Bioheat Equation Research Articles

An Alternative Approach for Evaluating Induced and Contact Currents for Compliance with Their Exposure Limits (100 kHz to 110 MHz) in IEEE Std C95.1-2019.

The Institute of Electrical and Electronics Engineers establishes exposure reference levels (ERLs) for electric fields (E-fields) (0-300 GHz) and both induced (IIND) and contact currents (ISC) (<110 MHz) in its standard, IEEE Std C95.1™-2019 (IEEE C95.1). The "classical" scenarios addressed in IEEE C95.1 include a free-standing, grounded "reference" person (IIND) or an ungrounded reference person in manual contact with an adjacent grounded conductor (ISC), each exposed to a vertically oriented E-field driving the currents. The ERLs for current from 100 kHz to 110 MHz were established to limit heating in the finger (from touch), ankle (IIND), and wrist (ISC from grasp contact), specifying the 6-min average specific absorption rate (SAR, W kg-1) as the dosimetric reference limit (DRL); whole-body E-field ERLs are 30-min averages. The DRLs were established assuming a default "effective" local cross-section (9.5 cm2) and consistent with a composite tissue conductivity of ~0.5 S m-1. A previous publication described the misalignment of the ERLs for E-fields with the ERLs for IIND (which extends to ISC) and also proposed a ramped E-field ERL from 100 kHz to 30 MHz. For the frequency range 100 kHz to 110 MHz, this paper proposes temperature increase (ΔT) in ankle and wrist as the preferred effect metric associated with IIND and ISC; applying the E-field ERLs as surrogates for limits to these currents; and adopting the proposed ramp. The analysis of ΔT is based on the tissue mix in realistic anatomic depictions of ankle and wrist cross-sections; relevant tissue properties posted online; published tissue perfusion data; and anthropometric data on a large sample of male and female adults in the US military, allowing an estimate of effects over a range of body size. To evaluate ΔT versus frequency and time, the Penne bioheat equation was adapted with convective cooling from arterial blood as the lone cooling mechanism. The analysis revealed that IINDs and ISCs induced by ERL-level E-fields produce SARs in excess of the local DRLs (in some cases far exceed). Calculations of time to ΔT of 5 °C, reflective of a potentially adverse (painful) response, resulted in worst-case times for effects in the ankle on the order of minutes but on the order of 10s of s in wrist. Thus, compliance with the E-field ERL, as assessed as a 30-min whole-body average is incompatible with the time course of potentially adverse effects in ankle and wrist from IIND and ISC, respectively. Further analysis of the relevant exposure/dose scenarios and consensus of stakeholders with a multi-disciplinary perspective will enable the development of a revised standard, practical from a compliance perspective and protective of all persons.

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.

Simulation and clinical validation of the breast temperature field based on a multi-point heat source model

To investigate the relationship between cell metabolism heat production and breast diseases, and to differentiate the benign and malignant nature of breast tumors based on this foundation, this study established a refined three-dimensional model of the breast suitable for analyzing the temperature field of the breast, based on the anatomical structure and physiological characteristics of the breast, using the Pennes bio-heat transfer equation. Compared to traditional breast models, this model closely approximates the physiological structure of the breast, thereby enabling a more accurate simulation of the temperature distribution within the breast for both normal and embedded tumors. This study obtains the heat production of the corresponding position of the lesion area in patients with breast tumors through the multi-point heat source model. The heat production is embedded in the breast model containing the tumor. Then, the temperature field analysis is conducted on the normal breast model and the breast model with malignant and benign tumors. Finally, the obtained temperature values are compared. The analysis reveals that the temperature values in the malignant tumor regions are higher than those in the benign tumor regions. Furthermore, based on the distribution of temperature fields, tumor sizes are estimated and compared with those observed in ultrasound images, demonstrating a close correspondence between the results. Therefore, this paper provides an essential novel analytical approach for distinguishing between benign and malignant breast cancer.

Numerical simulations to analyze the impact of vascular network complexity over cryosurgical treatment process of two-dimensional liver tumor tissue

Cryosurgery is a minimally invasive surgery widely used for liver cancer. The vascular network present in the tissue affects the temperature distribution across the tissue. The present study focuses upon the numerical simulations of cryosurgery for liver tumor with vascular network. The phase change which occurs in bioheat equation has been tackled using Effective heat capacity method and the vessels are constructed following Murray’s Law. Blood flow in the vascular network is assumed to be Newtonian and laminar. The continuity equation, Navier’s Stoke Equation coupled with heat energy equation is solved for the vascular network. Finite Element Method (FEM) has been implemented for the numerical simulations using COMSOL Multiphysics software. The ice balls generated in 600s around the cryoprobe are analyzed. Necrosis of the tissue with the presence of vascular network have been determined for tissue kept under freezing for 600s. The numerical results have been compared with experimental results of Ge et al.[1] and found to be in good agreement with the experimental study. Further, impact of vascular network for optimal planning of the surgery have been numerically simulated in the present study.

Numerical simulation in magnetic resonance imaging radiofrequency dosimetry

Magnetic Resonance Imaging (MRI) employs a radiofrequency electromagnetic field to create pictures on a computer. The prospective biological consequences of exposure to radiofrequency electromagnetic fields (RF EMFs) have not yet been demonstrated, and there is not enough evidence on biological hazards to offer a definite response concerning possible RF health dangers. Therefore, it is crucial to research the health concerns in reaction to RF EMFs, considering the entire exposure in terms of patients receiving MRI. Monitoring increases in temperature in-vivo throughout MRI scan is extremely invasive and has resulted in a rise in the utilization of computational methods to estimate distributions of temperatures. The purpose of this study is to estimate the absorbed power of the brain exposed to RF in patients undergoing brain MRI scan. A three-dimensional Penne’s bio-heat equation was modified to computationally analyze the temperature distributions and potential thermal effects within the brain during MRI scans in the 0.3 T to 1.5 T range (12.77 MHz to 63.87 MHz). The instantaneous temperature distributions of the in-vivo tissue in the brain temperatures measured at a time, t = 20.62 s is 0.2 °C and t = 30.92 s is 0.4 °C, while the highest temperatures recorded at 1.03 min and 2.06 min were 0.4 °C and 0.6 °C accordingly. From the temperature distributions of the in-vivo tissue in the brain temperatures measured, there is heat build-up in patients who are exposed to electromagnetic frequency ranges, and, consequently, temperature increases within patients are difficult to prevent. The study has, however, indicated that lengthier imaging duration appears to be related to increasing body temperature.

Solid-state laser (266 nm) as an alternative to ArF excimer laser (193 nm) for corneal reshaping: Comparative numerical study of the thermal effect.

Laser corneal reshaping is a safe and effective technique utilized to treat common vision disorders. An advanced laser delivery system equipped with a pulsed UV laser with specific parameters is used to ablate parts of the cornea surface to correct the existing refractive error. The argon fluoride (ArF) excimer pulsed gas laser at 193 nm is the most employed type in the commercial devices for such treatments. This laser is generated using a mixture of Argon, Fluorine, and a significant amount of Neon gases. However, due to the ongoing Russian-Ukraine war, the availability of Neon gas is currently very limited, as this region is considered the primary supplier of pure Neon gas. Consequently we suggest replacing the common ArF laser source in the commercial devices with a solid-state (forth harmonic neodymium-doped yttrium aluminum garnet laser at 266 nm). This replacement uses the same operation parameters, optics, and scanning algorithm. Parameters from five commercial devices (Zeiss MEL 90, Technolas TENEO 317, Alcon Wave Light EX 500, Schwind Amaris 750 s, OptoSystems MICROSCAN VISUM) were compared with those of the i-ablation device, a research device that uses a 266 nm laser source. Our goal is to reduce production costs through a simple modification that has a significant impact. Consequently, the present study aims to find an alternative laser source for the current ArF laser without exchanging the complete system's design. This recommendation is based on a numerical simulation study. The thermal effect on a human cornea model was numerically evaluated using finite-element solutions of Pennes' bioheat equation on the COMSOL platform by applying two laser wavelengths. The results demonstrated that changing the laser source significantly impacts the thermal effect, even with the same laser settings. All studied devices showed a reduction in the thermal effect to below 40°C, compared with nearly 100°C under ordinary conditions.

Model to identify comfortable cloth fabric for human body during thermal stress due to physical exercise

Physical exercise enhances heat generation in human skin and subcutaneous tissues causing thermal stress. This thermal stress causes discomfort in the human body and deteriorates the physical performance of the human subjects. Appropriate choice of cloth for outer covering of human body is necessary to prevent this to provide comfort during the thermal stress. A mathematical model is proposed in this study to analyze the thermal stresses in human skin and subcutaneous tissues covered with various different cloth fabrics. The model considers four compartments namely cloth, epidermis, dermis, subcutaneous tissues. The bioheat equation along with appropriate boundary condition is employed in this model for one dimensional unsteady state case. The numerical simulation is performed using forward and central finite difference formulas. The findings have been utilized to examine how different types of fabric impact thermal stress experienced by the layers of human skin during physical activity. The polyester is found to be superior in comparison to cotton fabric as it shows less thermal stress and thus can be concluded to be more comfortable as a dress material.

Effect of high blood flow on heat distribution and ablation zone during microwave ablation-numerical approach.

Microwave ablation has become a viable alternative for cancer treatment for patients who cannot undergo surgery. During this procedure, a single-slot coaxial antenna is employed to effectively deliver microwave energy to the targeted tissue. The success of the treatment was measured by the amount of ablation zone created during the ablation procedure. The significantly large blood vessel placed near the antenna causes heat dissipation by convection around the blood vessel. The heat sink effect could result in insufficient ablation, raising the risk of local tumor recurrence. In this study, we investigated the heat loss due to large blood vessels and the relationship between blood velocity and temperature distribution. The hepatic artery, with a diameter of 4 mm and a height of 50 mm and two branches, is considered in the computational domain. The temperature profile, localized tissue contraction, and ablation zones were simulated for initial blood velocities 0.05, 0.1, and 0.16 m/s using the 3D Pennes bio-heat equation, temperature-time dependent model, and cell death model, respectively. Temperature-dependent blood velocity is modeled using the Navier-Stokes equation, and the fluid-solid interaction boundary is treated as a convective boundary. For discretization, we utilized elements for the wave propagation model, elements for the Pennes bio-heat model, and elements for the Navier-Stokes equation, where represents the computational domain. The simulated results show that blood vessels and blood velocity have a significant impact on temperature distribution, tissue contraction, and the volume of the ablation zone.

Physical activities aid in tumor prevention: A finite element study of bio-heat transfer in healthy and malignant breast tissues

The objective of the present research is to explore the temperature diffusion in healthy and cancerous tissues, with a specific focus on how physical activity impacts on the weakening of breast tumors. Previous research lacked numerical analysis regarding the effectiveness of physical activity in tumor prevention or attenuation, prompting an investigation into the mechanism behind physical activity and tumor prevention from a bio-heat transfer perspective. The study employs a realistic model of human breasts and tumors in COMSOL Multiphysics® to analyze temperature distribution by utilizing Penne's bio-heat equation. The research examines their influence on tissue temperature by varying tumor diameter (10–20 mm) and exercise intensities (such as walking speeds and other activities like carpentry, swimming, and marathon running). Results demonstrate that cancerous tissues generate notably more heat than normal tissues at rest and during physical activity. Smaller tumors exhibit higher temperatures during exercise, emphasizing the significance of tumor size in treatment effectiveness. Tumor temperatures range between 40 and 43.2 °C, while healthy tissue temperatures remain below 41 °C during physical activity. High-intensity exercises, particularly swimming, walking at 1.8 m/s, and marathon running, display a therapeutic effect on tumors, increasing effectiveness with intensity. The temperatures of healthy and malignant tissues rise noticeably due to constant metabolic heat and decreased blood flow. The study also identifies the optimal duration of high-intensity exercise, recommending at least 20 min for optimal therapeutic outcomes. The outcomes of this research would help individuals, doctors, and cancer researchers understand and weaken malignant tissues.

Analytical solutions in the modeling of the endovenous laser ablation

We modeled the operative treatment of incompetent truncal veins using endovenous laser ablation (EVLA). The main concern regarding the thermoablative technique is tissue damage, which is correlated with (1) the energy provided by the laser power and (2) temperature distribution. Our objective was to accurate the two functions, namely the fluence rate and the temperature, depending on the thermoablative technique and the endovenous laser treatment (ELT). First, we considered three differential equations: diffusion, heat, and bioheat equations in the endovenous-perivenous multidomain to describe the lumen, the vein wall, the tissue pad, and the skin. Second, we examined the power source according to the Beer-Lambert law in the incident beam irradiance and the heat source as the so-called absorbed optical power density. Third, we checked out the heat transfer at the skin boundary according to Newton’s law of cooling, which stands for a Robin boundary condition. For this new model, we proposed exact solutions: applying differential equations techniques, we solved (1) a diffusion approximation of the radiative transfer equation under the considered power source, and (2) the coupled heat and bioheat equations under the considered heat source accomplished with the Robin boundary condition. Then, we graphically illustrated the fluence rate profile and discussed its time dependence and steady state. Besides, we discuss thermal damage to the vein-tissue system and present open problems.

Magnetic Nanoparticles in Cancer Thermotherapy: A Mathematical Approach to Optimal Treatment Design

Thermotherapy, often called Hyperthermia treatment is a cancer treatment modality that involves raising the temperature of the tumor mass to over 315 K (42°C) for a specific duration, which leads to cell death through apoptosis or necrosis. Magnetic Particle Hyperthermia (MPH) is a non-invasive technique where magnetic nanoparticles are introduced into the tumor and then exposed to a magnetic field which convert magnetic energy into heat. Due to their high acidity, tumor cells are more sensitive to heat than healthy cells, meaning that heating the tumor to 315-319 K (42°C–46°C) can destroy it with minimal damage to the surrounding healthy tissues. During hyperthermia treatment, blood perfusion helps protect the healthy tissues around the tumor by dissipating excess heat. This paper presents a study where the temperature profiles within a spherical hepatic tumor mass are estimated by solving Pennes’ Bio-heat Equation, incorporating a power term. The study uses analytical methods to examine the effects of magnetic fluid hyperthermia treatment. Numerical illustrations are carried out using magnetite (Fe3O4) nanoparticles having an average diameter of 10.9 nm with mineral oil as a carrier liquid, subjected to magnetic fields of varying intensities. By analysing the model, the present work helps in designing an optimal treatment protocol by identify the time threshold of the therapy for varying magnetic field strengths.

Theoretical and Experimental Analysis of the Effect of Vaporization Heat on the Interaction between Laser and Biological Tissue

A theoretical model, based on the classical Pennes’ bioheat theory, incorporating various boundary conditions, was established and compared to analyze the influence of the latent heat of vaporization via simulation. The aim was to elucidate the extent of its influence. The thermal damage rate, governed by the vaporization heat of biological tissue, is introduced as a key factor. Functional relationships between temperature and incident laser power, spatial position, and time are derived from the classical Pennes’ bioheat equation. According to the theoretical model, numerical simulations and experimental validations are conducted using Comsol Multiphysics 6.0, considering the tissue latent heat of vaporization. The model incorporating the latent heat of vaporization proved more suitable for analyzing the interactions between laser and biological tissue, evident from the degree of fit between simulated and experimental data. The minimum deviations between theoretical and experimental observations were determined to be 2.43% and 5.11% in temperature and thermal damage, respectively. Furthermore, this model can be extended to facilitate the theoretical analysis of the impact of vaporization heat from different primary tissue components on laser-tissue interaction.

Effect of radius-dependent diffusion behavior of various gold nanoparticles on photothermal therapy

Among the various anti-cancer treatments, photothermal therapy (PTT) is gaining traction as it is a non-invasive treatment. PTT is a treatment technique involving the use of a laser to raise the temperature of the target tumor until it dies. In this study, the effects of PTT under various conditions of squamous cell carcinoma (SCC) occurring in the skin were numerically analyzed and optimized. Gold nanoparticles (AuNPs) with different radii were injected into the center of the SCC. Subsequently, the diffusion behavior of the AuNPs was analyzed to calculate the distribution area of the AuNPs that changed over time. Furthermore, at each elapsed time point after injection, the temperature distribution in the tissue was calculated, as treatment was performed using varying laser intensities. The diffusion coefficient of AuNPs was calculated using the Stokes–Einstein equation, and diffusion behavior of AuNPs in biological tissues was analyzed using the convection–diffusion equation. Additionally, temperature distribution was analyzed using the Pennes bioheat equation. The effect of PTT under each condition was quantitatively analyzed using apoptotic variables. As a result, As the radius of AuNPs increased, the optimal treatment start time was derived as 2 h, 8 h, 8 h, and 12 h, respectively, and the laser intensity at that time was derived as 0.44 W, 0.46 W, 0.42 W, and 0.42 W, respectively. The study findings will provide reference for the optimization of the efficacy of PTT.

Assessment of local temperature elevation at the surface of tissue exposed to radiation of milimeter waves using simplified analytical approach

Dominant effect of human exposure to electromagnetic fields in GHz frequency range corresponding to operation of 5G mobile communications systems is tissue heating i.e. local temperature elevation at the body surface, i.e. skin, ear and eyes. For the frequencies below transition frequency of 6GHz specific absorption rate (SAR) is used to quantify the volume heating. On the other hand, the surface heating above 6GHz is quantified via absorbed power density (Sab ). Once these quantities are determined by means of internal field dosimetry procedures it is possible to determine the local surface temperature increase by solving the bio-heat transfer equation. The present paper deals with the calculation of tissue surface heating due to exposure to millimeter waves. Internal dosimetry is based on the planar tissue model exposed to dipole antenna radiation. Electromagnetic model is based on the analytical solution of Pocklington integro-differential equation while the assessment of tissue surface heating in planar tissue model has been carried by analytically solving a simplified variant of the bio-heat transfer equation. Some illustrative results for power density and temperature elevations will be presented for different antenna parameters.

Numerical study of the induction of intratumoral apoptosis under microwave ablation by changing slot length of microwave coaxial antenna.

Recent advances in technology have led to an increase in the detection of previously undetected deep-located tumor tissue. As a result, the medical field is using a variety of methods to treat deep-located tumors, and minimally invasive treatment techniques are being explored. In this study, therapeutic effect of microwave ablation (MWA) on tumor generated inside liver tissue was analyzed through numerical analysis. The distribution of electromagnetic fields in biological tissues emitted by microwave coaxial antenna (MCA) was calculated through the wave equation, and the thermal behavior of the tissue was analyzed through the Pennes bioheat equation. Among various treatment conditions constituting MWA, tumor radius and the slot length inside the MCA were changed, and the resulting treatment effect was quantitatively confirmed through three apoptotic variables. As a result, each tumor radius has optimal power condition for MWA, 2.6W, 2.4W, and 3.0W respectively. This study confirmed optimal therapeutic conditions for MWA. Three apoptotic variables were used to quantitatively identify apoptotic temperature maintenance inside tumor tissue and thermal damage to surrounding normal tissue. The findings of this study are expected to serve as a standard for treatment based on actual MWA treatment.

Proactive esophageal cooling during laser cardiac ablation: A computer modeling study.

Laser ablation is increasingly used to treat atrial fibrillation (AF). However, atrioesophageal injury remains a potentially serious complication. While proactive esophageal cooling (PEC) reduces esophageal injury during radiofrequency ablation, the effects of PEC during laser ablation have not previously been determined. We aimed to evaluate the protective effects of PEC during laser ablation of AF by means of a theoretical study based on computer modeling. Three-dimensional mathematical models were built for 20 different cases including a fragment of atrial wall (myocardium), epicardial fat (adipose tissue), connective tissue, and esophageal wall. The esophagus was considered with and without PEC. Laser-tissue interaction was modeled using Beer-Lambert's law, Pennes' Bioheat equation was used to compute the resultant heating, and the Arrhenius equation was used to estimate the fraction of tissue damage (FOD), assuming a threshold of 63% to assess induced necrosis. We modeled laser irradiation power of 8.5 W over 20 s. Thermal simulations extended up to 250 s to account for thermal latency. PEC significantly altered the temperature distribution around the cooling device, resulting in lower temperatures (around 22°C less in the esophagus and 9°C in the atrial wall) compared to the case without PEC. This thermal reduction translated into the absence of transmural lesions in the esophagus. The esophagus was thermally damaged only in the cases without PEC and with a distance equal to or shorter than 3.5 mm between the esophagus and endocardium (inner boundary of the atrial wall). Furthermore, PEC demonstrated minimal impact on the lesion created across the atrial wall, either in terms of maximum temperature or FOD. PEC reduces the potential for esophageal injury without degrading the intended cardiac lesions for a variety of different tissue thicknesses. Thermal latency may influence lesion formation during laser ablation and may play a part in any collateral damage.

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.

Model-based correction of rapid thermal confounds in fluorescence neuroimaging of targeted perturbation.

An array of techniques for targeted neuromodulation is emerging, with high potential in brain research and therapy. Calcium imaging or other forms of functional fluorescence imaging are central solutions for monitoring cortical neural responses to targeted neuromodulation, but often are confounded by thermal effects that are inter-mixed with neural responses. Here, we develop and demonstrate a method for effectively suppressing fluorescent thermal transients from calcium responses. We use high precision phased-array 3MHz focused ultrasound delivery integrated with fiberscope-based widefield fluorescence to monitor cortex-wide calcium changes. Our approach for detecting the neural activation first takes advantage of the high inter-hemispheric correlation of resting state dynamics and then removes the ultrasound-induced thermal effect by subtracting its simulated spatio-temporal signature from the processed profile. The focused -sized ultrasound stimulus triggered rapid localized activation events dominated by transient thermal responses produced by ultrasound. By employing bioheat equation to model the ultrasound heat deposition, we can recover putative neural responses to ultrasound. The developed method for canceling transient thermal fluorescence quenching could also find applications with optical stimulation techniques to monitor thermal effects and disentangle them from neural responses. This approach may help deepen our understanding of the mechanisms and macroscopic effects of ultrasound neuromodulation, further paving the way for tailoring the stimulation regimes toward specific applications.

Thermal relaxation parameters estimation of non-Fourier heat transfer in laser-irradiated living tissue using the Levenberg-Marquardt algorithm

The present work is concerned with solving the inverse heat transfer problem (IHTP) to estimate the thermal relaxation parameters corresponding to the dual phase lag (DPL) model-based bio-heat transfer in laser-irradiated living tissue. This problem is divided into two parts: direct and inverse problems. The solution of the inverse problem has been obtained using the Levenberg–Marquardt algorithm. On the other hand, the solution to the direct problem is obtained by solving the DPL model-based bio-heat transfer equation (BHTE) with the transient radiative transfer equation (TRTE). So, the TRTE has been numerically solved by the modified discrete ordinate method (DOM) to find the intensity field in the living tissue subjected to short-pulsed laser radiation, and it acts as a heat source in the DPL model-based BHTE. So, the DPL model-based BHTE has been analytically solved by employing the finite integral transform technique to get the temperature variation inside the laser-irradiated living tissue. First, the computer code developed for estimating unknown thermal relaxation parameters using the Levenberg–Marquardt algorithm has been verified against the data given in the literature, and found good agreement between them. Then, the thermal response of laser-irradiated living tissue has been investigated. After that, the influence of sensor position on the sensitivity of the IHTP solution has been discussed. The impact of the total transient readings and the measurement error on estimating the unknown parameters have been investigated. The present study’s findings can significantly contribute to various parameter estimation problems where the conventional methods for direct measurements of parameters are impossible or very difficult. Furthermore, the current results may considerably impact the study of the thermic response of living tissue during laser-based photothermal therapy.

Bio-heat transfer modeling in lungs

In cardiac surgery where extracorporeal circulation is used, the lungs are temporarily disconnected from the body and are connected to a device that provides air and blood. To minimize the risk of tissue damage, the lungs are subjected to mild hypothermia. Heat transfer modeling offers the potential to enhance temperature regulation through a more advanced approach. A thermal model, based on a thermal quadrupoles, also called two-port network, offers a wide frequency range applicability, making it suitable for modeling the human breathing. This modeling approach can also be adapted to incorporate the influence of blood flow, which also serves as a natural temperature regulator in the human body. This is accomplished by combining the thermal two-port network with the bio-heat equation. The main contributions are in the analytical expressions of the thermal impedances and by proposing a Butterworth approximation model for the equivalent impedances of lung thermal transfers.