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Analytical solution of unsteady one-dimensional bioheat transfer equation

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Chinese Science Bulletin 1995年第19期40卷 1663-1665页

作者：蔡睿贤 Institute of Engineering Thermophysics Chinese Academy of Sciences Beijing 100080 China

A basic bioheat transfer equation based upon porous medium model was derived by Wang et al. in 1993 to improve the Pennes equation in common use previously. A steady one-dimensional general analytical solution of this new equation was given by Wang et al. later under the condition of constant coefficients and rectangular coordinates. This analytical solution compared well with experimental data. In order to expand the understanding of the new equation, an unsteady one-dimensional particular analytical solution

关键词： bioheat transfer unsteady analytical solution.

Generalized time delay bioheat equation and preliminary analysis on its wave nature

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Chinese Science Bulletin 1997年第4期42卷 289-292页

作者： Liu, J Zhang, XX Wang, CC Lu, WQ Ren, ZP Thermal Engineering Department Tsinghua University Beijing China Physics Department Graduate School of Chinese Academy of Sciences Beijing China

As a new developing field, the science of bioheat transfer is making its fundamental propositions and theories much more complete and thus postulates new concepts based on the new discovery and knowledge. In this note... 详细信息

关键词： bioheat transfer time delay thermal wave.

Investigation of nonlinear temperature distribution in biological tissues by using bioheat transfer equation of Pennes’ type

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Natural Science 2010年第3期2卷 131-138页

作者： Ahmed Lakhssassi Emmanuel Kengne Hicham Semmaoui 不详

In this paper, a two level finite difference scheme of Crank-Nicholson type is constructed and used to numerically investigate nonlinear temperature distribution in biological tissues described by bioheat transfer equation of Pennes’ type. For the equation under consideration, the thermal conductivity is either depth-dependent or tem-perature-dependent, while blood perfusion is temperature-dependent. In both cases of depth- dependent and temperature-dependent thermal conductivity, it is shown that blood perfusion decreases the temperature of the living tissue. Our numerical simulations show that neither the localization nor the magnitude of peak tempera-ture is affected by surface temperature;however, the width of peak temperature increases with surface temperature.

关键词： bioheat Transfer Equation of Pennes Type Pennes’ bioheat Transfer Equation Modified Crank-Nicholson Method Two-Level Finite Difference Scheme

Numerical solution of generalized DPL model using wavelet method during thermal therapy applications

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International Journal of Biomathematics 2019年第3期12卷 169-190页

作者： P.Kumar K.N.Rai Department of Mathematics H. R. College Amnour (A Constituent Unit of J. P. University) Saran-841401 India Department of Mathematical Sciences IIT (BHU) Varanasi India

In this paper, generalized dual-phase-lag (DPL) model has been studied for the numerical analysis of spatial variation of temperature within living biological tissues during thermal therapy applications. A new hybrid numerical scheme based on finite difference scheme and Chebyshev wavelet Galerkin method are used to solve the generalized DPL model with constant heat flux boundary condition. Multi-resolution and multi-scale computational property of Chebyshev wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. Our study demonstrates that due to presence of coupling factor (convection–perfusion), generalized DPL model predicts lower temperature than classical DPL and Pennes model at the tumor position. Higher values of phase lag times results in lower temperature at the tumor position. But, in case of variation of phase lag time due to temperature gradient, the nature of temperature profile also depends on the spatial coordinate. The effect of the blood temperature, porosity and interfacial convective heat transfer on temperature distribution has been investigated. It is found that larger values of porosity and interfacial convective heat transfer results in lower temperature at the tumor position. Also, both porosity and interfacial convective heat transfer are pronounced more at higher values. The whole analysis is presented in dimensionless form.

关键词： Chebyshev wavelet Galerkin method Generalized DPL model Nonequilibrium bioheat transfer Thermal therapy

Experimental Validation and Simulation of Fourier and Non-Fourier Heat Transfer Equation during Laser Nano-Phototherapy of Lung Cancer Cells: An <i>in Vitro</i>Assay

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Journal of Modern Physics 2014年第18期5卷 2125-2141页

作者： Mohammad E. Khosroshahi Lida Ghazanfari Payam Khoshkenar Center for Advanced Diffusion-Wave Technologies (CADIFT) Department of Mechanical and Industrial Engineering University of Toronto Toronto Canada Laser and Nanobiophotonics Laboratory Biomaterial Group Faculty of Biomedical Engineering Amirkabir University of Technology Tehran Iran Max Planck Institute for the Science of Light Erlangen Germany Department of Biomedical Engineering College of Engineering & Science Louisiana Technology University Ruston USA

This paper investigated the numerical scheme extended to solve the hyperbolic non-Fourier form of bioheat transfer equation and the experimental trials were conducted to validate the numerical simulation. MNPs were prepared via co-precipitation and modified with a silica layer. The amino modified Fe3O4/SiO2 nanoshells were covered with gold colloids producing nanoshells of Fe3O4/SiO2/Au (MNSs). In vitro assays were performed to determine the effect of apoptosis of QU-DB lung cancer cells based on the cells morphology changes. Cell damage was reduced by decreasing the power density of laser. Also, a larger area of damage on cell culture plates was observed at longer intervals of laser irradiation. The effect of nanoshell concentration and irradiation rate has been evaluated. A maximum temperature rise of 6°C was achieved at 184 W/cm2 and concentration of 0.01 mg/ml. The experiment confirmed a hyperbolic behaviour of thermal propagation. The results revealed that the three-dimensional implementation of bioheat equation is likely to be more accurate than the two-dimensional study.

关键词： bioheat Equation Gold Nanoshells Laser Hyperthermia Lung Cancer Cells Surface Plasmon Resonance

FEM Model of the Temperature Distribution in the Brain during Enhanced Infrared Neural Stimulation Using Nanoparticles

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Journal of Applied Mathematics and Physics 2019年第2期7卷 381-393页

作者： Rui Zhou Haoling Chen Zongxia Mou Key Laboratory of Biomaterials of Guangdong Higher Education Institutes Institution of Biomedical Engineering Jinan University Guangzhou China

Objectives: Enhanced infrared neural stimulation (EINS) using nanoparticles is a new research hotspot. In this paper, the numerical modeling of the interaction between a light source and brain tissue during EINS is studied. Materials and Methods: This model is built with the finite element method (FEM) to mimic the propagation and absorption of light in brain tissue with EINS. Only the thermal change is considered in this model since the photothermal effect is the main mechanism of EINS. The temperature response of brain irradiation is governed by the extensively used Pennes’ bio-heat equation in a multilayer model. Results: The temperature distribution in the brain under laser irradiation is determined. And the relationships between the brain tissue temperature and the three factors (the laser pulse time, the laser energy and the enhanced absorption coefficient of the tissue caused by the nanoparticles) are analyzed. Conclusions: The results indicate that the brain tissue is easier to warm up with the enhancement of nanoparticles and parameters of the laser can alter the temperature increase of the brain tissue. These findings offer a theoretical basis for future animal experiments.

关键词： Enhanced Infrared Neural Stimulation Pennes bioheat Equation Finite Element Method Temperature Distribution Nanoparticles