Numerical evaluation of myoglobin facilitated oxygen diffusion in the heart

Myoglobin facilitated oxygen diffusion and Michaelis-Menten kinetics are added to an experimentally-validated oxygen transport to cardiac tissue model to determine the steady-state function of myoglobin in working heart tissue. Previous modeling of tissue oxygen partial pressure (pO₂) data suggests that the oxygen diffusion coefficient in working heart tissue is greater than expected. To fit the pO₂ data, the tissue oxygen diffusion coefficient in the model must be elevated to 8 to 12 times reported values. These elevated values of the tissue oxygen diffusion coefficient are not acceptable based upon current understanding of cardiac muscle physiology. In this paper the effect of including myoglobin facilitated diffusion in the model is evaluated to determine if this phenomenon can explain the need for an elevated oxygen diffusion coefficient. The radially-averaged, axially-distributed (RAAD) model considers axial diffusion of oxygen in tissue, myoglobin facilitation of oxygen transport, and pO₂-dependent oxygen consumption. Models are solved numerically using a variable-mesh finite-difference scheme. Parameters are optimized with Nelder-Mead simplexing and are chosen to minimize the sum-of-squares error between model pO₂ predictions and pO₂ data. The addition of myoglobin to the RAAD model does not provide a better data fit. Simulations lead to the conclusion that myoglobin facilitation is not responsible for the elevated oxygen diffusion found through modeling pO₂ data. Also, simulations indicate that myoglobin does not act to facilitated diffusive transport of oxygen in the steady-state isolated perfused cat heart preparation. A possible explanation for the elevated oxygen diffusion coefficient is tissue stirring by contractile elements