Evaluation of myoglobin function in the presence of axial diffusion

Abstract

Facilitation of oxygen transport by myoglobin has been assessed by many researchers. Yet, the models used in these studies often assume that radial diffusion is the primary transport mechanism in tissue. Axial diffusion is typically neglected. In this study, oxygen transport by myoglobin facilitation is added to a proven cardiac tissue model which contains axial diffusion in the tissue and capillary regions, the Radially-Averaged, Axially-Distributed (RAAD) model. Previous research has shown that the axial diffusion in the capillary and tissue regions becomes coupled, causing a reduction in the pO2 at the capillary inlet. The objective is to determine if this coupling effect increases the facilitation of oxygen transport by myoglobin. The RAAD model consists of non-interacting cylinders of tissue (Krogh cylinders), with each perfused by a central capillary. Derivation of the equations describing the RAAD model yields a stiff, fourth-order, non-linear, ODE, BVP. The equation set is solved numerically. Parameters for myoglobin concentration and diffusion coefficient are chosen to maximize myoglobin facilitation. The effect of myoglobin is assessed by observing changes in the pO2 profiles for the model with and without myoglobin. Also, the RAAD model is compared to experimental pO2 data to determine if the inclusion of myoglobin improves the model prediction. The computer simulations show that myoglobin does facilitate diffusion, but only to a small extent. The changes in the capillary pO2 profiles for the model with and without myoglobin are not significant, pO2 reductions are 0.8% at the inlet and 2% at the outlet. The model prediction is not substantially improved with the addition of myoglobin. The sum of squared error is reduced by 0.1%, from 5.6834 without myoglobin, to 5.6779 with myoglobin. The steady state solution of the RAAD model with myoglobin suggests that, in the presence of axial diffusion, facilitation of oxygen diffusion to tissue is not myoglobin's primary function. No conclusion can be made about the transient function of myoglobin.