A new theoretical model supported by ultrastructural studies and high-spatial resolution temperature measurements is presented for surface tissue heat transfer in a two-part study. In this first paper, vascular casts of the rabbit thigh prepared by the tissue clearance method were serially sectioned parallel to the skin surface to determine the detailed variation of the vascular geometry as a function of tissue depth. Simple quantitative models of the basic vascular structures observed were then analyzed in terms of their characteristic thermal relaxation lengths and a new three-layer conceptual model proposed for surface tissue heat transfer. Fine wire temperature measurements with an 80-micron average diameter thermocouple junction and spatial increments of 20 micrometers between measurement sites have shown for the first time the detailed temperature fluctuations in the microvasculature and have confirmed the fundamental assumptions of the proposed three-layer model for the deep tissue, skeletal muscle and cutaneous layers.

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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.

This study was undertaken to gain a better understanding of the fundamental mechanisms of micro- and macrovascular heat transfer by experimentally identifying those vessels most important in the process. Tissue temperature fields around thermally nonequilibrated vessels were determined using a small temperature sensor that was guided through the rabbit thigh to generate a detailed temperature map. The measurements revealed that the lower limit of vessel size for thermal nonequilibration was 100 microns for arteries and 400 microns for veins. Local temperature fields were found around four of the five (80%) arteries that were greater than 300 microns in diameter but in only 3 of the 12 (25%) veins greater than 400 microns. These experimental results are in good agreement with previously published theoretical studies (5) in which it was concluded that thermal equilibration in the branching countercurrent vascular network of the rabbit limb occurs in vessels an order of magnitude larger than the capillaries. In those studies the smallest vessels capable of carrying heat were predicted to be 50 microns ID with the major blood tissue heat exchange occurring in vessels greater than 100 micron ID. These findings contrast with the view that most heat transfer occurs in the capillaries and suggest that vascular heat transfer analysis must take into account the vascular architecture of the 50- to 1,000-micron vessels where most heat transfer occurs.

Our results suggest that two fundamentally different responses to shear stress are mediated by microvascular endothelium: one vasodilation is elicited by shear stress changes on a time scale of a few seconds or less and another is elicited by shear stress changes on a longer time scale. The former response is potent, transient, and rate sensitive; the latter is more modest, sustained, and magnitude sensitive.