillary density values obtained from biopsy samples do not fully reflect the oxygen transport capacity of the capillaries in skeletal muscle. The model is also used to predict decreases in oxygen consumption in maximally exercising muscle due to reductions in the inspired partial pressure of oxygen. In general, observed reductions in maximal oxygen consumption rates due to hypoxic breathing conditions are larger than predicted by the model, suggesting that responses to hypoxia not currently included in the model, such as decreases in oxygen demand or in muscle blood flow, may be important in determining maximal oxygen consumption in hypoxic conditions.