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K N Rai - One of the best experts on this subject based on the ideXlab platform.

  • a study of fractional order dual phase lag Bioheat Transfer model
    Journal of Thermal Biology, 2020
    Co-Authors: Mahesh Kumar, K N Rai
    Abstract:

    Abstract In this study, we have established a space-time fractional DPL Bioheat Transfer model in the presence of temperature-dependent metabolic and space-time dependent electromagnetic heat sources. Applying the Legendre wavelet collocation method, the fractional order partial differential equation is reduced into the system of algebraic equations, which has been solved using the Newton iteration method. The error bound as well as stability analysis and numerical scheme validation are provided. The time to achieve for the position of hyperthermia is discussed in three cases: the DPL model, the time-fractional DPL model, and the space-time-fractional DPL model. The effect of variability of time and space fractional derivative orders (α and β), transmitted power (P) and lagging times on the temperature profile in biological tissue at a different time are discussed in detail. We conclude that a suitable value of α, β, τ T , τ q , and P provides a desirable temperature at a particular time in thermal therapies. Such knowledge will be very useful in the clinical therapeutic application.

  • three phase lag Bioheat Transfer model and its validation with experimental data
    Mechanics Based Design of Structures and Machines, 2020
    Co-Authors: Dinesh Kumar, K N Rai
    Abstract:

    In this study, we introduce a three-phase-lag (TPL) Bioheat Transfer model for living biological tissue by considering the heat conduction law that includes heat flux, temperature gradient and ther...

  • verified non linear dpl model with experimental data for analyzing heat Transfer in tissue during thermal therapy
    International Journal of Thermal Sciences, 2018
    Co-Authors: Dinesh Kumar, Surjan Singh, Neha Sharma, K N Rai
    Abstract:

    Abstract In this paper, mathematical modeling and simulation of heat Transfer in tissue using non-linear dual-phase-lag Bioheat Transfer (DPLBHT) model under Dirichlet boundary condition has been studied for therapeutic treatment of cancerous or tumorous cells. The components of volumetric heat source in non-linear DPLBHT model such as blood perfusion and metabolism are assumed experimentally validated temperature-dependent function which results in non-linear DPLBHT model in order to predict more accurate. A hybrid numerical method which is based on finite difference and Runge-Kutta (4, 5) schemes, is used to solve the present non-linear problem. The exact solution has been obtained in a particular case and compared with the present numerical scheme, and we found that those are in good agreement. A comparison of models has been made when the variation of blood perfusion rate and metabolism is realistic function of temperature, is of non-linear DPLBHT model, non-linear single-phase-lag Bioheat Transfer (SPLBHT) model and non-linear Pennes Bioheat Transfer (PBHT) model with experimental data in same situation and it has been found that non-linear DPL model is closest to the experimental data. The whole paper is analyzed and presented in dimensionless form. The effect of coefficient of blood perfusion rate, dimensionless heating source parameters, relaxation and thermalisation time on dimensionless temperature distribution has been analyzed in treatment process.

  • numerical solution of non linear dual phase lag Bioheat Transfer equation within skin tissues
    Bellman Prize in Mathematical Biosciences, 2017
    Co-Authors: Dinesh Kumar, P Kumar, K N Rai
    Abstract:

    Abstract This paper deals with numerical modeling and simulation of heat Transfer in skin tissues using non-linear dual-phase-lag (DPL) Bioheat Transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL Bioheat Transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge–Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes Bioheat Transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form.

  • fractional modeling of hyperbolic Bioheat Transfer equation during thermal therapy
    Journal of Mechanics in Medicine and Biology, 2017
    Co-Authors: P Kumar, K N Rai
    Abstract:

    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.

Hossein Ahmadikia - One of the best experts on this subject based on the ideXlab platform.

  • analytical study on the transient heating of a two dimensional skin tissue using parabolic and hyperbolic Bioheat Transfer equations
    Applied Mathematical Modelling, 2015
    Co-Authors: Hossein Askarizadeh, Hossein Ahmadikia
    Abstract:

    Abstract In this study, exact analytical analysis of two-dimensional Fourier and non-Fourier Bioheat Transfer equations in skin tissue exposed to an instantaneous heating condition is presented. The effects of blood perfusion and metabolic heat generation on the tissue thermal behavior are considered. Corresponding analytical approach is developed through Laplace transform (LT) technique in conjunction with the separation of variables method and inversion theorem. The dual-phase-lag (DPL), thermal wave (TW) and Pennes models of Bioheat Transfer equation are studied by utilizing a generalized model. The reliability of the presented results has been evidenced through enforcing appropriate circumstances on the DPL model and comparing the outcome results with that of predicted by the Pennes and TW models. It is proved that the DPL Bioheat Transfer equation with the effects of blood perfusion and metabolic heat generation can be reduced to the Pennes Bioheat Transfer equation when τ q = τ T . The effects of local non-equilibrium on the tissue thermal behavior are examined and discussed by comparing the gradient precedence (GP) and flux precedence (FP) heat flow regimes of the DPL model. The first- and second-degree burn times of a 2D skin tissue for different Bioheat models are introduced and compared with the 1D case.

  • Analytical analysis of the dual-phase-lag model of Bioheat Transfer equation during transient heating of skin tissue
    Heat and Mass Transfer, 2014
    Co-Authors: Hossein Askarizadeh, Hossein Ahmadikia
    Abstract:

    Dual-phase-lag model of Bioheat Transfer equation is utilized in treating the transient heat Transfer problems in skin tissue considering prevalent heating conditions in thermal therapy applications, namely, pulse train and periodic heat flux. Comparisons between the presented analytical results for limiting cases and previous studies display an excellent agreement. The effects of temperature gradient relaxation time on the tissue temperature, damage, and also on the blood perfusion in skin tissue are studied.

  • analytical solution of non fourier and fourier Bioheat Transfer analysis during laser irradiation of skin tissue
    Journal of Mechanical Science and Technology, 2012
    Co-Authors: Hossein Ahmadikia, A Moradi, R Fazlali, Basiri A Parsa
    Abstract:

    The thermal wave and the Pennes Bioheat Transfer models are solved analytically by employing the Laplace transform method for small and large values of reflection power (albedo) during laser irradiation. Most of the previous studies have been based on the infinite heat diffusion velocity, but non-Fourier thermal behavior has been observed experimentally in biological tissue. At low initial albedo values, the temperature in the skin depth that directly results from conduction heat Transfer process is caused by the lengthy thermal relaxation time in skin tissue. This condition generates a big difference between the thermal wave and Pennes results at the beginning of the heating process. This difference increases under short-time heating condition and high heat flux. However, with high initial albedo, the temperature distribution in the skin depth becomes negligible because of the skin absorption of laser beams. The non-Fourier effect should be considered during laser heating with low albedo, because errors in the predicted temperature values may occur.

  • analytical solution of the parabolic and hyperbolic heat Transfer equations with constant and transient heat flux conditions on skin tissue
    International Communications in Heat and Mass Transfer, 2012
    Co-Authors: Hossein Ahmadikia, R Fazlali, A Moradi
    Abstract:

    Abstract In this article, the parabolic (Pennes Bioheat equation) and hyperbolic (thermal wave) Bioheat Transfer models for constant, periodic and pulse train heat flux boundary conditions are solved analytically by applying the Laplace transform method for skin as a semi-infinite and finite domain. The Bioheat Transfer analysis with transient heat flux on skin tissue has only been studied by Pennes equation for a semi-infinite domain. For modeling heat Transfer in short duration of an initial transient, or when the propagation speed of the thermal wave is finite, there are major differences between the results of parabolic and hyperbolic heat Transfer equations. The non-Fourier Bioheat Transfer equation describes the thermal behavior in the biological tissues better than Fourier equation. The outcome of transient heat flux condition shows that by penetrating into the depths beneath the skin subjected to heat, the amplitude of temperature response decreases significantly. The blood perfusion rate can be predicted using the phase shift between the surface temperature and transient surface heat flux. The thermal damage of the skin is studied by applying both the parabolic and hyperbolic Bioheat Transfer equations.

A Moradi - One of the best experts on this subject based on the ideXlab platform.

  • Bioheat Transfer analysis of biological tissues induced by laser irradiation
    International Journal of Thermal Sciences, 2015
    Co-Authors: P Hooshmand, A Moradi, B Khezry
    Abstract:

    Abstract This paper develops an analytical solution for a generalized dual phase lag (DPL) model based on the nonequilibrium heat Transfer in biological tissues during laser irradiation achieved by performing volume average to the local instantaneous energy equation for blood and tissue. The obtained energy equation is solved by employing the separation of variables and Duhamel's integral method for both absorbing and scattering tissues. The generalized DPL model anticipates different results than that of the predicted by the classical DPL and Pennes Bioheat Transfer (parabolic) models. It is found that the generalized DPL model calculates lower temperature than that of obtained by the classical DPL model due to considering heat convection between blood vessels and tissue. The obtained analytical results are also compared with existing numerical and experimental data to verify the accuracy of the analytical solution. The results indicate that the generalized DPL model reduces to Pennes Bioheat Transfer model when both thermal lag times are zero. It is shown that effects of blood perfusion rate, coupling factor and the lag time τT on the temperature response of tissue are similar. Furthermore, the comparison between the analytical results and existed experimental data shows that the present mathematical model is an efficient tool for evaluation of Bioheat Transfer in biological tissues.

  • analytical solution of non fourier and fourier Bioheat Transfer analysis during laser irradiation of skin tissue
    Journal of Mechanical Science and Technology, 2012
    Co-Authors: Hossein Ahmadikia, A Moradi, R Fazlali, Basiri A Parsa
    Abstract:

    The thermal wave and the Pennes Bioheat Transfer models are solved analytically by employing the Laplace transform method for small and large values of reflection power (albedo) during laser irradiation. Most of the previous studies have been based on the infinite heat diffusion velocity, but non-Fourier thermal behavior has been observed experimentally in biological tissue. At low initial albedo values, the temperature in the skin depth that directly results from conduction heat Transfer process is caused by the lengthy thermal relaxation time in skin tissue. This condition generates a big difference between the thermal wave and Pennes results at the beginning of the heating process. This difference increases under short-time heating condition and high heat flux. However, with high initial albedo, the temperature distribution in the skin depth becomes negligible because of the skin absorption of laser beams. The non-Fourier effect should be considered during laser heating with low albedo, because errors in the predicted temperature values may occur.

  • analytical solution of the parabolic and hyperbolic heat Transfer equations with constant and transient heat flux conditions on skin tissue
    International Communications in Heat and Mass Transfer, 2012
    Co-Authors: Hossein Ahmadikia, R Fazlali, A Moradi
    Abstract:

    Abstract In this article, the parabolic (Pennes Bioheat equation) and hyperbolic (thermal wave) Bioheat Transfer models for constant, periodic and pulse train heat flux boundary conditions are solved analytically by applying the Laplace transform method for skin as a semi-infinite and finite domain. The Bioheat Transfer analysis with transient heat flux on skin tissue has only been studied by Pennes equation for a semi-infinite domain. For modeling heat Transfer in short duration of an initial transient, or when the propagation speed of the thermal wave is finite, there are major differences between the results of parabolic and hyperbolic heat Transfer equations. The non-Fourier Bioheat Transfer equation describes the thermal behavior in the biological tissues better than Fourier equation. The outcome of transient heat flux condition shows that by penetrating into the depths beneath the skin subjected to heat, the amplitude of temperature response decreases significantly. The blood perfusion rate can be predicted using the phase shift between the surface temperature and transient surface heat flux. The thermal damage of the skin is studied by applying both the parabolic and hyperbolic Bioheat Transfer equations.

Kullervo Hynynen - One of the best experts on this subject based on the ideXlab platform.

  • temperature change near microbubbles within a capillary network during focused ultrasound
    Physics in Medicine and Biology, 2010
    Co-Authors: Alexander R Klotz, Liis Lindvere, Bojana Stefanovic, Kullervo Hynynen
    Abstract:

    Preformed gas bubbles can increase energy absorption from an ultrasound beam and therefore they have been proposed for an enhancer of ultrasound treatments. Although tissue temperature measurements performed in vivo using invasive thermocouple probes and MRI thermometry have demonstrated increased tissue temperature, the microscopic temperature distribution has not been investigated so far. In this study the Transfer of heat between bubbles and tissue during focused ultrasound was simulated. Microbubble oscillations were simulated within a rat cortical microvascular network reconstructed from in vivo dual-photon microscopy images and the power density of these oscillations was used as an input term in the Pennes Bioheat Transfer equation. The temperature solution from the Bioheat Transfer equation was mapped onto vascular data to produce a three-dimensional temperature map. The results showed high temperatures near the bubbles and slow temperature rise in the tissue. Heating was shown to increase with increasing bubble frequency and insonation pressure, and showed a frequency-dependent peak. The goal of this research is to characterize the effect of various parameters on bubble-enhanced therapeutic ultrasound to allow better treatment planning. These results show that the induced temperature elevations have nonuniformities which may have a significant impact on the bio-effects of the exposure.

Jing Liu - One of the best experts on this subject based on the ideXlab platform.

  • a coupled continuum discrete Bioheat Transfer model for vascularized tissue
    International Journal of Heat and Mass Transfer, 2017
    Co-Authors: Jing Liu
    Abstract:

    Abstract For a living tissue embedded with multiscale and heterogeneous vascular network, the thermal transport process is considerable complicated so that it is hard to establish a credible and feasible Bioheat Transfer model for many biomedical applications. This paper is aimed at establishing a novel Bioheat Transfer model to characterize the heat Transfer process in the vascularized tissue. The coupled continuum-discrete model denoted by CCD was proposed in this work. CCD model consists of 3D temperature equation for solid tissue and 1D equation for blood vessel, which are coupled through the discrete heat-source terms. The blood vessels are classified as visible vessel with detailed geometry information obtained from medical image or vascular tree generation method, and invisible capillary without configuration information. The discrete terms for different vascular sizes were separately established to represent the multiscale conjugated blood-tissue thermal interaction. The comparison of CCD model and the existing Bioheat models was discussed in detailed. An efficient numerical scheme for CCD model was also developed and demonstrated to accurately predict temperature field of the vascularized tissue, which is furthermore applied to investigate the heat Transfer in a realistic vascularized liver.

  • an efficient parallel numerical modeling of Bioheat Transfer in realistic tissue structure
    International Journal of Heat and Mass Transfer, 2016
    Co-Authors: Jing Liu
    Abstract:

    Abstract A fast and accurate numerical method of solving Bioheat Transfer problems is critical for many biomedical applications, such as efficient implementation of thermal therapy planning in a clinical setup, and evaluation of the thermal effects induced by specific energy absorption rate (SAR) from external electromagnetic field. This paper developed a parallel finite-difference method based on alternating direction explicit (ADE) scheme to solve three dimensional transient Bioheat equation for the realistic tissue structure. An optimized processing pipeline for accurate presentation of the irregular boundary condition was established to considerably reduce the staircase errors induced by cubic voxel. The voxels order aligned along diagonal direction was designed to allow fast parallel strategy for the lower and upper matrix solution involved in ADE scheme for irregular tissue. The test cases including a real head model have indicated that the developed method can support large time step and cubic voxel approximation of irregular interface and boundary, and also produce significant parallel efficiency.

  • an effective finite difference method for simulation of Bioheat Transfer in irregular tissues
    Journal of Heat Transfer-transactions of The Asme, 2013
    Co-Authors: Xu Xue, Jing Liu
    Abstract:

    A three-dimensional (3D) simulation of Bioheat Transfer is crucial to analyze the physiological processes and evaluate many therapeutic/diagnostic practices spanning from high to low temperature medicine. In this paper we develop an efficient numerical scheme for solving 3D transient Bioheat Transfer equations based on the alternating direction implicit finite-difference method (ADI-FDM). An algorithm is proposed to deal with the boundary condition for irregular domain which could capture accurately the complex boundary and reduce considerably the staircase effects. Furthermore, the local adaptive mesh technology is introduced to improve the computational accuracy for irregular boundary and the domains with large temperature gradient. The detailed modification to ADI-FDM is given to accommodate such special grid structure, in particular. Combination of adaptive-mesh technology and ADI-FDM could significantly improve the computational accuracy and decrease the computational cost. Extensive results of numerical experiments demonstrate that the algorithm developed in the current work is very effective to predict the temperature distribution during hyperthermia and cryosurgery. This work may play an important role in developing a computational planning tool for hyperthermia and cryosurgery in the near future. [DOI: 10.1115/1.4024064]

  • analytical solutions to 3 d Bioheat Transfer problems with or without phase change
    2012
    Co-Authors: Zhongshan Deng, Jing Liu
    Abstract:

    Theoretical analysis on the Bioheat Transfer process has been an extremely important issue in a wide variety of bioengineering situations such as cancer hyperthermia, burn injury evaluation, brain hypothermia, disease diagnostics, thermal comfort analysis, cryosurgery and cryopreservation etc. In this chapter, the theoretical strategies towards exactly solving the three-dimensional (3-D) Bioheat Transfer problems for both cases with and without phase change were systematically illustrated based on the authors’ previous works. Typical closed form analytical solutions to the hyperthermia Bioheat Transfer problems with space or transient heating on skin surface or inside biological bodies were summarized. In addition, exact solutions to the 3-D temperature transients of tissues under various phase change processes such as cryopreservation of biomaterials or cryosurgery of living tissues subject to freezing by a single or multiple cryoprobes were also outlined. Such solution is comprehensive enough by taking full account of many different factors such as generalized initial and boundary conditions, blood perfusion heat Transfer, volumetric heating of hyperthermia apparatus or heat sink of cryoprobes etc. For illustrating the applications of the present methods, part of the solutions were adopted to analyze the selected Bioheat Transfer problems. The versatility of these theoretical approaches to tackle more complex issues was also discussed. The obtained solutions are expected to serve as the basic foundation for theoretically analyzing Bioheat Transfer problems.

  • Bioheat Transfer model
    Wiley Encyclopedia of Biomedical Engineering, 2006
    Co-Authors: Jing Liu
    Abstract:

    Bioheat Transfer models have significant applications in a wide variety of clinical, basic, and environmental sciences. In particular, understanding the heat Transfer in biological tissues is a necessity for many therapeutic practices involving either raising or lowering temperature such as cancer hyperthermia, burn injury, brain hypothermia resuscitation, disease diagnostics, thermal comfort analysis, cryosurgery and cryopreservation, and so on. In this section, aiming to provide a fundamental background for theoretically tackling the above bioengineering issues, an overview on the most basic Bioheat Transfer model, its extended forms as well as typical applications under various high- or low-temperature situations was summarized. Meanwhile, solutions either analytical or numerical to the Bioheat Transfer model with or without phase change and particularities for choosing the model parameters were illustrated. Some possible extensions of the classic Bioheat Transfer model were also discussed. Keywords: Bioheat Transfer; hyperthermia therapy; burn injury; brain cooling; disease diagnostics; thermal comfort; cryosurgery; cryopreservation; phase change; numerical calculation