Abstract
Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues.
Highlights
Heat transfer in biological systems is relevant in many diagnostic and therapeutic applications involving either decrease or increase of temperature and often requires precise monitoring of the spatial distribution of thermal histories that are produced during a treatment protocol [1,2,3,4,5,6,7,8,9]
With the help of Riccati equation, we investigate the thermal traveling-wave distribution in biological tissues through the bio-heat transfer (BHT) Equation (1.1) with the temperature-dependent blood perfusion (1.2)
We use the analytical solutions found in the previous section to discuss thermal traveling-wave distribution in biological tissues
Summary
Heat transfer in biological systems is relevant in many diagnostic and therapeutic applications involving either decrease or increase of temperature and often requires precise monitoring of the spatial distribution of thermal histories that are produced during a treatment protocol [1,2,3,4,5,6,7,8,9]. Since the pioneering work by Henriques and Moritz [10] and by Pennes [11] on heat transfer in biological system, the problem of heat transfer in biological systems has received renewed attention and has been the focus of considerable research [12,13,14,15,16] The investigation of such heat transfer problems requires the evaluation of spatiotemporal distributions of temperature and has been traditionally addressed using the Pennes model which is originally designed for predicting temperature fields in the human forearm [10,11]. The generalized one-dimensional Pennes BHT equation can be written in the following form [17,18,19,20,21]
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