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Oxygen Depleted Regions by the Theory of Krogh

Oxygen depleted regions in the tissue of Krogh in cartesian coordinates is derived. Simultaneous diffusion and reaction is considered and the concentration profile solved for. Michaelis-Menten kinetics is supposed for the reaction rate. The critical distance in the tissue, less than the length of the tissue, is given by a quadratic equation. This is obtained from the governing equation by solving for the appropriate boundary conditions. The analysis is at steady state.