Finite Element Analysis of Oxygen Transport in Tissue and Capillaries with a Second Order Metabolic Consumption

This study presents a numerical investigation into the oxygen transport through a Krogh-type capillary-tissue model with second-order tissue metabolism. The governing non-linear equations are solved by implementing a Galerkin finite element method with a fixed-point iteration scheme. The resulting code and solution algorithm were successfully validated against available analytical solutions for zeroth- and first-order kinetics, showing very good agreement. Numerical simulations indicated, that under the parameters investigated, relative to zeroth- and first-order kinetics, a second-order metabolism leads to less overall oxygen consumption within the tissue phase. This yields higher oxygen partial pressures at the outer tissue boundary and higher oxygen levels present throughout the capillary. Results also supported other studies in showing that the oxygen concentration decreased most rapidly near the capillary inlet, where partial pressure gradients are largest. This reinforces the idea that diffusion effects strongly influence oxygen distribution not only within the tissue, but also in the capillary phase. In addition, increasing inlet arterial oxygen partial pressures were found to enhance oxygen delivery into the tissue.