Vasculature based model for characterizing the oxygen transport in skin tissues – analogy to the Weinbaum-Jiji bioheat equation

Based on the conceptual three-layer microvascular structure of skin tissues proposed by Weinbaum et al. 20–25] and in analogy to the well known Weinbaum-Jiji (W-J) bioheat equation, a new oxygen transport model was established in this paper, which collectively included the contributions of the vascular geometry and the blood flow condition. The new one-dimensional three-layer oxygen transport model was then applied to predict the average oxygen concentration distribution in skin tissues and numerical solutions for the boundary value problem coupling the three layers were obtained. A simple expression for the tensor diffusivity (D_eff) of oxygen transport over the deep tissue layer was presented, which was orders of magnitude higher than the intrinsic diffusivity (D_t) in tissue without blood flow. Effects of blood flow velocity and vascular geometry to the oxygen transport were investigated. Calculations indicated that the vascular geometry had significant effects on oxygen transport. The oxygen exchange between the arteries and veins was relatively small for the deep tissue layer. Further, the average oxygen concentration gradient appears low in intermediate layer due to large capillary perfusion. The theoretical results were implemented to interpret some previous experimental results and a better understanding on the oxygen transport across the vascularized living tissues was obtained. The strategy proposed in this paper may provide a feasible way to comprehensively characterize the oxygen transport behaviors in living tissues with real and complex vasculature.