Готові списки джерел за темами / Transient nonlinear bioheat transfer

Добірка наукової літератури з теми "Transient nonlinear bioheat transfer"

Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 29 січня 2023

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Статті в журналах з теми "Transient nonlinear bioheat transfer"

Zhang, Ze-Wei, Hui Wang, and Qing-Hua Qin. "Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues." International Journal of Molecular Sciences 16, no. 1 (January 16, 2015): 2001–19. http://dx.doi.org/10.3390/ijms16012001.

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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 (May 13, 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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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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Deng, Zhong-Shan, and Jing Liu. "Analytical Study on Bioheat Transfer Problems with Spatial or Transient Heating on Skin Surface or Inside Biological Bodies." Journal of Biomechanical Engineering 124, no. 6 (December 1, 2002): 638–49. http://dx.doi.org/10.1115/1.1516810.

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Several closed form analytical solutions to the bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were obtained using Green’s function method. The solutions were applied to study several selected typical bioheat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, thermal comfort analysis, and tissue thermal parameter estimation. Thus a straightforward way to quantitatively interpret the temperature behavior of living tissues subject to constant, sinusoidal, step, point or stochastic heatings etc. both in volume and on boundary were established. Further solution to the three-dimensional bioheat transfer problems was also given to illustrate the versatility of the present method. Implementations of this study to the practical problems were addressed.

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ZHANG, ZE-WEI, HUI WANG, and QING-HUA QIN. "METHOD OF FUNDAMENTAL SOLUTIONS FOR NONLINEAR SKIN BIOHEAT MODEL." Journal of Mechanics in Medicine and Biology 14, no. 04 (July 3, 2014): 1450060. http://dx.doi.org/10.1142/s0219519414500602.

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In this paper, the method of fundamental solution (MFS) coupling with the dual reciprocity method (DRM) is developed to solve nonlinear steady state bioheat transfer problems. A two-dimensional nonlinear skin model with temperature-dependent blood perfusion rate is studied. Firstly, the original bioheat transfer governing equation with nonlinear term induced by temperature-dependent blood perfusion rate is linearized with the Taylor's expansion technique. Then, the linearized governing equation with specified boundary conditions is solved using a meshless approach, in which the DRM and the MFS are employed to obtain particular and homogeneous solutions, respectively. Several numerical examples involving linear, quadratic and exponential relations between temperature and blood perfusion rate are tested to verify the efficiency and accuracy of the proposed meshless model in solving nonlinear steady state bioheat transfer problems, and also the sensitivity of coefficients in the expression of temperature-dependent blood perfusion rate is analyzed for investigating the influence of blood perfusion rate to temperature distribution in skin tissues.

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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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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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Zomordikhani, Zahed, Mohammadmahdi Attar, Alireza Jahangiri, and Farzan Barati. "Analysis of nonlinear bioheat transfer equation in magnetic fluid hyperthermia." Journal of Mechanical Science and Technology 34, no. 9 (September 2020): 3911–18. http://dx.doi.org/10.1007/s12206-020-0841-9.

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Ahmedou Bamba, Salem, and Abdellatif Ellabib. "Nonoverlapping Dirichlet–Neumann method for transient bioheat transfer in the human eye." International Journal of Biomathematics 13, no. 05 (May 28, 2020): 2050035. http://dx.doi.org/10.1142/s1793524520500357.

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This paper presents a 2D simulation of transient heat transfer in the human eye using appropriate boundary conditions. The mathematical model governing bioheat transfer in the human eye is discussed and the existence and uniqueness of the solution are proven. Four methods based on finite element method and nonoverlapping domain decomposition method to obtain transient heat transfer in the human eye are presented and described in details. After conducting numerous simulations using realistic parameters obtained from the open literature and after comparison with measurements reported by previous experimental studies, all proposed methods gave an accurate representation of transient heat transfer in the human eye. The results obtained by the domain decomposition of the human eye into four subdomains are found to be the closest to reality.

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Chan, Cho Lik. "Boundary Element Method Analysis for the Bioheat Transfer Equation." Journal of Biomechanical Engineering 114, no. 3 (August 1, 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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Дисертації з теми "Transient nonlinear bioheat transfer"

Buckley, Donovan O. "Solution of Nonlinear Transient Heat Transfer Problems." FIU Digital Commons, 2010. http://digitalcommons.fiu.edu/etd/302.

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In the presented thesis work, meshfree method with distance fields was extended to obtain solution of nonlinear transient heat transfer problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the meshfree method with distance fields were investigated. Convergence and accuracy of the methodology was validated by analytical solutions, and solutions produced by commercial FEM software (ANSYS 12.1). The research was focused on nonlinearities caused by temperature-dependent thermal conductivity. The behavior of the developed numerical algorithms was observed for both weak and strong temperature-dependency of thermal conductivity. Oseen and Newton-Kantorovich linearization techniques were applied to linearized the governing equation and boundary conditions. Results of the numerical experiments showed that the meshfree method with distance fields has the potential to produced fast accurate solutions. The method enables all prescribed boundary conditions to be satisfied exactly.

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Korvink, Jan Gerrit. "Transient nonlinear heat transfer using finite elements." Master's thesis, University of Cape Town, 1986. http://hdl.handle.net/11427/17618.

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Includes bibliographical references.
This thesis is concerned with the numerical modelling of the transient nonlinear heat conduction problem in solid continua. The hyperbolic governing equation is specialised to a parabolic equation which is sufficient for most engineering applications. The theoretical development includes the effects of conduction, specific heat, internal heat generation and the boundary conditions of convection, radiation, specified temperatures and flux, as well as point sources in the domain. The finite element spatial semidiscretisation of the equations is formally derived from the weak form of the governing equations. Temporal discretisation is obtained through an implicit/explicit difference scheme. The material properties are allowed to be temperature dependent, and consequently a modified Newton-Raphson iterative scheme is employed to solve the equations. The fully discretised equations are solved by implementing the algorithm in an existing finite element stress analysis code. Modelling is possible using four or eight-noded isoparametric elements, and solution control is possible through choice of time step size and choice of time integration method. Five examples are employed to demonstrate the ability of the program. The results compare well with published analytical solutions.

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French, L. de F. "Transient nonlinear heat transfer analysis using the finite element method in the context of the requirements of thermal analysis in a mine." Master's thesis, University of Cape Town, 1990. http://hdl.handle.net/11427/8297.

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Bibliography: leaves 106-108.
The aim of this thesis is to develop a computer program, together with a users' guide, to analyse two-dimensional; nonlinear, transient heat conduction in non-isotropic solids using the finite element method. This program is an extension of an existing program that analyses thermomechanical stress in solids which may have prescribed temperature and flux boundary conditions. The program has been extended using the requirements for modelling heat transfer in mines as a guide. The theory of conduction, thermal radiation, convection and heat transfer due to evaporation and condensation is presented.

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Liu, Li. "Propriétés photo-physiques de nouveaux matériaux moléculaires pour la conversion de photons en énergie." Thesis, Strasbourg, 2017. http://www.theses.fr/2017STRAE010/document.

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Plusieurs processus photo-induits d'énergie et de transfert d'énergie ont été étudiés en solution et dans le film par spectroscopie d'absorption transitoire et de fluorescence pour deux types de cellules solaires. Combinés avec d'autres expériences et par une analyse globale, ces phénomènes ultrarapides avec leur durée de vie ont été observés et les scénarios photo-induits ont été déterminés. La compréhension approfondie des matériaux moléculaires pourrait aider les chimistes à concevoir des cellules solaires efficaces. La première étude sur l'influence des conceptions chimiques sur la formation et la séparation des charges implique différentes fractions donneuses et différents solvants et les résultats ont été expliqués par la théorie de Marcus-Jortner combinée avec le calcul quantique. La deuxième étude porte sur les complexes Fe (II) comme photosensibilisateurs pour les cellules solaires sensibilisées aux colorants. On a étudié une série de complexes de Fe (II) homo et hétérotéptiques avec des ligands de carbène et de terpyridine en solution et dans le film. La durée de vie de l'état de transfert de la charge métal-ligand du triplet d'enregistrement du complexe Fe (II) est obtenue en solution. La compréhension du film est en cours
Various photo-induced energy and energy transfer processes were investigated in solution and in the film by transient absorption and fluorescence spectroscopies for two types of solar cells. Combined with other experiments and through a global analysis, those ultrafast phenomena with their lifetimes were observed and the photo-induced scenarios were determined. The insight understanding of molecular materials could help chemists to design efficient solar cells.The first study about the influence of chemical designs on charge formation and separation involves different donor moieties and different solvents and the results were explained by Marcus-Jortner theory combined with quantum calculationThe second investigation is about Fe(II) complexes as photosensitizers for dye-sensitized solar cells. A series of homo- and heteroleptic Fe(II) complexes with carbene and terpyridine ligands have been studied in solution and in the film. The record triplet metal-to-ligand charge transfer state lifetime of Fe(II) complex is achieved in solution. The further understanding in the film is in progress

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Zhang, Zewei. "Transient bioheat transfer analysis in biological tissues by fundamental-solution-based numerical methods." Phd thesis, 2015. http://hdl.handle.net/1885/15827.

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Taylor's expansion approach was applied to linearize the nonlinear term in the original nonlinear bioheat transfer governing equation. Then the DRM and the MFS was established to obtain the particular and homogeneous solutions. The influence of blood perfusion rate on temperature distribution in the skin tissue was analysed by changing the coefficients in the three expressions of blood perfusion rate. Numerical results showed that the variation of blood perfusion rate plays a significant role in the temperature distribution within the skin tissue. Finally, a meshless numerical scheme combining the operator splitting method (OSM), the RBF interpolation and the MFS was developed for solving transient nonlinear bioheat problems in two-dimensional skin tissue. In the numerical scheme, the nonlinearity caused by the temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the procedure, the OSM is used to separate the Laplacian operator and the nonlinear source term, and then second-order time-stepping schemes are employed for approximating two splitting operators in order to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. The full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations to determine unknowns at each time step. The proposed method was verified by comparison with other methods. Furthermore, the sensitivity of the coefficients in cases of a linear and an exponential relationship of TDBPR was investigated to reveal their bioheat effect on the skin tissue.

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Книги з теми "Transient nonlinear bioheat transfer"

National Aeronautics and Space Administration (NASA) Staff. Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code. Independently Published, 2018.

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Cina, Jeffrey A. Getting Started on Time-Resolved Molecular Spectroscopy. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780199590315.001.0001.

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This textbook details the basic theory of ultrafast molecular spectroscopy starting from time-dependent quantum mechanical perturbation theory in Hilbert space. The emphasis is on the dynamics of nuclear and electronic motion initiated and monitored by femtosecond laser pulses that underlies nonlinear optical signal formation and interpretation. Topics include short-pulse optical absorption, the molecular adiabatic approximation, transient-absorption spectroscopy, vibrational adiabaticity during conformational change, femtosecond stimulated Raman spectroscopy, multi-dimensional electronic spectroscopy and wave-packet interferometry, and two-dimensional wave-packet interferometry of electronic excitation-transfer systems. Numerous exercises embedded in the text explore and expand upon the physical concepts encountered in this important research field.

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Частини книг з теми "Transient nonlinear bioheat transfer"

HEATON, J. M., and L. SOLYMAR. "Transient energy transfer during hologram formation in photorefractive crystals." In Landmark Papers on Photorefractive Nonlinear Optics, 223–34. WORLD SCIENTIFIC, 1995. http://dx.doi.org/10.1142/9789812832047_0024.

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Joel Moitsheki, Raseelo, Partner Luyanda Ndlovu, and Basetsana Pauline Ntsime. "Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces." In Heat Transfer - Design, Experimentation and Applications. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.95490.

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In this chapter we provide the review and a narrative of some obtained results for steady and transient heat transfer though extended surfaces (fins). A particular attention is given to exact and approximate analytical solutions of models describing heat transfer under various conditions, for example, when thermal conductivity and heat transfer are temperature dependent. We also consider fins of different profiles and shapes. The dependence of thermal properties render the considered models nonlinear, and this adds a complication and difficulty to solve these model exactly. However, the nonlinear problems are more realistic and physically sound. The approximate analytical solutions give insight into heat transfer in fins and as such assist in the designs for better efficiencies and effectiveness.

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C. Mehta, Rakhab. "Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem." In Inverse Heat Conduction and Heat Exchangers. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.91000.

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A one-dimensional transient heat conduction equation is solved using analytical and numerical methods. An iterative technique is employed which estimates unknown boundary conditions from the measured temperature time history. The focus of the present chapter is to investigate effects of input parameters such as time delay, thermocouple cavity, error in the location of thermocouple position and time- and temperature-dependent thermophysical properties. Inverse heat conduction problem IHCP is solved with and without material conduction. A two-time level implicit finite difference numerical method is used to solve nonlinear heat conduction problem. Effects of uniform, nonuniform and deforming computational grids on the estimated convective heat transfer are investigated in a nozzle of solid rocket motor. A unified heat transfer analysis is presented to obtain wall heat flux and convective heat transfer coefficient in a rocket nozzle. A two-node exact solution technique is applied to estimate aerodynamic heating in a free flight of a sounding rocket. The stability of the solution of the inverse heat conduction problem is sensitive to the spatial and temporal discretization.

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Deliiski, Nencho, Ladislav Dzurenda, and Natalia Tumbarkova. "Modeling of the Two-Dimensional Thawing of Logs in an Air Environment." In Modeling and Simulation in Engineering - Selected Problems. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.93177.

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A two-dimensional mathematical model has been created, solved, and verified for the transient nonlinear heat conduction in logs during their thawing in an air environment. For the numerical solution of the model, an explicit form of the finite-difference method in the computing medium of Visual FORTRAN Professional has been used. The chapter presents solutions of the model and its validation towards own experimental studies. During the validation of the model, the inverse task of the heat transfer has been solved for the determination of the logs’ heat transfer coefficients in radial and longitudinal directions. This task has been solved also in regard to the logs’ surface temperature, which depends on the mentioned coefficients. The results from the experimental and simulative investigation of 2D nonstationary temperature distribution in the longitudinal section of poplar logs with a diameter of 0.24 m, length of 0.48 m, and an initial temperature of approximately –30°C during their many hours thawing in an air environment at room temperature are presented, visualized, and analyzed.

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Тези доповідей конференцій з теми "Transient nonlinear bioheat transfer"

Biniazan, Maral, and Kamran Mohseni. "Inverse Heat Transfer Analysis of Micro Heater Strength and Locations for Hyperthermia Treatment of Brain Tumors." In ASME 2007 2nd Frontiers in Biomedical Devices Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/biomed2007-38046.

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Hyperthermia, also called thermal therapy or thermotherapy, is a type of cancer treatment in which the aim is to maintain the surrounding healthy tissue at physiologically normal temperatures and expose the cancerous region to high temperatures between 43°C–45°C. Several methods of hyperthermia are currently under study, including local, regional, and whole-body hyperthermia. In local hyperthermia, Interstitial techniques are used to treat tumors deep within the body, such as brain tumors. heat is applied to the tumor, usually by probes or needles which are inserted into the tumor. The heat source is then inserted into the probe. Invasive interstitial heating technique offer a number of advantages over external heating approaches for localizing heat into small tumors at depth. e. g interstitial technique allows the tumor to be heated to higher temperatures than external techniques. This is why an innovative internal hyperthermia research is being conducted in the design of an implantable microheater [1]. To proceed with this research we need complete and accurate data of the strength, number and location of the micro heaters, which is the objective of this paper. The location, strength, and number of implantable micro heaters for a given tumor size is calculated by solving an Inverse Heat Transfer Problem (IHTP). First we model the direct problem by calculating the transient temperature field via Pennies bioheat transfer equation. A nonlinear least-square method, modified by addition of a regularization term, Levenberg Marquardt method is used to determine the inverse problem [2].

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Echeverria, Esteban, and Chandrasekhar Thamire. "Development of an Ultrasound Hyperthermia Simulator for Therapeutic Applications." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-64205.

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In recent times, Ultrasound for therapeutic applications is becoming increasingly popular due to its high practicality and efficiency. However, determination of adequate dosages presents a great challenge due to the difficulty of measuring tissue temperatures during the process. Further, accurate calculation of temperature field induced by ultrasound within the tissue is difficult to develop because of the time-scale differences between pressure and temperature analyses. In order to overcome this issue, practical and accurate methods to couple both analyses are needed. In the present study, Westervelt’s nonlinear wave equation is used to simulate ultrasonic propagation driven by an unfocused piston source in an axisymmetric biological tissue phantom. Using the Finite Difference Time Domain (FDTD) method, a pressure field was calculated for different sinusoidal bursts, frequencies, and source pressures. Average heat generation fields were calculated from the pressure field within an adequate time range for practical purposes. The Pennes bioheat transfer equation with the calculated heat generation fields were used to acquire transient temperature distributions. Effect of source pressure, frequency, source radius, and trial duration on the temperature profiles was examined. It can be observed from the simulations that continuous wave signals increase temperature at a focus in shorter times, while discrete pulses with adequate duty factors can be useful in maintaining required temperatures constant while diffusing heat along the tissue. The methodology presented here can be of use in many applications such as increasing necrotic volume for tissue ablation purposes.

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Kolios, Michael C., Michael D. Sherar, and John W. Hunt. "Temperature Dependent Tissue Properties and Ultrasonic Lesion Formation." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0591.

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Abstract High intensity focused ultrasound has considerable potential for the noninvasive treatment of localised disease. A detailed understanding of the kinetics of tissue coagulation is required to optimise ultrasonic parameters. In this presentation a theoretical model was used to examine the effects of temperature dependent ultrasonic attenuation and absorption on the transient tissue temperature distributions and lesion dimensions. A finite difference algorithm was used to solve numerically the nonlinear form of the bioheat transfer equation in cylindrical coordinates. The lesion dimensions were calculated based on the time-temperature distributions in tissue by using a thermal dose threshold to define the lesion boundaries. The results were compared to published experimental data in which the the location of maximal energy deposition during short duration high intensity focused ultrasound irradiation of in vitro tissue was examined. It was found that the theoretical model did not predict the size and shape of the experimental lesions. To correctly predict lesion size and shape much higher values of attenuation and absorption were required than can be accounted for by thermal coagulation of the tissue alone. The values used suggest that for intensities greater than 3030 W/cm2 the effective local attenuation/absorption in the focal region increased by a factor of 10–20. It is finally shown that temperature dependent tissue changes should be incorporated in thermal models to avoid underestimation of the induced temperature distributions during high intensity focused ultrasound therapy.

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Sarkar, Daipayan, A. Haji-Sheikh, and Ankur Jain. "Theoretical Analysis of Transient Bioheat Transfer in Multi-Layer Tissue." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-53392.

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Heat conduction in skin tissue is a problem of significant technological importance. A theoretical understanding of such a problem is essential as it may lead to design potential therapeutic measures for needed cancer therapy or novel medical devices for various applications including hyperthermia. To understand the physical phenomenon of energy transport in biological systems a transient model is chosen for this study. The most common transport equation to estimate temperature distribution in humans was developed by H.H. Pennes and is popularly known as the Pennes bioheat transfer equation. A generalized Pennes bioheat transfer equation accounts for the effect of various physical phenomena such as conduction, advection, volumetric heat generation, etc. are considered. In this paper, a general transient form of the Pennes bioheat transfer equation is solved analytically for a multilayer domain. The boundary value problem considers the core of the tissue is maintained at uniform temperature of 37°C, convective cooling is applied to the external surface of the skin and the sidewalls are adiabatic. The computation of transient temperature in multidimensional and multilayer bodies offers unique features. Due to the presence of blood perfusion in the tissue, the reaction term in the Pennes governing equation is modeled similar to a fin term. The eigenvalues may become imaginary, producing eigenfunctions with imaginary arguments. In addition the spacing between the eigenvalues between zero and maximum value varies for different cases; therefore the values need to be determined with precision using second order Newton’s method. A detailed derivation of the temperature solution using the technique of separation of variables is presented in this study. In addition a proof of orthogonality theorem for eigenfunctions with imaginary eigenvalues is also presented. The analytical model is used to study the thermal response of skin tissue to different parameters with the aid of some numerical examples. Results shown in this paper are expected to facilitate a better understand of bioheat transfer in layered tissue such as skin.

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Al-Othmani, Mohamad, Nesreen Ghaddar, and Kamel Ghali. "Transient Human Thermal Comfort Response in Convective and Radiative Environments." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56101.

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In this work, human transient thermal responses and comfort are studied in non-uniform radiant heating and convective heating environments. The focus was on a change from walking activity of human in outdoor cold environment at high clothing insulation to warm indoor environment at sedentary activity level associated with lower clothing insulation. A transient multi-segmented bioheat model sensitive to radiant asymmetry is used to compare how fast the human body approaches steady state thermal conditions in both radiative and convective warm environments. A space thermal model is integrated with the bioheat model to predict the transient changes in skin and core temperature of a person subject to change in metabolic rate and clothing insulation when entering conditioned indoor space. It was found that overall thermal comfort and neutrality were reached in 6.2 minutes in the radiative environment compared to 9.24 minutes in convective environment. The local thermal comfort of various body segments differed in their response to the convective system where it took more than 19 minutes for extremities to reach local comfort unlike the radiative system where thermal comfort was attained within 7 minutes.

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Kudryashov, Nikolay A., and Kirill E. Shilnikov. "Nonlinear bioheat transfer models and multi-objective numerical optimization of the cryosurgery operations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952018.

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Kengne, Emmanuel, Idir Mellal, and Ahmed Lakhssassi. "Bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies." In 2014 7th International Conference on Biomedical Engineering and Informatics (BMEI). IEEE, 2014. http://dx.doi.org/10.1109/bmei.2014.7002880.

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Gayzik, F. Scott, Elaine P. Scott, and Tahar Loulou. "Optimal Control of Thermal Damage to Targetted Regions in a Biological Material." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56426.

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A numerical technique with potential applications in hyperthermia treatment planning is presented. The treatment is simulated using a 2D transient computational model of the Pennes bioheat equation within an optimization algorithm. The algorithm recovers the heating protocol which will lead to a desired damage field. The relationship between temperature, time and thermal damage is expressed as a first order rate process using the Arrhenius equation. The objective function of the control problem is based on this thermal damage model. The adjoint method in conjunction with the conjugate gradient algorithm is used to minimize the objective function. The results from a numerical simulation show good agreement between the optimal damage field and the damage field recovered by the algorithm. A comparison between the recovered damage field and the commonly used thermal dose is also made.

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Westin, Johan K., Jayanta S. Kapat, and Louis C. Chow. "Evaluating a Thermoregulatory Model for Cooling Garment Applications With Transient Metabolic Rates." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56319.

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Current state-of-the-art thermoregulatory models do not predict body temperatures with the accuracies that are required for the development of automatic cooling control in liquid cooling garment (LCG) systems. Automatic cooling control would be beneficial in a variety of space, aviation, military, and industrial environments for optimizing cooling efficiency, for making LCGs as portable and practical as possible, for alleviating the individual from manual cooling control, and for improving thermal comfort and cognitive performance. In this paper, we adopt the Fiala thermoregulatory model, which has previously demonstrated state-of-the-art predictive abilities in air environments, for use in LCG environments. We compare the model’s tissue temperature predictions with analytical solutions to the bioheat equation, and with experimental data for a 700 W rectangular type activity schedule. The thermoregulatory model predicts rectal temperature, mean skin temperature, and body heat storage (BHS) with mean absolute errors of 0.13°C, 0.95°C, and 11.9 W·hr, respectively. Even though these accuracies are within state-of-the-art variations, the model does not satisfy the target BHS accuracy of ±6.5 W·hr. We identify model deficiencies, which will be addressed in future studies in order to achieve the strict BHS accuracy that is needed for automatic cooling control development.

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Zhou, X., K. Tamma, and D. Sha. "Recent developments in linear/nonlinear computational algorithms for transient heat transfer." In 39th Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2001. http://dx.doi.org/10.2514/6.2001-370.

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