Journal articles: 'Pennes bioheat transfer equations'

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SHIH, TZU-CHING, HONG-SEN KOU, CHIHNG-TSUNG LIAUH, and WIN-LI LIN. "THERMAL MODELS OF BIOHEAT TRANSFER EQUATIONS IN LIVING TISSUE AND THERMAL DOSE EQUIVALENCE DUE TO HYPERTHERMIA." Biomedical Engineering: Applications, Basis and Communications 14, no. 02 (2002): 86–96. http://dx.doi.org/10.4015/s1016237202000139.

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This review focuses both on the basic formulations of bioheat equation in the living tissue and on the determination of thermal dose during thermal therapy. The temperature distributions inside the heated tissues, generally controlled by heating modalities, are obtained by solving the bioheat transfer equation. However, the major criticism for the Pennes' model focused on the assumption that the heat transfer by blood flow occurs in a non-directional, heat sink- or source-like term. Several bioheat transfer models have been introduced to compare their convective and perfusive effects in vascular tissues. The present review also elucidates thermal dose equivalence that represents the extent of thermal damage or destruction of tissue in the clinical treatment of tumor with local hyperthermia. In addition, this study uses the porous medium concept to describe the heat transfer in the living tissue with the directional effect of blood flow, and the polynomial expression of thermal dose in terms of the curve fitting of the experimental isosurvival curve data by Dewey et al. Results show that the values of factor R is a function of the heating temperature instead of the two different constants suggested by Sapareto and Dewey.

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El-Nabulsi, Rami Ahmad. "Fractal Pennes and Cattaneo–Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth." Journal of The Royal Society Interface 18, no. 182 (2021): 20210564. http://dx.doi.org/10.1098/rsif.2021.0564.

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In this study, the Pennes and Cattaneo–Vernotte bioheat transfer equations in the presence of fractal spatial dimensions are derived based on the product-like fractal geometry. This approach was introduced recently, by Li and Ostoja-Starzewski, in order to explore dynamical properties of anisotropic media. The theory is characterized by a modified gradient operator which depends on two parameters: R which represents the radius of the tumour and R 0 which represents the radius of the spherical living tissue. Both the steady and unsteady states for each fractal bioheat equation were obtained and their implications on living cells in the presence of growth of a large tumour were analysed. Assuming a specific heating/cooling by a constant heat flux equivalent to the metabolic heat generation in the tissue, it was observed that the solutions of the fractal bioheat equations are robustly affected by fractal dimensions, the radius of the tumour growth and the dimensions of the living cell tissue. The ranges of both the fractal dimensions and temperature were obtained, analysed and compared with recent studies. This study confirms the importance of fractals in medicine.

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Liu, Kuo-Chi, Po-Jen Cheng, and Yan-Nan Wang. "Analysis of non-Fourier thermal behavior for multi-layer skin model." Thermal Science 15, suppl. 1 (2011): 61–67. http://dx.doi.org/10.2298/tsci11s1061l.

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This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes? model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.

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Adeola, Lawal Hamid, and Oluwole Daniel Makinde. "Buoyancy Effects on Human Skin Tissue Thermoregulation due to Environmental Influence." Defect and Diffusion Forum 401 (May 2020): 107–16. http://dx.doi.org/10.4028/www.scientific.net/ddf.401.107.

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This paper theoretically examines the impact of thermal buoyancy on human skin tissue’s blood flow, heat exchange and their interaction with the surrounding environment using a two phase mathematical model that relies on continuity, momentum and energy conservation equations in continuum mechanics. The tissue blood flows and heat transfer characteristics are determined numerically based on Darcy’s Brinkman model for a saturated porous medium coupled with modified Pennes bioheat equation while analytical approach is employed to tackle the model of interacting surrounding environmental buoyancy driven air flow with heat sink. The influence of embedded biophysical parameters on the skin tissue’s blood flow rate and temperature distribution together with friction coefficient at skin tissue surface and Nusselt number are display graphically and discussed quantitatively. It is found that a boost in thermal buoyancy enhances skin tissue heat transfer and blood flow rates.

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Chen, Zong-Ping, and Robert B. Roemer. "The Effects of Large Blood Vessels on Temperature Distributions During Simulated Hyperthermia." Journal of Biomechanical Engineering 114, no. 4 (1992): 473–81. http://dx.doi.org/10.1115/1.2894097.

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Several three-dimensional vascular models have been developed to study the effects of adding equations for large blood vessels to the traditional bioheat transfer equation of Pennes when simulating tissue temperature distributions. These vascular models include “transiting” vessels, “supplying” arteries, and “draining” veins, for all of which the mean temperature of the blood in the vessels is calculated along their lengths. For the supplying arteries this spatially variable temperature is then used as the arterial temperature in the bioheat transfer equation. The different vascular models produce significantly different locations for both the maximum tumor and the maximum normal tissue temperatures for a given power deposition pattern. However, all of the vascular models predict essentially the same cold regions in the same locations in tumors: one set at the tumors’ corners and another around the inlets of the large blood vessels to the tumor. Several different power deposition patterns have been simulated in an attempt to eliminate these cold regions; uniform power in the tumor, annular power in the tumor, preheating of the blood in the vessels while they are traversing the normal tissue, and an “optimal” power pattern which combines the best features of the above approaches. Although the calculations indicate that optimal power deposition patterns (which improve the temperature distributions) exist for all of the vascular models, none of the heating patterns studied eliminated all of the cold regions. Vasodilation in the normal tissue is also simulated to see its effects on the temperature fields. This technique can raise the temperatures around the inlet of the large blood vessles to the tumor (due to the higher power deposition rates possible), but on the other hand, normal tissue vasodilation makes the temperatures at the tumor corners slightly colder.

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CONSIGLIERI, LUISA. "ANALYTICAL SOLUTIONS IN THE MODELING OF THE LOCAL RF ABLATION." Journal of Mechanics in Medicine and Biology 16, no. 05 (2016): 1650071. http://dx.doi.org/10.1142/s0219519416500718.

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Coupled mathematical models for the radiofrequency (RF) ablation performed in biomedical sciences have been developed based on the bioheat transfer theory. The heat exchange problem is important to be analytically studied in order to control the size of the necrosis zone caused by RF ablation. This lesion size in the tissue may be predicted by the knowledge of the internal tissue temperature. We propose an analytical solution for the Pennes heat transfer equation in bi- and tri-region domains, applicable to the RF ablation of cancerigeneous tissue — a clinical relevant problem. The model consists of two partial differential equations describing the spatio-temporal interactions between the electric and thermic effects. The aim is to find simple algebraic expressions of analytical solutions that may allow to generate quantitative results which in turn may be interpreted (including uncertainties). The dependence of the temperature as function of the electrothermal parameters in both diseased and surrounding healthy tissues is pointed out. Two cases, namely the tumor–tissue and tumor–tissue–skin systems, are graphically computed, and important findings include the fact that the presence of tissue with smaller value parameters protects somehow healthy cells. Moreover, the graphical representations are conducted to highlight the link of the profile of current density distribution in the physiological problem with the (neither oval nor circular) shape of the temperature isoclinic lines.

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Grysa, Krzysztof, and Artur Maciag. "Trefftz method in solving the pennes’ and single-phase-lag heat conduction problems with perfusion in the skin." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 6 (2019): 3231–46. http://dx.doi.org/10.1108/hff-09-2018-0488.

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Purpose The purpose of this paper is to derive the Trefftz functions (T-functions) for the Pennes’ equation and for the single-phase-lag (SPL) model (hyperbolic equation) with perfusion and then comparing field of temperature in a flat slab made of skin in the case when perfusion is taken into account, with the situation when a Fourier model is considered. When considering the process of heat conduction in the skin, one needs to take into account the average values of its thermal properties. When in biological bodies relaxation time is of the order of 20 s, the thermal wave propagation appears. The initial-boundary problems for Pennes’ model and SPL with perfusion model are considered to investigate the effect of the finite velocity of heat in the skin, perfusion and thickness of the slab on the rate of the thermal wave attenuation. As a reference model, the solution of the classic Fourier heat transfer equation for the considered problems is calculated. A heat flux has direction perpendicular to the surface of skin, considered as a flat slab. Therefore, the equations depend only on time and one spatial variable. Design/methodology/approach First of all the T-functions for the Pennes’ equation and for the SPL model with perfusion are derived. Then, an approximate solutions of the problems are expressed in the form of a linear combination of the T-functions. The T-functions satisfy the equation modeling the problem under consideration. Therefore, approximating a solution of a problem with a linear combination of n T-functions one obtains a function that satisfies the equation. The unknown coefficients of the linear combination are obtained as a result of minimization of the functional that describes an inaccuracy of satisfying the initial and boundary conditions in a mean-square sense. Findings The sets of T-functions for the Pennes’ equation and for the SPL model with perfusion are derived. An infinite set of these functions is a complete set of functions and stands for a base functions layout for the space of solutions for the equation used to generate them. Then, an approximate solutions of the initial-boundary problem have been found and compared to find out the effect of finite velocity of heat in the skin, perfusion and thickness of the slab on the rate of the thermal wave attenuation. Research limitations/implications The methods used in the literature to find an approximate solution of any bioheat transfer problems are more complicated than the one used in the presented paper. However, it should be pointed out that there is some limitation concerning the T-function method, namely, the greater number of T-function is used, the greater condition number becomes. This limitation usually can be overcome using symbolic calculations or conducting calculations with a large number of significant digits. Originality/value The T-functions for the Pennes’ equation and for the SPL equation with perfusion have been reported in this paper for the first time. In the literature, the T-functions are known for other linear partial differential equations (e.g. harmonic functions for Laplace equation), but for the first time they have been derived for the two aforementioned equations. The results are discussed with respect to practical applications.

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Paruch, Marek. "Identification of the cancer ablation parameters during RF hyperthermia using gradient, evolutionary and hybrid algorithms." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 3 (2017): 674–97. http://dx.doi.org/10.1108/hff-03-2016-0114.

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Purpose The purpose of this study is to show that the methods of the numerical simulation can be a very effective tool for a proper choice of control parameters of artificial hyperthermia. An electromagnetic field induced by two external electrodes and a temperature field resulting from electrodes action in a 3D domain of biological tissue is considered. An important problem is the appropriate directing of heat in the region of tumor, so as to avoid damaging healthy cells surrounding the tumor. Recently, to concentrate the heat on the tumor, magnetic nanoparticles, which are introduced into the tumor, were used. The nanoparticles should be made of material that ensures appropriate magnetic properties and has a high biocompatibility with the biological tissue. External electric field causes the heat generation in the tissue domain. Design/methodology/approach The distribution of electric potential in the domain considered is described by the Laplace system of equations, while the temperature field is described by the Pennes’ system of equations. These problems are coupled by source function being the additional component in the Pennes’ equation and resulting from the electric field action. The boundary element method is applied to solve the coupled problem connected with the heating of biological tissues. Findings The aim of investigations is to determine an electric potential of external electrodes and the number of nanoparticles introduced to a tumor region to obtain the artificial hyperthermia state. The tests performed showed that the proposed tool to solve the inverse problem provides correct results. Research limitations/implications In the paper the steady state bioheat transfer problem is considered, so the thermal damage is a function of the temperature only. Therefore, the solution can be considered as the maximum ablation zone of cancer. Additionally, the choice of appropriate parameters will be affected on the position and shape of the tumor and the electrodes. Originality/value In the paper the inverse problem has been solved using the evolutionary algorithm, gradient method and hybrid algorithm which is a combination of the two previous.

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Pacheco, César, Helcio R. B. Orlande, Marcelo Colaco, and George S. Dulikravich. "State estimation problems in PRF-shift magnetic resonance thermometry." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 2 (2018): 315–35. http://dx.doi.org/10.1108/hff-10-2016-0427.

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Purpose The purpose of this paper is to apply the Steady State Kalman Filter for temperature measurements of tissues via magnetic resonance thermometry. Instead of using classical direct inversion, a methodology is proposed that couples the magnetic resonance thermometry with the bioheat transfer problem and the local temperatures can be identified through the solution of a state estimation problem. Design/methodology/approach Heat transfer in the tissues is given by Pennes’ bioheat transfer model, while the Proton Resonance Frequency (PRF)-Shift technique is used for the magnetic resonance thermometry. The problem of measuring the transient temperature field of tissues is recast as a state estimation problem and is solved through the Steady-State Kalman filter. Noisy synthetic measurements are used for testing the proposed methodology. Findings The proposed approach is more accurate for recovering the local transient temperatures from the noisy PRF-Shift measurements than the direct data inversion. The methodology used here can be applied in real time due to the reduced computational cost. Idealized test cases are examined that include the actual geometry of a forearm. Research limitations/implications The solution of the state estimation problem recovers the temperature variations in the region more accurately than the direct inversion. Besides that, the estimation of the temperature field in the region was possible with the solution of the state estimation problem via the Steady-State Kalman filter, but not with the direct inversion. Practical implications The recursive equations of the Steady-State Kalman filter can be calculated in computational times smaller than the supposed physical times, thus demonstrating that the present approach can be used for real-time applications, such as in control of the heating source in the hyperthermia treatment of cancer. Originality/value The original and novel contributions of the manuscript include: formulation of the PRF-Shift thermometry as a state estimation problem, which results in reduced uncertainties of the temperature variation as compared to the classical direct inversion; estimation of the actual temperature in the region with the solution of the state estimation problem, which is not possible with the direct inversion that is limited to the identification of the temperature variation; solution of the state estimation problem with the Steady-State Kalman filter, which allows for fast computations and real-time calculations.

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Kaur, J., and S. A. Khan. "Thermal changes in Human Abdomen Exposed to Microwaves: A Model Study." Advanced Electromagnetics 8, no. 3 (2019): 64–75. http://dx.doi.org/10.7716/aem.v8i3.1092.

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The electromagnetic energy associated with microwave radiation interacts with the biological tissues and consequently, may produce thermo-physiological effects in living beings. Traditionally, Pennes’ bioheat equation (BTE) is employed to analyze the heat transfer in biological medium. Being based on Fourier Law, Pennes’ BTE assumes infinite speed of propagation of heat transfer. However, heat propagates with finite speed within biological tissues, and thermal wave model of bioheat transfer (TWBHT) demonstrates this non-Fourier behavior of heat transfer in biological medium. In present study, we employed Pennes’ BTE and TWMBT to numerically analyze temperature variations in human abdomen model exposed to plane microwaves at 2450 MHz. The numerical scheme comprises coupling of solution of Maxwell's equation of wave propagation within tissue to Pennes’ BTE and TWMBT. Temperatures predicted by both the bioheat models are compared and effect of relaxation time on temperature variations is investigated. Additionally, electric field distribution and specific absorption rate (SAR) distribution is also studied. Transient temperatures predicted by TWMBT are lower than that by traditional Pennes’ BTE, while temperatures are identical in steady state. The results provide comprehensive understanding of temperature changes in irradiated human body, if microwave exposure duration is short.

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Ezzat, Magdy A., Noorah S. AlSowayan, Zeid I. A. Al-Muhiameed, and Shereen M. Ezzat. "Fractional modelling of Pennes’ bioheat transfer equation." Heat and Mass Transfer 50, no. 7 (2014): 907–14. http://dx.doi.org/10.1007/s00231-014-1300-x.

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Charny, C. K., S. Weinbaum, and R. L. Levin. "An Evaluation of the Weinbaum-Jiji Bioheat Equation for Normal and Hyperthermic Conditions." Journal of Biomechanical Engineering 112, no. 1 (1990): 80–87. http://dx.doi.org/10.1115/1.2891130.

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The predictions of the simplified Weinbaum-Jiji (WJ) bioheat transfer equation in one dimension are compared to those of the complete one-dimensional three-equation model that represented the starting point for the derivation of the WJ equation, as well as results obtained using the traditional bioheat transfer equation of Pennes [6]. The WJ equation provides very good agreement with the three-equation model for vascular generations 2 to 9, which are located in the outer half of the muscle layer, where the paired vessel diameters are less than 500 μm, under basal blood flow conditions. At the same time, the Pennes equation yields a better description of heat transfer in the first generation, where the vessels’ diameters are greater than 500 μm and ε, the vessels’ normalized thermal equilibration length, is greater than 0.3. These results were obtained under both normothermic and hyperthermic conditions. A new conceptual view of the blood source term in the Pennes equation has emerged from these results. This source term, which was originally intended to represent an isotropic heat source in the capillaries, is shown to describe instead the heat transfer from the largest countercurrent microvessels to the tissue due to small vessel bleed-off. The WJ equation includes this effect, but significantly overestimates the second type of tissue heat transfer, countercurrent convective heat transfer, when ε > 0.3. Indications are that a “hybrid” model that applies the Pennes equation in the first generation (normothermic) and first two to three generations (after onset of hyperthermia) and the Weinbaum-Jiji equation in the subsequent generations would be most appropriate for simulations of bioheat transfer in perfused tissue.

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Attanayake, Champike, and So-Hsiang Chou. "An immersed interface method for Pennes bioheat transfer equation." Discrete & Continuous Dynamical Systems - B 20, no. 2 (2015): 323–37. http://dx.doi.org/10.3934/dcdsb.2015.20.323.

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Brinck, H., and J. Werner. "Efficiency function: improvement of classical bioheat approach." Journal of Applied Physiology 77, no. 4 (1994): 1617–22. http://dx.doi.org/10.1152/jappl.1994.77.4.1617.

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In view of the complex vascular architecture and the intricate physical heat transfer processes in the human body, convective heat transfer via the blood is generally described by simple substitutional processes (“non-vascular models”). The classical “bioheat” approach of Pennes (J. Appl. Physiol. 1: 93–122, 1948), defining the heat flow to or from the tissue as being proportional to the product of perfusion rate and the difference of arterial and tissue temperature, has been seriously questioned after having been used for > 40 yr in many applications. In our laboratory, we have at our disposal a complex three-dimensional vascular model for the special case of tissue in a human extremity. This was used to test the performance of simple nonvascular models. It turned out that the Pennes approach may deliver acceptable results if the body is in the thermoneutral zone or if heat stress acts uniformly on the whole body. However, when cold stress or local hyperthermia is present, unreliable results must be expected. As the vascular model is not generally practicable because of its extreme complexity, we offer the efficiency function concept as a simple way of correcting the classical bioheat approach by factor multiplication. Efficiency function is determined as a function of perfusion rate and tissue depth in a way that compensates for the deficiencies of the Pennes bioheat term. The results are reasonable compared with those of the vascular model and experimental results.

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Luitel, Kabita, Dil Bahadur Gurung, Harihar Khanal, and Kedar Nath Uprety. "Bioheat Transfer Equation with Protective Layer." Mathematical Problems in Engineering 2021 (January 25, 2021): 1–12. http://dx.doi.org/10.1155/2021/6639550.

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The human thermal comfort is the state of mind, which is affected not only by the physical and body’s internal physiological phenomena but also by the clothing properties such as thermal resistance of clothing, clothing insulation, clothing area factor, air insulation, and relative humidity. In this work, we extend the one-dimensional Pennes’ bioheat transfer equation by adding the protective clothing layer. The transient temperature profile with the clothing layer at the different time steps has been carried out using a fully implicit Finite Difference (FD) Scheme with interface condition between body and clothes. Numerically computed results are bound to agree that the clothing insulation and air insulation provide better comfort and keep the body at the thermal equilibrium position. The graphical representation of the results also verifies the effectiveness and utility of the proposed model.

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Liu, Kuo-Chi, and Fong-Jou Tu. "Numerical Solution of Bioheat Transfer Problems with Transient Blood Temperature." International Journal of Computational Methods 16, no. 04 (2019): 1843001. http://dx.doi.org/10.1142/s0219876218430016.

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In the heat treatment process, blood perfusion starts up a negative feedback mechanism. The blood temperature undergoes a transient process before onset of equilibrium and then changes the situation of temperature distribution. In substance, the blood temperature undergoes a transient process for heat exchange between blood and tissue. For more fully exploring the heat transfer behavior of biological tissue, this paper analyzes the bioheat transfer problems with the nonconstant blood temperature based on the Pennes bioheat equation. A numerical scheme based on the Laplace transform is proposed for solving the present problems.

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Charny, C. K., and R. L. Levin. "Bioheat Transfer in a Branching Countercurrent Network During Hyperthermia." Journal of Biomechanical Engineering 111, no. 4 (1989): 263–70. http://dx.doi.org/10.1115/1.3168377.

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A bioheat transfer model which computes the spatial variations in the arteriole, venule, and muscle temperatures in a human extremity under both resting and hyperthermic conditions is presented. This model uses the two-parameter model first proposed by Baish et al. [2] to account for the heat exchange between tissue and the paired arterioles and venules that comprise the microcirculation. Thermoregulation of the muscle blood flow during hyperthermia is also incorporated into the model. Results show that even when the paired arteriole and venule are assumed to have equal radii, the mean temperature under both steady and transient conditions is not equal to the mean of the arteriole and venule blood temperatures. Tissue temperature profiles during hyperthermia computed with the three-equation model presented in this study are similar in shape and magnitude to those predicted by the traditional one-equation Pennes bioheat transfer model [1]. This is due primarily to the influence of thermoregulatory mechanism in the heated muscle. The unexpected agreement is significant given the inherent relative simplicity of the traditional Pennes model. An “experimental” thermal conductivity is presented to relate the theoretical results to experimental procedures that are widely used to estimate the enhancement of conductivity by perfusion.

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Sarkar, N. "A novel Pennes’ bioheat transfer equation with memory-dependent derivative." Mathematical Models in Engineering 2, no. 2 (2016): 151–57. http://dx.doi.org/10.21595/mme.2016.18024.

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Bojdi, Z. Kalateh, and A. Askari Hemmat. "Wavelet collocation methods for solving the Pennes bioheat transfer equation." Optik 130 (February 2017): 345–55. http://dx.doi.org/10.1016/j.ijleo.2016.10.102.

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Roca Oria, E. J., L. E. Bergues Cabrales, and And J. Bory Reyes. "Analytical solution of the bioheat equation for thermal response induced by any electrode array in anisotropic tissues with arbitrary shapes containing multiple-tumor nodules." Revista Mexicana de Física 65, no. 3 (2019): 284. http://dx.doi.org/10.31349/revmexfis.65.284.

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The Pennes bioheat transfer equation is the most used model to calculate the temperature induced in a tumor when physical therapies like electrochemical treatment, electrochemotherapy and/or radiofrequency are applied. In this work, a modification of the Pennes bioheat equation to study the temperature distribution induced by any electrode array in an anisotropic tissue containing several nodules (primary or metastatic) with arbitrary shape is proposed. For this, the Green functions approach is generalized to include boundaries among two or more media. The analytical solution we obtain in a very compact way, under quite general suppositions, allows calculating the temperature distributions in the tumor volumes and their surfaces, in terms of heat sources, initial temperature and calorific sources at the boundary of tumors.

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KUMAR, P., and K. N. RAI. "FRACTIONAL MODELING OF HYPERBOLIC BIOHEAT TRANSFER EQUATION DURING THERMAL THERAPY." Journal of Mechanics in Medicine and Biology 17, no. 03 (2016): 1750058. http://dx.doi.org/10.1142/s0219519417500580.

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In this paper, we have developed a fractional hyperbolic bioheat transfer (FHBHT) model by applying fractional Taylor series formula to the single-phase-lag constitutive relation. A new hybrid numerical scheme that combines the multi-resolution and multi-scale computational property of Legendre wavelets based on fractional operational matrix has been used to find the numerical solution of the present problem. This study demonstrates that FHBHT model can provide a unified approach for analyzing heat transfer within living biological tissues, as standard hyperbolic bioheat transfer (SHBHT) and Pennes models are particular cases of FHBHT model. The effect of phase lag time and order of fractional derivative on temperature distribution within living biological tissues for both SHBHT and FHBHT models have been studied and shown graphically. It has been observed that thermal signal propagates more easily with larger values of order of fractional derivative within living biological tissues. The time interval for achieving temperature range of thermal treatment for different models have been studied and compared. It is least for Pennes model, highest for FHBHT model and in between them for SHBHT model. The whole analysis is presented in dimensionless form.

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Wang, Hongyun, Wesley A. Burgei, and Hong Zhou. "Analytical solution of one-dimensional Pennes’ bioheat equation." Open Physics 18, no. 1 (2020): 1084–92. http://dx.doi.org/10.1515/phys-2020-0197.

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Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

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Zhang, Ze Wei, Hui Wang, and Qing Hua Qin. "Analysis of Transient Bioheat Transfer in the Human Eye Using Hybrid Finite Element Model." Applied Mechanics and Materials 553 (May 2014): 356–61. http://dx.doi.org/10.4028/www.scientific.net/amm.553.356.

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Simulation of transient bioheat transfer in a two dimensional (2D) human eye model is conducted using a newly developed hybrid fundamental solution-finite element method (HFS-FEM) coupling with the radial basis function (RBF) approximation. Firstly, a time stepping scheme based on the finite difference method (FDM) is used to handle time variable in the transient Pennes bioheat equation. Secondly, the particular solution of the governing equation is approximated by a RBF approach. Then, the homogeneous solution is calculated by means of HFS-FEM. The obtained results are compared with those from ABAQUS and a good agreement between them is observed.

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Chan, Cho Lik. "Boundary Element Method Analysis for the Bioheat Transfer Equation." Journal of Biomechanical Engineering 114, no. 3 (1992): 358–65. http://dx.doi.org/10.1115/1.2891396.

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In this paper, the boundary element method (BEM) approach is applied to solve the Pennes (1948) bioheat equation. The objective is to develop the BEM formulation and demonstrate its feasibility. The basic BEM formulations for the transient and steady-state cases are first presented. To demonstrate the usefulness of the BEM approach, numerical solutions for 2-D steady-state problems are obtained and compared to analytical solutions. Further, the BEM formulation is applied to model a conjugate problem for an artery imbedded in a perfused heated tissue. Analytical solution is possible when the conduction in the x-direction is negligible. The BEM and analytical results have very good agreement.

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Tan, Qiaolai, Xiao Zou, Hu Dong, Yajun Ding, and Xinmin Zhao. "Influence of Blood Vessels on Temperature during High-Intensity Focused Ultrasound Hyperthermia Based on the Thermal Wave Model of Bioheat Transfer." Advances in Condensed Matter Physics 2018 (September 6, 2018): 1–10. http://dx.doi.org/10.1155/2018/5018460.

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The coupled effects of blood vessels and thermal relaxation time on temperature and thermal lesion region in biological tissue during high-intensity focused ultrasound (HIFU) hyperthermia are numerically investigated. Considering the non-Fourier behavior of heat conduction in biological tissue, the traditional Pennes bioheat equation was modified to thermal wave model of bioheat transfer (TWMBT). Consequently, a joint physical model, which combines TWMBT for tissue and energy transport equation for blood vessel, is presented to predict the evolution of temperature and the thermal lesion region. In this study, pulsatile blood flow is first introduced into numerical study of HIFU hyperthermia, and thermal relaxation time, ultrasonic focus location, blood vessel radius, and blood flow velocity are all taken into account. The results show that the thermal relaxation time plays a key role in the temperature and the thermal lesion region. Larger thermal relaxation time results in lower temperature and smaller thermal lesion region, which indicates that TWMBT leads to lower temperature and smaller thermal lesion region compared to Pennes bioheat transfer model. In addition, we found that the ultrasonic focus location and blood vessel radius significantly affected the temperature and thermal lesion region, while the heartbeat frequency and amplitude factor of pulsating blood flow as well as the average velocity of blood flow had only a slight effect.

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Łaszczyk, Joanna, Anna Maczko, Wojciech Walas, and Andrzej J. Nowak. "Inverse thermal analysis of the neonatal brain cooling process." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 4 (2014): 949–68. http://dx.doi.org/10.1108/hff-04-2013-0112.

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Purpose – This paper aims to test the inverse analysis, based on the standard least-square method, which will finally lead to find the appropriate parameters of modelling of the brain cooling process. Design/methodology/approach – To test the presented in this paper method of inverse analysis the numerical simulations of the bioheat transfer process in the neonatal body were performed. To model the bioheat transfer the Pennes bioheat equation and the modified Fiala model were applied. Findings – The performed tests of the inverse analysis proved that it is possible to estimate the proper parameters of the process using this tool, but always with the small mistake. Research limitations/implications – The presented method still requires a lot of tests. The test with the data from real measurements can be very valuable. Practical implications – The determination of the proper parameters of the bioheat transfer in the neonatal body can finally be used to perform the numerical simulations of the brain cooling process. Social implications – The performance of the numerical simulations of the brain cooling process in the proper way can finally helps protect newborns’ health and life. Originality/value – In the paper the attempt of the inverse analysis in order to determine the parameters of bioheat transfer in the newborn's body is made.

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Ghazanfarian, J., R. Saghatchi, and D. V. Patil. "Implementation of Smoothed-Particle Hydrodynamics for non-linear Pennes’ bioheat transfer equation." Applied Mathematics and Computation 259 (May 2015): 21–31. http://dx.doi.org/10.1016/j.amc.2015.02.036.

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Cui, Zhou Jin, Gui Dong Chen, and Rui Zhang. "Analytical Solution for the Time-Fractional Pennes Bioheat Transfer Equation on Skin Tissue." Advanced Materials Research 1049-1050 (October 2014): 1471–74. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.1471.

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This study focuses on analytical solution of a fractional Pennes bioheat transfer equation on skin tissue. The method of separating variables, finite Fourier sine transformation, Laplace transformation and their corresponding inverse transforms are used to solve this equation with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin boundary value conditions. The exact solutions are discussed and derived in the form of generalized Mittag-Leffler function. In addition, numerical results are presented graphically for various values of order factional derivative.

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Arkin, H., K. R. Holmes, and M. M. Chen. "Theory on Thermal Probe Arrays for the Distinction Between the Convective and the Perfusive Modalities of Heat Transfer in Living Tissues." Journal of Biomechanical Engineering 109, no. 4 (1987): 346–52. http://dx.doi.org/10.1115/1.3138692.

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Recent suggestions for an improved model of heat transfer in living tissues emphasize the existence of a convective mode due to flowing blood in addition to, or even instead of, the perfusive mode, as proposed in Pennes’ “classic” bioheat equation. In view of these suggestions, it might be beneficial to develop a technique that will enable one to distinguish between these two modes of bioheat transfer. To this end, a concept that utilizes a multiprobe array of thermistors in conjunction with a revised bioheat transfer equation has been derived to distinguish between, and to quantify the perfusive and convective contribution of blood to heat transfer in living tissues. The array consists of two or more temperature sensors one of which also serves to locally insert a short pulse of heat into the tissue prior to the temperature measurements. A theoretical analysis shows that such a concept is feasible. The construction of the system involves the selection of several important design parameters, i.e., the distance between the probes, the heating power, and the pulse duration. The choice of these parameters is based on computer simulations of the actual experiment.

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Weinbaum, S., L. X. Xu, L. Zhu, and A. Ekpene. "A New Fundamental Bioheat Equation for Muscle Tissue: Part I—Blood Perfusion Term." Journal of Biomechanical Engineering 119, no. 3 (1997): 278–88. http://dx.doi.org/10.1115/1.2796092.

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A new model for muscle tissue heat transfer has been developed using Myrhage and Eriksson’s [23] description of a muscle tissue cylinder surrounding secondary (s) vessels as the basic heat transfer unit. This model provides a rational theory for the venous return temperature for the perfusion source term in a modified Pennes bioheat equation, and greatly simplifies the anatomical description of the microvascular architecture required in the Weinbaum-Jiji bioheat equation. An easy-to-use closed-form analytic expression has been derived for the difference between the inlet artery and venous return temperatures using a model for the countercurrent heat exchange in the individual muscle tissue cylinders. The perfusion source term calculated from this model is found to be similar in form to the Pennes’s source term except that there is a correction factor or efficiency coefficient multiplying the Pennes term, which rigorously accounts for the thermal equilibration of the returning vein. This coefficient is a function of the vascular cross-sectional geometry of the muscle tissue cylinder, but independent of the Peclet number in contrast to the recent results in Brinck and Werner [8]. The value of this coefficient varies between 0.6 and 0.7 for most muscle tissues. In part II of this study a theory will be presented for determining the local arterial supply temperature at the inlet to the muscle tissue cylinder.

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Revathy, P., V. Sadasivam, and T. Ajith Bosco Raj. "Intensity Based Simulation of the Temperature Prediction in the Focal Region of Liver Using MRI-Guided High Intensity Focused Ultrasound (HIFU)." Journal of Computational and Theoretical Nanoscience 13, no. 10 (2016): 6728–32. http://dx.doi.org/10.1166/jctn.2016.5620.

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In this research paper a new temperature prediction method is proposed to predict the temperature in liver during thermal ablation which also takes in to account the blood flow cooling. The proposed method suggest a modification of Pennes bioheat transfer equation (PBHTE) inorder to more accurately predict the treatment temperature. The temperature elevation by the proposed heat transfer model is compared with the PBHTE model and the other two heat continuum models by Wulff and Klinger. Appropriate temperature prediction is useful in treatment planning. This may reduce the recurrence level of cancer. Further the reduction in treatment time increases patient safety.

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Das, Sanatan, Tilak Kumer Pal, Rabindra Nath Jana, and Oluwole Daniel Makinde. "Temperature Response in Living Skin Tissue Subject to Convective Heat Flux." Defect and Diffusion Forum 387 (September 2018): 1–9. http://dx.doi.org/10.4028/www.scientific.net/ddf.387.1.

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This paper examines the heat transfer in living skin tissue that is subjected to a convective heating. The tissue temperature evolution over time is classically described by the one-dimensional Pennes' bioheat transfer equation which is solved by applying Laplace transform method. The heat transfer analysis on skin tissue (dermis and epidermis) has only been studied defining the Biot number. The result shows that the temperature in skin tissue is less subject to the convected heating skin compared to constant skin temperature. The study also shows that the Biot number has a significant impact on the temperature distribution in the layer of living tissues. This study finds its application in thermal treatment.

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Yue, Kai, Xinxin Zhang, and Fan Yu. "An analytic solution of one-dimensional steady-state Pennes’ bioheat transfer equation in cylindrical coordinates." Journal of Thermal Science 13, no. 3 (2004): 255–58. http://dx.doi.org/10.1007/s11630-004-0039-y.

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Aghayan, Seyed Ali, Dariush Sardari, Seyed Rabii Mahdi Mahdavi, and Mohammad Hasan Zahmatkesh. "An Inverse Problem of Temperature Optimization in Hyperthermia by Controlling the Overall Heat Transfer Coefficient." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/734020.

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A novel scheme to obtain the optimum tissue heating condition during hyperthermia treatment is proposed. To do this, the effect of the controllable overall heat transfer coefficient of the cooling system is investigated. An inverse problem by a conjugated gradient with adjoint equation is used in our model. We apply the finite difference time domain method to numerically solve the tissue temperature distribution using Pennes bioheat transfer equation. In order to provide a quantitative measurement of errors, convergence history of the method and root mean square of errors are also calculated. The effects of heat convection coefficient of water and thermal conductivity of casing layer on the control parameter are also discussed separately.

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Mir, Aijaz, Ibrahim M. Almanjahie, and Javid Gani Dar. "Energy Balance Approach to Study the Role of Perspiration in Heat Distribution of Human Skin." Computational and Mathematical Methods in Medicine 2020 (March 9, 2020): 1–5. http://dx.doi.org/10.1155/2020/3154908.

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This paper develops a model to identify the role of perspiration in temperature distribution of human skin. The model has been solved by using the energy balance equation on the surface of human skin. The role played by thermal conductance, convection, and heat radiation during heat transfer in human skin has been considered, and the relevant laws such as Fourier law for conduction, Newton’s Law for convection, and Stefan–Boltzmann’s law for radiation have been used in the model. Pennes’ bioheat equation has been employed to estimate the heat flow in the dermal region of skin including subcutaneous tissue.

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Lakhssassi, Ahmed, Emmanuel Kengne, and Hicham Semmaoui. "Investigation of nonlinear temperature distribution in biological tissues by using bioheat transfer equation of Pennes’ type." Natural Science 02, no. 03 (2010): 131–38. http://dx.doi.org/10.4236/ns.2010.23022.

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Shih, Tzu-Ching, Ping Yuan, Win-Li Lin, and Hong-Sen Kou. "Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface." Medical Engineering & Physics 29, no. 9 (2007): 946–53. http://dx.doi.org/10.1016/j.medengphy.2006.10.008.

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Dehghan, Mehdi, and Mania Sabouri. "A spectral element method for solving the Pennes bioheat transfer equation by using triangular and quadrilateral elements." Applied Mathematical Modelling 36, no. 12 (2012): 6031–49. http://dx.doi.org/10.1016/j.apm.2012.01.018.

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Huang, H. W., Z. P. Chen, and R. B. Roemer. "A Counter Current Vascular Network Model of Heat Transfer in Tissues." Journal of Biomechanical Engineering 118, no. 1 (1996): 120–29. http://dx.doi.org/10.1115/1.2795937.

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A fully conjugated blood vessel network model (FCBVNM) for calculating tissue temperatures has been developed, tested, and studied. This type of model represents a more fundamental approach to modeling temperatures in tissues than do the generally used approximate equations such as the Pennes’ BHTE or effective thermal conductivity equations. As such, this type of model can be used to study many important questions at a more basic level. For example, in the particular hyperthermia application studied herein, a simple vessel network model predicts that the role of counter current veins is minimal and that their presence does not significantly affect the tissue temperature profiles: the arteries, however, removed a significant fraction of the power deposited in the tissue. These more fundamental models can also be used to check the validity of approximate equations. For example, using the present simple model, when the temperatures calculated by the FCBVNM are used for comparing predictions from two approximation equations (a simple effective thermal conductivity and a simple Pennes’ bio-heat transfer equation formulation of the same problem) it is found that the Pennes’ equation better approximates the FCBVNM temperatures than does the keff model. These results also show that the “perfusion” value (W˙) in the Pennes’ BHTE is not necessarily equal to the “true” tissue perfusion (P˙) as calculated from mass flow rate considerations, but can be greater than, equal to, or less than that value depending on (1) how many vessel levels are modeled by the BHTE, and (2) the “true” tissue perfusion magnitude. This study uses a simple, generic vessel network model to demonstrate the potential usefulness of such fully conjugated vessel network models, and the associated need for developing and applying more complicated and realistic vascular network models. As more realistic vascular models (vessel sizes, orientations, and flow rates) are developed, the predictions of the fully conjugated models should more closely model and approach the true tissue temperature distributions, thus making these fully conjugated models more accurate and valuable tools for studying tissue heat transfer processes.

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Chen, Cuiye, and Lisa X. Xu. "A Vascular Model for Heat Transfer in an Isolated Pig Kidney During Water Bath Heating." Journal of Heat Transfer 125, no. 5 (2003): 936–43. http://dx.doi.org/10.1115/1.1597625.

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Isolated pig kidney has been widely used as a perfused organ phantom in the studies of hyperthermia treatments, as blood perfusion plays an essential role in thermoregulation of living tissues. In this research, a vascular model was built to describe heat transfer in the kidney phantom during water bath heating. The model accounts for conjugate heat transfer between the paired artery and vein, and their surrounding tissue in the renal medulla. Tissue temperature distribution in the cortex was predicted using the Pennes bioheat transfer equation. An analytical solution was obtained and validated experimentally for predicting the steady state temperature distribution in the pig kidney when its surface kept at a uniform constant temperature. Results showed that local perfusion rate significantly affected tissue temperature distributions. Since blood flow is the driving force of tissue temperature oscillations during hyperthermia, the newly developed vascular model provides a useful tool for hyperthermia treatment optimization using the kidney phantom model.

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Liu, Jing, Liang Zhu, and Lisa X. Xu. "Studies on the Three-Dimensional Temperature Transients in the Canine Prostate During Transurethral Microwave Thermal Therapy." Journal of Biomechanical Engineering 122, no. 4 (2000): 372–79. http://dx.doi.org/10.1115/1.1288208.

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Thermal therapy of benign prostatic hyperplasia requires accurate prediction of the temperature distribution induced by the heating within the prostatic tissue. In this study, the Pennes bioheat transfer equation was used to model the transient heat transfer inside the canine prostate during transurethral microwave thermal therapy. Incorporating the specific absorption rate of microwave energy in tissue, a closed-form analytical solution was obtained. Good agreement was found between the theoretical predictions and in-vivo experimental results. Effects of blood perfusion and the cooling at the urethral wall on the temperature rise were investigated within the prostate during heating. The peak intraprostatic temperatures attained by application of 5, 10, or 15 W microwave power were predicted to be 38°C,41°C, and 44°C. Results from this study will help optimize the thermal dose that can be applied to target tissue during the therapy. [S0148-0731(00)01004-9]

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Majchrzak, E., Bohdan Mochnacki, M. Dziewoński, and M. Jasiński. "Numerical Modelling of Hyperthermia and Hypothermia Processes." Advanced Materials Research 268-270 (July 2011): 257–62. http://dx.doi.org/10.4028/www.scientific.net/amr.268-270.257.

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In the paper the results of different numerical solutions of bioheat transfer problems are presented. The base of numerical algorithms constitute the models containing the bioheat transfer equation (or equations) and the adequate geometrical, physical, boundary and initial conditions. In the first part of the paper the solutions concerning the transient temperature field in the biological tissue subjected to the strong external heat sources (freezing, burns) are presented. Next, the examples of sensitivity analysis application in the range of bioheat transfer are discussed. In the final part of the paper the inverse problems are formulated and the example concerning the identification of thermal parameters is shown.

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JANKOWSKA, Małgorzata, and Grażyna SYPNIEWSKA-KAMIŃSKA. "AN INTERVAL FINITE DIFFERENCE METHOD FOR THE BIOHEAT TRANSFER PROBLEM DESCRIBED BY THE PENNES EQUATION WITH UNCERTAIN PARAMETERS." Mechanics and Control 31, no. 2 (2012): 77. http://dx.doi.org/10.7494/mech.2012.31.2.77.

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Liu, Kuo Chi, Cheng Chi Wang, and Po Jen Cheng. "Analysis of Non-Fourier Thermal Behavior in Layered Tissue with Pulse Train Heating." Applied Mechanics and Materials 479-480 (December 2013): 496–500. http://dx.doi.org/10.4028/www.scientific.net/amm.479-480.496.

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This paper investigates the thermal behavior in laser-irradiated layered tissue, which was stratified into skin, fat, and muscle. A modified nonFourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase lag model. This equation is a fourth order partial differential equation and can be simplified as the bio-heat transfer equations derived from Pennes model, thermal wave model, and the linearized form of dual-phase lag model. The boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The deviations of the results from the bio-heat transfer equations based on Pennes model, thermal wave model and dual-phase lag model are presented and discussed.

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Fahmy, Mohamed Abdelsabour. "Boundary Element Algorithm for Modeling and Simulation of Dual-Phase Lag Bioheat Transfer and Biomechanics of Anisotropic Soft Tissues." International Journal of Applied Mechanics 10, no. 10 (2018): 1850108. http://dx.doi.org/10.1142/s1758825118501089.

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The main aim of this paper is to propose a new boundary element algorithm for describing thermomechanical interactions in anisotropic soft tissues. The governing equations are studied based on the dual-phase lag bioheat transfer and Biot’s theory. Due to the advantages of convolution quadrature boundary element method (CQBEM), such as low CPU usage, low memory usage and suitability for treatment of soft tissues that have complex shapes, it is a versatile and powerful method for modeling of bioheat distribution in anisotropic soft tissues and the related deformation. The resulting linear systems for bioheat and mechanical equations are solved by Transpose-free quasi-minimal residual (TFQMR) solver with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner that reduces the iterations number and total CPU time. Numerical results demonstrate the validity, efficiency and accuracy of the proposed algorithm and technique.

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Torvi, D. A., and J. D. Dale. "A Finite Element Model of Skin Subjected to a Flash Fire." Journal of Biomechanical Engineering 116, no. 3 (1994): 250–55. http://dx.doi.org/10.1115/1.2895727.

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A variable property, multiple layer finite element model was developed to predict skin temperatures and times to second and third degree burns under simulated flash fire conditions. A sensitivity study of burn predictions to variations in thermal physical properties of skin was undertaken using this model. It was found that variations in these properties over the ranges used in multiple layer skin models had minimal effects on second degree burn predictions, but large effects on third degree burn predictions. It was also found that the blood perfusion source term in Pennes’ bioheat transfer equation could be neglected in predicting second and third degree burns due to flash fires. The predictions from this model were also compared with those from the closed form solution of this equation, which has been used in the literature for making burn predictions from accidents similar to flash fires.

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Zhai, Fei, Qun Nan, Hui Juan Zhang, and Xue Mei Guo. "The Comparison of Two Simulation Methods on the Thermal Ablation with Large Blood Vessel." Applied Mechanics and Materials 444-445 (October 2013): 1177–81. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.1177.

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Purpose: The aim of this study is to contrast the coupling algorithm (CEE) and boundary heat exchange coefficients (Nu) used in treatment of the large blood vessel in thermal ablation. Methods: Based on the Pennes bioheat transfer equation, the models with blood vessel parallel to microwave antenna were built with finite element method. In two kind of simulation, blood flow rate was set in 0.2 m/s or boundary heat exchange coefficients was set in 1750 W / (m2 °C), respectively. Results and conclusions : There was no significant difference on shape of effective ablation areas and 54°C temperature contours by using two kinds of simulation methods, especially the place far away from the blood vessel. At the place near the blood vessel, the method of CEE is closer to real condition which considers directivity of blood. Whats more, there are higher temperature by using method of Nu inside effective ablation areas.

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ELSAYED, ASSMA F., and O. ANWAR BÉG. "NEW COMPUTATIONAL APPROACHES FOR BIOPHYSICAL HEAT TRANSFER IN TISSUE UNDER ULTRASONIC WAVES: THE VARIATIONAL ITERATION AND CHEBYSCHEV SPECTRAL SIMULATIONS." Journal of Mechanics in Medicine and Biology 14, no. 03 (2014): 1450043. http://dx.doi.org/10.1142/s0219519414500432.

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A mathematical and numerical study is presented for simulating temperature distribution in a two-dimensional tissue medium using Pennes bioheat transfer equation, when the tissue is subjected to ultrasonic waves. Following nondimensionalization of the governing partial differential equation, a novel variational iteration method (VIM) solution is developed. This excellent technique introduced by He [Variational iteration method — a kind of non-linear analytical technique: Some examples, Int J Non-Linear Mech.34:699–708, 1999] employs Lagrange multipliers which can be identified optimally via variational theory. The space and time distributions of temperature are studied and solutions visualized via Mathematica. The influence of thermal conductivity and relaxation time are also examined. Excellent stability and convergence characteristics of VIM are demonstrated. Validation is achieved with a Chebyschev spectral collocation method (CSCM). The present work demonstrates the excellent potential of this powerful semi-numerical method in nonlinear biological heat transfer and furthermore provides an alternative strategy to conventional finite element and finite difference computational simulations. The model finds applications in minimally-invasive spinal laser treatments, glaucoma therapy in ophthalmology and thermoradiotherapy for malignant tumors.

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ZHU, WEIPING, FANGBAO TIAN, and PENG RAN. "ANALYTICAL SOLUTIONS OF NON-FOURIER PENNES AND CHEN–HOLMES EQUATIONS." International Journal of Biomathematics 05, no. 04 (2012): 1250022. http://dx.doi.org/10.1142/s1793524511001647.

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The analytical solutions of non-Fourier Pennes and Chen–Holmes equations are obtained using the Laplace transformation and particular solution method in the present paper. As an application, the effects of the thermal relaxation time τ, the blood perfusion wb, and the blood flow velocity v on the biological skin and inner tissue temperature T are studied in detail. The results obtained in this study provide a good alternative method to study the bio-heat and a biophysical insight into the understanding of the heat transfer in the biotissue.

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Su, YL, KT Chen, CJ Chang, and K. Ting. "Experiment and simulation of biotissue surface thermal damage during laser surgery." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 231, no. 3 (2015): 581–89. http://dx.doi.org/10.1177/0954408915616933.

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In medical cosmetology, laser energy must be properly controlled to avoid unnecessary thermal damage of normal tissue due to excessive irradiation. When a laser source is applied to a specific target that is very close to the surface tissue, residual heat can damage the surface tissue even after the laser treatment is halted. This study aims to determine the proper conditions for the laser treatment and the prediction of the thermal damage of surface tissue after the laser is applied. An 810 nm diode laser was used to irradiate porcine liver and the surface temperature was measured using infrared thermography for different laser application processes. The Pennes bioheat transfer equation was solved using the ANSYS software package to simulate the surface temperature and thermal damage zone in laser surgery. The double ellipsoid function represented the laser source term in the heat transfer simulation. The results of the simulation were compared with the experimental data. Finally, a transient analysis of the estimations of thermal damage after laser surgery was conducted for different conditions of power, laser irradiation time, and laser depth under the surface of the porcine liver.

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Journal articles on the topic 'Pennes bioheat transfer equations'

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