Numerical Analysis of an Extremity in a Cold Environment Including Countercurrent Arterio-Venous Heat Exchange

Abstract

A model of the thermal behavior of an extremity, e.g., a finger, is presented. The model includes the effects of heat conduction, metabolic heat generation, heat transport by blood perfusion, heat exchange between the tissue and the large blood vessels, and arterio-venous heat exchange. Heat exchange with the environment through a layer of thermal insulation, depicting thermal handwear, is also considered. The tissue is subdivided into four concentric layers simulating, from the center outward, core, muscle, fat, and skin. Differential heat balance equations are formulated for the tissue and for the major artery and the major vein traversing the finger. These coupled equations are solved numerically by a finite-difference, alternating direction method employing a Thomas algorithm. The numerical scheme was extensively tested for its stability and convergence. This paper presents the model equations and results of the convergence tests, and shows plots of blood and tissue temperatures along the axis of the model for combinations of parameters including the effect of countercurrent heat exchange between the artery and the vein.

Characterization of a three-phase response in gloved cold-stressed fingers

“…Thus, a con¯ict of tendencies is observed in a cold exposure since the body tends naturally to constrict thē ow of warm blood to the extremities, thereby decreasing heat loss to the environment. This, in turn, will result in a rapid drop in ®nger temperature with the wind playing a signi®cant role, even in the gloved ®nger, as has recently been demonstrated by Shitzer et al (1994).…”

Thermal comfort range of a military cold protection glove: database by thermophysiological simulation

“…The inXuence of air velocity (wind chill eVect) or humidity on the estimation of environmental limit temperatures was not considered in this thermophysiological simulation study. It is known from the studies by Shitzer et al (1994) that wind can play a signiWcant role in hand cooling, even for gloved Wngers. Because of the special construction of the investigated military wet/cold protection glove, equipped with a three-layer laminate which is providing a "wind stopper"-function and a wadding insulation underneath, the contribution of the wind chill eVect to the hand cooling was rated as less determinant in this particular case.…”

“…Several studies by Shitzer and co-workers give an excellent theoretical description of the heat exchange processes from the Wngers to the environment (Shitzer 1996;Shitzer et al 1997). In these studies, the Wnger is depicted as a cylinder with an internal heat source taking into account eVects of heat generation (metabolic rate), heat conduction and heat transport by blood perfusion.…”

“…In the case of a long-lasting cold exposure, this eVect is followed after a couple of minutes by periodically increasing the blood Xow to the Wnger, termed as "cold-induced vasodilation" (CIVD). As this phenomenon is mostly pronounced at the Wnger tips, Shitzer et al (1993Shitzer et al ( , 1996 developed a separate, lumpedparameter heat exchange model especially describing this behaviour. So far there is a very good theoretical basis in the understanding of the essential processes of hand cooling during cold exposure.…”

An analytical study of heat transfer in a finite tissue region with two blood vessels and general Dirichlet boundary conditions

“…applications such as thermoregulation and thermal therapy [8][9][10][11][12][13][14][15][16][17][18][19][20]. Thus a number of researchers have attempted to define and quantify the vessel-vessel and vessel-tissue heat transfer rates and the corresponding shape factors for the geometry of paired vessels in both infinite [8][9][10]12,15,[21][22][23]28] and finite [11,14,17,18,[24][25][26][27]29,30], and unheated [8][9][10][11][12]14,15,17,18,[21][22][23][24][25][26][27][28][29] and heated …”