Bioheat Transfer Research Articles

Analytical Investigation of Non-Fourier Bioheat Transfer in the Axisymmetric Living Tissue Exposed to Pulsed Laser Heating Using Finite Integral Transform Technique

Abstract This article proposes the closed-form solution of the generalized non-Fourier model-based bioheat transfer equation (BHTE) in Cylindrical coordinates to understand the thermal behavior of living tissue heated by a pulsed laser. The axisymmetric living tissue exposed to the non-Gaussian temporal profile of laser heating has been considered to investigate the non-Fourier bioheat transfer phenomena. The closed-form solution of the generalized non-Fourier model-based BHTE with time-dependent thermal energy generation has been obtained through the finite integral transform (FIT) technique. The analytical solution was juxtaposed to the corresponding numerical solution in order to determine its reliability. The numerical solution of the aforementioned governing equation has been obtained by the finite volume method (FVM). The results of both analytical and numerical solutions have been verified using results given in published literature. Subsequently, the dual-phase-lag (DPL) model's findings were juxtaposed to those obtained using the hyperbolic and traditional Fourier models. The effect of different parameters like relaxation times corresponding to the temperature gradient and heat flux, metabolic energy generation, and blood perfusion on the resultant temperature distribution inside the axisymmetric living tissue exposed to pulsed laser heating has been discussed. The importance of this study might be found in various applications such as laser-based-photothermal therapy, melting of the surface of metal and alloys by laser heating.

Numerical evaluation of the duodenal mucosal resurfacing technique for the treatment of Type 2 diabetes

Backgrounds and objectivesThis work presents a numerical analysis of the Duodenal Mucosal Resurfacing (DMR) technique, which is a relatively new treatment for Type 2 diabetes that has been already tested in human beings. In this innovative strategy, an endoscopic catheter is placed inside the duodenum thus serving as a guide to an ablation device. A circumferential ablation is then performed by using a balloon filled with a hot fluid with pre- and post-cooling stages that allows for a controlled thermal procedure. Clinical outcomes indicate that the damaged duodenal lining induces a better control of glycemic levels. Therefore, a numerical evaluation of the efficiency of this treatment is carried out by utilizing the bioheat transfer equation in the transient form. MethodsThe finite volume method is used in the discretization of the energy equation and the results are verified by exploring the same mathematical model in a commercial finite-element package. The Arrhenius criterion for the evaluation of the thermally affected tissue is employed in this study. ResultsA systematic analysis of the simulations is performed by investigating two scenarios: one in which the lifting of the mucosal duodenum layer is achieved and another one where the lifting strategy is not implemented. The role of the magnitude of the blood perfusion coefficient, tissue thermal conductivity, peak, pre- and post-cooling temperatures is thoroughly explored, especially in connection with the evaluation of the extent of the thermally affected region. ConclusionsAccording to the simulations discussed in the present contribution, this treatment is capable of accurately targeting the cells in the mucosal layer without significantly affecting the outermost stratum of the organ if the lifting process is applied. However, for the case without lifting, the muscularis propria layer may reach temperatures above 42 °C during a short time interval and thus the treatment should be considered with caution by the physician.

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.

A numerical study of space‐fractional three‐phase‐lag bioheat transfer model during thermal therapy

AbstractPrediction of accurate temperature profile and control of temperature are two important factors to treat the cancerous cells effectively in the living tissue during thermal therapy. To deal with this, we have generated a space‐fractional mathematical model of bioheat transfer within the living skin tissue by using three‐phase‐lag constitutive relation. The present model with Dirichlet's boundary condition is investigated in the companionship of the metabolic and external heat source during the thermal therapy. Exponentially decaying (with position) laser heat source is used as an external heating source term. To find out the solution, the model is converted to an initial value problem by using a fractional backward finite difference scheme and then Runge–Kutta (4,5) scheme is applied for determining the temperature profile within the living biological skin tissue. The effect on the dimensionless temperature profile during thermal therapy due to variations in the value of parameters like an order of space‐fractional derivative, relaxation times, blood perfusion coefficient, rate of thermal conductivity, and the external laser heat source incorporated in the current bioheat transfer model is discussed graphically. Results obtained from the study are beneficial in the field of medicine, especially for oncologists.

Non-Fourier bioheat model for bone grinding with application to skull base neurosurgery.

Bone grinding is used to remove the skull bone and access tumors through the nasal passage during cranial base neurosurgery. The generated heat of the spherical diamond tool propagates and could damage the nerves or coagulate the arteries blood. Little is known about the non-Fourier behavior of heat propagation during bone grinding. Therefore, this study develops an analytical model of the hyperbolic Pennes bioheat transfer equation (HPBTE) to calculate the three-dimensional temperature and necrosis in the grinding region. In vitro experimental investigations were carried out, and the contact zone temperature was measured using an infrared thermography system to validate the proposed thermal model. The results demonstrate that the HPBTE provides more reliable temperature evaluation and thermal damage than Fourier or parabolic heat transfer equation (PHTE). Due to the low thermal diffusivity of the bone, the lower grinding feed rate leads to higher temperature amplitude and a smaller radius of the affected zone in the surface and depth of the bone. Also, the intensity of bone necrosis decreases with the increase of the feed rate, and the shape of the damage zone becomes stretched. This analytical model can assess the potential risk of the surgery before clinical trials. Also, it could be used for comparing the different operating conditions to minimize bone necrosis and improve the control process in neurosurgeries.

Fluid–Structure Interaction and Non-Fourier Effects in Coupled Electro-Thermo-Mechanical Models for Cardiac Ablation

In this study, a fully coupled electro-thermo-mechanical model of radiofrequency (RF)-assisted cardiac ablation has been developed, incorporating fluid–structure interaction, thermal relaxation time effects and porous media approach. A non-Fourier based bio-heat transfer model has been used for predicting the temperature distribution and ablation zone during the cardiac ablation. The blood has been modeled as a Newtonian fluid and the velocity fields are obtained utilizing the Navier–Stokes equations. The thermal stresses induced due to the heating of the cardiac tissue have also been accounted. Parametric studies have been conducted to investigate the effect of cardiac tissue porosity, thermal relaxation time effects, electrode insertion depths and orientations on the treatment outcomes of the cardiac ablation. The results are presented in terms of predicted temperature distributions and ablation volumes for different cases of interest utilizing a finite element based COMSOL Multiphysics software. It has been found that electrode insertion depth and orientation has a significant effect on the treatment outcomes of cardiac ablation. Further, porosity of cardiac tissue also plays an important role in the prediction of temperature distribution and ablation volume during RF-assisted cardiac ablation. Moreover, thermal relaxation times only affect the treatment outcomes for shorter treatment times of less than 30 s.

BNS: A Framework for Wireless Body Area Network Realistic Simulations.

Simulation is a useful and common technique to evaluate the performance of networks when the implementation of a real scenario is not available. Specifically for Wireless Body Area Networks (WBAN), it is crucial to perform evaluations in environments as close as possible to the real conditions of use. To achieve that, simulations must include different protocol layers involved in WBAN and models close to reality to create realistic simulation environments for e-health applications. To satisfy these needs, this work presents the BNS framework, a flexible tool for WBAN simulations. The proposal is an extension of the Castalia framework, which includes: (1) a new wireless channel model considering real radio-propagation over the human body; (2) an updated implementation of the WBAN MAC protocol in Castalia, with functionalities and requirements in accordance with the IEEE 802.15.6 standard; (3) a new comprehensive and configurable mobility model for simulating intra-WBAN communication; (4) a temperature module based on the Pennes bioheat transfer equation, to model the temperature of a WBAN node based on the activity of the node; and (5) a Healthcare Application Layer that implements data representation and a communication protocol between Personal Health Devices (PHD) following the ISO/IEEE 11073 standard. Three use cases are presented, where WBAN scenarios are simulated and evaluated using the proposed BNS framework. Results show that BNS is a valid and flexible tool to evaluate WBAN solutions through simulation.

Fractional thermal wave bio-heat equation based analysis for living biological tissue with non-Fourier Neumann boundary condition in laser pulse heating

In the present paper, the different heat transfer mechanisms in living biological tissue during pulse laser irradiation are studied with the fractional thermal wave bio-heat transfer (FTWBT) equation, the thermal wave bio-heat transfer (TWBT) equation and the Pennes bio-heat transfer (PBT) equation, respectively. The corresponding non-Fourier boundary condition is established and the analytical solutions based on the three models are obtained by employing the Fourier and Laplace transform methods. The heat wave propagation characteristics in biological tissues are revealed and discussed in detail. The results show that the FTWBT model has advantages over the others to describe the bio-heat transfer in laser therapy as long as the boundary condition is correct. The heat transfer predicted by the FTWBT model reveals the thermal diffusion feature as well as the thermal wave behavior, which is dependent on the fractional order parameter and biological tissue relaxation time.

Two-dimensional thermo-mechanical fractional responses to biological tissue with rheological properties

PurposeThe system of equations for fractional thermo-viscoelasticity is used to investigate two-dimensional bioheat transfer and heat-induced mechanical response in human skin tissue with rheological properties.Design/methodology/approachLaplace and Fourier’s transformations are used. The resulting formulation is applied to human skin tissue subjected to regional hyperthermia therapy for cancer treatment. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions.FindingsComparisons are made with the results anticipated through the coupled and generalized theories. The influences of volume materials properties and fractional order parameters for all the regarded fields are examined. The results indicate that volume relaxation parameters, as well as fractional order parameters, play a major role in all considered distributions.Originality/valueBio-thermo-mechanics includes bioheat transfer, biomechanics, burn injury and physiology. In clinical applications, knowledge of bio-thermo-mechanics in living tissues is very important. One can infer from the numerical results that, with a finite distance, the thermo-mechanical waves spread to skin tissue, removing the unrealistic predictions of the Pennes’ model.

Thermoelastic behavior of skin tissue induced by laser irradiation based on the generalized dual-phase lag model.

This paper analyzes the thermoelastic responses of skin tissue during laser irradiation based on a generalized dual-phase-lag (DPL) model. The method of separation of variables is utilized to obtain the analytical solutions for thermal and mechanical responses. The influences of some crucial parameters on temperature, displacement and stress evolutions are discussed, including the phase lag of heat flux, the phase lag of temperature gradient and the phase lag of laser pulse, the coupling factor between tissue and blood, the porosity of tissue, the equivalent diameter of tissue and the diameter of blood vessels. The generalized DPL bio-heat transfer model predicts different results from those by the classical DPL model and Pennes model. The equivalent diameter of tissue affects the coupling factor between tissue and blood, while the diameter of blood vessels mainly affects the porosity of tissue.

An integral transform solution for bioheat transfer in skin tissue subjected to surface laser irradiation

Two-dimensional non-Fourier heat conduction in soft skin tissue irradiated by a laser beam on its surface is investigated on the basis of biothermomechanics. A new semianalytic solution to the thermal wave model of bioheat transfer in terms of integrals of a known function is obtained by using Laplace and Hankel transforms as well as their inverse transforms. Based on the obtained semianalytic solution, the result of numerical example indicates the thermal wave behavior caused by the non-Fourier effect is distinct. There is significant difference between the thermal wave and classical Pennes bioheat transfer.

A three-dimensional model of transient bioheat transfer in the lower extremity during cryotherapy.

The purpose of this research was to create a computational model of the human thigh undergoing cryotherapy. The tissue temperatures were measured for five cold pack temperatures of -8°C, -4°C, 0°C, 4°C, and 8°C in addition to six different time intervals of cold application and ice removal. The depth of cold penetration and duration of local tissue cooling were investigated at 10 points during 30 min of application and 7 h of post-application. The model was created in CATIA, using a mid-axial cut of the human thigh MRI without pathology. After validation by the available clinical data, this research applied the finite-volume discretization method to solve bioheat transfer equations. A 16°C decrease in the cold pack temperature reduced the tissue temperatures located 1 and 2 cm below the fat by almost 3.34°C and 1.4°C, respectively, after 30 min of cold application. It took the tissues 10-15 min to start cooling down, and the temperature reached its plateau after 100 min. Thirty minutes of cold application declined the superficial tissue and deep tissue temperatures near the bone by 22.59°C and 0.48°C, respectively. Intense cryotherapy led to an insignificant change in the deep tissue temperature at 2 cm and deeper below the fat tissue. After ice removal, tissues continued cooling down for about 8 min until 40 min, depending on the tissue depth. This study proposed a 100-min cold therapy with 10 min of ice removal to optimize tissue cooling.

Bio-heat transfer analysis based on fractional derivative and memory-dependent derivative heat conduction models

The fractional derivative (FD) and memory-dependent derivative (MDD) are efficient methods to predict the transient thermal responses. In the present paper, for the first time, the FD and MDD are introduced into classical Pennes bio-heat conduction equation with single phase-lag and the corresponding bio-heat transfer models have been formulated with the aids of thermal energy conservation equation. The Laplace transform and numerical inverse transform method are adopted to get access to thermal responses due to temperature shock. Reductions of the present models to classical Pennes and single phase-lag bio-heat transfer models are presented and comparison between different FD and MDD in transient bio-heat transfer is carried out firstly. An approximate formulation of propagation speed of thermal signal in FD models is given according to results firstly. Influences of fractional derivative parameter and tempered parameter in FD, delay time in MDD, phase-lag time and rate of blood perfusion on temperature variation and distribution are carried out numerically. Both fractional derivative and memory-dependent derivative have the ability to predict thermal response between diffusion and wave behavior and CF fractional derivative and MDD with K3 may be suitable methods.

Identification of the thermo-physical properties of a stratified tissue. Adiabatic hypodermic wall

Biological living tissues possess thermophysical properties that are difficult to measure directly and their estimation is very important in order to decide the appropriate treatment procedure (e.g. place of inoculation and appropriate amount of drug dosage) in case an abnormality is detected. In the present paper, we numerically investigate, for the first time, the determination of several thermo-physical blood-tissue properties of a one-dimensional, multi-layered biological skin tissue subjected to external heating. In contrast to the usual parabolic model that assumes infinitely fast propagation of the heat signal, in the present paper, the bio-heat transfer in such a biological body is mathematically modelled by a hyperbolic partial differential equation, which takes into account that the thermal wave speed is finite. On the skin surface a convective boundary condition holds taking into account the heat exchange with the environment, whilst on the most inner wall of the tissue an adiabatic boundary condition applies. Then, in this framework, the piecewise constant thermo-physical properties of interest given by the thermal conductivity, heat capacity and blood perfusion rate are accurately and stably reconstructed from non-intrusive temperature measurements on the inner and outer boundaries of the multi-layered tissue by minimizing a weighted nonlinear least-squares objective function.

Design, simulation, and construction an air-conditioning system to eliminate any pathogenic microorganisms in the air

In this paper, for the first time, we have designed, simulated, and constructed an efficient air-conditioning system via a microwave plasma source to eliminate pathogens in the air, which can be found in crowded places such as hospitals and subways, and prevent the diseases' outbreak. The plasma air-conditioning system designed in this paper, besides having a high plasma density (increasing the probability of electrons collision with contaminants), uses a very high-temperature plasma (gas), which is an effective factor to eliminate any contamination. Also, to design and simulate the introduced system, COMSOL software, and its Electromagnetic Waves, Plasma, Laminar Flow, Heat Transfer in Fluids, and Bioheat Transfer modules were used; and the performance of the system has been entirely investigated. Finally, we have shown that the designed system, via an output power of 1000 W, a frequency of 2.45 GHz, and a standard airflow of 170 l/min, can destroy any microorganisms and pathogenic respiratory droplets in the air.

Determination of the thermo-physical properties of multi-layered biological tissues

Abnormal biological tissues possess unknown properties that must be estimated in order to decide the appropriate method of treatment in terms of amount of dosage and appropriate place of inoculation. The current work numerically investigates, for the first time, the simultaneous estimation of several thermo-physical properties of multi-layered tissues from internal temperature measurements. The heat propagation within the tissues is modelled by the thermal-wave model of bio-heat transfer, accounting for the finite speed of heat propagation. On the skin surface, a convective boundary condition holds taking into account the heat exchange with the environment, whilst on the most inner wall of the tissues a Dirichlet boundary temperature condition is prescribed. Accurate and stable reconstruction of the piecewise constant properties given by the thermal conductivity, heat capacity and blood perfusion rate is successfully achieved for two physical examples concerning three- and four-layered, one-dimensional tissues, subjected to externally induced aggression.

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

In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments.

Measurement of Ex Vivo Liver, Brain and Pancreas Thermal Properties as Function of Temperature.

The ability to predict heat transfer during hyperthermal and ablative techniques for cancer treatment relies on understanding the thermal properties of biological tissue. In this work, the thermal properties of ex vivo liver, pancreas and brain tissues are reported as a function of temperature. The thermal diffusivity, thermal conductivity and volumetric heat capacity of these tissues were measured in the temperature range from 22 to around 97 °C. Concerning the pancreas, a phase change occurred around 45 °C; therefore, its thermal properties were investigated only until this temperature. Results indicate that the thermal properties of the liver and brain have a non-linear relationship with temperature in the investigated range. In these tissues, the thermal properties were almost constant until 60 to 70 °C and then gradually changed until 92 °C. In particular, the thermal conductivity increased by 100% for the brain and 60% for the liver up to 92 °C, while thermal diffusivity increased by 90% and 40%, respectively. However, the heat capacity did not significantly change in this temperature range. The thermal conductivity and thermal diffusivity were dramatically increased from 92 to 97 °C, which seems to be due to water vaporization and state transition in the tissues. Moreover, the measurement uncertainty, determined at each temperature, increased after 92 °C. In the temperature range of 22 to 45 °C, the thermal properties of pancreatic tissue did not change significantly, in accordance with the results for the brain and liver. For the three tissues, the best fit curves are provided with regression analysis based on measured data to predict the tissue thermal behavior. These curves describe the temperature dependency of tissue thermal properties in a temperature range relevant for hyperthermia and ablation treatments and may help in constructing more accurate models of bioheat transfer for optimization and pre-planning of thermal procedures.

Analysis of the time-space fractional bioheat transfer equation for biological tissues during laser irradiation

Laser technology has been widely used in biomedical therapies and external surgeries. To promote its applications, a good thermal model is required to analyze the temperature distribution within the living tissues. In this paper, we develop a time-space fractional hyperbolic bioheat transfer model to study the non-Fourier bioheat transfer process within the living biological tissues during laser irradiation. Based on the the L1 approximation for the Caputo time fractional derivative and the central difference scheme for the Riesz fractional derivative, the finite difference algorithm is developed for the laser irradiation problem. The efficiency and accuracy of this method have been verified by using three numerical examples. In view of the thermophysical properties of the biological tissues, the effect of time and space fractional parameters, phase lag time and blood perfusion rate on temperature distribution within living biological tissues have been analyzed and shown graphically.

Development of heat and moisture transfer model for predicting skin burn of firefighter in fire environments

A model of heat and moisture transfer based on partial differential equations was developed to establish a functional design platform for predicting safety and health of firefighter in fire-fighting and emergency rescue. This model consisted of heat and moisture transfer in clothing, Pennes bio-heat transfer and Henriques burn integral equations. The clothing model was based on the traditional heat transfer model, but considered the effects of phase change, absorption/desorption and moisture transfer on heat exchange in the clothing. The experimental results were used to validate the predictive precision of the model, indicating that the skin temperature obtained from the model presented a good consistency with the experiment. The design platform was used to predict the minimum exposure time of firefighter for avoiding the skin burn injuries. Besides, the design platform was the preliminary evaluation tool of functional development on firefighting protective clothing, which could be used to represent heat and moisture transfer and carry out parameter study for providing suitable instructions for developing new products.