Статті в журналах: "Transient nonlinear bioheat transfer"

1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Kaur, J., and S. A. Khan. "Thermal changes in Human Abdomen Exposed to Microwaves: A Model Study." Advanced Electromagnetics 8, no. 3 (June 11, 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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12

Marin, Marin, Aatef Hobiny, and Ibrahim Abbas. "Finite Element Analysis of Nonlinear Bioheat Model in Skin Tissue Due to External Thermal Sources." Mathematics 9, no. 13 (June 22, 2021): 1459. http://dx.doi.org/10.3390/math9131459.

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In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments.

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13

Charny, C. K., and R. L. Levin. "Bioheat Transfer in a Branching Countercurrent Network During Hyperthermia." Journal of Biomechanical Engineering 111, no. 4 (November 1, 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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14

Jasinski, Marek. "Sensitivity analysis of transient bioheat transfer during thermal injury formation of biological tissue." Journal of Applied Mathematics and Computational Mechanics 13, no. 2 (June 2014): 33–42. http://dx.doi.org/10.17512/jamcm.2014.2.04.

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15

Fahmy, Mohamed Abdelsabour. "A Computational Model for Nonlinear Biomechanics Problems of FGA Biological Soft Tissues." Applied Sciences 12, no. 14 (July 16, 2022): 7174. http://dx.doi.org/10.3390/app12147174.

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The principal objective of this work was to develop a semi-implicit hybrid boundary element method (HBEM) to describe the nonlinear fractional biomechanical interactions in functionally graded anisotropic (FGA) soft tissues. The local radial basis function collocation method (LRBFCM) and general boundary element method (GBEM) were used to solve the nonlinear fractional dual-phase-lag bioheat governing equation. The boundary element method (BEM) was then used to solve the poroelastic governing equation. To solve equations arising from boundary element discretization, an efficient partitioned semi-implicit coupling algorithm was implemented with the generalized modified shift-splitting (GMSS) preconditioners. The computational findings are presented graphically to display the influences of the graded parameter, fractional parameter, and anisotropic property on the bio-thermal stress. Different bioheat transfer models are presented to show the significant differences between the nonlinear bio-thermal stress distributions in functionally graded anisotropic biological tissues. Numerical findings verified the validity, accuracy, and efficiency of the proposed method.

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16

Al-Othmani, M., N. Ghaddar, and K. Ghali. "A multi-segmented human bioheat model for transient and asymmetric radiative environments." International Journal of Heat and Mass Transfer 51, no. 23-24 (November 2008): 5522–33. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2008.04.017.

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17

Gayzik, F. Scott, Elaine P. Scott, and Tahar Loulou. "Experimental Validation of an Inverse Heat Transfer Algorithm for Optimizing Hyperthermia Treatments." Journal of Biomechanical Engineering 128, no. 4 (February 3, 2006): 505–15. http://dx.doi.org/10.1115/1.2205375.

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Hyperthermia is a cancer treatment modality in which body tissue is exposed to elevated temperatures to destroy cancerous cells. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol with the goal of isolating thermal damage to predetermined treatment areas. This paper presents an algorithm to optimize a hyperthermia treatment protocol using the conjugate gradient method with the adjoint problem. The output of the minimization algorithm is a heating protocol that will cause a desired amount of thermal damage. The transient temperature distribution in a cylindrical region is simulated using the bioheat transfer equation. Temperature and time are integrated to calculate the extent of thermal damage in the region via a first-order rate process based on the Arrhenius equation. Several validation experiments are carried out by applying the results of the minimization algorithm to an albumen tissue phantom. Comparisons of metrics describing the damage region (the height and radius of the volume of thermally ablated phantom) show good agreement between the desired extent of damage and the measured extent of damage. The sensitivity of the bioheat transfer model and the Arrhenius damage model to their constituent parameters is calculated to create a tolerable range of error between the desired and measured extent of damage. The measured height and radius of the ablated region fit well within the tolerable range of error found in the sensitivity analysis.

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18

Rodrigues, D. B., P. J. S. Pereira, P. Limão-Vieira, P. R. Stauffer, and P. F. Maccarini. "Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications." International Journal of Heat and Mass Transfer 62 (July 2013): 153–62. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.11.082.

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19

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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20

Jiang, Xiaoyun, and Haitao Qi. "Thermal wave model of bioheat transfer with modified Riemann–Liouville fractional derivative." Journal of Physics A: Mathematical and Theoretical 45, no. 48 (November 19, 2012): 485101. http://dx.doi.org/10.1088/1751-8113/45/48/485101.

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21

Askarizadeh, Hossein, and Hossein Ahmadikia. "Analytical analysis of the dual-phase-lag model of bioheat transfer equation during transient heating of skin tissue." Heat and Mass Transfer 50, no. 12 (May 14, 2014): 1673–84. http://dx.doi.org/10.1007/s00231-014-1373-6.

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22

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 (March 22, 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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23

Askarizadeh, Hossein, and Hossein Ahmadikia. "Analytical study on the transient heating of a two-dimensional skin tissue using parabolic and hyperbolic bioheat transfer equations." Applied Mathematical Modelling 39, no. 13 (July 2015): 3704–20. http://dx.doi.org/10.1016/j.apm.2014.12.003.

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24

Hien, Tran Duong, and Michałl Kleiber. "On solving nonlinear transient heat transfer problems with random parameters." Computer Methods in Applied Mechanics and Engineering 151, no. 3-4 (January 1998): 287–99. http://dx.doi.org/10.1016/s0045-7825(97)00152-7.

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25

Polyanin, A. D., and V. V. Dil'man. "Integral transform ?infixing? method for nonlinear transient mass-transfer problems." Journal of Engineering Physics 55, no. 4 (October 1988): 1161–66. http://dx.doi.org/10.1007/bf01155227.

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26

Ajzoul, T., C. Chaussavoine, and M. Amouroux. "Finite element analysis of a transient nonlinear heat transfer problem." Computers & Chemical Engineering 19, no. 4 (April 1995): 423–36. http://dx.doi.org/10.1016/0098-1354(94)00053-q.

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27

Zhang, Huichen, and Markus BrÃ¼hl. "GENERATION OF EXTREME TRANSIENT WAVES IN EXPERIMENTAL MODELS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 51. http://dx.doi.org/10.9753/icce.v36.waves.51.

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The transfer of natural waves and sea states into small- and large-scale model teste contributes to the proper design of offshore and coastal structure. Such shallow-water ocean surface waves are highly nonlinear and subject to wave transformation and nonlinear wave-wave interactions. However, the standard methods of wave generation according to conventional wave theories and wave analysis methods are limited to simple regular waves, simple sea states and low-order wave generation without considering the nonlinear wave-wave interactions. The research project Generation of Extreme Transient Waves in Experimental Models (ExTraWaG) aims to accurately generate target transient wave profile at a pre-defined position in the wave flume (transfer point) under shallow water conditions. For this purpose, the KdV-based nonlinear Fourier transform is introduced as a continuative wave analysis method and is applied to investigate the nonlinear spectral character of experimental wave data. Furthermore, the method is applied to generate transient nonlinear waves as specific locations in the wave flume, considering the nonlinear transformation and interactions of the propagating waves.

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28

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 (February 5, 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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29

KUMAR, P., S. NARAYANAN, and S. GUPTA. "Targeted energy transfer in stochastically excited system with nonlinear energy sink." European Journal of Applied Mathematics 30, no. 5 (September 18, 2018): 869–86. http://dx.doi.org/10.1017/s0956792518000505.

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This study investigates the phenomenon of targeted energy transfer (TET) from a linear oscillator to a nonlinear attachment behaving as a nonlinear energy sink for both transient and stochastic excitations. First, the dynamics of the underlying Hamiltonian system under deterministic transient loading is studied. Assuming that the transient dynamics can be partitioned into slow and fast components, the governing equations of motion corresponding to the slow flow dynamics are derived and the behaviour of the system is analysed. Subsequently, the effect of noise on the slow flow dynamics of the system is investigated. The Itô stochastic differential equations for the noisy system are derived and the corresponding Fokker–Planck equations are numerically solved to gain insights into the behaviour of the system on TET. The effects of the system parameters as well as noise intensity on the optimal regime of TET are studied. The analysis reveals that the interaction of nonlinearities and noise enhances the optimal TET regime as predicted in deterministic analysis.

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30

Vakakis, Alexander F. "Passive nonlinear targeted energy transfer." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (July 23, 2018): 20170132. http://dx.doi.org/10.1098/rsta.2017.0132.

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Nonlinearity in dynamics and acoustics may be viewed as scattering of energy across frequencies/wavenumbers. This is in contrast with linear systems when no such scattering exists. Motivated by irreversible large-to-small-scale energy transfers in turbulent flows, passive targeted energy transfers (TET) in mechanical and structural systems incorporating intentional strong nonlinearities are considered. Transient or permanent resonance captures are basic mechanisms for inducing TET in such systems, as well as nonlinear energy scattering across scales caused by strongly nonlinear resonance interactions. Certain theoretical concepts are reviewed, and some TET applications are discussed. Specifically, it is shown that the addition of strongly nonlinear local attachments in an otherwise linear dynamical system may induce energy scattering across scales and ‘redistribution' of input energy from large to small scales in the linear modal space, in similarity to energy cascades that occur in turbulent flows. Such effects may be intentionally induced in the design stage and may lead to improved performance, e.g. it terms of vibration and shock isolation or energy harvesting. In addition, a simple mechanical analogue in the form of a nonlinear planar chain of particles composed of linear stiffness elements but exhibiting strong nonlinearity due to kinematic and geometric effects is discussed, exhibiting similar energy scattering across scales in its acoustics. These results demonstrate the efficacy of intentional utilization of strong nonlinearity in design to induce predictable and controlled intense multi-scale energy transfers in the dynamics and acoustics of a broad class of systems and structures, thus achieving performance objectives that would be not possible in classical linear settings. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

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31

Sharma, Neha, Surjan Singh, and Dinesh Kumar. "Analytical Solution of Non Linear DPL Bioheat Transfer Model for Temperature Dependent Metabolic Heat Source During Thermal Therapy." International Journal of Innovative Technology and Exploring Engineering 11, no. 8 (July 30, 2022): 78–86. http://dx.doi.org/10.35940/ijitee.h9174.0711822.

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In this research paper, the simulation based modelling of heat transfer in tissue under periodic boundary condition has been considered. The dual phase lag bioheat transfer (DPLBHT) model is implemented for computation of the temperature based thermal therapy treatment. The elements of volumetric heat source such as perfusion of blood, metabolism heat source and external heat source are considered in nonlinear DPL model. In this paper we have taken three cases for metabolic heat source namely, constant, linear and exponential. The combined two numerical methods which are based on finite difference scheme and Runge Kutta (4,5) scheme are exerted to solve the non-linear problem. We compute the exact solution for particular case. Numerical conclusions which are computed by numerical hybrid method are equated with exact result. It has been found that non linear DPL model with exponential metabolic heat source is closed to exact solution. We also expressed the effect of different parameters such as relaxation time, perfusion rate, metabolic heat source parameter, associated blood perfusion heat, heat source because of heat flux and temperature gradient etc.

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32

Li, Zi Liang, and Mei Hong Liu. "Numerical Simulation of the Transient Temperature Field during Gas Quenching." Advanced Materials Research 683 (April 2013): 275–79. http://dx.doi.org/10.4028/www.scientific.net/amr.683.275.

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Based on the theory of heat transfer, phase transformation and thermal non-elasticity, a nonlinear coupling heat-conduction equation considering phase transformation, nonlinear surface heat transfer coefficient and variable physical properties during gas quenching is proposed and solved by means of Finite Element Method (F.E.M). The transient temperature field is obtained and the influencing factors are analyzed and discussed. It might be valuable for some practical applications and for the development of theory.

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33

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 (November 30, 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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34

Liew, A., N. S. Feng, and E. J. Hahn. "On Using the Transfer Matrix Formulation for Transient Analysis of Nonlinear Rotor Bearing Systems." International Journal of Rotating Machinery 10, no. 6 (2004): 425–31. http://dx.doi.org/10.1155/s1023621x04000429.

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For many years transfer matrices have been used to evaluate the steady-state vibration response of linear rotor bearing systems. More recently, they have been used to evaluate the steady-state periodic vibration response of nonlinear rotor bearing systems. For quasi-periodic and chaotic response, a transient solution is mandated and transient solution software can also be gainfully used to evaluate the stability of the above-mentioned periodic solutions. To date, transient solutions generally necessitate a different lumped parameter discretization of the rotor and involve solving simultaneously the differential equations for every degree of freedom. This article shows how transient analysis can be performed while maintaining the transfer matrix lumped parameter discretization. The technique is illustrated for a non symmetric unbalanced flexible rotor supported on hydrodynamic journal bearings or deep-groove ball bearings.

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35

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 (March 13, 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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36

Paik, Seungho, Hoa D. Nguyen, and Jacob N. Chung. "Transient Conjugated Heat Transfer Analysis from a Sphere with Nonlinear Boundary Conditions." Journal of Computational Physics 115, no. 2 (December 1994): 423–30. http://dx.doi.org/10.1006/jcph.1994.1207.

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37

Malekzadeh, P., and H. Rahideh. "Two-dimensional nonlinear transient heat transfer analysis of variable section pin fins." Energy Conversion and Management 50, no. 4 (April 2009): 916–22. http://dx.doi.org/10.1016/j.enconman.2008.12.025.

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38

Majchrzak, Ewa, Marek Jasiński, and Łukasz Turchan. "Modeling of Laser-Soft Tissue Interactions Using the Dual-Phase Lag Equation: Sensitivity Analysis with Respect to Selected Tissue Parameters." Defect and Diffusion Forum 379 (November 2017): 108–23. http://dx.doi.org/10.4028/www.scientific.net/ddf.379.108.

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Thermal processes occurring in soft tissues are subjected to laser irradiation are analyzed. The transient bioheat transfer is described by the generalized dual-phase lag model. This model consists of two coupled equations concerning the tissue and blood temperatures supplemented by the appropriate boundary and initial conditions. The efficiency of the internal heat source connected to the laser irradiation results from the solution of the diffusion equation. This approach is acceptable when the scattering dominates over the absorption for wavelengths between 650 and 1300 nm, and just such a situation occurs in the case of soft tissues. Sensitivity analysis with respect to the parameters occurring in the mathematical model is done using the direct approach (differentiation of the basic equations and the boundary-initial conditions with respect to the parameter considered), especially the absorption coefficient and scattering coefficient of the soft tissue are considered. At the stage of numerical modeling the basic problem and additional problems connected with the sensitivity functions are solved using the finite difference method. In the final part the conclusions and examples of computations are presented.

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39

McBranch, Duncan W., Eric S. Maniloff, Dan Vacar, and Alan J. Heeger. "Ultrafast Nonlinear Optical Properties of Charge-Transfer Polymers." Journal of Nonlinear Optical Physics & Materials 07, no. 03 (September 1998): 313–30. http://dx.doi.org/10.1142/s0218863598000259.

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Charge-transfer polymers are a new class of nonlinear optical materials which can be used for generating femtosecond holographic gratings. Using semiconducting polymers sensitized with varying concentrations of C 60, holographic gratings were recorded by individual ultrafast laser pulses; the diffraction efficiency and time decay of the gratings were measured using nondegenerate four-wave mixing. Using a figure of merit for dynamic data processing, the temporal diffraction efficiency, this new class of materials exhibits between two and 12 orders of magnitude higher response than previous reports. The charge-transfer range at polymer/ C 60 interfaces was further studied using transient absorption spectroscopy. The fact that charge transfer occurs in the picosecond-time scale in bilayer structures (thickness 200 Å) implies that diffusion of localized excitations to the interface is not the dominant mechanism; the charge-transfer range is a significant fraction of the film thickness. From analysis of the excited state decay curves, we estimate the charge-transfer range to be 80 Å and interpret that range as resulting from quantum delocalization of the photoexcitations.

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40

Garg, Rajul, Harish chandra, and Thakur Brajesh Tripathi. "Nonlinear and Transient Heat Transfer in the Fin by a Truly Meshless Method." Indian Journal of Science and Technology 10, no. 31 (September 16, 2017): 1–7. http://dx.doi.org/10.17485/ijst/2017/v10i31/113859.

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41

Malekzadeh, P., and H. Rahideh. "IDQ two-dimensional nonlinear transient heat transfer analysis of variable section annular fins." Energy Conversion and Management 48, no. 1 (January 2007): 269–76. http://dx.doi.org/10.1016/j.enconman.2006.04.005.

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42

LEE, KANG IL, IMBO SIM, GWAN SUK KANG, and MIN JOO CHOI. "NUMERICAL SIMULATION OF TEMPERATURE ELEVATION IN SOFT TISSUE BY HIGH INTENSITY FOCUSED ULTRASOUND." Modern Physics Letters B 22, no. 11 (May 10, 2008): 803–7. http://dx.doi.org/10.1142/s0217984908015413.

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In focused ultrasound surgery, high intensity focused ultrasound (HIFU) can be used to destroy pathological tissue deep inside the body without any damage to the surrounding normal tissue. This noninvasive technique has been used to treat malignant tumors of the liver, prostate, kidney, and benign breast tumors via a percutaneous or transrectal approach without the need for general anaesthesia. In the present study, a finite element method was used for the simulation of temperature elevation in soft tissue by HIFU. First, the HIFU field was modeled using the Westervelt equation for the propagation of finite-amplitude sound in a thermoviscous fluid in order to account for the effects of diffraction, absorption, and nonlinearity. Second, the Pennes bioheat transfer equation was used to predict the temperature elevation in soft tissue by HIFU. In order to verify the numerical simulation, the simulated temperature elevation at the focus in a tissue-mimicking phantom was compared with the measurements, using a concave focused transducer with a focal length of 62.6 mm, a radius of 35.0 mm, and a center frequency of 1.1 MHz.

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43

Liauh, C. T., and R. B. Roemer. "A Semilinear State and Parameter Estimation Algorithm for Inverse Hyperthermia Problems." Journal of Biomechanical Engineering 115, no. 3 (August 1, 1993): 257–61. http://dx.doi.org/10.1115/1.2895484.

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An improved state and parameter estimation algorithm has been developed which decreases the total computational time required to accurately reconstruct complete hyperthermia temperature fields. Within this improved iterative estimation algorithm, if the change in the unknown perfusion parameters is small a linear approximation scheme is implemented in which the old Jacobian matrix (the sensitivity matrix) is used, instead of recalculating the new Jacobian matrix for the next iteration. In the hyperthermia temperature estimation problem the relationship between the temperature and the blood perfusion based on the bioheat transfer equation is generally nonlinear. However, the temperature can be approximated as a linear function of the blood perfusion over a certain range thus allowing this improved approach to work. Results show that if the temperature is approximated as a linear (or quasi-linear) function of the blood perfusion, the linearizing approach considerably reduces the CPU time required to accurately reconstruct the temperature field. The limiting case of implementing this approach is to calculate the Jacobian matrix for each iteration, which is identical to the approach used in the original nonlinear algorithm. Critical values of determining whether or not there is a need to recalculate the new Jacobian matrix during the iterations are presented for several inverse hyperthermia temperature estimation problems.

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44

Subbiah, R., and N. F. Rieger. "On the Transient Analysis of Rotor-Bearing Systems." Journal of Vibration and Acoustics 110, no. 4 (October 1, 1988): 515–20. http://dx.doi.org/10.1115/1.3269559.

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The transient dynamic response of a flexible rotor in nonlinear supports has been investigated using time marching methods. Several marching techniques such as Newmark β, Wilson θ, and Houbolt have been utilized in this study of rotor-bearing dynamic systems, to examine the stability of the system, and the suitability of each technique for predicting the onset of instability. The given rotor system has been modeled both in space and time using the transfer matrix method and the Houbolt method. The transient orbital response data so obtained have been compared with those obtained by a finite element model. Differences in the order of 6 percent were found. A nonlinear representation of a finite bearing has been included in the transient matrix model and the stability characteristics of different rotor systems of varied complexity have been studied. The nonlinear results have been compared with earlier results obtained using linear bearing representations.

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45

Li, Q. H., S. S. Chen, and X. M. Luo. "Using Meshless Local Natural Neighbor Interpolation Method to Solve Two-Dimensional Nonlinear Problems." International Journal of Applied Mechanics 08, no. 05 (July 2016): 1650069. http://dx.doi.org/10.1142/s1758825116500691.

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Based on the meshless local natural neighbor interpolation method (MLNNI), a novel solution procedure is developed for the analysis of nonlinear steady and transient heat transfer of two-dimensional structures in this paper. Nonlinearities arising from temperature dependence of material properties and nonlinear boundary conditions have been taken into account. The present method is developed based on the natural neighbor interpolation (NNI) for constructing shape functions at scattered nodes. The three-node triangular FEM shape function is employed as the test function, which reduces the orders of integrands involved in domain integrals. Due to the delta function property of the natural neighbor shape functions, there is no need to employ special techniques to enforce the essential boundary conditions. The backward difference method is employed for the time integration scheme in transient analysis and the Newton–Raphson iterative procedure is required at each time step. Three numerical examples with different geometries and boundary conditions are presented at the end to demonstrate the validity and accuracy of the proposed method for the solution of a wide class of nonlinear steady and transient heat transfer problems.

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46

Liu, Ji’ang, Youbo Liu, Gao Qiu, and Xiao Shao. "Learning-Aided Optimal Power Flow Based Fast Total Transfer Capability Calculation." Energies 15, no. 4 (February 11, 2022): 1320. http://dx.doi.org/10.3390/en15041320.

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Total transfer capability (TTC) is a vital security indicator for power exchange among areas. It characterizes time-variants and transient stability dynamics, and thus is challenging to evaluate efficiently, which can jeopardize operational safety. A leaning-aided optimal power flow method is proposed to handle the above challenges. At the outset, deep learning (DL) is utilized to globally establish real-time transient stability estimators in parametric space, such that the dimensionality of dynamic simulators can be reduced. The computationally intensive transient stability constraints in TTC calculation and their sensitivities are therewith converted into fast forward and backward processes. The DL-aided constrained model is finally solved by nonlinear programming. The numerical results on the modified IEEE 39-bus system demonstrate that the proposed method outperforms several model-based methods in accuracy and efficiency.

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47

Liew, A., N. Feng, and E. Hahn. "On Using the Transfer Matrix Formulation for Transient Analysis of Nonlinear Rotor Bearing Systems." International Journal of Rotating Machinery 10, no. 6 (November 1, 2004): 425–31. http://dx.doi.org/10.1080/10236210490447755.

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48

Ramadan, K., and M. A. Al-Nimr. "Analysis of transient heat transfer in multilayer thin films with nonlinear thermal boundary resistance." International Journal of Thermal Sciences 48, no. 9 (September 2009): 1718–27. http://dx.doi.org/10.1016/j.ijthermalsci.2009.01.014.

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49

Zhang, Hengliang, Weimin Kan, and Xuejiao Hu. "Green's function approach to the nonlinear transient heat transfer analysis of functionally graded materials." International Journal of Thermal Sciences 71 (September 2013): 292–301. http://dx.doi.org/10.1016/j.ijthermalsci.2013.04.025.

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50

Malekzadeh, P., H. Rahideh, and G. Karami. "A Differential Quadrature Element Method for Nonlinear Transient Heat Transfer Analysis of Extended Surfaces." Numerical Heat Transfer, Part A: Applications 49, no. 5 (August 2006): 511–23. http://dx.doi.org/10.1080/10407780500436840.

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