Blood Perfusion Rate Research Articles

Analytical solution of three-dimensional temperature field for skin tissue considering blood perfusion rates under laser irradiation and thermal damage analysis

An analytical solution of the three-dimensional transient temperature distribution for skin tissue when heated by a laser heat source is presented in this work. An equation for the three-dimensional bioheat transfer of skin tissue is obtained firstly, and the transient temperature value at any point inside the skin tissue can be solved using the separation variable method and the Newton-Cotes method. Previous research primarily focused on semi-infinite domains, while this work presents an analytical solution for finite domains. A comparison of present analytical solution with simulation software results and numerical solution is given to demonstrate the feasibility of the analytical solution. The three-dimensional temperature distribution of skin tissue irradiated by a laser is theoretically studied. The extent of thermal damage to skin tissue is assessed by substituting the analytical solution of the temperature field for laser-irradiated skin tissue into the thermal damage equation. The calculations in this work reveal that the variation of temperature field in biological tissues is dependent not only on the laser incident light intensity and the optical parameters of the tissues but also on the heat transfer properties of the biological tissues, such as the blood perfusion rates.

Thermoviscoelastic response of skin tissue via fractional Pennes bioheat and fractional viscoelasticity

In this paper, the thermoviscoelastic response of skin tissue, as a typical class of viscoelastic biological tissue, subject to thermal shock is studied based on the fractional Kelvin-Voigt model and fractional Pennes bioheat conduction. A time-fractional biothermoviscoelastic governing equation is derived and initial-boundary value conditions are given for monolayer skin tissue of finite thickness. The temperature change and thermal stress of viscoelastic skin tissue are obtained by the Laplace transform and its inversion using matlab software. The influences of viscosity coefficient, relaxation times, fractional-order viscosity/heat parameter, and blood perfusion rate of skin tissue on the temperature distribution and the elastic displacement are analyzed. The numerical results show that fractional-order viscosity does not affect temperature, whereas fractional-order heat flow does. Moreover, fractional-order heat flow affects the sensitivity of blood perfusion rate to the thermodynamic response.

Bio-thermal response during laser haemorrhoidoplasty: an exclusive analytical and numerical approach for theoretical investigation.

Haemorrhoidal disease is identified by declension of the inflamed and bleeding of vascular tissues of the anal canal. Traditionally, haemorrhoids are associated with chronicconstipation and the most common symptoms are irritation in anus region, pain and discomfort, swelling around anus, tender lumps around the anus and rectal bleeding (depending upon the grade of haemorrhoid). Among the several conventional treatment procedures (commonly mentioned as, rubber band litigation, sclerotherapy and electrotherapy), laser haemorrhoidoplasty is an out-patient and less-invasive laparoscopic procedure. From literature survey it has been observed that an exclusive theoretical model depicting the impact of 1064nm wavelength laser wave on living tissues subjected to haemorrhoid therapy is not available. This research work is a pioneering attempt to develop a theoretical study attributing specifically on laser therapy of haemorrhoid treatment based on Pennes' biological heat transfer model. The corresponding mathematical model has been solved by analytical method to establish thermal response of tissue during the treatment and also the same has been solved a numerical approach based on finite difference method to validate the feasibility of former method due to unavailability of any theoretical model. Impact of variation of blood perfusion term, laser pulse time and optical penetration depth on temperature response of skin tissue is captured. The tissue temperature decreases along with time of laser exposure with increasing the blood perfusion rate as it carries away large amount of heat. With the increase in laser pulse time, tissue temperature declines due to shorter pulse time resulting in higher energy consumed by electrons. The research outcome is successfully validated with less than 1% of error observed between the appointed analytical and numerical scheme.

Investigating the protective performance of turnout gears for firefighters under diverse exposure conditions: Effect of age and body segments

Present work investigates the impact of different exposures (flame, 50/50 convection and radiation, and radiation alone) on thermal performance of firefighters' clothing. The protective performance is evaluated across various body segments for firefighters of different ages. Transient heat transport equations are numerically discretized using finite difference approach. The computational domain comprises of a three-layer fabric assembly, a single-layer skin, and a microclimate between the fabric and skin. Heat transfer in the porous fabric assembly results from the interaction of both conduction and incident radiation penetrating through confined hot air within the fabric. The energy equation of fabric employs a two-flux model, encompassing self-emission originating from absorbed incident radiation in the encapsulated hot air. A nonlinear bioheat transfer model, accounting for age and body segment, incorporates temperature-dependent thermal conductivity, blood perfusion rate, skin thickness, and heat generation from metabolism, shivering, and external work. Results found that first and second-degree burn durations decrease by 30.85 % and 37.92 %, 26.73 % and 29.76 %, and 24.23 % and 26.63 % for flame, 50/50 convection-radiation and pure radiation heat exposure respectively as firefighter’s age from 25 to 65 years. The protective attire excels the best for the torso against direct flame but is the least effective for shielding arms from radiant heat. Moreover, the transition time from first to second-degree burn injury decreases by 64.77 %, 65.73 %, and 66.03 % for arms, and by 70.93 %, 66.29 %, and 67.22 % for legs in flame, 50/50 convective-radiative, and purely radiant heat exposures, respectively, with a 100 % reduction in skin conductivity coefficient.

Running water as first aid for burn and early hypothermia: A numerical investigation on human skin

The cooling rate of the running water on the burn wound depends on both physiological and water parameters. Prolonged use of cold water on the burn wound may cause hypothermia. We aimed to investigate the running water as first aid for burns and find out the cooling effect of bio-heat transfer to avoid hypothermia. Measuring the temperature variation across the tissue layers is the main limitation of working with in vivo experiments and a one-dimensional model. Moreover, multiple boundary conditions cannot be used in one-dimensional models. These limitations motivate us to develop ADVENTURE Thermal to perform a finite element analysis of the bio-heat equation in the 3D skin model for the burn analysis. A circular wound was developed on a 3-layered skin with a hot disk of 92 °C for 15 s. Then the wound area was cooled with the running water, which had different parameters. Running water at 15 °C takes 20–30 % less time than being immersed in water at the same temperature. Results reveal that cooling rates of burns significantly depend on the temperature and heat transfer coefficient of the water. To avoid hypothermia, the use of the running water with a heat transfer coefficient ranging from 800 to 1000 W/m2 °C (flow rate around 1.6 L/min) and temperature ranging from 15 to 20 °C for not more than 10 min is recommended. In the end, the running water cools the tissue with a small blood perfusion rate faster. The results agree with the experiment.

A fully automatic deep learning-based method for segmenting regions of interest and predicting renal function in pediatric dynamic renal scintigraphy.

Accurate delineation of renal regions of interest (ROIs) is critical for the assessment of renal function in pediatric dynamic renal scintigraphy (DRS). The purpose of this study was to develop and evaluate a deep learning (DL) model that can fully automatically delineate renal ROIs and calculate renal function in pediatric 99mTechnetium-ethylenedicysteine (99mTc-EC) DRS. This study retrospectively analyzed 1,283 pediatric DRS data at a single center from January to December 2018. These patients were divided into training set (n = 1027), validation set (n = 128), and testing set (n = 128). A fully automatic segmentation of ROIs (FASR) model was developed and evaluated. The pixel values of the automatically segmented ROIs were calculated to predict renal blood perfusion rate (BPR) and differential renal function (DRF). Precision, recall rate, intersection over union (IOU), and Dice similarity coefficient (DSC) were used to evaluate the performance of FASR model. Intraclass correlation (ICC) and Pearson correlation analysis were used to compare the consistency of automatic and manual method in assessing the renal function parameters in the testing set. The FASR model achieved a precision of 0.88, recall rate of 0.94, IOU of 0.83, and DSC of 0.91. In the testing set, the r values of BPR and DRF calculated by the two methods were 0.94 (P < 0.01) and 0.97 (P < 0.01), and the ICCs (95% confidence interval CI) were 0.94 (0.90-0.96) and 0.94 (0.91-0.96). We propose a reliable and stable DL model that can fully automatically segment ROIs and accurately predict renal function in pediatric 99mTc-EC DRS.

Magnetic resonance imaging of blood perfusion rate based on Helmholtz decomposition of heat flux.

Objective.Thermal property (TP) maps of human tissues are useful for tumor treatment and diagnosis. In particular, the blood perfusion rate is significantly different for tumors and healthy tissues. Noninvasive techniques that reconstruct TPs from the temperature measured via magnetic resonance imaging (MRI) by solving an inverse bioheat transfer problem have been developed. A few conventional methods can reconstruct spatially varying TP distributions, but they have several limitations. First, most methods require the numerical Laplacian computation of the temperature, and hence they are sensitive to noise. In addition, some methods require the division of a region of interest (ROI) into sub-regions with homogeneous TPs using prior anatomical information, and they assume an unmeasurable initial temperature distribution. We propose a novel robust reconstruction method without the division of an ROI or the assumption of an initial temperature distribution.Approach.The proposed method estimates blood perfusion rate maps from relative temperature changes. This method avoids the computation of the Laplacian by using integral representations of the Helmholtz decomposition of the heat flux.Main Result.We compare the reconstruction results of the conventional and proposed methods using numerical simulations. The results indicate the robustness of the proposed method.Significance.This study suggests the feasibility of thermal property mapping with MRI using the robust proposed method.

Optimization and experimental characterization of the innovative thermo-brachytherapy seed for prostate cancer treatment.

Adjuvant administration of hyperthermia (HT) with radiation therapy in the treatment of cancer has been extensively studied in the past five decades. Concurrent use of the two modalities leads to both complementary and synergetic enhancements in tumor management, but presents a practical challenge. Their simultaneous administration using the same implantable thermo-brachytherapy (TB) seed source has been established theoretically through magnetically mediated heat induction with ferromagnetic materials. Careful consideration, however, showed that regular ferromagnetic alloys lack the required conductivity to generate enough power through eddy current to overcome heat dissipation due to blood perfusion at clinically measuredrates. We characterized the TB implant that combines a sealed radioactive source with a ferrimagnetic ceramic (ferrite) core, serving as a self-regulating HT source when placed in an alternating electromagnetic field. To increase the heat production and uniformity of temperature distribution the empty spacers between radioisotope seeds were replaced by hyperthermia-only (HT-only)seeds. The heat generation due to eddy currents circulating in the seed's thin metal shell, surrounding the core, depends drastically on the core permeability. We identified a soft ferrite material ( ) as the best candidate for the core, owing to its high permeability, the HT-range Curie temperature, adjustable through material composition, and a sharp Curie transition, leading to heat self-regulation, with no invasive thermometry required. The core permeability as a function of temperature was calculated based on measured resistor-inductor (RL) circuit parameters and material B-H curves. The thickness of the shell was optimized separately for TB and HT-only seeds, having slightly different dimensions. Heat generation was calculated using the power versus temperature approximation. Finally, the temperature distribution for a realistic prostate LDR brachytherapy plan was modeled with COMSOL Multiphysics for a set of blood perfusion rates found in theliterature. The small size of the investigated ferrite core samples resulted in demagnetization significantly decreasing the relative permeability from its intrinsic value of ∼5000 to about 11 in the range of magnetic field amplitude and frequency values relevant to HT. The power generated by the seed dropped sharply as the shell thickness deviated from the optimal value. The optimized TB and HT-only seeds generated 45 and 267 mW power, respectively, providing a HT source sufficient for >90% volume coverage even for the highest blood perfusion rates. The toxicity of the surrounding normal tissues was minimal due to the rapid temperature fall off within a few millimeters distance from aseed. The investigated TB and HT-only seed prototypes were shown to provide sufficient power for the concurrent administration of radiation and HT. In addition to being used as a source for both radiation and heat at the onset of cancer therapy, these implanted seeds would be available for treatment intensification in the setting of salvage brachytherapy for locally radiorecurrent disease, possibly as a sensitizer to systemic therapies or as a modulator of the immune response, without another invasive procedure. Experimentally determined parameters of the ferrite material cores provided in this study establish a mechanistic foundation for future pre-clinical and clinical validationstudies.

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.

Developing computational methods of heat flow using bioheat equation enhancing skin thermal modeling efficiency

PurposeThe main objective of this paper is to investigate the response of human skin to an intense temperature drop at the surface. In addition, this paper aims to evaluate the efficiency of finite difference and finite volume methods in solving the highly nonlinear form of Pennes’ bioheat equation.Design/methodology/approachOne-dimensional linear and nonlinear forms of Pennes’ bioheat equation with uniform grids were used to study the behavior of human skin. The specific heat capacity, thermal conductivity and blood perfusion rate were assumed to be linear functions of temperature. The nonlinear form of the bioheat equation was solved using the Newton linearization method for the finite difference method and the Picard linearization method for the finite volume method. The algorithms were validated by comparing the results from both methods.FindingsThe study demonstrated the capacity of both finite difference and finite volume methods to solve the one-dimensional and highly nonlinear form of the bioheat equation. The investigation of human skin’s thermal behavior indicated that thermal conductivity and blood perfusion rate are the most effective properties in mitigating a surface temperature drop, while specific heat capacity has a lesser impact and can be considered constant.Originality/valueThis paper modeled the transient heat distribution within human skin in a one-dimensional manner, using temperate-dependent physical properties. The nonlinear equation was solved with two numerical methods to ensure the validity of the results, despite the complexity of the formulation. The findings of this study can help in understanding the behavior of human skin under extreme temperature conditions, which can be beneficial in various fields, including medical and engineering.

Detection of multiple tumors through temperature response of a human brain using inverse bioheat transfer based on swarm optimization

In this article, an innovative inverse regularized framework has been proposed for a bio-medical problem to detect tumors in the human brain via temperature. Most of the thermal data obtained through infrared thermography is sensitive towards errors, thus a regularized approach is sought from the literature. The best inversion algorithm, WOA, together with a hybrid GWOCS are utilized. Pennes model is used for the formulation of heat transfer within the human brain. Using inverse analysis, the unknown blood perfusion rate ωi is retrieved in the regularized environment. The current research reported that at positions where tumor cells are present, the temperature rises. Moreover, with an increase in time, the temperature of the cancer cells increases, whereas no change in the temperature of tissue without tumor is seen. This observation marks the presence of tumor. Elastic net regularization (λ=0.1, α=10−2) for WOA and (λ=0.9, α=10−4) for GWOCS shows the least relative error. After regularization, the perfusion rate is retrieved. A clear distinction of two tumors from the brain tissue is observed. The obtained perfusion rate is used to reconstruct the temperature profile. An excellent matching of the reconstructed temperature field and the exact field is obtained, even when the forward data contain measurement errors. The obtained set of perfusion rate is appropriate for tumor detection, up to 7% error in the measured data. Thus, the proposed comparative procedure is found suitable for the bio-heat transfer problem.

Influence of different heat transfer models on therapeutic temperature prediction and heat-induced damage during magnetic hyperthermia

Magnetic hyperthermia regulates the therapeutic temperature within a specific range to damage malignant cells after exposing the magnetic nanoparticles inside tumor tissue to an alternating magnetic field. The therapeutic temperature of living tissues can be generally predicted using Pennes' bio-heat equation after ignoring both the inhomogeneity of biological structure and the microstructural responses. Although various of the bio-heat transfer models proposed in literature fix these shortages, there is still a lack of a comprehensive report on investigating the discrepancy for different models when applied in the magnetic hyperthermia context. This study compares four different bio-heat equations in terms of the therapeutic temperature distribution and the heat-induced damage situation for a proposed geometric model, which is established based on computed tomography images of a tumor bearing mouse. The therapeutic temperature is also used as an index to evaluate the effect of two key relaxation times for the phase lag behavior on bio-heat transfer. Moreover, this work evaluates the effects of two blood perfusion rates on both the treatment temperature and the cumulative equivalent heating minutes at 43 °C. Numerical analysis results reveal that relaxation times for phase-lag behavior as well as the porosity for living tissues directly affect the therapeutic temperature variation and ultimately the thermal damage for the malignant tissue during magnetic hyperthermia. The dual-phase-lag equation can be converted into Pennes’ equation and simple-phase-lag equation when relaxation times meet specific conditions during the process of heat transfer. In addition, different blood perfusion rates can result in an amplitude discrepancy for treatment temperature, but this parameter does not change the characteristics of thermal propagation during therapy.

Model-Optimizing Radiofrequency Parameters of 3D Finite Element Analysis for Ablation of Benign Thyroid Nodules.

Radiofrequency (RF) ablation represents an efficient strategy to reduce the volume of thyroid nodules. In this study, a finite element model was developed with the aim of optimizing RF parameters, e.g., input power and treatment duration, in order to achieve the target volume reduction rate (VRR) for a thyroid nodule. RF ablation is modelled as a coupled electro-thermal problem wherein the electric field is applied to induce tissue heating. The electric problem is solved with the Laplace equation, the temperature distribution is estimated with the Pennes bioheat equation, and the thermal damage is evaluated using the Arrhenius equation. The optimization model is applied to RF electrode with different active tip lengths in the interval from 5 mm to 40 mm at the 5 mm step. For each case, we also explored the influence of tumour blood perfusion rate on RF ablation outcomes. The model highlights that longer active tips are more efficient as they require lesser power and shorter treatment time to reach the target VRR. Moreover, this condition is characterized by a reduced transversal ablation zone. In addition, a higher blood perfusion increases the heat dispersion, requiring a different combination of RF power and time treatment to achieve the target VRR. The model may contribute to an improvement in patient-specific RF ablation treatment.

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.

Parameter variation effects on millimeter wave dosimetry based on precise skin thickness in real rats

This study presents a parametric analysis of the steady-state temperature elevation in rat skin models due to millimeter wave exposure at frequencies from 6–100 GHz. The statistical data of the thickness of skin layers, namely epidermis, dermis, dermal white adipose tissue, and panniculus carnosus, were measured for the first time using the excised tissues of real male Sprague–Dawley rats. Based on the precise structure obtained from the histological analysis of rat skin, we solve the bioheat transfer equation to investigate the effects of changes in parameters, such as body parts and thermal constants, on the absorbed power density and temperature elevation of biological tissues. Owing to the notably thin dermal white adipose tissue layer, the surface temperature elevation in the rat head and dorsal skin at 6–100 GHz is 52.6–32.3% and 83.3–58.8% of the average values of different human skin models, respectively. Our results also reveal that the surface temperature elevation of rat skin may correlate with the tissue thickness and deep blood perfusion rates.

Effect of Bronchial Blood Flow on Respiratory Heat Exchange: A Mathematical Analysis for Infectious Diseases

Abstract The present study aims to mathematically analyze the role of bronchial blood flow on heat transfer in respiratory infections. In general, the exchange of heat transfer in various infectious diseases like COVID-19 caused by SARS-CoV-2 has adversely affected respiration by reducing the physiological efficiency of the human respiratory tract. The mechanism of heat exchange through airway walls with the bronchial blood circulation still needs to be thoroughly studied for infectious diseases. In this article, a three-dimensional (3D) spatio-temporal theoretical model is developed to estimate the possible role of bronchial blood on heat exchange during breathing. The local description of the model is presented in a comprehensive and consistent dimensionless framework to explicitly state the actual physiological background. The global description is framed by a multicompartment-based approach, and the algorithm is solved using an advanced numerical scheme to ensure computational tractability. The numerical study elucidates the role of inhalation air temperature, breathing cycles, blood perfusion rate, and mucosal hydration. The outcomes of the algorithm estimate the parameters of the isothermal saturation boundary (ISB), which is defined as the position in the respiratory tract where the temperature of inhaled air comes in equilibrium with the body core saturation temperature. The derived results help to understand the pathophysiological threshold limits and recommend the values to evaluate respiratory distress. With the variations of inspiratory flow conditions, it is observed that the ISB position shifts to the distal branches with the increment in inhalation temperature, breathing rate and virus infection, and decrement in blood perfusion rate. The two antiparallel effects are observed: inhalation of cold air transmits the viral infection, and inhalation of warm air produces thermal injury. However, both can be well controlled by suitable ventilation rates. The observed threshold values may be helpful in clinical trials to correlate the anatomic configuration with pathophysiology.

Thermal damage analysis in tissue caused by electromagnetic radiation using space–time collocation method

Over the past half-century, the usage of external heat sources in medical applications has increased substantially. Controlling heat damage is essential for ensuring the efficacy of the treatment. Living tissues are highly non-homogeneous; hence, it is important to take into account the effects of local non-equilibrium on their thermal behavior. In the present study, two- and three- space dimensional time-space fractional single-phase-lag (SPL) and dual-phase-lag (DPL) models for bio-heat transfer in tissue are considered to study the thermal damage and temperature in tissue caused by electromagnetic radiation as an external heat source. The considered mathematical models are more general and consider non-Fourier as well as non-local effects. We obtain the numerical solution for the models by combining Gaussian RBFs and shifted Chebyshev polynomials in the space and time directions, respectively. The RBFs depend on Euclidean distance, so they can easily be used in multidimensional space domain, and the use of Chebyshev polynomials gives spectral accuracy in time direction. It is also explored how different parameters, such as blood perfusion rate Wb, phase lags τq, τt, and fractional derivatives α, β, affect the temperature distribution and thermal damage in the tissue.

Numerical simulation of non–linear skin model with energy dissipation during hyperthermia and its validation with experimental data

This work deals with a non–linear skin model with energy dissipation exposed to hyperthermia therapy based on a Gaussian–type external heat source and also consider that the blood perfusion rate relies linearly on temperature. Since skin tissue is very sensitive to temperature, it is crucial to predict the temperature response with energy dissipation to ensure hyperthermia efficacy and minimize adverse effects. The present model, which is supported by experimental data, indicates that the temperature profile of skin tissue increases less in comparison to the non–linear Pennes model due to energy dissipation. A hybrid strategy is utilized to get computed outcomes for the present problem and obtained outcome is compared to the analytical outcome in a specific situation and is confirmed with high precision through table and graph. To damage a significant number of cancerous cells width, we have to manage or reduce enough value of the antenna constant accordingly, and the length of the probe region may be changed according to the position of the tumor or cancer cells in skin tissue. The temperature profile at the targeted area reduces when the values of rate of thermal conductivity, rate of blood perfusion per unit volume and blood perfusion constant increase.

Treatment Modelling of a 3D Tumour in Brain by Laser-Induced Interstitial Thermotherapy.

Introduction: There are some ways to examine heat transfer in tumor tissue, which is an important issue in bioengineering. One of these ways uses the bioheat equation, proposed by Pennes, in a continuous medium. Another one uses a porous medium to model heat transfer in living tissues. The objective of this paper was to study an approach to modelling the temperature distribution and tumour ablation in brain tissue and compare results to Pennes' approach. Methods: This approach presents and uses a porous medium as the tissue instead of a continuous medium. In addition, the two approaches (simulation in continuous and porous medium) are compared in terms of temperature simulation and amount of cell ablation. The density, heat conduction factor, and blood perfusion rate are considered functions of temperature. Results: In these approaches, after an 85-second treatment, the temperature increases to about 90°C. The temperature increase of the porous medium is relatively the same as that of the continuous medium and for this reason, the amount of cancerous cells that are ablated in a porous medium is approximately the same as that in a continuous medium. The volume of cell ablation is about 6500 mm3 for two ideas. In addition, the degree of damage, computed from the Arrhenius integral method, and the ablated volume of the tumour endorse equality at the end of treatment. According to the results, similar to the continuous approach, the porous approach predicts the temperature and amount of volume of damaged cells. Conclusion: Therefore, it is possible to use the porous approach instead of the Pennes approach for tumour treatment.

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.