A numerical study on heat transfer in tissues during hyperthermia

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.

Thermal analysis of different shape nanoparticles on hyperthermia therapy on breast cancer in a porous medium: A fractional model

Cancer is clearly a major cause of disease and fatality around the world, yet little is known about how it starts and spreads. In this study, a model in mathematical form of breast cancer guided by a system of (ODE'S) ordinary differential equations is studied in depth to examine the thermal effects of various shape nanoparticles on breast cancer hyperthermia therapy in the existence of a porous media with fractional derivative connection, when utilizing microwave radiative heating. The unsteady state is determined precisely using the Laplace transform approach to crop a more decisive examination of temperature dissemination of blood temperature inside the breast tissues. Durbin's and Zakian's techniques are used to find Laplace inversion. Mild temperature hyperthermia is used in the treatment, which promotes cell death by increasing cell nervousness to radiation therapy and flow of blood in tumor. In the graphical findings, we can witness the distinct behavior of hyperthermia therapy on tumor cells by applying various metabolic heat generation rates across various time intervals to attain the optimal therapeutic temperature point. Particularly, we used graphs to visualize the behavior of different Nanoparticles with different shaped during hypothermia therapy. In comparison to other nanoparticles and shapes, it demonstrates that gold nanoparticles with a platelet shape are the best option for improving heat transmission. Which assess of heat transfer up to 16.412%.

A Fractional Analysis of Hyperthermia Therapy on Breast Cancer in a Porous Medium along with Radiative Microwave Heating

Cancer is a prominent source of mortality and morbidity globally, but little is known about how it develops and spreads. Tumor cells are unable to thrive in high-temperature environments, according to recent research. Hyperthermia is the name for this therapy method. This study provides insights into hyperthermia therapy on breast cancer in the presence of a porous material with fractional derivative access when using radiative microwave heating. The mathematical model is formulated by PDE, while the time-fractional Caputo derivative is applied to make our equation more general as compared to the classical model. To produce a more efficient analysis of blood temperature distributions inside the tissues of the breast, the unsteady state is calculated by using the Laplace transform technique. The Laplace inversion is found by Durbin’s and Zakian’s algorithms. The treatment involves mild temperature hyperthermia, which causes cell death by enhancing cell sensitivity to radiation therapy and blood flow in the tumor. The variations of different parameters to control the temperate profile during therapy are discussed; we can also see how a fractional parameter makes our study more realistic for further experimental study.

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.

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.

Self-monitored and optically powered fiber-optic device for localized hyperthermia and controlled cell death in vitro

Localized hyperthermia therapy involves heating a small volume of tissue in order to kill cancerous cells selectively and with limited damage to healthy cells and surrounding tissue. However, these features are only achievable through real-time control of the tissue temperature and heated volume, both of which are difficult to obtain with current heating systems and techniques. This work introduces an optical fiber-based active heater that acts both as a miniature heat source and as a thermometer. The heat-induced damage in the tissue is caused by the conductive heat transfer from the surface of the device, while the heat is generated in an absorptive coating on the fiber by near-infrared light redirected from the fiber core to the surface by a tilted fiber Bragg grating inscribed in the fiber core. Simultaneous monitoring of the reflection spectrum of the grating provides a measure of the local temperature. Localized temperature increases between 0°C and 100°C in 10 mm-long/5 mm-diameter cylindrical volumes are obtained with continuous-wave pump power levels up to 1.8 W. Computational and experimental results further indicate that the temperature rise and dimensions of the heated volume can be maintained at a nearly stable level determined by the input optical power.

The effects of exterior boundary conditions on a internally heated tumor tissue with a thermoporoelastic model

Modeling flow field in tumor regions interstitial space is of primary importance, because of the importance of advection in macromolecule drug delivery. Its deformation has also to be taken into account because of the forces caused by the fluid; if the tumor region is not isothermal, this deformation can be also strongly affected by temperature fields. In this paper, the effects of thermal boundary conditions on a tumor region periphery with an internal heat source are investigated. The tumor region is modeled as a deformable sphere, in which two phases can be distinguished. The fluid phase is the interstitial fluid, while the rest of the tumor is modeled as the solid phase, including also capillaries and tissues. Transient-state governing equations for mass, momentum and energy are written for both phases, by also considering tumor deformation under the linear elastic material assumption. A situation of Tumor Blood Flow (TBF) rapid decay, in which vascular pressure rapidly approaches to zero, is considered, while the heat source is modeled as a fourth-grade radial-decay function. Boundary conditions for the energy equation are varied on the external surface of the sphere, in order to appreciate the effects of the surrounding on flow and temperature fields inside the tumor. After scaling equations, a finite-element scheme is employed for the numerical solution. Comparisons with analytical solutions from literature show a good agreement. Results are shown for different dimensionless parameters that are referred to temperature, volumetric strain, pressure and velocity, showing in which case external boundary conditions strongly affect tumor region flow fields and a third-kind boundary condition is needed.

Modeling Heat Transfer in Tumors: A Review of Thermal Therapies

It is quite challenging to describe heat transfer phenomena in living systems because of the involved phenomena complexity. Indeed, thermal conduction and convection in tissues, blood perfusion, heat generation due to metabolism, complex vascular structure, changing of tissue properties depending on various conditions, are some of the features that make hard to obtain an accurate knowledge of heat transfer in living systems for all the clinical situations. This theme has a key role to predict accurately the temperature distribution in tissues, especially during biomedical applications, such as hyperthermia treatment of cancer, in which tumoral cells have to be destroyed and at the same time the surrounding healthy tissue has to be preserved. Moreover, the lack of experimentation in this field, due to ethical reasons, makes bioheat models even more significant. The first simple bioheat model was developed in 1948 by Pennes (J Appl Physiol 1:93-122, 1948) but it has some shortcomings that make the equation not so accurate. For this reason, over the years it has been modified and more complex models have been developed. The purpose of this review is to give a clear overview of how the bioheat models have been modified when applied in various hyperthermia treatments of cancer.

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.

MAGNETIC FLUID HYPERTHERMIA IN A CYLINDRICAL GEL CONTAINS WATER FLOW

In magnetic fluid hyperthermia (MFH), nanoparticles are injected into a diseased tissue and then subjected to an alternating high frequency magnetic field. The produced heat may have a key asset to destroy the cancerous cells. The blood flow in a tissue is considered as the most complicated part of the MFH which should be taken into account in the analysis of the MFH. This study was aimed to perform an experimental study to investigate the heat transfer of agar gel which contains fluid flow. Fe 3 O 4 as a nanoparticle was injected into the center of a cylindrical gel. It was also embedded with other cylindrical gels and subjected to an alternating magnetic field of 7.3 (kA/m) and a frequency of 50 (kHz) for 3600 (s). The temperature of the gel was measured at three points. The temperature distribution was measured via the experimental data. Moreover, specific absorption rate (SAR) was quantified with time differential temperature function at t = 0 by means of experimental data. Finite element method (FEM) was employed to establish a model to validate the SAR function. Results revealed the effects of fluid flow and accuracy of the SAR function for heat production in gel. The proposed function have implications in hyperthermia studies as a heat generation source. Finally, the condition of experimental setup was simulated to find the blood perfusion.

Diagnosis of breast tumor using thermal tomography q-r curve

Metabolic heat, the product following the metabolism of cells, is closely related to the pathological information of living organisms, which means there are strong connections between the heat distribution and the pathological state of the living organism. The mathematical function δ is introduced in the classical Pennes bioheat transfer equation as a point heat source, and by simplifying the boundary condition, a bioheat transfer model is established. Based on the temperature distribution of the human body surface, the q−r curve of heat intensity q varying with depth r is acquired while combining the fitting method of the Lorentz curve. According to 34,977 clinical confirmed cases and the corresponding classified statistics, diagnostic criteria (for breast diseases) for judging diseases by the q−r curve are proposed. The P -value of our statistics is <0.05 , which means our classified statistics are reliable. Six typical clinical examinations are performed, and the diagnosis results are very consistent with those of B-ultrasonic images, molybdenum target x-ray, and pathological examination, which suggests that the method of diagnosing diseases with a q−r curve has very good prospects for application. It is radiation free and noninvasive to the human body.

Q-r curve of thermal tomography and its clinical application on breast tumor diagnosis

Heat is the product following the metabolism of cells, and the metabolism is closely related with the pathological information of living organism. So, there are strong ties between the heat distribution and the pathological state in living organism. In this paper, the mathematical function δ is introduced in the classical Pennes bio-heat transfer equation as the point heat source. By simplifying the boundary conditions, a novel bio-heat transfer model is established and solved in a spherical coordinate system. Based on the temperature distribution of human body surface, the information of heat source is mined layer by layer, and the corresponding q-r curve of heat intensity varying with depth is acquired combining the fitting method of Lorentz curve. According to a large number of clinical confirmed cases and statistics, the diagnostic criteria judging diseases by q-r curve are proposed. Five typical clinical practices are performed and four of the diagnosis results are very consistent with those of molybdenum target (MT) X-ray, B-ultrasonic images and pathological examination, one gives the result of early stage malignant tumor that MT X-ray and B-ultrasonic can't check out. It is a radiation-free green method with noninvasive diagnostic procedure and accurate diagnosis result.

Cylindrical agar gel with fluid flow subjected to an alternating magnetic field during hyperthermia

PURPOSE

In magnetic fluid hyperthermia (MFH), nanoparticles are injected into diseased tissue and subjected to an alternating high frequency magnetic field. The process triggers sufficient heat to destroy the cancerous cells. One of the challenging problems during MFH is blood flow in tissue. In real conditions the heat which is transferred by blood flow should be considered in the analysis of MFH.

METHODS

In this study, heat transfer was investigated in an agar gel phantom containing fluid flow. Fe3O4 as a nano-fluid was injected into the centre of a gel cylinder which was filled with another gel cylinder and subjected to an alternating magnetic field of 7.3 kA/m and a frequency of 50 kHz for 3600 s. The temperature was measured at three points in the gel. Temperature distributions regarding the time at these three points were experimentally measured. Moreover, the specific absorption rate (SAR) function was calculated with a temperature function.

RESULTS

The SAR function was a key asset in the hyperthermia and was obtained on the condition that the fluid flowed through the gel. Finally, a finite element analysis (FEA) was performed to verify the SAR function. The results revealed that there was good agreement between the measured temperature and the one obtained from FEA. In addition, the effects of fluid flow and accuracy of function obtained for heat production in the gel were presented.

CONCLUSION

It is believed that the proposed model has the potential ability to get close to reality in this type of investigation. The proposed function has implications for use in further modelling studies as a heat generation source.