Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface

Thermal simulation of the lower limb in vascular medicine: A proof-of-concept by using computed tomography images

Simulations of physiology based on patient-specific anatomical structures have several potential applications in medicine. A few fields, such as radiotherapy and neurophysiology already utilize such methods in clinical practice, yet a number of disciplines could benefit from similar technologies, especially when imaging data is already available. The major problem in patient-specific simulation is the data conversion to simulation-compatible form i.e., data preparation and the coupling of the underlying physics to the anatomical model. In this work we present such a methodology in the context of vascular medicine, consisting of a three-dimensional blood flow-temperature simulation model of the lower limb built from computed tomography data. We also simulate a clinical condition of chronic limb-threatening ischemia, a severe complication of peripheral arterial disease. This proof-of-concept model simulates the limb's surface temperature with respect to the vascular structure. The methodology, depicting accurate patient anatomy, is a promising step towards individualized physiological simulations in vascular medicine, although more research and validation are required. Such a model could eventually outline a deeper understanding of the relation between vascular changes and peripheral thermal behavior.

Thermal wave and Pennes' models of bioheat transfer in human skin: A transient comparative analysis

The primary focus of this study is to analyze comparative heat transfer in a two-dimensional (2D) multilayered human skin using thermal waves and Pennes' bioheat transfer models. The model comprises the epidermis, dermis, hypodermis tissue, and inner cells, and aims to understand their response to microwave (MW) power and electromagnetic (EM) frequency. The system of equations involves EM wave frequency and bioheat equations and uses the finite element method (FEM) for solving. It encompasses a range of microwave power levels (4-16 W), frequencies (0.9-4 GHz), and exposure durations (0-180 s). It examines how MW power and frequency affect temperature predictions due to different relaxation times. The results are visually represented, illustrating microwave power dissipation, isothermal profiles within the skin tissue, temperature trends at several locations, relaxation times, specific absorption rate (SAR), and the mean surface temperature of the multilayered dermal cell. Thermal analysis shows that Pennes' equation predicts higher temperatures than the thermal wave model of bioheat transfer (TWMBT). A notable disparity in temperature evolution is observed between the two models, especially in high-frequency transient heating scenarios. The TWMBT forecasts a delay in heat transfer, offering valuable insights into the more realistic short-term thermal behavior that the classical Pennes' model fails to capture. This comparative study underscores the significance of selecting an appropriate bioheat transfer model for precise thermal analysis in biomedical applications, such as hyperthermia treatment and thermal diagnostics. The findings emphasize the potential of the TWMBT to enhance the accuracy of thermal treatments in clinical settings.

Miniaturized implantable temperature sensors for the long-term monitoring of chronic intestinal inflammation

Diagnosing and monitoring inflammatory bowel diseases, such as Crohn's disease, involves the use of endoscopic imaging, biopsies and serology. These infrequent tests cannot, however, identify sudden onsets and severe flare-ups to facilitate early intervention. Hence, about 70% of patients with Crohn's disease require surgical intestinal resections in their lifetime. Here we report wireless, miniaturized and implantable temperature sensors for the real-time chronic monitoring of disease progression, which we tested for nearly 4 months in a mouse model of Crohn's-disease-like ileitis. Local measurements of intestinal temperature via intraperitoneally implanted sensors held in place against abdominal muscular tissue via two sutures showed the development of ultradian rhythms at approximately 5 weeks before the visual emergence of inflammatory skip lesions. The ultradian rhythms showed correlations with variations in the concentrations of stress hormones and inflammatory cytokines in blood. Decreasing average temperatures over the span of approximately 23 weeks were accompanied by an increasing percentage of inflammatory species in ileal lesions. These miniaturized temperature sensors may aid the early treatment of inflammatory bowel diseases upon the detection of episodic flare-ups.

Computer Simulation of Catheter Cryoablation for Pulmonary Vein Isolation

Cryoablation is a well-established medical procedure for surgically treating atrial fibrillation. Cryothermal catheter therapy induces cellular necrosis by freezing the insides of pulmonary veins, with the goal of disrupting abnormal electrical heart signals. Nevertheless, tissue damage induced by cold temperatures may also lead to other complications after cardiac surgery. In this sense, the simulation of catheter ablation can provide safer environments for training and the performance of cryotherapy interventions. Therefore, in this paper, we propose a novel approach to help better understand how temperature rates can affect this procedure by using computer tools to develop a simulation framework to predict lesion size and determine optimal temperature conditions for reducing the risk of major complications. The results showed that a temperature profile of around -40 °C caused less penetration, reduced necrotic damage, and smaller lesion size in the tissue. Instead, cryotherapy close to -60 °C achieved a greater depth of temperature flow inside the tissue and a larger cross-section area of the lesion. With further development and validation, the framework could represent a cost-effective strategy for providing personalized modeling, better planning of cryocatheter-based treatment, and preventing surgical complications.

Helmet Radio Frequency Phased Array Applicators Enhance Thermal Magnetic Resonance of Brain Tumors

Thermal Magnetic Resonance (ThermalMR) integrates Magnetic Resonance Imaging (MRI) diagnostics and targeted radio-frequency (RF) heating in a single theranostic device. The requirements for MRI (magnetic field) and targeted RF heating (electric field) govern the design of ThermalMR applicators. We hypothesize that helmet RF applicators (HPA) improve the efficacy of ThermalMR of brain tumors versus an annular phased RF array (APA). An HPA was designed using eight broadband self-grounded bow-tie (SGBT) antennae plus two SGBTs placed on top of the head. An APA of 10 equally spaced SGBTs was used as a reference. Electromagnetic field (EMF) simulations were performed for a test object (phantom) and a human head model. For a clinical scenario, the head model was modified with a tumor volume obtained from a patient with glioblastoma multiforme. To assess performance, we introduced multi-target evaluation (MTE) to ensure whole-brain slice accessibility. We implemented time multiplexed vector field shaping to optimize RF excitation. Our EMF and temperature simulations demonstrate that the HPA improves performance criteria critical to MRI and enhances targeted RF and temperature focusing versus the APA. Our findings are a foundation for the experimental implementation and application of a HPA en route to ThermalMR of brain tumors.

The impact of multiple stenosis and aneurysms on arterial diseases: A cardiovascular study

The comparative effect of serial stenosis and aneurysms arteries on blood flow is examined to identify atherosclerotic diseases. The finite element approach has been used to solve the continuity, momentum, and Oldroyd-B partial differential equations to analyze the blood flow. Newtonian and non-Newtonian both cases are taken for the viscoelastic response of blood. In this study, the impact of multiple stenotic and aneurysmal arteries on blood flow have been studied to determine the severity of atherosclerosis diseases through the analysis of blood behavior. The novel aspect of the study is its assessment of the severity of atherosclerotic disorders for the occurrence of serial stenosis and aneurysm simultaneously in the blood vessel wall in each of the four cases. The maximum abnormal arterial blood flow effect is found for the presence of serial stenoses compared to aneurysms which refers to the severity of atherosclerosis. At the hub of stenosis, the blood velocity magnitude and wall shear stress (WSS) are higher, whereas the arterial wall normal gradient values are lower. For all cases, the contrary results are observed at the hub of the aneurysmal model. The blood flow has been affected significantly by the increases in Reynolds number for both models. The influence of stenotic and aneurysmal arteries on blood flow is graphically illustrated in terms of the velocity profile, pressure distribution, and WSS. Medical experts may use this study's findings to assess the severity of cardiovascular diseases.

Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks

The primary objective of this research is to develop a mathematical model, analyze the dynamic occurrence of thermal shock and exploration of how thermal memory with moving line impact of heat transfer within biological tissues. An extended version of the Pennes equation as its foundational framework, a new fractional modelling approach called the Prabhakar fractional operator to investigate and a novel time-fractional interpretation of Fourier's law that incorporates its historical behaviour. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fractional formulation of heat flow, achieved through a generalized fractional operator with a non-singular type kernel, enables the representation of the finite propagation speed of heat waves. Furthermore, the dynamics of thermal source continually generates a linear thermal shock at predefined locations within the tissue. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also expressed the solution in the form of special functions. The article derives analytical solutions for the heat transfer phenomena of both the generalized model, in the Laplace domain, and the ordinary model in the real domain, employing Laplace inverse transformation. The pertinent parameter's influence, such as α, β, γ, a0, b0, to gain insights into the impact of the thermal memory parameter on heat transfer, is brought under consideration to reveal the interesting results with graphical representations of the findings.

Simultaneous estimation of SAR, thermal diffusivity, and damping using periodic power modulation for MRgFUS quality assurance

Purpose: A crucial aspect of quality assurance in thermal therapy is periodic demonstration of the heating performance of the device. Existing methods estimate the specific absorption rate (SAR) from the temperature rise after a short power pulse, which yields a biased estimate as thermal diffusion broadens the apparent SAR pattern. To obtain an unbiased estimate, we propose a robust frequency-domain method that simultaneously identifies the SAR as well as the thermal dynamics.Methods: We propose a method consisting of periodic modulation of the FUS power while recording the response with MR thermometry (MRT). This approach enables unbiased measurements of spatial Fourier coefficients that encode the thermal response. These coefficients are substituted in a generic thermal model to simultaneously estimate the SAR, diffusivity, and damping. The method was tested using a cylindrical phantom and a 3 T clinical MR-HIFU system. Three scenarios with varying modulation strategies are chosen to challenge the method. The results are compared to the well-known power pulse technique.Results: The thermal diffusivity is estimated at 0.151 mm2s-1 with a standard deviation of 0.01 mm2s-1 between six experiments. The SAR estimates are consistent between all experiments and show an excellent signal-to-noise ratio (SNR) compared to the well established power pulse method. The frequency-domain method proved to be insensitive to B0-drift and non steady-state initial temperature distributions.Conclusion: The proposed frequency-domain estimation method shows a high SNR and provided reproducible estimates of the SAR and the corresponding thermal diffusivity. The findings suggest that frequency-domain tools can be highly effective at estimating the SAR from (biased) MRT data acquired during periodic power modulation.

Noninvasive and Continuous Monitoring of the Core Body Temperature through the Quantitative Measurement of Blood Perfusion Rate

Core body temperature (CBT) is one of the four vital signs that must be monitored continuously. The continuous recording of CBT is possible through invasive methods by inserting a temperature probe into specific body sites. We report a novel method to monitor CBT through the quantitative measurement of skin blood perfusion rate (ωb,skin). By monitoring the skin temperature, heat flux, and ωb,skin, the arterial blood temperature, equivalent to CBT, can be extracted. ωb,skin is quantitatively evaluated thermally via sinusoidal heating with regulated thermal penetration depth so that the blood perfusion rate is acquired only in the skin. Its quantification is significant because it indicates various physiological events including hyper- or hypothermia, tissue death, and delineation of tumors. A subject showed promising results with steady values of ωb,skin and CBT of 5.2 ± 1.05 × 10-4 s-1 and 36.51 ± 0.23 °C, respectively. For periods where the subject's actual CBT (axillary temperature) did not fall within the estimated range, the average deviation from the actual CBT was only 0.07 °C. This study aims to develop a competent methodology capable of continuously monitoring the CBT and blood perfusion rate at a distant location from the core body region for the diagnosis of a patient's health condition with wearable devices.

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.

Mathematical Modelling with the Exact Solution of Three Different Bioheat Conduction Models of a Skin Tissue Shocked by Thermoelectrical Effect

This research deals with the temperature increment and responsiveness of skin tissue to a continuous flow of surface heat induced by a constant-voltage electrical current. The exact analytical solution for the dual-phase-lag (DPL) of bioheat transfer has been obtained. It is used to confine the variables to a limited domain to solve the governing equations. The transition temperature reactions have been measured and investigated. The figures provide a comparison of the Pennes, Tzou models, and Vernotte-Cattaneo models. The numerical results demonstrate the values of the voltage, resistance, electric shock time, and dual-phase-lag time parameters which have significant influences on the distributions of the dynamic and conductive temperature rise through the skin tissue.

Computational study on 2D three-phase lag bioheat model during cryosurgery using RBF meshfree method

Biological tissue has a multidimensional and non-homogeneous inner structure by nature. The temperature distribution and freezing front locations in biological tissue are crucial to optimizing the damage to tissue during cryosurgery. There is a need for a good mathematical model and effective simulation techniques to predict the effectiveness of the therapy. The present study concerns the numerical study of phase change phenomena during cryosurgery using the three-phase lag (TPL) bioheat model in arbitrary soft tissue domains, i.e., circular (Γ₁), ameba-like (Γ₂), and multiconnected (Γ₃). We employ the effective heat capacity formulation to solve the nonlinear governing equation. The Gaussian radial basis function and Crank-Nicolson finite difference approximation are applied for spatial and time derivatives, respectively. Using the present algorithm, we study the impact of phase lag (τ_v) due to thermal displacement involved in the TPL model on phase change interface position and thermal distribution in all three domains. The obtained results may be beneficial in the field of oncology.

A 3D Approach Using a Control Algorithm to Minimize the Effects on the Healthy Tissue in the Hyperthermia for Cancer Treatment

According to the World Health Organization, cancer is a worldwide health problem. Its high mortality rate motivates scientists to study new treatments. One of these new treatments is hyperthermia using magnetic nanoparticles. This treatment consists in submitting the target region with a low-frequency magnetic field to increase its temperature over 43 °C, as the threshold for tissue damage and leading the cells to necrosis. This paper uses an in silico three-dimensional Pennes' model described by a set of partial differential equations (PDEs) to estimate the percentage of tissue damage due to hyperthermia. Differential evolution, an optimization method, suggests the best locations to inject the nanoparticles to maximize tumor cell death and minimize damage to healthy tissue. Three different scenarios were performed to evaluate the suggestions obtained by the optimization method. The results indicate the positive impact of the proposed technique: a reduction in the percentage of healthy tissue damage and the complete damage of the tumors were observed. In the best scenario, the optimization method was responsible for decreasing the healthy tissue damage by 59% when the nanoparticles injection sites were located in the non-intuitive points indicated by the optimization method. The numerical solution of the PDEs is computationally expensive. This work also describes the implemented parallel strategy based on CUDA to reduce the computational costs involved in the PDEs resolution. Compared to the sequential version executed on the CPU, the proposed parallel implementation was able to speed the execution time up to 84.4 times.

Analytical and numerical analysis of the dual-pulse lag heat transfer in a three-dimensional tissue subjected to a moving multi-point laser beam

An extensive algorithm based on both analytical and numerical solution methodologies is proposed to obtain transient temperature distributions in a three-dimensional living tissue subjected to a moving single-point and multi-point laser beam by considering metabolic heat generation and blood perfusion rate. Here, the dual-phase lag/Pennes equation is analytically solved by using the method of Fourier series and the Laplace transform. The ability to model single-point or multi-point laser beams as an arbitrary function of place and time is a significant advantage of the proposed analytical approach, which can be used to solve similar heat transfer problems in other living tissues. Besides, the related heat conduction problem is numerically solved based on the finite element method. The effects of laser beam transitional speed, laser power, and the number of laser points on the temperature distribution within the skin tissue are investigated. Moreover, the temperature distribution predicted by the dual-phase lag model is compared with that of the Pennes model under different working conditions. For the studied cases, it is observed that the maximum tissue temperature decreased about 63% by an increase of 6mm/s in the speed of the laser beam. An increase in the laser power from 0.8W/cm³ to 1.2W/cm³ results in a 28 °C increase in the maximum temperature of the skin tissue. It is observed that the maximum temperature predicted by the dual-phase lag model is always lower than that of the Pennes model and the temperature variations over time are sharper, while their results are entirely consistent over the simulation time. The obtained numerical results indicated that the dual-phase lag model is preferred in heating processes occurring at short intervals. Among the investigated parameters, the laser beam speed has the most considerable effect on the difference between the results of the Pennes and the dual-phase lag models.

Fractal Pennes and Cattaneo-Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

In this study, the Pennes and Cattaneo-Vernotte bioheat transfer equations in the presence of fractal spatial dimensions are derived based on the product-like fractal geometry. This approach was introduced recently, by Li and Ostoja-Starzewski, in order to explore dynamical properties of anisotropic media. The theory is characterized by a modified gradient operator which depends on two parameters: R which represents the radius of the tumour and R0 which represents the radius of the spherical living tissue. Both the steady and unsteady states for each fractal bioheat equation were obtained and their implications on living cells in the presence of growth of a large tumour were analysed. Assuming a specific heating/cooling by a constant heat flux equivalent to the metabolic heat generation in the tissue, it was observed that the solutions of the fractal bioheat equations are robustly affected by fractal dimensions, the radius of the tumour growth and the dimensions of the living cell tissue. The ranges of both the fractal dimensions and temperature were obtained, analysed and compared with recent studies. This study confirms the importance of fractals in medicine.

Theoretical analysis on thermal treatment of skin with repetitive pulses

Thermal ablation is an efficient method of medical treatment, such as cancer therapy, wound closure, laser cutting, freckle removal and other treatments. In order to guarantee the curative effect and the safety of the patients, the thermal response of the tissue which is subjected to the heat source need to be carefully monitored. However, it is too difficult to achieve real-time monitoring on the full-field temperature. In the present study, efforts were made to build up a theoretical model for the prediction of the thermal response in the human skin. The Dual-Phase-Lag (DPL) bio-heat transfer model and the Henrique’s burn assessment model were employed to describe the interaction of multi-pulse heat source and the skin. The repeated multi-pulse laser is a common heat source in the thermal treatment and the thermal responses of the skin would be complicated under the common effects of the non-Fourier effects and the multi-pulse source. The Green’s function approach was used to solve the governing equations analytically. The closed-form solution for the temperature distribution of the skin was obtained and the thermal damage was estimated based on the temperature results. The influences of the biological parameters (the phase lags of the heat flux and the temperature gradient) and the heat source parameters (the pulse number and the duty ratio) on the temperature distribution, the burn degree and the irreversible burn depth of the irradiated region were discussed.

Contrast agent shell properties effects on heat deposition in bubble enhanced high intensity focused ultrasound

The effects of the viscoelastic shell properties of ultrasound contrast agents on heat deposition in bubble enhanced high intensity focused ultrasound (HIFU) are studied numerically using a model that solves the ultrasound acoustic field and the multi-bubble dynamics. The propagation of the nonlinear acoustic waves in the test medium is modeled using the compressible Navier-Stokes equations in a fixed Eulerian grid, while the microbubbles are modeled as discrete flow singularities, which are tracked in a Lagrangian fashion. These two models are intimately coupled such that both the acoustic field and the bubbles influence each other at each time step. The resulting temperature rise in the field is then calculated by solving a heat transfer equation applied over a much longer time scale than the computed high frequency dynamics. Three shell models for the contrast agent are considered, and the effect of each of these models on the heat deposition at the focus is studied. The differences obtained in the bubble dynamics results between the shell models are discussed. The importance of modeling the elasticity of the shell is addressed by comparing the results between Newtonian and non-Newtonian shell models. Next, a parametric study varying the shell properties is carried out, and the relative roles of the shell viscosity and elasticity in affecting the heat deposition are discussed. These observations are then used to give recommendations for the design of innovative contrast agents, specifically for the purpose of obtaining higher heat deposition in bubble enhanced HIFU.

On the possibility of using temperature to aid in thyroid nodule investigation

Thyroid nodules are common, and their investigation is very important to exclude the possibility of cancer. The increase in blood vessels of malignant tumours may be related to local temperature augmentation detectable on the skin surface. The objective of this paper is to evaluate the feasibility of Infrared Thermography for cancer identification. For this purpose, two studies were performed. One used numerical modelling to simulate regional metabolic temperature propagation to evaluate whether a nodule is perceptible on the skin surface. A second study considered thyroid nodule identification by using convolutional neural networks (CNNs). First, variations in nodular size and fat thickness were investigated, showing that the fat layer has an important role in regional heat transfer. In the second study, the training process achieved accuracy of 96% for in-sample and 95% for validation. In the testing phase, 92% accuracy, 100% precision and 80% recall were achieved. Thus, the presented studies suggest the feasibility of using Infrared Thermography with the CNN Artificial Intelligence technique as additional information in the investigation of thyroid nodules for patients without a very thick subcutaneous fat layer.

Analysis of the effect of external heating in the human tissue: A finite element approach

Thermal therapy which involves either raising or lowering tissue temperature to treat malignant cells needs precise acknowledgment of thermal history inside the biological system to ensure effective treatment. For this purpose, this study presents a two-dimensional unsteady finite element model (FEM) of the bioheat transfer problem based on Pennes bio-heat equation to analyze the thermal response of tissue subject to external heating. Crank-Nikolson scheme was used for the unsteady solution. A finite element code was developed using C language to calculate results. The obtained numerical result was compared with the analytical and other numerical results available in the literature. A good agreement was found from the comparison. Temperature distribution inside the human body due to constant and sinusoidal spatial and surface heating were analyzed. Response to point heating was also investigated. Moreover, a sensitivity analysis was carried out to know the effect of various parameters, i.e. blood temperature, thermal conductivity, and blood perfusion rate on tissue temperature. The outcome of this study will be helpful for the researchers and physicians involved in the thermal treatment of human tissue.

Evaluation of human brain hyperthermia using exergy balance equation

Hyperthermia is caused by disturbance in the thermoregulatory system of the human body and requires emergency treatment to prevent disability or possible mortality. To design any therapeutic device for hyperthermia, an exhaustive effort is required to establish the extremities of such thermal traumas. In this context, the authors have incorporated the human-body exergy-balance equation to compute the hyperthermia thresholds. This is a pioneer attempt to model hyperthermia states. An induced-hyperthermia technique is used to evaluate the extremities of metabolic heat generation and other dependent parameters. Moreover, a case study is also presented to calculate the parameters of prime importance i.e. exergy consumption (EC) and entropy generation rate (δS_g) to provide the body's accumulative and exhaustive thermal energy maxima, respectively. Furthermore, the thresholds have been evaluated and simulated by the varying body and/or environmental conditions. The resulting states have been analysed to setup critical ranges to provide the guidelines for rehabilitation therapy. A thermal manikin has also been developed, mimicking the blood circulation in humans, to further substantiate the use of an exergy-based approach. The results indicate that the exergy-based approach is well suited to model hyperthermia at pathophysiological boundaries, contrary to existing approaches which predominantly are limited to the physiological domain.

The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

The effects of thermal and mechanical material properties on tumorous tissue during hyperthermia treatment

Although there have been numerous reports in several articles about the viscoelastic properties of biological tissues, no effort has been made to investigate the combined thermal and mechanical behavior of the viscoelastic tissue. At present, the model of thermo-viscoelasticity theory with variable thermal conductivity and rheological properties of the volume is considered to investigate bio-thermo-mechanics behavior in living tissue within the context of the Lord-Shulman theory. The model is applied to a limited thickness, cancerous layer problem. The problem was solved analytically in the transformed domain using Laplace transform as a tool. The exact solution is obtained in the context of transformation Laplace. Numerical results are given and illustrated graphically for the distributions of temperature, displacement, and stress. Some correlations are produced with the results obtained for the absence of the thermal relaxation parameter. The effects of variable thermal and volume materials properties, blood perfusion rate on the behavior of various fields are examined.

Investigation of non-uniformly emitting optical fiber diffusers on the light distribution in tissue

The influence of inhomogeneities in the emission characteristics of optical fiber diffusers on the light distribution within biological tissue was evaluated by Monte Carlo (MC) simulations and by experiments on optical phantoms. Due to the strong scattering of light within biological tissue, inhomogeneities in the emission profile become blurred within a short light propagation distance, so that the light distribution within the tissue approaches that of a homogeneous diffuser. The degree of feature vanishing in the light distribution is mainly determined by the width of the inhomogeneities. It was shown that the influence of local inhomogeneities on top of a homogeneous light distribution fades away very effectively within 1 mm of tissue depth, which results in a light distribution very close to that for a homogeneously emitting diffuser. Emission profiles composed of multiple narrow peaks distributed over the full diffuser length with a peak-to-peak distance of less than 2 mm result in an almost homogeneous light distribution after approximately 1 mm of tissue depth. While this article is focused on the impact of diffuser inhomogeneities on the light distribution within the tissue, the importance of further investigations on the related thermal effects is also discussed.

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.

Temperature-dependent heating efficiency of magnetic nanoparticles for applications in precision nanomedicine

The power released by magnetic nanoparticles submitted to an alternating driving field is temperature dependent owing to the variation of the fundamental magnetic properties. Therefore, the heating efficiency of magnetic nanoparticles for applications in precision nanomedicine (such as magnetic hyperthermia or heat-assisted drug delivery) can be significantly affected by the local instantaneous temperature of the host medium. A rate equation approach is used to determine the hysteretic properties and the power released by magnetite nanoparticles, and the heat transport equation is solved in a simple geometry with boundary conditions appropriate to both in-lab experiments and in vivo applications. Size plays a fundamental role in determining the heating efficiency of magnetic nanoparticles; above a critical size, nanoparticles remain inactive, although they can undergo secondary activation. The experimental conditions for optimal thermal efficiency are expressed by a thermal activity diagram for nanoparticles. In the light of the model's results, features, methods, advantages and dangers of magnetic-particle assisted precision nanomedicine ought to be reconsidered. In vivo antitumor applications should take into account the hazards arising from the heat generated by magnetic nanoparticles that diffuse into the neighboring healthy tissue.

Modeling of One-Dimensional Thermoelastic Dual-Phase-Lag Skin Tissue Subjected to Different Types of Thermal Loading

This work introduces a mathematical model of thermoelastic skin tissue in the context of the dual-phase-lag heat conduction law. One-dimensional skin tissue has been considered with a small thickness and its outer surface traction free. The bounding plane of the skin tissue is subjected to three different types of thermal loading; thermal shock, ramp type heating, and harmonic heating. The inner surface has no temperature increment and traction free. Laplace transform techniques have been used, and its inversions have been calculated by using the Tzuo method. The numerical results have been represented in figures. The thermal shock time parameter, the ramp-type heat parameter, and the angular thermal parameter have significant effects on the temperature increment, the strain, the displacement, and the stress distributions, and they play vital roles in the speed propagation of the thermomechanical waves through the skin tissue.

Intraoperative Speckle Variance Optical Coherence Tomography for Tissue Temperature Monitoring During Cutaneous Laser Therapy

Background: Tissue temperature monitoring during cutaneous laser therapy can lead to safer and more effective treatments. In this study, we investigate the use of speckle variance optical coherence tomography (svOCT) to monitor real-time temperature changes in the excised human skin tissue sample during laser irradiation. Methods: To accomplish this, we combined the pulse laser system with a reference-based svOCT system. To calibrate the svOCT, the ex-vivo human skin samples from three individuals with tissues collected from the arm, face, and back were heated with 1-degree increments. Additionally, linear regression was used to extract and evaluate the linear relationship between the temperature and normalized speckle variance value. Experiments were conducted on excised human skin sample to monitor the temperature change during laser therapy with a svOCT system. Thermal modeling of ex-vivo human skin was used to numerically simulate the laser-tissue interaction and estimate the thermal diffusion and peak temperature of the tissue during the laser treatment. Results and Conclusion: These results showed that normalized speckle variance had a linear relationship with the tissue temperature before the onset of tissue coagulation (52°) and we were able to measure the rapid increase of the tissue temperature during laser therapy. The result of the experiment is also in good agreement with the numerical simulation result that estimated the laser-induced peak temperature and thermal relaxation time.

Numerical study on the effects of blood perfusion and body metabolism on the temperature profile of human forearm in hyperthermia conditions

The development of mathematical models for describing the thermal behavior of living tissues under normal or hyperthermia conditions is of increasing importance. In this research, a 3D forearm model based on anthropometric measurement of 25 samples in Tehran, Iran was developed. The tissue temperature distribution is obtained via the Finite Volume Method (FVM) by considering the appropriate boundary conditions, blood perfusion, body metabolism, and the application of hyperthermia conditions on the tissue. The Pennes Bioheat Transfer Equation (PBHTE) is considered in this regard. Also, various thermophysical properties are assumed for the model in order to clarify the effects of such parameters on the tissue temperature distribution. The results of this study indicate that it is possible to provide the desired conditions for many therapeutic processes by controlling the parameters such as blood perfusion, body metabolism and the type of external heat source applied on the tissue. Generally, by decreasing the body metabolism, increasing the blood perfusion rate in tissue and applying a fluctuating heat flux, instead of uniform heat flux on the surface of the forearm skin, it is possible to provide the hyperthermia conditions without causing damages such as burn injuries to the other parts of the tissue. By using the results of this study, the appropriate conditions of hyperthermia can be obtained.

Thermal damage in three-dimensional vivo bio-tissues induced by moving heat sources in laser therapy

The thermal damage of a three-dimensional bio-tissue model irradiated by a movable laser beam was studied in this work. By employing the DPL biological heat conduction model and Henriques' thermal damage assessment model, the distribution of burn damage of vivo human tissue during laser therapy was analytically obtained. The influences of laser moving velocity, laser spot size, phase lags of heat flux and temperature gradient were discussed. It was found that the laser moving speed and the laser spot size greatly influence the thermal damage degree by affecting the energy concentration degree. The increases of the laser moving speed and laser spot size can enlarge the irradiated region and reduce the burn degree. A greater phase lag of temperature gradient led to lower accumulation of thermal energy and lower burn degree. However, the increment of heat flux phase lag leads to the thermal energy accumulation and more serious burn degree in the irradiated region.

Theoretical analysis of nanoshell-assisted thermal treatment for subcutaneous tumor

The hyperthermia is an efficient technique for tumor treatment, in which the tumor is subjected to a heating source, such as laser, supersonic or electromagnetic field. In order to improve the therapeutic efficiency and to protect the surrounding healthy tissues, gold nanoshells are embedded in the tumor as the additive to make it absorb more thermal energy than the healthy tissues. In the present study, a one-dimensional three-layered model is established to investigate the thermal response of the bio-tissue in the hyperthermia treatment for subcutaneous tumor. The governing equations are solved analytically by using the Green's function method and the Henriques' model is employed to evaluate the degree of thermal damage in the target tissue. The influences of the volumetric density of gold nanoshells on the temperature distribution and thermal damage are discussed in detail. When the gold nanoshells are embedded with a proper density, it can improve the efficiency of tumor killing and protecting the subcutaneous tissue from being burnt. The closed-form solution for the governing equations in multilayered tissues can be a theoretical guideline to selection of appropriate parameters of the gold nanoshells.

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.

Development of Temperature Distribution and Light Propagation Model in Biological Tissue Irradiated by 980 nm Laser Diode and Using COMSOL Simulation

Introduction: The purpose of this project is to develop a mathematical model to investigate light distribution and study effective parameters such as laser power and irradiated time to get the optimal laser dosage to control hyperthermia. This study is expected to have a positive impact and a better simulation on laser treatment planning of biological tissues. Moreover, it may enable us to replace animal tests with the results of a COMSOL predictive model. Methods: We used in this work COMSOL5 model to simulate the light diffusion and bio-heat equation of the mouse tissue when irradiated by 980 nm laser diode and the effect of different parameters (laser power, and irradiated time) on the surrounding tissue of the tumor treatment in order to prevent damage from excess heat Results: The model was applied to study light propagation and several parameters (laser power, irradiated time) and their impact on light-heat distribution within the tumor in the mouse back tissue The best result is at laser power 0.5 W and time irradiation 0.5 seconds in order to get the maximum temperature hyperthermia at 52°C. Conclusion: The goal of this study is to simulate a mouse model to control excess heating of tissue and reduce the number of animals in experimental research to get the best laser parameters that was safe for use in living animals and in human subjects.

DEVELOPING ANALYTICAL MODELS OF PREDICTING SKIN TEMPERATURE AND DAMAGE EXTENT FROM SINGLE-LAYER INTO MULTI-LAYER ONES

As a starting point for developing analytical models of predicting skin temperature and damage extent into multi-layer ones, a double-layer model consisting of two distinguished and attached layers is considered: a tissue layer containing blood vessels and a tissue layer containing no blood vessels. The Pennes model is applied for the tissue containing blood vessels. Applying the Laplace transform, then the inversion theorem for Laplace transforms and the Cauchy residue theorem, the desired skin temperature function is obtained. Applying the temperature function in a damage model, the severity and degree of damage can be determined. Validating this model against previous analytical, numerical and experimental data, the error rate is determined.

Tissue responses to fractional transient heating with sinusoidal heat flux condition on skin surface

A fractional model of Bioheat equation for describing quantitatively the thermal responses of skin tissue under sinusoidal heat flux conditions on skin surface is given. Laplace transform technique is used to obtain the solution in a closed form. The resulting formulation is applied to one-dimensional application to investigate the temperature distribution in skin with instantaneous surface heating for different cases. According to the numerical results and its graphs, conclusion about the fractional bioheat transfer equation has been constructed. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature. The comparisons are made with the results obtained in the case of the absence of time-fractional order. © 2016 Japanese Society of Animal Science.

Study of thermal behavior of a biological tissue: an equivalence of Pennes bioheat equation and Wulff continuum model

Equivalence of Pennes bioheat equation (PBHE) and Wulff continuum model (WCM) is established for a 1-D planar tissue. The derived condition of equivalence is specific to tissue without metabolic heat generation. Mathematical analysis is carried out to relate blood perfusion rate and local mean blood velocity that are needed in the analysis of WCM. It is found that the local mean blood velocity in a tissue is a direct function of square root of blood perfusion rate. This functional dependence is also established numerically by having same solution obtained from PBHE and WCM. Analysis is also done to check how closely the derived relation can be used for practical cases of breast tissue with and without a tumor. Blood velocity is a very important physiological quantity. Its measurement is a difficult process and requires a state-of-the-art technique. The proposed relation allows its computation merely from the knowledge of blood perfusion rate.

Lock-in thermal imaging for the early-stage detection of cutaneous melanoma: a feasibility study

This paper theoretically evaluates lock-in thermal imaging for the early-stage detection of cutaneous melanoma. Lock-in thermal imaging is based on the periodic thermal excitation of the specimen under test. Resulting surface temperature oscillations are recorded with an infrared camera and allow the detection of variations of the sample's thermophysical properties under the surface. In this paper, the steady-state and transient skin surface temperatures are numerically derived for a different stage of development of the melanoma lesion using a two-dimensional axisymmetric multilayer heat-transfer model. The transient skin surface temperature signals are demodulated according to the digital lock-in principle to compute both a phase and an amplitude image of the lesions. The phase image can be advantageously used to accurately detect cutaneous melanoma at an early stage of development while the maximal phase shift can give precious information about the lesion invasion depth. The ability of lock-in thermal imaging to suppress disturbing subcutaneous thermal signals is demonstrated. The method is compared with the previously proposed pulse-based approaches, and the influence of the modulation frequency is further discussed.

ANALYTICAL SOLUTIONS OF BIO-HEAT CONDUCTION ON SKIN IN FOURIER AND NON-FOURIER MODELS

In general, the transport of thermal energy in living tissue is a complex process. The analysis of the heat conduction of skin tissue is helpful for understanding of the bio-thermo-mechanical behavior of skin tissue. So far, three kinds of conduction law — (1) the Fourier model, (2) the C-V model and (3) dual-phase-lag (DPL) model — are often investigated in bio-thermal transfer process. In this study, the mathematical model of heat conduction of the skin tissue subjected to a general transient heating at the skin surface was established. The analytical solutions of these three conduction models are presented. In addition, the measure of thermal injury of the skin tissue subjected to a harmonic heating was investigated. It was found that the phenomenon of Fourier model is greatly different to those of the C-V and DPL models. Moreover, the effects of the phase lags, the heating frequency, and the heat quantity on the temperature variation and the index of thermal injury were significant. In sum, the analytical method can be used to solve the conduction problem of any one-layer tissue.

An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

This study analytically analyzes the changes in the temperature profile of a homogenous and isotropic medium having the same thermal parameters as a muscular tissue, due to the heat released by a single magnetic nanoparticle (MNP) to its surroundings when subject to different magnetic field profiles. Exploring the temperature behavior of a heated MNP can be very useful predicting the temperature increment of it immediate surroundings. Therefore, selecting the most effective magnetic field profile (MFP) in order to reach the necessary temperature for cancer therapy is crucial in hyperthermia treatments. In order to find the temperature profile caused by the heated MNP immobilized inside a homogenous medium, the 3D diffusive-heat-flow equation (DHFE) was solved for three different types of boundary conditions (BCs). The change in the BC is caused by the different MF profiles (MFP), which are analyzed in this article. The analytic expressions are suitable for describing the transient temperature response of the medium for each case. The analysis showed that the maximum temperature increment surrounding the MNP can be achieved by radiating periodic magnetic pulses (PMPs) on it, making this MFP more effective than the conventional cosine profile.