A mathematical simulation of oxygen delivery in rat peripheral nerve.

We have performed a mathematical simulation on a CYBER computer of the release, diffusion, and consumption of oxygen in the capillaries and surrounding tissue of peripheral nerve under steady-state conditions. The Krogh-Erlang equation was used to calculate oxygen tension in tissue, while numerical solution of the differential equation governing oxygen release from hemoglobin and diffusion was used to calculate oxygen tension in the capillary. Using average measured values for the parameters of oxygen solubility, diffusion coefficient, capillary diameter, capillary density, nerve blood flow, oxygen consumption rate, and arterial oxygen tension in rat peripheral nerve, we calculated the endoneurial oxygen tension as a function of distance from the nearest capillary and distance along the capillary from the arterial end to the venous end. The range of calculated values agreed with experimental measurements obtained from the sciatic nerves of rats. Alterations in these parameters produced changes in the calculated oxygen tension distributions. Conditions which adversely affected oxygen delivery include reduced capillary diameter, increased intercapillary distance, reduced blood flow, and reduced arterial oxygen tension. The lower experimentally obtained oxygen tensions in sciatic nerves of diabetic rats could be accounted for reasonably by this model on the basis of a 33% reduction in nerve blood flow (consistent with previously measured flow reduction). However, the measured reduction in oxygen tensions in sciatic nerves of rats with experimental galactose neuropathy were not as marked as those predicted on the basis of a 22% increase in tissue cylinder radius in the model (consistent with experimental observations). This may be due to the fact that the oxygen consumption rate is reduced in hypoxic regions of tissue.