title: Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer--Part II: Model formulation and solution.
abstract: In this paper the conceptual three-layer representation of surface tissue heat transfer proposed in Weinbaum, Jiji and Lemons [1], is developed into a detailed quantitative model. This model takes into consideration the variation of the number density, size and flow velocity of the countercurrent arterio-venous vessels as a function of depth from the skin surface, the directionality of blood perfusion in the transverse vessel layer and the superficial shunting of blood to the cutaneous layer. A closed form analytic solution for the boundary value problem coupling the three layers is obtained. This solution is in terms of numerically evaluated integrals describing the detailed vascular geometry, a capillary bleed-off distribution function and parameters describing the shunting of blood to the cutaneous layer. Representative heat transfer results for typical physiological conditions are presented.
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D001833:Body Temperature Regulation; D008433:Mathematics; D008833:Microcirculation / Q000502:physiology*; D008954:Models, Biological; D011817:Rabbits; D012039:Regional Blood Flow; D012867:Skin / Q000098:blood supply*; D012879:Skin Physiological Phenomena; D012881:Skin Temperature