Pennes Bioheat Transfer Equation Research Articles

Microwave Ablation Therapy for Hepatocellular Carcinoma: The Effect of Metabolic Heat on Temperature Distribution

Hepatocellular carcinoma is the main cause of liver cancer and one of the most occurring cancers worldwide. Microwave Ablation (MWA) is a method to destroy cancer cells by heating tumors above 50°C. Cancerous tissues can have high metabolic heat rates and affect temperature gain and distribution in thermal therapies. This research clarifies the metabolic heat effects in MWA therapy of liver cancer. Using Pennes Bioheat transfer equation with finite element numerical method, this research simulates temperature distribution with metabolic heat value ranging from 368,1 W/m3 to 29000 W/m3. The heat generated by metabolic heat is lower than the MWA heat source. However, the temperature increase should be considered as it can increase healthy surrounding tissue temperature to dangerous levels.

Patient-specific temperature distribution prediction in laser interstitial thermal therapy: single-irradiation data-driven method

Laser interstitial thermal therapy (LITT) is popular for treating brain tumours and epilepsy. The strict control of tissue thermal damage extent is crucial for LITT. Temperature prediction is useful for predicting thermal damage extent. Accurately predicting in vivo brain tissue temperature is challenging due to the temperature dependence and the individual variations in tissue properties. Considering these factors is essential for improving the temperature prediction accuracy. Objective. To present a method for predicting patient-specific tissue temperature distribution within a target lesion area in the brain during LITT. Approach. A magnetic resonance temperature imaging (MRTI) data-driven estimation model was constructed and combined with a modified Pennes bioheat transfer equation (PBHE) to predict patient-specific temperature distribution. In the PBHE for temperature prediction, the individual specificity and temperature dependence of thermal tissue properties and blood perfusion, as well as the individual specificity of optical tissue properties were considered. Only MRTI data during one laser irradiation were required in the method. This enables the prediction of patient-specific temperature distribution and the resulting thermal damage region for subsequent ablations. Main results. Patient-specific temperature prediction was evaluated based on clinical data acquired during LITT in the brain, using intraoperative MRTI data as the reference standard. Our method significantly improved the prediction performance of temperature distribution and thermal damage region. The average root mean square error was decreased by 69.54%, the average intraclass correlation coefficient was increased by 37.5%, the average Dice similarity coefficient was increased by 43.14% for thermal damage region prediction. Significance. The proposed method can predict temperature distribution and thermal damage region at an individual patient level during LITT, providing a promising approach to assist in patient-specific treatment planning for LITT in the brain.

Quantitative investigation on the effects of eyeball geometry, blood perfusion and natural convection in retinal laser surgery

The photothermal effects of laser on tissue are widely used in ophthalmology to treat retinal diseases. The accurate modelling of retinal laser surgery will prove valuable guidance for clinic treatment. There are several important issues should be carefully evaluated during retinal laser surgery modelling, including the eye geometry (whole eye or fundus only, retinal pigment epithelium layer incorporated or not), blood perfusion and natural convection. In previous publications, the existence of the anterior part of eyeball and retinal pigment epithelium layer is neglected to simply the eye geometry due to low laser light absorption (anterior part of eyeball) or small volume occupation (retinal pigment epithelium layer), respectively. However, the justification of this treatment has not been conducted. In this study, we will quantitatively investigate these factors systemically in a large pulse duration range that covers all the retinal laser surgery used in clinic. To do this, we present a bioheat transfer model for the simulation of the thermal response of the eye to laser irradiation. In the simulation, the 3D whole-eye geometry is considered. The Pennes bioheat transfer equation is adopted for the whole-eye temperature modelling. Simultaneously, we treat the fundus as a multilayered medium that all primary components, including RPE layer, are considered for first time in whole eye modelling. Our model calculates the thermal responses of the eye during laser retinal surgery with the pulse duration from nanosecond to tens of second. The effects of eye geometry, blood perfusion and natural convection are clearly clarified based on the laser pulse duration and incident energy used. The results show that neglecting the anterior part of eyeball will introduce the computational error more than 27 %. The existence of the retinal pigment epithelium layer should always be considered in retinal laser surgery modelling in all pulse durations used in clinic, otherwise more than 20 % computational error will be generated. When the pulse duration is longer than 10s, the effect of blood perfusion and natural convection in vitreous body should both be considered.

Analysis of Optimal Treatment Starting Time for Photothermal Therapy Through Analysis of Diffusion Behavior of Gold Nanoparticles.

Due to its distinct advantage of non-invasive application in treatment, photothermal therapy (PTT) is being studied by many researchers to reduce the need for surgical incisions. It is characterized by the injection of nanoparticles into biological tissue as photothermal agents (PTAs) which diffuse within the tissue. In this study, the diffusion behavior of various doses of gold nanoparticles (AuNPs) injected into tumor tissues is analyzed and the effectiveness of PTT at each elapsed time after injection is confirmed by numerical analysis. The diffusion behavior of AuNPs within biological tissues is assessed using the convection-diffusion equation, while the temperature distribution is determined using the Pennes bioheat transfer equation. In addition, the effect of the diffusion behavior of AuNPs on the effectiveness of PTT is quantitatively confirmed by analyzing the temperature distribution in the medium through the apoptotic variable. Numerical simulation parameters are selected with doses ranging from 100 to 400 μg/mL, elapsed time after injection from 1 min to 24 h, and laser power ranging from 0 to 1 W. After evaluating PTT's efficacy in every situation, it was discovered that a dosage of 100-300 μg/mL produced the best therapeutic result, with the highest impact occurring 12 hours after injection. In contrast, when the dosage was 400 μg/mL, the highest therapeutic effect was achieved after 18 hours post-injection. Additionally, it was discovered that the ideal laser power at each injection dose was 0.22, 0.14, 0.12, and 0.12 W, respectively. The conditions required to achieve the optimal treatment effect at each dosage, presented here, are expected to accelerate the commercialization of PTT.

Application of multipoint heat source model to breast surface temperature map

This paper proposed a new method of the clinical analysis of breast tumors based on infrared thermal imaging. The theoretical foundation was constructed on the basis of the widely-used Pennes bio-heat transfer equation to find the relationship between the body surface temperature distribution and the inner heat source. Then, a multi-point heat source model was established. Benign and malignant lesions could be distinguished by analyzing the feature parameters of inner heat source. Moreover, without harm to and contact with human body, this method was suitable for breast cancer screening for its good sensitivity and rapid diagnosis process.

Effect of porous heat transfer model on different equivalent thermal dose methods considering an experiment-based nanoparticle distribution during magnetic hyperthermia

Magnetic fluid hyperthermia damages malignant cells by keeping the therapeutic temperature within a specific range after magnetic nanoparticles (MNPs) are exposed to an alternating magnetic field. The temperature distribution inside bio-tissue is usually predicted by a classic Pennes bio-heat transfer equation, which considers a heat source due to a homogeneous distribution for MNPs. Aiming at this problem, this study compares the Pennes model to a porous heat transfer model, named local thermal non-equilibrium equation, by considering an experiment-based MNPs distribution, and evaluates the thermal damage degree for malignant tissue by two different thermal dose methods. In addition, this study evaluates the effect of porosity and different blood perfusion rates on both effective treatment temperature and equivalent thermal dose. Simulation results demonstrate that different bio-heat transfer models can result in significant differences in both the treatment temperature profile and the thermal damage degree for tumor region under the same power dissipation of MNPs. Furthermore, scenarios considering a temperature-dependent blood perfusion rate or a lower porosity can have a positive effect on the temperature distribution inside tumor, while having a lower value in the maximum equivalent thermal dose in both thermal dose evaluation methods.

Adaptive PID Control Approach Considering Simulated Annealing Algorithm for Thermal Damage of Brain Tumor During Magnetic Hyperthermia

Magnetic nanofluid hyperthermia (MNH) damages malignant cells by the heat generated by magnetic nanoparticles (MNPs) exposed to an alternating magnetic field during therapy. The key point for magnetic hyperthermia is to maintain the treatment temperature to a safe range for bio-tissue, in which malignant tissue will be damaged due to its higher heat sensitivity but not the healthy tissue. However, the therapeutic system for MNH should be a non-linear one since the treatment temperature is generally determined by many certain and uncertain factors, which result in the difficulty to modulate the temperature to a specific range in a practical application. This study proposes a control method for a MNH system by introducing a proportional-integral-derivative control (PID) algorithm, and dynamically optimizes the PID coefficients for the proposed system by considering simulated annealing algorithm during therapy. The treatment temperature distribution for bio-tissue is obtained by solving an improved Pennes bio-heat transfer equation using finite element method. The simulation results demonstrate that the proposed control system can effectively modulate the power dissipation for MNPs and further exactly regulate the transient treatment temperature to an expected value. In addition, this proposed system can also automatically adapt to different cases during therapy, in which the nanofluid concentration distribution inside tumor region changes with nanofluid injection strategy.

Numerical study of high-intensity focused ultrasound (HIFU) in fat reduction.

This study aimed to investigate the effect of fat-layer thickness and focal depth on the pressure and temperature distribution of tissue. Computer simulations were performed for the skin-fat layer models during high-intensity focused ultrasound (HIFU) treatment. The acoustic pressure field was calculated using the nonlinear Westervelt equation and coupled with the Pennes bioheat transfer equation to obtain the temperature distribution. To investigate the effect of the thickness of the fat layer on pressure and thermal distributions, the thickness of the fat layer behind the focal point (z=13.5mm) changed from 8 to 24mm by 2mm step. The pressure and temperature distribution spectra were extracted. The simulated results were validated using the experimental results with a 98% correlation coefficient (p<0.05). There was a significant difference between the pressure amplitude and temperature distribution for the 8-14mm thickness of the fat layer (p<0.05). By changing the focal point from 11.5 to 13.5mm, the maximum acoustic pressure at the focal point increased 66%, and the maximum temperature was 56%, respectively. Considering the specific treatment plan for each patient, according to the skin and fat layer thicknesses, can help prevent side effects and optimize the treatment process of HIFU.

On the magnetic nanoparticle injection strategy for hyperthermia treatment

We developed a dedicated computational framework by coupling the lattice-Boltzmann-method (LBM) modeling and the particle-swarm-optimization (PSO) algorithm to search optimal strategies of magnetic nanoparticle (MNP) injection for hyperthermia-based cancer treatment. Two simplified tumor models were considered: a circular model representing geometrically regular tumors and an elliptic model representing geometrically irregular tumors, both sharing the same area. The temperature distribution in the tumor and its surrounding healthy tissue was predicted by solving the Pennes’ bio-heat transfer equation (PBHTE). Both single- and multi-site injection strategies were explored. The results suggest that the multi-site injection strategies generally work well, while the single-site injection strategy fails even on the simplest circular tumor model. The more the injection sites, the better the performance. In particular, when the number of injection sites reaches eight, all temperature requirements can be nearly 100% satisfied in both tumor models. Whether or not including the minimum dose requirement in the objective function only affects the optimization results by less than 2%. The thermal dose was also assessed by considering both temperature and heat exposure time. It was found that the optimal multi-site injection strategies perform reasonably well for both tumor models. Although the setting is only two dimensional and the optimization is on very simplified tumor models, the framework adopted in this present study works well and can provide useful insights into magnetic hyperthermia treatment.

A coupled BioHeat transfer model for customized whole-eye modeling in retinal laser surgery

The photothermal effects of laser on tissue are widely used in ophthalmology to treat retinal diseases. The multiscale retinal lesion from the micrometer size to the millimeter size can be thermally targeted by adjusting the pulse duration from nanoseconds to tens of seconds. A large-scale difference among target lesions has brought extra challenge for retinal laser surgery modeling. In this study, we developed a coupled whole-eye model for retinal laser surgery. In the model, the Pennes bioheat transfer equation was adapted for the whole-eye temperature modeling. Simultaneously, we treated the fundus as a multilayered porous medium made of a tissue matrix buried with highly absorbing chromophores (melanin or blood). Two-temperature equations, one for the chromophore and the other for the surrounding tissue, were developed on the basis of the local thermal nonequilibrium theory of porous media. The Pennes and two-temperature models were coupled together to calculate the thermal responses of eye during several laser retinal surgery processes with pulse duration from nanoseconds to tens of seconds. Simulation results proved that our model was capable of modeling the laser retinal surgery process at different time scales. Furthermore, the coupled model was applied in a real fundus anatomy from a patient with diabetic retinopathy to illustrate its feasibility in customized laser protocol planning.

Conjugate heat transfer analysis of laser-irradiated cylindrical-shaped biological tissue embedded with the optical inhomogeneity

The current study is associated with the numerical investigation of the thermal behavior of cylindrical-shaped biological tissue during laser-based photo-thermal therapy. The light-tissue interaction has been modeled using the transient radiative transfer equation (TRTE). The TRTE in a cylindrical coordinate system is solved using the modified discrete ordinate method to obtain the intensity distribution inside the biological tissue. The solution of TRTE is coupled with Pennes bio-heat transfer equation (BHTE) to understand the thermic response of biological tissue. The Pennes BHTE is solved using the finite volume method (FVM). The two different types of optical inhomogeneity (absorption and scattering inhomogeneity) are considered in the current study. The inhomogeneity's optical and thermophysical properties may be the same/different from the homogeneous biological tissue. This conjugate heat transfer problem (CHTP) is solved using the harmonic mean technique. First, the present result is verified with the data available in the literature. Subsequently, the effect of inhomogeneity's optical properties on the temperature distribution is investigated. A comparative study between the same and different thermophysical properties of the biological tissue and inhomogeneity is performed. This study will help to accurately model the thermal characteristics of the laser-irradiated biological tissue having different thermophysical properties than the inhomogeneity.

Numerical simulation of the effect of injection sites arrangement on the thermal ablation in the magnetic fluid hyperthermia

Magnetic hyperthermia ablates malignant cells by the heat-dissipating from magnetic nanoparticles (MNPs) when subjects to an alternate magnetic field. To reveal the heat transfer mechanism for magnetic fluid hyperthermia (MFH) and analyze the effect of injection site arrangement on the temperature distribution during magnetic fluid hyperthermia. A three-dimensional multi-physical model was established to obtain the temperature distribution of the treated tumor tissues, the concentration distribution of magnetic fluid, effective treatment volume (Veff), and thermal damage fraction of the tumor. The treatment temperature distribution for a proposed physical model is predicted by solving Pennes bio-heat transfer equation using the finite element method, in which a heat source in form of a Gaussian distribution is used as the power dissipation of MNPs. The results demonstrate that the size of the heat source has a greater effect on the maximum temperature of the heat source center under a single injection site. Additionally, it found that the effective treatment volume is not the sum of the effective treatment volumes at each injection site for the multisite injections. The effective treatment volume shows a strong nonlinear increase with the number of injection site increases compared with the single injection site. The multisite injection can significantly increase the effective treatment volume during the hyperthermia process and achieve the effect of agglomeration heating. For eight injection sites, the optimal effective treatment volume change rate (εV) reached 94.7%. Additionally, the temperature distribution uniformity of eight injection sites is greatly improved compared with other injection site arrangements under an equal dose. The damage fraction of single site injection from 0.12 up to 0.55 when the magnetic hyperthermia treatment time increases from 0 to 40 min while the damage fraction of eight sites injection from 0.23 up to 0.94. In the clinical treatment process, the distance between the injection sites and the time of magnetic hyperthermia can be reasonably arranged according to the size, shape, and type of the tumor, which not only can obtain a good thermal ablation effect but can effectively reduce the thermal damage to normal tissues.

A 3-D virtual human model for simulating heat and cold stress.

In this study, we extended our previously developed anatomically detailed three-dimensional (3-D) thermoregulatory virtual human model for predicting heat stress to allow for predictions of heat and cold stress in one unified model. Starting with the modified Pennes bioheat transfer equation to estimate the spatiotemporal temperature distribution within the body as the underlying modeling structure, we developed a new formulation to characterize the spatial variation of blood temperature between body elements and within the limbs. We also implemented the means to represent heat generated from shivering and skin blood flow that apply to air exposure and water immersion. Then, we performed simulations and validated the model predictions with experimental data from nine studies, representing a wide range of heat- and cold-stress conditions in air and water and physical activities. We observed excellent agreement between model predictions and measured data, with average root mean squared errors of 0.2°C for core temperature, 0.9°C for mean skin temperature, and 27 W for heat from shivering. We found that a spatially varying blood temperature profile within the limbs was crucial to accurately predict core body temperature changes during very cold exposures. Our 3-D thermoregulatory virtual human model consistently predicted the body's thermal state accurately for each of the simulated hot and cold environmental conditions and exertional heat stress. As such, it serves as a reliable tool to assess whole body, localized tissue, and, potentially, organ-specific injury risks, helping develop injury prevention and mitigation strategies in a systematic and expeditious manner.NEW & NOTEWORTHY This work provides a new, unified modeling framework to accurately predict the human body's thermal response to both heat and cold stress caused by environmental conditions and exertional physical activity in one mathematical model. We show that this 3-D anatomically detailed model accurately predicts the spatiotemporal temperature distribution in the body under extreme conditions for exposures to air and water and could be used to help design medical interventions and countermeasures to prevent injuries.

Thermoelastic response of skin using time-fractional dual-phase-lag bioheat heat transfer equation

In this paper, a time-fractional dual-phase-lag (DPL) bioheat heat conduction model is presented to treat thermoelastic response of skin subjected to sudden temperature shock. The skin tissue is treated as a monolayered thermoelastic material. A modified Pennes bioheat transfer equation with non-Fourier effect is introduced to capture the influence of blood perfusion rate in the skin tissue on temperature distribution. The transient response of the temperature field of skin tissue is derived analytically and calculated numerically. The mechanical response is considered and the elastic displacement induced by temperature change is evaluated. The effects of two relaxation times and fractional orders of heat flux and temperature gradient together with blood flow on the temperature distribution in the skin tissue are analyzed.

Effects of non-Fourier bioheat transfer on bone drilling temperature in orthopedic surgery: Theoretical and in vitro experimental investigation.

The mechanical drilling process is a typical step in treating bone fractures to fix broken parts with screws and plates. Drilling generates a significant amount of heat and elevates the temperature of the bone, which can cause thermal osteonecrosis and damage to the surrounding bone tissue and nerves. Thermal inertia between heat flux and temperature gradient in nonhomogeneous interior structural medium-like biological tissues is arguable. Therefore, this paper proposes an analytical model of heat propagation in bone drilling for orthopedic surgery based on the hyperbolic Pennes bioheat transfer equation (HPBTE). Drilling experiments in bovine cortical bone samples were also carried out using an infrared thermography approach to confirm the proposed analytical model. Around the drilled hole surface, thermal necrosis is spread out from 1 to 10 mm. Increased feed rate reduces necrosis penetration distance and increases intense bone necrosis. The HPBTE includes thermal relaxation time effect and internal convective function of tissue perfusion rate. As these factors are not considered in the parabolic heat transfer equation (PHTE), the results show that the HPBTE is more accurate in predicting temperature and thermal osteonecrosis than the PHTE. As a result, proposed analytical model is a handy tool for calculating temperature to avoid thermal damage while improving process efficiency. Furthermore, it has the capability of controlling the manual or robotic drilling procedure for minimally invasive operations.

A computational model of radiofrequency ablation in the stomach, an emerging therapy for gastric dysrhythmias.

Gastric ablation has recently emerged as a promising potential therapy for bioelectrical dysrhythmias that underpin many gastrointestinal disorders. Despite similarities to well-developed cardiac ablation, gastric ablation is in early development and has thus far been limited to temperature-controlled, non-irrigated settings. A computational model of gastric ablation is needed to enable in silico testing and optimization of ablation parameters and techniques. In this study, we developed a computational model of radio-frequency (RF) gastric ablation. Model parameters and boundary conditions were established based on the current in vivo experimental application of serosal gastric ablation with a non-irrigated RF catheter. The Pennes bioheat transfer equation was used to model the thermal component of RF ablation, and Laplace's equation was used to model the Joule heating component. Tissue, blood, and catheter parameters were obtained from literature. The performance of the model was compared to previously established experimental values of temperature measured from various distances from the catheter tip. The model produced temperature estimations that were within 6% of the maximum experimental temperature at 2.5 mm from the catheter, and within 13% of the maximum temperature change at 4.7 mm. This model now provides a computational basis through which to conduct in silico testing of gastric ablation, and can be usefully applied to optimize gastric ablation parameters. In future, the model can be expanded to include irrigation of the catheter tip and power-controlled RF settings.Clinical Relevance- This work presents a computational model of gastric ablation that can now guide the in silico development of effective ablation parameters and therapeutic strategies, expanding the breadth of this promising therapy.

Microbubble-cloud behavior Simulation to Improve Focused Ultrasound Heating Effect using an Ultrasound Contrast Agent

The thermal effect ability of an ultrasound contrast agent (UCA) in high-intensity focused ultrasound (HIFU) therapy was evaluated. This was done using a thermal effect simulation program using a microbubble-cloud model and modified Pennes Bio-Heat Transfer Equation (BHTE). In order to design the proposed simulation program, a spherical microbubble-cloud model was developed. Next, the proposed simulation program was experimentally investigated by ultrasound phantom experiments using commercial HIFU equipment and UCA, and the change of thermal effect according to the microbubble-cloud population ratio was measured. The HIFU thermal effect simulations using the properties of UCA were compared with the phantom experiments, which provided concordant results.

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.

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.