A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment

Magnetic Nanoparticles: A Comprehensive Review from Synthesis to Biomedical Frontiers

Nanotechnology has opened new doors of exploration, particularly in materials science and healthcare. Magnetic nanoparticles (MNP), the tiny magnets, because of their various properties, have the potential to bring about radical changes in the field of medicine. The distinctive surface chemistry, nontoxicity, biocompatibility, and, in particular, the inducible magnetic moment of magnetic materials has attracted a great deal of interest in morphological structures from a variety of scientific domains. This review presents a concise overview of MNPs and their crucial properties and synthesis routes. It also aims to highlight the continuous synthesis methods available for MNP production. In recent years, the use of computational methods for understanding the behavior of nanoparticles has been on the rise. Thus, we also discuss the numerical models developed to understand how magnetic nanoparticles can be used in magnetic hyperthermia and targeting the Circle of Wilis. With the increasing use of MNPs in biomedical applications, it becomes necessary to understand the mechanisms of toxicity, which are elucidated in this review. The review focuses on the biomedical applications of MNPs in drug delivery, theranostics, and MRI contrasting agents. We anticipate that this article will broaden the perspective on magnetic nanoparticles and help to understand their functionality and applicability better.

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy

The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods.

Advances in screening hyperthermic nanomedicines in 3D tumor models

Hyperthermic nanomedicines are particularly relevant for tackling human cancer, providing a valuable alternative to conventional therapeutics. The early-stage preclinical performance evaluation of such anti-cancer treatments is conventionally performed in flat 2D cell cultures that do not mimic the volumetric heat transfer occurring in human tumors. Recently, improvements in bioengineered 3D in vitro models have unlocked the opportunity to recapitulate major tumor microenvironment hallmarks and generate highly informative readouts that can contribute to accelerating the discovery and validation of efficient hyperthermic treatments. Leveraging on this, herein we aim to showcase the potential of engineered physiomimetic 3D tumor models for evaluating the preclinical efficacy of hyperthermic nanomedicines, featuring the main advantages and design considerations under diverse testing scenarios. The most recent applications of 3D tumor models for screening photo- and/or magnetic nanomedicines will be discussed, either as standalone systems or in combinatorial approaches with other anti-cancer therapeutics. We envision that breakthroughs toward developing multi-functional 3D platforms for hyperthermia onset and follow-up will contribute to a more expedited discovery of top-performing hyperthermic therapies in a preclinical setting before their in vivo screening.

Generalized thermomechanical interaction in two-dimensional skin tissue using eigenvalues approach

The aim of this work is to analytically study the thermo-mechanical response of two-dimensional skin tissues when subjected to instantaneous heating. A complete understanding of the heat transfer process and the associated thermal and mechanical effects on the patient's skin tissues is critical to ensuring the effective applications of thermal therapy techniques and procedures. The surface boundary of the half-space undergoes a heat flux characterized by an exponentially decaying pulse, while maintaining a condition of zero traction. The utilization of Laplace and Fourier transformations is employed, and the resulting formulations are then applied to human tissues undergoing regional hyperthermia treatment for cancer therapy. To perform the inversion process for Laplace and Fourier transforms, a numerical programming method based on Stehfest numerical inverse method is employed. The findings demonstrate that blood perfusion rate and thermal relaxation time significantly influence all the analyzed distributions. Numerical findings suggest that thermo-mechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

Influence of thermal relaxation time on thermomechanical interactions in biological tissue during hyperthermia treatment

This study presents an analytical analysis of thermo-mechanical interactions within living tissues using a generalized biothermoelastic model with one thermal relaxation time. Utilizing Laplace transforms and associated techniques, we investigate the response of living tissue to a pulse boundary heat flux that decays exponentially on a traction-free surface. Through detailed graphical illustrations, we elucidate the influence of key parameters such as thermal relaxation time, blood perfusion rate, and the characteristic time of the pulsing heat flux on temperature distribution, displacement, and thermal strain. Our results are presented through comprehensive graphical representations. Furthermore, a parametric analysis is conducted to guide the selection of optimal design factors, enhancing the accuracy of hyperthermia treatments.

Numerical simulation of burn injuries with temperature-dependent thermal conductivity and metabolism under different surface heat sources

In the present paper, the phenomena of heat transport inside human forearm tissue are studied through a one-dimensional nonlinear bioheat transfer model under the influence of various boundary and interface conditions. In this study, we considered temperature-dependent thermal conductivity and metabolic heat to predict temperature distribution inside the forearm tissue. We have studied the temperature distribution inside inner tissue and bone because it has been found that burn injuries are mostly affected by layer thickness. The temperature distribution inside human forearm tissue is analyzed using the finite difference and bvp4c numerical techniques. To examine the accuracy of present numerical code, we compare the obtained numerical result with the exact analytical result in a specific case and find an excellent agreement with the exact results. We also validated our present numerical code with a hybrid scheme based on Runge-Kutta (4,5) and finite difference technique and found it in good compliance. From the obtained results, we observed that the homogeneous heat flux has a greater impact on the temperature at the outer surface of the skin, but the sinusoidal heat flux has a greater impact on the temperature of the subcutaneous layer and inner tissue. It is found that there is no burn injury in the first type of heat source (Tw=44°C), but it may occur in the second and third types of heat sources. It has been observed that by raising the blood perfusion rate and reducing the values of reference metabolic heat, coefficient of thermal conductivity, and heat fluxes, we can manage and reduce burn injuries and achieve hyperthermia temperature.

Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma

Hyperthermia therapy is now being used to treat cancer. However, understanding the pattern of temperature increase in biological tissues during hyperthermia treatment is essential. In recent years, many physicians and engineers have studied the use of computational and mathematical models of heat transfer in biological systems. The rapid progress in computing technology has intrigued many researchers. Many medical procedures also use engineering techniques and mathematical modeling to ensure their safety and assess the risks involved. One such model is the modified Pennes bioheat conduction equation. This paper provides an analytical solution to the modified Pennes bioheat conduction equation with a single relaxation time by incorporating in it the (MGT) equation. The suggested model examines heat transport in biological tissues as forming an infinite concentric spherical region during magnetic fluid hyperthermia. To investigate thermal reactions caused by temperature shock, specifically the influence of heat generation through heat treatment on a skin tumor [AEGP9], the Laplace transformation, and numerical inverse transformation methods are used. This model was able to explain the effects of different therapeutic approaches such as cryotherapy sessions, laser therapy, and physical occurrences, transfer, metabolism support, and blood perfusion. Comparison of the numerical results of the suggested model with those in the literature confirmed the validity of the model's numerical results.

Finite Element Analysis of Nonlinear Bioheat Model in Skin Tissue Due to External Thermal Sources

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.

Analysis of thermal injuries using classical Fourier and DPL models for multi-layer of skin under different boundary conditions

In this paper, the temperature distribution in the multi-layer of the skin is studied when the skin surface is subjected to most generalized boundary condition. Our skin model consists of three layers known as the epidermis, dermis, and subcutaneous layers. All layers of skin are assumed to be connected with point of interface condition and taking the barrier in between each of the two layers by symmetric flux condition and analyzing each layer separately. The classical Fourier and non-Fourier (DPL) models are extended to analyze the behavior of heat transfer in the multi-layer of the skin. The Laplace transform technique is used to derive analytical solutions for the multi-layer of skin models. The effects of the variability of different parameters such as relaxation time, layer thickness, and different types of boundary conditions on the behavior of temperature distribution in the multi-layer of skin are analyzed and discussed in detail. All the effects are shown graphically. It has been observed that during temperature distribution in the multi-layer of skin, the measurement of skin damage is less on the DPL model ([Formula: see text]) in comparison to the classical Fourier model.

A Fibonacci Wavelet Method for Solving Dual-Phase-Lag Heat Transfer Model in Multi-Layer Skin Tissue during Hyperthermia Treatment

In this article, a novel wavelet collocation method based on Fibonacci wavelets is proposed to solve the dual-phase-lag (DPL) bioheat transfer model in multilayer skin tissues during hyperthermia treatment. Firstly, the Fibonacci polynomials and the corresponding wavelets along with their fundamental properties are briefly studied. Secondly, the operational matrices of integration for the Fibonacci wavelets are built by following the celebrated approach of Chen and Haiso. Thirdly, the proposed method is utilized to reduce the underlying DPL model into a system of algebraic equations, which has been solved using the Newton iteration method. Towards the culmination, the effect of different parameters including the tissue-wall temperature, time-lag due to heat flux, time-lag due to temperature gradient, blood perfusion, metabolic heat generation, heat loss due to diffusion of water, and boundary conditions of various kinds on multilayer skin tissues during hyperthermia treatment are briefly presented and all the outcomes are portrayed graphically.

Comparative study of heat transfer and thermal damage assessment models for hyperthermia treatment

Appropriate heating of the tumor can ablate tumor cells with minimal damage to healthy tissue and low side effects to the patient. Therefore, it is important to estimate power dissipation requirement and predict thermal damage in tumor before hyperthermia treatment. This work applied a mathematical model on heat transfer in two-layered spherical tissue to predict the temperature profile within hyperthermia domain. The present bioheat transfer problem was analyzed based on the Pennes equation, the thermal wave and dual-phase lag modes in order to explore the effect of analysis mode on the power dissipation requirement. The Arrenius equation, the modified thermal damage model with regeneration term, and the equivalent thermal dose equation were used to evaluate the thermal damage and discuss their effects on thermal damage prediction. The computation results show that the model of bioheat transfer and the non-Fourier effect significantly affects the power dissipation requirement. The damage parameter value predicted by the modified thermal damage model with regeneration term seems to have a limit value of Ω = 1. The results imply that the regeneration of biological tissue can prevent the tissue from thermal damage, the equivalent thermal dose equation is more related to heating time, and the Arrenius equation is more related to heating temperature.

A study of fractional order dual-phase-lag bioheat transfer model

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.

A review on numerical modeling for magnetic nanoparticle hyperthermia: Progress and challenges

Recent progress in nanotechnology has advanced the development of magnetic nanoparticle (MNP) hyperthermia as a potential therapeutic platform for treating diseases. Due to the challenges in reliably predicting the spatiotemporal distribution of temperature in the living tissue during the therapy of MNP hyperthermia, critical for ensuring the safety as well as efficacy of the therapy, the development of effective and reliable numerical models is warranted. This article provides a comprehensive review on the various mathematical methods for determining specific loss power (SLP), a parameter used to quantify the heat generation capability of MNPs, as well as bio-heat models for predicting heat transfer phenomena and temperature distribution in living tissue upon the application of MNP hyperthermia. This article also discusses potential applications of the bio-heat models of MNP hyperthermia for therapeutic purposes, particularly for cancer treatment, along with their limitations that could be overcome.

A Study on Non-Linear DPL Model for Describing Heat Transfer in Skin Tissue during Hyperthermia Treatment

The article studies the simulation-based mathematical modeling of bioheat transfer under the Dirichlet boundary condition. We used complex non-linear dual-phase-lag bioheat transfer (DPLBHT) for analyzing the temperature distribution in skin tissues during hyperthermia treatment of infected cells. The perfusion term, metabolic heat source, and external heat source were the three parts of the volumetric heat source that were used in the model. The non-linear DPLBHT model predicted a more accurate temperature within skin tissues. The finite element Runge–Kutta (4,5) (FERK (4,5)) method, which was based on two techniques, finite difference and Runge–Kutta (4,5), was applied for calculating the result in the case of our typical non-linear problem. The paper studies and presents the non-dimensional unit. Thermal damage of normal tissue was observed near zero during hyperthermia treatment. The effects of the non-dimensional time, non-dimensional space coordinate, location parameter, regional parameter, relaxation and thermalization time, metabolic heat source, associated metabolic heat source parameter, perfusion rate, associated perfusion heat source parameter, and external heat source coefficient on the dimensionless temperature profile were studied in detail during the hyperthermia treatment process.

Thermal ablation of biological tissues in disease treatment: A review of computational models and future directions

Percutaneous thermal ablation has proven to be an effective modality for treating both benign and malignant tumours in various tissues. Among these modalities, radiofrequency ablation (RFA) is the most promising and widely adopted approach that has been extensively studied in the past decades. Microwave ablation (MWA) is a newly emerging modality that is gaining rapid momentum due to its capability of inducing rapid heating and attaining larger ablation volumes, and its lesser susceptibility to the heat sink effects as compared to RFA. Although the goal of both these therapies is to attain cell death in the target tissue by virtue of heating above 50°C, their underlying mechanism of action and principles greatly differs. Computational modelling is a powerful tool for studying the effect of electromagnetic interactions within the biological tissues and predicting the treatment outcomes during thermal ablative therapies. Such a priori estimation can assist the clinical practitioners during treatment planning with the goal of attaining successful tumour destruction and preservation of the surrounding healthy tissue and critical structures. This review provides current state-of-the-art developments and associated challenges in the computational modelling of thermal ablative techniques, viz., RFA and MWA, as well as touch upon several promising avenues in the modelling of laser ablation, nanoparticles assisted magnetic hyperthermia and non-invasive RFA. The application of RFA in pain relief has been extensively reviewed from modelling point of view. Additionally, future directions have also been provided to improve these models for their successful translation and integration into the hospital work flow.

Nonlocal heat conduction approach in a bi-layer tissue during magnetic fluid hyperthermia with dual phase lag model

In this work, a nonlocal dual-phase-lag (NL DPL) model is introduced to accommodate the effects of thermomass and size-dependent thermophysical properties at nanoscale heat transport. Heat transfer at nanoscale is essentially nonlocal and quite different from that at the micro- or macro scale. To illustrate the nonlocal effect, a bi-layered structure is considered during magnetic fluid hyperthermia (MFH) treatment which is used successfully in prostate, liver, and breast tumors and the effect of size-dependent characteristic lengths is discussed in tumor and normal region of tissue. The problem is solved by using the finite difference scheme in space coordinate and Legendre wavelet Galerkin approach in time coordinate with the Dirichlet, Neumann and Robin boundary conditions. The effect of boundary conditions, characteristic lengths, phase lag parameters and nanomaterial parameters is discussed in tumor and healthy tissue domain and the results are presented graphically. This study is expected to be helpful for modeling of bioheat transfer equation at nano-scale, and may be beneficial to design nano-sized and multi-layered devices for heat transfer.

A study of heat transfer during cryosurgery of lung cancer

In this study, a mathematical model describing two-dimensional bio-heat transfer during cryosurgery of lung cancer is developed. The lung tissue is cooled by a cryoprobe by imposing its surface at a constant temperature or a constant heat flux or a constant heat transfer coefficient. The freezing starts and the domain is distributed into three stages namely: unfrozen, mushy and frozen regions. In stage I where the only unfrozen region is formed, our problem is an initial-boundary value problem of the hyperbolic partial differential equation. In stage II where mushy and unfrozen regions are formed, our problem is a moving boundary value problem of parabolic partial differential equations and in stage III where frozen, mushy, and unfrozen regions are formed, our problem is a moving boundary value problem of parabolic partial differential equations. The solution consists of the three-step procedure: (i) transformation of problem in non-dimensional form, (ii) by using finite differences, the problem converted into ordinary matrix differential equation and moving boundary problem of ordinary matrix differential equations, (iii) applying Legendre wavelet Galerkin method the problem is transferred into the generalized system of Sylvester equations which are solved by applying Bartels-Stewart algorithm of generalized inverse. The complete analysis is presented in the non-dimensional form. The consequence of the imposition of boundary conditions on moving layer thickness and temperature distribution are studied in detail. The consequence of Stefan number, Kirchoff number and Biot number on moving layer thickness are also studied in specific.

Risk of breast cancer based on thermal tomography characteristics

Background

There is no uniform standard for the diagnosis of breast lesions by thermal tomography (TT). This study aimed to widely analyse the predictive value of TT in patients with breast cancer and establish a uniform standard for the diagnosis of breast lesions.

Methods

We retrospectively analysed data from women who suffered from non-inflammatory unilateral single breast lesion and underwent TT from January 2014 to July 2016. Changes in TT parameters were correlated with the pathologic diagnosis, and its predictive value was assessed.

Results

A total of 407 patients underwent TT examinations during the study period, including 196 subsequently diagnosed with breast cancer. Several characteristics were found to be significantly correlated with breast cancer: age ≥60 years [odds ratio (OR) =109.296, P<0.001], age ≥35 and <60 years (OR =25.720, P<0.001), q-r curve as an angle of 30°–45° (OR =14.895, P<0.001), ΔTs (surface temperature difference between the neoplastic side and the healthy side) ≥0.65 °C (OR =4.129, P<0.001), ΔTn (nipple temperature difference between the neoplastic side and the healthy side) ≥0.45 °C (OR =2.683, P=0.006), isotherm asymmetry (OR =2.297, P=0.035), and vascular plentiful (OR =3.333, P=0.004). Q value as a novel predictive indicator based on the multiple predictor modelling improved the diagnostic rate for breast cancer, and the accuracy in this study was up to 86.7%.

Conclusions

Age, q-r curve, ΔTs, ΔTn, isotherm, and vascular features were independent predictors of breast cancer. Q value could be used to assess the risk of breast cancer as an additional diagnostic tool for breast cancer screening and diagnosis.

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

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.

A study of cryosurgery of lung cancer using Modified Legendre wavelet Galerkin method

In this paper, we have developed a new mathematical model describing bio-heat transfer during cryosurgery of lung cancer. The lung tissue cooled by a flat probe whose temperature decreases linearly with time. The freezing process occurs in three stages and the whole region is divided into solid, mushy and liquid region. The heat released in the mushy region is considered as discontinuous heat generation. The model is an initial-boundary value problem of the hyperbolic partial differential equation in stage 1 and moving boundary value problem of parabolic partial differential equations in stage 2 and 3. The method of the solution consists of four-step procedure as transformation of problem in dimensionless form, the problem of hyperbolic partial differential equation converted into ordinary matrix differential equation and the moving boundary problem of parabolic partial differential equations converted into moving boundary problem of ordinary matrix differential equations by using finite differences in space, transferring the problem into the generalized system of Sylvester equations by using Legendre wavelet Galerkin method and the solution of the generalized system of Sylvester equation are solved by using Bartels-Stewart algorithm of generalized inverse. The whole analysis is presented in dimensionless form. The effect of cryoprobe rate on temperature distribution and the effect of Stefan number on moving layer thickness is discussed in detail.

Numerical Simulation of Thermal Processes in a Domain of Thin Metal Film Subjected to an Ultrashort Laser Pulse

A thin metal film subjected to an ultrashort laser pulse is considered. With a sufficiently high laser intensity the process of the film heating may cause metal melting and even ablation. In this work, the numerical model of the melting and resolidification processes is presented. The mathematical model is based on the dual phase lag equation in which two positive constants appear, this means the relaxation and thermalization times. The considered equation contains a second-order time derivative and higher order mixed derivative in both time and space and should be supplemented by the appropriate boundary and initial conditions. The model of the melting and resolidification is presented in two versions. The first can be called 'the introduction of the artificial mushy zone sub-domain', while the second 'the two forms of the basic energy equation'. At the stage of numerical computations, the implicit scheme of the finite difference method is used. The numerical algorithm is tested for the two proposed models which are applied to the computations concerning the thermal processes occurring in the cylindrical micro-domain (chromium, gold) subjected to an ultrashort laser pulse.

Two-dimensional closed-form model for temperature in living tissues for hyperthermia treatments

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.

Thermal tomography for monitoring tumor response to neoadjuvant chemotherapy in women with locally advanced breast cancer

BACKGROUND & AIMS

This study aims to analyze the feasibility and predictive value of thermal tomography (TT) for monitoring early treatment response in patients with locally advanced breast cancer (LABC) receiving neoadjuvant chemotherapy (NAC).

METHODS

Patients with LABC who were due to receive six cycles of NAC were examined by TT prior to NAC, the second cycle of NAC, the fourth cycle of NAC and surgery. Changes in TT parameters and ultrasonography were correlated with pathologic response to NAC, and the predictive value was assessed.

RESULTS

Forty-four patients were evaluable for response (25 pathologic responders and 19 nonresponders). As early as after the first cycle of NAC, changes in the TT parameters ΔTs, ΔTn, and ΔTa correlated significantly with pathologic response (P < 0.05). The best predictor of pathologic response after the 6th cycle of NAC was TT (area under the receiver operating characteristic curve, 0.794), as opposed to cross-sectional areas and the longest diameter by ultrasonography.

CONCLUSIONS

TT allows for monitoring early tumor response to NAC and can predict pathologic response in the early stages of therapy. Therefore, TT could be used as a novel imaging modality to monitor NAC treatment.

SEMI-ANALYTICAL SOLUTION OF BIO-HEAT CONDUCTION FOR MULTI-LAYERS SKIN SUBJECTED TO LASER HEATING AND FLUID COOLING

A semi-analytical solution of bio-heat conduction on the three-layer skin is presented. The performance of the typical heat treatment (heating by laser and cooling by fluid at skin surface) is studied. The transient temperature field and thermal damage of skin are investigated. Effects of several parameters on temperature variation and thermal damage are discussed. The results of the paper will be useful for heat therapy in clinics. In addition, the presented result is very consistent to that by the finite element method. The semi-analytical method can be easily applied for solving the general problem of heat conduction in any multilayer structure.

FRACTIONAL MODELING OF HYPERBOLIC BIOHEAT TRANSFER EQUATION DURING THERMAL THERAPY

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.

Inverse investigation of non-Fourier heat conduction in tissue

This paper attempts to describe the heat conduction in tissue using the dual-phase-lag mode. Evaluating the thermo-physical parameters is one of the ways to certify the thermal behavior. As a result, the paper simultaneously and inversely estimates the values of τ_q, τ_T and α for bologna based on the dual-phase-lag mode with the measurement data in the literature. The inconsistence in theory discovered in the literatures is eliminated. The calculated results of temperature variation with the estimated values of τ_q, τ_T and α at the measurement location are very close to the experimental data and address the rationality of the present results.