Calculation of oxygen diffusion across the surface of isolated perfused hearts

Although exact mathematical descriptions of oxygen diffusion into unperfused isolated organs are known, no analytic solution is available for perfused organs. Here, we derive an equation for oxygen diffusion across the epicardial surface of perfused hearts. Our oxygen transport model incorporates oxygen delivery from the capillary perfusate, oxygen consumption, diffusion among adjacent capillary exchange regions, and diffusion across the epicardial surface. The wall of the heart is modeled by a slab of tissue. The derived equation fits experimental data on the diffusive oxygen flux across the surface of isolated saline-perfused guinea pig hearts, obtained by measuring oxygen uptake from the perfusate at various oxygen tensions in the surroundings of the isolated heart. The model predicts that in isolated arrested guinea pig hearts suspended in air, 25% of the oxygen taken up from the saline perfusate (PO2 approximately 680 mmHg) diffuses out of the heart across the surface. In beating isolated guinea pig hearts, 5% of the oxygen taken up from the perfusate diffuses across the surface.