Myoglobin facilitated oxygen diffusion in the heart: a mathematical assessment

Previous theoretical assessments of myoglobin facilitation have failed to validate modeling results with a comparison to experimental data. In this study, myoglobin reaction kinetics is added to a proven cardiac tissue model in an effort to determine the extent of myoglobin facilitation. The mathematical model is compared to experimental pO₂ measurements taken from an isolated perfused cat heart preparation. The model is based upon the Krogh cylinder. In the tissue region there is axial diffusion, zero-order oxygen consumption, and myoglobin kinetics. Oxygen flux leaving the capillary is represented by a concentration difference times a mass transport coefficient, meaning that the tissue is considered “well mixed” radially. The tissue model is called the Radially-Averaged-Axially-Distributed (RAAD) model. Formulation of the mathematical problem describing the RAAD model yields a stiff, fourth-order, nonlinear, ordinary differential equation, boundary value problem. The equation set was solved numerically using a finite difference routine on a mainframe computer. The amount of diffusion facilitation by myoglobin was estimated by observing the inlet arteriolar pO₂ for the model with and without myoglobin. The computer simulations show that myoglobin does facilitate diffusion, but only to a small extent. The change in arteriolar pO₂ was less than 1% (0.76%). The facilitation is limited due to the low concentration and low diffusability of myoglobin in tissue. This suggests that facilitation of oxygen transport is not myoglobin´s main physiological function