A New Simplified Bioheat Equation for the Effect of Blood Flow on Local Average Tissue Temperature
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...This causes the tissue–blood medium to be anisotropic with respect to the thermal conductivity in addition to the corresponding anisotropy indicated by Weinbaum and Jiji [42] due to concurrent blood flows....
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...An important research work example that utilized Weinbaum and Jiji s [42] model is the work of Guiot et al. [43]....
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...They used the Weinbaum and Jiji s model, assuming a linear relation between the effective thermal conductivity and the blood perfusion rate, to determine the increase in the thermal conductivity in a perfused tissue....
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...Accordingly, Weinbaum and Jiji [42] modified the thermal conductivity in the Pennes equation by means of an ‘‘effective conductivity’’ related quadratically to blood perfusion rate which is affected by the dimensions and the directions of the vessels....
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...This density distribution is unstable, and convective motions are Table 3 Summary of presented bioheat transfer models Bioheat transfer model Main features Pennes [38] • simple • based on uniform perfusion • it is not valid for all tissues Weinbaum and Jiji [41] • valid when arteries and veins are close leading to negligible blood perfusion effects • utilizes an effective conductivity as function of the perfusion rate Wissler [44] • avoids assumptions of the Weinbaum and Jiji s [41] model Baish [45] • complex and statistical based model • considers simulation of a realistic vascular tree containing all thermally significant vessels Weinbaum et al. [46] • includes an efficiency term in Pennes source term to make Pennes equation applicable to muscle tissues Theory of porous media (Principle of local thermal equilibrium) Amiri and Vafai [50,51], Khanafer and Vafai [52], Marafie and Vafai [53], Alazmi and Vafai [37], Xuan and Roetzel [48,49] • modifies Pennes equation by considering the following effects (a) variations in the tissue porosity (b) blood dispersion (c) considers effective tissue conductivity (d) considers effective tissue capacitance Theory of porous media (Principle of local thermal non-equilibrium) Amiri and Vafai [50,51], Alazmi and Vafai [52], Khanafer and Vafai [54], Marafie and Vafai [55], Kuznetsov and Vafai [56], Xuan and Roetzel [48,49] • exact blood perfusion is included • complex and require more flow and thermal information • considers (a) variations in the tissue porosity (b) blood dispersion (c) considers effective tissue conductivity (d) considers effective tissue capacitance set up as in a shallow fluid heated from below....
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