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Zambe JIC, Simo E, Kuicheu DK, Fono Fotso PR, Abdel HS. Therapeutic processes for eradicating cancerous or benign tumours by laser beams using the excitonic approach of peptide groups. Laser Ther 2022. [DOI: 10.4081/ltj.2022.297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
The aim of the present study was to develop a protocol for the treatment of cancerous or benign tumours making use of laser rays, also demonstrating that the destruction process remains exclusively confined in the defective organ. Thermal effects of lasers on biological tissue have been elucidated using vibrational excitations approach of peptide groups (PGs). It was proposed a Hamiltonian which integrate excitations induced by laser pulses and it was shown that the system is governed by a nonlinear equation with strong nonlinearity. It was also exactly described what happens in polypeptide chain once the unwanted organ is irradiated by the Neodymium-doped yttrium aluminium garnet, chosen as incident laser. It was shown that, the advent of incident laser beams contributes to a sudden reinforcement of the vibrational excitations of PGs frequencies and amplitudes. It was also demonstrated that the heating process leads to transverse and longitudinal deformation of the polypeptide chain and these sudden changes lead to the denaturation and subsequently to the destruction of the bulky organ. The drawn curves make it possible to estimate the spatial expansion of the denaturation, in order to effectively control the spread of the heat. Laser irradiation leads to a drastic increase in the vibration amplitudes of the PGs and subsequently results in the destruction of the undesirable tissue. An appropriate choice of the laser can make it possible to circumscribe the destruction only in the defective zone and to protect healthy cells.
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Eltayeb IA, Hughes DW, Proctor MRE. The convective instability of a Maxwell-Cattaneo fluid in the presence of a vertical magnetic field. Proc Math Phys Eng Sci 2020; 476:20200494. [PMID: 33071592 PMCID: PMC7544336 DOI: 10.1098/rspa.2020.0494] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 09/02/2020] [Indexed: 11/12/2022] Open
Abstract
We study the instability of a Bénard layer subject to a vertical uniform magnetic field, in which the fluid obeys the Maxwell-Cattaneo (MC) heat flux-temperature relation. We extend the work of Bissell (Proc. R. Soc. A 472, 20160649 (doi:10.1098/rspa.2016.0649)) to non-zero values of the magnetic Prandtl number p m . With non-zero p m , the order of the dispersion relation is increased, leading to considerably richer behaviour. An asymptotic analysis at large values of the Chandrasekhar number Q confirms that the MC effect becomes important when C Q 1/2 is O(1), where C is the MC number. In this regime, we derive a scaled system that is independent of Q. When CQ 1/2 is large, the results are consistent with those derived from the governing equations in the limit of Prandtl number p → ∞ with p m finite; here we identify a new mode of instability, which is due neither to inertial nor induction effects. In the large p m regime, we show how a transition can occur between oscillatory modes of different horizontal scale. For Q ≫ 1 and small values of p, we show that the critical Rayleigh number is non-monotonic in p provided that C > 1/6. While the analysis of this paper is performed for stress-free boundaries, it can be shown that other types of mechanical boundary conditions give the same leading-order results.
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Affiliation(s)
- I. A. Eltayeb
- Department of Mathematical and Physical Sciences, College of Arts and Science, University of Nizwa, Birkat Al Mouz, Nizwa 616, Oman
| | - D. W. Hughes
- School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
| | - M. R. E. Proctor
- DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
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Kabiri A, Talaee MR. Thermal field and tissue damage analysis of moving laser in cancer thermal therapy. Lasers Med Sci 2020; 36:583-597. [PMID: 32594347 DOI: 10.1007/s10103-020-03070-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2020] [Accepted: 06/11/2020] [Indexed: 10/24/2022]
Abstract
In this paper, a closed-form analytical solution of hyperbolic Pennes bioheat equation is obtained for spatial evolution of temperature distributions during moving laser thermotherapy of the skin and kidney tissues. The three-dimensional cubic homogeneous perfused biological tissue is adopted as a media and the Gaussian distributed function in surface and exponentially distributed in depth is used for modeling of laser moving heat source. The solution procedure is Eigen value method which leads to a closed form solution. The effect of moving velocity, perfusion rate, laser intensity, absorption and scattering coefficients, and thermal relaxation time on temperature profiles and tissue thermal damage are investigated. Results are illustrated that the moving velocity and the perfusion rate of the tissues are the main important parameters in produced temperatures under moving heat source. The higher perfusion rate of kidney compared with skin may lead to lower induced temperature amplitude in moving path of laser due to the convective role of the perfusion term. Furthermore, the analytical solution can be a powerful tool for analysis and optimization of practical treatment in the clinical setting and laser procedure therapeutic applications and can be used for verification of other numerical heating models.
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Affiliation(s)
- Ali Kabiri
- School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran
| | - Mohammad Reza Talaee
- School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran.
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Computational study on constant and sinusoidal heating of skin tissue using radial basis functions. Comput Biol Med 2020; 121:103808. [DOI: 10.1016/j.compbiomed.2020.103808] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Revised: 05/01/2020] [Accepted: 05/02/2020] [Indexed: 10/24/2022]
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Two-dimensional closed-form model for temperature in living tissues for hyperthermia treatments. J Therm Biol 2017; 71:41-51. [PMID: 29301699 DOI: 10.1016/j.jtherbio.2017.10.012] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2017] [Revised: 10/20/2017] [Accepted: 10/23/2017] [Indexed: 10/18/2022]
Abstract
This research article determines an exact analytical expression for 2-D thermal field in single layer living tissues under a therapeutic condition by means of Fourier and non-Fourier heat transfer approaches. An actual spatially dependent initial condition has been adopted to analyze the heat propagation in tissues. The exact analytical determination for this actual initial condition for temperature may be difficult. However, in this study, an approximate analytical method has newly been established for an appropriate initial condition. With this initial expression, an exact temperature distribution for 2-D heat conduction in plane co-ordinates has been investigated for the predefined therapeutic boundary condition to have knowledge for practical aspects of the thermal therapy. Laplace Transform Method (LTM) in conjunction with the Inversion Theorem is used for the analytical solution treatment. We have utilized both Pennes' bioheat equation (PBHE) and thermal wave model of bioheat equation (TWMBHE) for the analysis. The influence of thermo-biological behavior on 2-D heat conduction in tissues has been studied with the variation of several dependable parameters in relation to the Hyperthermia treatment protocol in a moderate temperature range (42-45°C). The result in the present study has been evidenced for the biological heat transfer for the enforcement of different circumstances and also has been validated with the published value where the maximum temperature deviation of 2.6% has been recorded. We conclude that the temperature curve for TWMBHE model shows a higher waveform nature for low thermal relaxation time and this wavy nature gradually diminishes with an increase in relaxation time. The maximum peak temperature attains 46.3°C for the relaxation time = 2s and with the increase in the relaxation time the peak temperature gradually falls. The impact of blood perfusion rate on the relaxation time has also been established in this paper.
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Noroozi MJ, Goodarzi M. Nonlinear analysis of a non-Fourier heat conduction problem in a living tissue heated by laser source. INT J BIOMATH 2017. [DOI: 10.1142/s1793524517501078] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The effect of laser, as a heat source, on a one-dimensional finite living tissue was studied in this paper. The dual phase lagging (DPL) non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent, resulting in a nonlinear equation. The obtained equations were solved using the approximate-analytical Adomian decomposition method (ADM). It was concluded that the nonlinear analysis was important in non-Fourier heat conduction problems. Moreover, a good agreement between the present nonlinear model and experimental result was obtained.
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Affiliation(s)
| | - Majid Goodarzi
- Faculty of Engineering, University of Ayatollah Ozma Boroujerdi, Boroujerd, Iran
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Nonlinear Analysis of a One-Dimensional Non-Fourier Heat Conduction Problem. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES 2017. [DOI: 10.1007/s40010-017-0379-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Abstract
Motivated by the need to understand better the dynamics of non-Fourier fluids, we examine the linear and weakly nonlinear stabilities of a horizontal layer of fluid obeying the Maxwell–Cattaneo relationship of heat flux and temperature using three different forms of the time derivative of the heat flux. Linear stability mode regime diagrams in the parameter plane have been established and used to summarize the linear instabilities. The energy balance of the system is used to identify the mechanism by which the Maxwell–Cattaneo effect (i) introduces overstability, (ii) leads to preferred stationary modes with the critical Rayleigh and wavelengths either both increasing or both decreasing, (iii) gives rise to instabilities in a layer heated from above, and (iv) enhances heat transfer. A formal weakly nonlinear analysis leads to evolution equations for the amplitudes of linear instability modes. It is shown that the amplitude of the stationary mode obeys an equation of the Landau–Stuart type. The two equally excitable overstable modes obey two equations of the same type coupled by an interaction term. The evolution of the different amplitudes leads to supercritical stability, supercritical instability or subcritical instability depending on the model and parameter values. The results are presented in regime diagrams.
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Dutta J, Kundu B. A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments. J Therm Biol 2017; 66:33-48. [DOI: 10.1016/j.jtherbio.2017.03.015] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2017] [Revised: 03/03/2017] [Accepted: 03/27/2017] [Indexed: 12/27/2022]
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kashcooli M, Salimpour MR, Shirani E. Heat transfer analysis of skin during thermal therapy using thermal wave equation. J Therm Biol 2017; 64:7-18. [DOI: 10.1016/j.jtherbio.2016.12.007] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2016] [Revised: 12/15/2016] [Accepted: 12/15/2016] [Indexed: 11/28/2022]
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Kumar D, Rai K. A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach. J Therm Biol 2016; 62:170-180. [DOI: 10.1016/j.jtherbio.2016.06.020] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2015] [Accepted: 06/29/2016] [Indexed: 10/21/2022]
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Bissell JJ. Thermal convection in a magnetized conducting fluid with the Cattaneo-Christov heat-flow model. Proc Math Phys Eng Sci 2016; 472:20160649. [PMID: 27956886 PMCID: PMC5134317 DOI: 10.1098/rspa.2016.0649] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Accepted: 10/17/2016] [Indexed: 11/12/2022] Open
Abstract
By substituting the Cattaneo-Christov heat-flow model for the more usual parabolic Fourier law, we consider the impact of hyperbolic heat-flow effects on thermal convection in the classic problem of a magnetized conducting fluid layer heated from below. For stationary convection, the system is equivalent to that studied by Chandrasekhar (Hydrodynamic and Hydromagnetic Stability, 1961), and with free boundary conditions we recover the classical critical Rayleigh number [Formula: see text] which exhibits inhibition of convection by the field according to [Formula: see text] as [Formula: see text], where Q is the Chandrasekhar number. However, for oscillatory convection we find that the critical Rayleigh number [Formula: see text] is given by a more complicated function of the thermal Prandtl number [Formula: see text], magnetic Prandtl number [Formula: see text] and Cattaneo number C. To elucidate features of this dependence, we neglect [Formula: see text] (in which case overstability would be classically forbidden), and thereby obtain an expression for the Rayleigh number that is far less strongly inhibited by the field, with limiting behaviour [Formula: see text], as [Formula: see text]. One consequence of this weaker dependence is that onset of instability occurs as overstability provided C exceeds a threshold value CT(Q); indeed, crucially we show that when Q is large, [Formula: see text], meaning that oscillatory modes are preferred even when C itself is small. Similar behaviour is demonstrated in the case of fixed boundaries by means of a novel numerical solution.
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Affiliation(s)
- J. J. Bissell
- Department of Physics, University of Bath, BA2 7AY Bath, UK
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A study on DPL model of heat transfer in bi-layer tissues during MFH treatment. Comput Biol Med 2016; 75:160-72. [DOI: 10.1016/j.compbiomed.2016.06.002] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2016] [Revised: 05/31/2016] [Accepted: 06/01/2016] [Indexed: 11/23/2022]
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Forghani P, Ahmadikia H, Karimipour A. Non-Fourier Boundary Conditions Effects on the Skin Tissue Temperature Response. ACTA ACUST UNITED AC 2015. [DOI: 10.1002/htj.21196] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- P. Forghani
- Department of Mechanical Engineering; Najafabad Branch; Islamic Azad University; Isfahan Iran
| | - H. Ahmadikia
- Department of Mechanical Engineering; University of Isfahan; Isfahan Iran
| | - A. Karimipour
- Department of Mechanical Engineering; Najafabad Branch; Islamic Azad University; Isfahan Iran
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Bissell JJ. On oscillatory convection with the Cattaneo-Christov hyperbolic heat-flow model. Proc Math Phys Eng Sci 2015; 471:20140845. [PMID: 25792960 PMCID: PMC4353040 DOI: 10.1098/rspa.2014.0845] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2014] [Accepted: 01/21/2015] [Indexed: 11/12/2022] Open
Abstract
Adoption of the hyperbolic Cattaneo-Christov heat-flow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection, Rc and RS respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value CT≥8/27π2≈0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number [Formula: see text], which-in contrast to the classical stationary scenario-can impact on oscillatory modes significantly owing to the non-zero frequency of convection. Numerical investigation indicates that the behaviour found analytically for free boundaries applies in a qualitatively similar fashion for fixed boundaries, while the threshold Cattaneo number CT is computed as a function of [Formula: see text] for both boundary regimes.
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Affiliation(s)
- J. J. Bissell
- Department of Mathematical Sciences, University of Durham, Durham City DH1 3LE, UK
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Barton MD, Trembly BS. Measurement of the anisotropic thermal conductivity of the porcine cornea. Exp Eye Res 2013; 115:216-23. [PMID: 23933570 DOI: 10.1016/j.exer.2013.07.029] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2013] [Revised: 06/28/2013] [Accepted: 07/29/2013] [Indexed: 11/19/2022]
Abstract
Accurate thermal models for the cornea of the eye support the development of thermal techniques for reshaping the cornea and other scientific purposes. Heat transfer in the cornea must be quantified accurately so that a thermal treatment does not destroy the endothelial layer, which cannot regenerate, and yet is responsible for maintaining corneal transparency. We developed a custom apparatus to measure the thermal conductivity of ex vivo porcine corneas perpendicular to the surface and applied a commercial apparatus to measure thermal conductivity parallel to the surface. We found that corneal thermal conductivity is 14% anisotropic at the normal state of corneal hydration. Small numbers of ex vivo feline and human corneas had a thermal conductivity perpendicular to the surface that was indistinguishable from the porcine corneas. Aqueous humor from ex vivo porcine, feline, and human eyes had a thermal conductivity nearly equal to that of water. Including the anisotropy of corneal thermal conductivity will improve the predictive power of thermal models of the eye.
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Affiliation(s)
- Michael D Barton
- Thayer School of Engineering, Dartmouth College, 14 Engineering Drive, Hanover, NH 03755, USA.
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Abstract
A model is proposed for thermohaline convection when the heat flux satisfies a relaxation time law rather than the classical Fourier one. Here, we adopt the recent law due to Christov. That a Cattaneo-like law would be relevant in thermohaline convection in star evolution was proposed in 1995 by Herrera and Falcón. They do not develop a detailed model which we do here. We find that with the Cattaneo–Christov law, there is a transition curve (depending on the salt concentration) such that for Cattaneo numbers greater than this transition, the nature of convection changes dramatically.
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Affiliation(s)
- B. Straughan
- Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK
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Rivera MJ, López Molina JA, Trujillo M, Romero-Garcia V, Berjano EJ. Analytical validation of COMSOL Multiphysics for theoretical models of Radiofrequency ablation including the Hyperbolic Bioheat transfer equation. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2010; 2010:3214-3217. [PMID: 21096815 DOI: 10.1109/iembs.2010.5627405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In this paper we outline our main findings about the differences between the use of the Bioheat Equation and the Hyperbolic Bioheat Equation in theoretical models for Radiofrequency (RF) ablation. At the moment, we have been working on the analytical approach to solve both equations, but more recently, we have considered numerical models based on the Finite Element Method (FEM). As a first step to use FEM, we conducted a comparative study between the temperature profiles obtained from the analytical solutions and those obtained from FEM. Regarding the differences between both methods, we obtain agreement in less than 5% of relative differences. Then FEM is a good alternative to model heating of biological tissues using BE and HBE in, for example, more complex and realistic geometries.
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Affiliation(s)
- Maria J Rivera
- Departamento de Matemática Aplicada, Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Spain.
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