An asymptotic study of oxygen transport from multiple capillaries to skeletal muscle tissue

摘要: A mathematical model of the transport oxygen from capillaries to skeletal muscle tissue is a diffusion problem in two-dimensional, bounded domain with Neumann and mixed boundary conditions. We consider N small but arbitrary cross-sectional shape demonstrate, for > 1, that this singular perturbation involves an infinite expansion logarithmic terms parameter $\varepsilon$, which characterizes size capillary cross sections. For $\varepsilon \ll 1$, we use hybrid asymptotic-numerical method calculate steady-state partial pressure correct within all terms. Our results illustrate effect heterogeneities such as mitochondria, variable permeability walls, facilitation by presence myoglobin. The compare well full numerical solutions.