Date of Award

Winter 1997

Document Type


Degree Name

Doctor of Philosophy (PhD)


Biomedical Engineering

First Advisor

Roy Schubert


Myoglobin facilitated oxygen diffusion and Michaelis-Menten kinetics are added to an experimentally-validated cardiac tissue model to determine the steady-state function of myoglobin in working heart tissue. Previous modeling of tissue oxygen partial pressure (pO$\sb2)$ data suggests that the oxygen diffusion coefficient in working heart tissue is greater than expected. To fit the pO$\sb2$ 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 the current understanding of cardiac muscle physiology. In this dissertation 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 pO$\sb2$-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 pO$\sb2$ predictions and pO$\sb2$ data.

The addition of myoglobin to the RAAD model does not provide a better data fit. Simulations led to the conclusion that myoglobin facilitation is not responsible for the elevated oxygen diffusion found through modeling pO$\sb2$ data. Also, simulations indicate that myoglobin facilitated diffusive transport of oxygen can be disregarded in future steady-state oxygen transport models of the isolated perfused cat heart. Possible explanations for the elevated oxygen diffusion coefficient include tissue stirring by contractile elements, intercapillary oxygen exchange, and preparation-specific transport conditions of the isolated heart.