Conventional and newly developed bioheat transport models in vascularized tissues: A review

Role of periodic irradiation and incident beam radius for plasmonic photothermal therapy of subsurface tumors

Plasmonic photothermal therapy (PPTT) is a potential technique to treat tumors selectively. However, during PPTT, issue of high temperature region and damage to the surrounding healthy is still need to be resolved. Also, treatment of deeper tumors non-invasively is a challenge for PPTT. In this paper, the effect of periodic irradiation and incident beam radius (relative to tumor size) for various gold nanorods (GNRs) concentrations is investigated to avoid much higher temperatures region with limiting thermal damage to the surrounding healthy tissue during PPTT of subsurface breast tumors located at various depths. Lattice Boltzmann method is used to solve Pennes' bioheat model to compute the resulting photothermal temperatures for the subsurface tumor embedded with GNRs subjected to broadband near infrared radiation of intensity 1 W/cm2. Computation revealed that low GNRs concentration leads to uniform internal heat generation than higher GNRs concentrations. The results show that deeper tumors, due to attenuation of incident radiation, show low temperature rise than shallower tumors. For shallower tumors situated 3 mm deep, 70% irradiation period resulted in around 20 °C reduction (110 °C-90 °C) of maximum temperature than that with the continuous irradiation. Moreover, 70% beam radius (i.e., beam radius as 70% of the tumor radius) causes less thermal damage to the nearby healthy tissue than 100% beam radius (i.e., beam radius equal to the tumor radius). The thermal damage within the healthy tissue is minimized to the 1 mm in radial direction and 3 mm in axial direction for 70% beam radius with 70% irradiation period. Overall, periodic heating and changing beam radius of the incident irradiation lead to reduce high temperature and limit healthy tissue damage. Hence, discussed results are useful for selection of the irradiation parameters for PPTT of sub-surface tumors.

Generalized thermomechanical interaction in two-dimensional skin tissue using eigenvalues approach

The aim of this work is to analytically study the thermo-mechanical response of two-dimensional skin tissues when subjected to instantaneous heating. A complete understanding of the heat transfer process and the associated thermal and mechanical effects on the patient's skin tissues is critical to ensuring the effective applications of thermal therapy techniques and procedures. The surface boundary of the half-space undergoes a heat flux characterized by an exponentially decaying pulse, while maintaining a condition of zero traction. The utilization of Laplace and Fourier transformations is employed, and the resulting formulations are then applied to human tissues undergoing regional hyperthermia treatment for cancer therapy. To perform the inversion process for Laplace and Fourier transforms, a numerical programming method based on Stehfest numerical inverse method is employed. The findings demonstrate that blood perfusion rate and thermal relaxation time significantly influence all the analyzed distributions. Numerical findings suggest that thermo-mechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

Investigation of memory influences on bio-heat responses of skin tissue due to various thermal conditions

Advancement of new technologies such as laser, focused ultrasound, microwave and radio frequency for thermal therapy of skin tissue has increased numerous challenging situations in medical treatment. In this article, a new meticulous bio-heat transfer model based on memory-dependent derivative with dual-phase-lag has been developed under different thermal conditions such as thermal shock and harmonic-type heating. Laplace transform method is acquired to perceive the analytical consequences. Quantitative results are evaluated for displacement, strain and temperature along with stress distributions in time domain by adopting the technique of inverse Laplace transform. Impacts of the constituents of memory-dependent derivatives-kernel functions along with time-delay parameter are analysed on the studied fields (temperature, displacement, strain and stress) for both thermal conditions separately using computational results. It has been found that the insertion of the memory effect proves itself a unified model, and therefore, this model can better predict temperature field data for thermal treatment processes.

Numerical simulation of burn injuries with temperature-dependent thermal conductivity and metabolism under different surface heat sources

In the present paper, the phenomena of heat transport inside human forearm tissue are studied through a one-dimensional nonlinear bioheat transfer model under the influence of various boundary and interface conditions. In this study, we considered temperature-dependent thermal conductivity and metabolic heat to predict temperature distribution inside the forearm tissue. We have studied the temperature distribution inside inner tissue and bone because it has been found that burn injuries are mostly affected by layer thickness. The temperature distribution inside human forearm tissue is analyzed using the finite difference and bvp4c numerical techniques. To examine the accuracy of present numerical code, we compare the obtained numerical result with the exact analytical result in a specific case and find an excellent agreement with the exact results. We also validated our present numerical code with a hybrid scheme based on Runge-Kutta (4,5) and finite difference technique and found it in good compliance. From the obtained results, we observed that the homogeneous heat flux has a greater impact on the temperature at the outer surface of the skin, but the sinusoidal heat flux has a greater impact on the temperature of the subcutaneous layer and inner tissue. It is found that there is no burn injury in the first type of heat source (Tw=44°C), but it may occur in the second and third types of heat sources. It has been observed that by raising the blood perfusion rate and reducing the values of reference metabolic heat, coefficient of thermal conductivity, and heat fluxes, we can manage and reduce burn injuries and achieve hyperthermia temperature.

Numerical Modeling and Simulation of Non-Invasive Acupuncture Therapy Utilizing Near-Infrared Light-Emitting Diode

Acupuncture is one of the most extensively used complementary and alternative medicine therapies worldwide. In this study, we explore the use of near-infrared light-emitting diodes (LEDs) to provide acupuncture-like physical stimulus to the skin tissue, but in a completely non-invasive way. A computational modeling framework has been developed to investigate the light-tissue interaction within a three-dimensional multi-layer model of skin tissue. Finite element-based analysis has been conducted, to obtain the spatiotemporal temperature distribution within the skin tissue, by solving Pennes' bioheat transfer equation, coupled with the Beer-Lambert law. The irradiation profile of the LED has been experimentally characterized and imposed in the numerical model. The experimental validation of the developed model has been conducted through comparing the numerical model predictions with those obtained experimentally on the agar phantom. The effects of the LED power, treatment duration, LED distance from the skin surface, and usage of multiple LEDs on the temperature distribution attained within the skin tissue have been systematically investigated, highlighting the safe operating power of the selected LEDs. The presented information about the spatiotemporal temperature distribution, and critical factors affecting it, would assist in better optimizing the desired thermal dosage, thereby enabling a safe and effective LED-based photothermal therapy.

Bio-thermal response and thermal damage in biological tissues with non-equilibrium effect and temperature-dependent properties induced by pulse-laser irradiation

Comprehension of thermal behavior underlying the living biological tissues helps successful applications of current heat therapies. The present work is to explore the heat transport properties of irradiated tissue during tis thermal treatment, in which the local thermal non-equilibrium effect as well as temperature-dependent properties arose from complicated anatomical structure, is considered. Based on the generalized dual-phase lag (GDPL) model, a non-linear governing equation of tissue temperature with variable thermal physical properties is proposed. The effective procedure constructed on an explicit finite difference scheme is then developed to predict numerically the thermal response and thermal damage irradiated by a pulse laser as a therapeutic heat source. The parametric study on variable thermal physical parameters including the phase lag times, heat conductivity, specific heat capacity and blood perfusion rate has been performed to evaluate their influence on temperature distribution in time and space. On this basis, the thermal damage with different laser variables such as laser intensity and exposure time are further analyzed.

Comparisons of healthy human brain temperature predicted from biophysical modeling and measured with whole brain MR thermometry

Brain temperature is an understudied parameter relevant to brain injury and ischemia. To advance our understanding of thermal dynamics in the human brain, combined with the challenges of routine experimental measurements, a biophysical modeling framework was developed to facilitate individualized brain temperature predictions. Model-predicted brain temperatures using our fully conserved model were compared with whole brain chemical shift thermometry acquired in 30 healthy human subjects (15 male and 15 female, age range 18-36 years old). Magnetic resonance (MR) thermometry, as well as structural imaging, angiography, and venography, were acquired prospectively on a Siemens Prisma whole body 3 T MR scanner. Bland-Altman plots demonstrate agreement between model-predicted and MR-measured brain temperatures at the voxel-level. Regional variations were similar between predicted and measured temperatures (< 0.55 °C for all 10 cortical and 12 subcortical regions of interest), and subcortical white matter temperatures were higher than cortical regions. We anticipate the advancement of brain temperature as a marker of health and injury will be facilitated by a well-validated computational model which can enable predictions when experiments are not feasible.

Modeling a 3-D multiscale blood-flow and heat-transfer framework for realistic vascular systems

Modeling of biological domains and simulation of biophysical processes occurring in them can help inform medical procedures. However, when considering complex domains such as large regions of the human body, the complexities of blood vessel branching and variation of blood vessel dimensions present a major modeling challenge. Here, we present a Voxelized Multi-Physics Simulation (VoM-PhyS) framework to simulate coupled heat transfer and fluid flow using a multi-scale voxel mesh on a biological domain obtained. In this framework, flow in larger blood vessels is modeled using the Hagen–Poiseuille equation for a one-dimensional flow coupled with a three-dimensional two-compartment porous media model for capillary circulation in tissue. The Dirac distribution function is used as Sphere of Influence (SoI) parameter to couple the one-dimensional and three-dimensional flow. This blood flow system is coupled with a heat transfer solver to provide a complete thermo-physiological simulation. The framework is demonstrated on a frog tongue and further analysis is conducted to study the effect of convective heat exchange between blood vessels and tissue, and the effect of SoI on simulation results.

Photothermal conversion and transfer in photothermal therapy: From macroscale to nanoscale

Photothermal therapy (PTT) is a promising alternative therapy for benign or even malignant tumors. To improve the selective heating of tumor cells, target-specific photothermal conversion agents are often included, especially nanoparticles. Meanwhile, some indirect methods by manipulating the radiation and heat delivery are also adopted. Therefore, to gain a clear understanding of the mechanism, and to improve the controllability of PTT, a few issues need to be clarified, including bioheat and radiation transfer, localized and collective heating of nanoparticles, etc. In this review, we provide an introduction to the typical bioheat transfer and radiation transfer models along with the dynamic thermophysical properties of biological tissue. On this basis, we reviewed the most recent advances in the temperature control methods in PTT from macroscale to nanoscale. Most importantly, a comprehensive introduction of the localized and collective heating effects of nanoparticle clusters is provided to give a clear insight into the mechanism for PPT from the microscale and nanoscale point of view.

A Fractional Analysis of Hyperthermia Therapy on Breast Cancer in a Porous Medium along with Radiative Microwave Heating

Cancer is a prominent source of mortality and morbidity globally, but little is known about how it develops and spreads. Tumor cells are unable to thrive in high-temperature environments, according to recent research. Hyperthermia is the name for this therapy method. This study provides insights into hyperthermia therapy on breast cancer in the presence of a porous material with fractional derivative access when using radiative microwave heating. The mathematical model is formulated by PDE, while the time-fractional Caputo derivative is applied to make our equation more general as compared to the classical model. To produce a more efficient analysis of blood temperature distributions inside the tissues of the breast, the unsteady state is calculated by using the Laplace transform technique. The Laplace inversion is found by Durbin’s and Zakian’s algorithms. The treatment involves mild temperature hyperthermia, which causes cell death by enhancing cell sensitivity to radiation therapy and blood flow in the tumor. The variations of different parameters to control the temperate profile during therapy are discussed; we can also see how a fractional parameter makes our study more realistic for further experimental study.

Hemodynamic response to thermal stress varies with sex and age: a murine MRI study

PURPOSE

The cardiovascular (CV) system plays a vital role in thermoregulation because of its influence on heat transfer via forced convection and conduction by changes in blood distribution, blood velocity, and proximity of vessels to surrounding tissues. To fully understand the cardiovascular system's role in thermoregulation, blood distribution (influenced by cardiac output, vessel size, blood flow, and pressure) must be quantified, ideally across sex and age. Additionally, wall shear stress is quantified because it is an important metric in cardiovascular disease localization and progression. By investigating the effect of thermal conditions on wall shear stress at a healthy baseline, researchers can begin to study the confluence of thermal condition with pathology or exercise. The purpose of this study is to determine the influence of sex and age on the CV response to temperature. In this work, the effect of core body temperature on hemodynamics of the murine arterial and venous systems has been studied non-invasively, at multiple locations across age and sex.

METHODS

Male and female, adult and aged, mice (n = 20) were anesthetized and underwent MRI at 7 T. Data were acquired from four co-localized vessel pairs (the neck [carotid/jugular], torso [suprarenal and infrarenal aorta/inferior vena cava (IVC)], periphery [femoral artery/vein]) at core temperatures of 35, 36, 37, and 38 °C. Sixteen CINE, ECG-gated, phase contrast frames with one-directional velocity encoding (through plane) were acquired perpendicular to each vessel. Each frame was analyzed to quantify blood velocity and volumetric flow using a semi-automated in-house MATLAB script. Wall shear stress (WSS) was calculated using the Hagen-Poiseulle formula. A multivariable regression for WSS in the femoral artery was fitted with temperature, sex, age, body weight, and heart rate as variables.

RESULTS

Blood velocity and volumetric flow were quantified in eight vessels at four core body temperatures. Flow in the infrarenal IVC linearly increased with temperature for all groups (p = .002; adjusted means of slopes: male vs. female, 0.37 and 0.28 cm/(s × °C); adult vs. aged, 0.22 and 0.43 cm/(s × °C)). Comparing average volumetric flow response to temperature, groups differed for the suprarenal aorta (adult < aged, p < .05), femoral artery (adult < aged, p < .05), and femoral vein (adult male < aged male, p < .001). The two-way interaction terms of temperature and body weight and temperature and sex had the largest effect on wall shear stress.

CONCLUSIONS

Age, in particular, had a significant impact on hemodynamic response as measured by volumetric flow (e.g., aged males > adult males) and WSS at peak-systole (e.g., aged males < adult males). The hemodynamic data can provide physiologically-relevant parameters, including sex and age difference, to computational fluid dynamics models and provide baseline data for the healthy murine vasculature to use as a benchmark for investigations of a variety of physiological (thermal stress) and pathophysiological conditions of the cardiovascular system.

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.

The effect of heat flux distribution and internal heat generation on the thermal damage in multilayer tissue in thermotherapy

Proper analysis of the temperature distribution during heat therapy in the target tissue and around it will prevent damage to other adjacent healthy cells. In this study, the exact solution of steady and unsteady of the hyperbolic bioheat equations is performed for multilayer skin with tumor at different heat fluxes on its surface and the generation of internal heat in the tumor. By determining the temperature distribution in three modes of constant heat flux, parabolic heat flux and internal heat generation in tumor tissue, the amount of burn in all three modes is evaluated. The results indicated that the Fourier or non-Fourier behavior of tissue has no role in the rate of burns in thermotherapy processes. At equal powers applied to the tissue, the internal heat generation in the tumor, constant flux and parabolic flux on the skin surface have the most uniform and most non-uniform temperature distribution, respectively and cause the least and the most thermal damage in the tissue.

Dimension Estimate of Uniform Attractor for a Model of High Intensity Focussed Ultrasound-Induced Thermotherapy

High intensity focussed ultrasound (HIFU) has emerged as a novel therapeutic modality, for the treatment of various cancers, that is gaining significant traction in clinical oncology. It is a cancer therapy that avoids many of the associated negative side effects of other more well-established therapies (such as surgery, chemotherapy and radiotherapy) and does not lead to the longer recuperation times necessary in these cases. The increasing interest in HIFU from biomedical researchers and clinicians has led to the development of a number of mathematical models to capture the effects of HIFU energy deposition in biological tissue. In this paper, we study the simplest such model that has been utilized by researchers to study temperature evolution under HIFU therapy. Although the model poses significant theoretical challenges, in earlier work, we were able to establish existence and uniqueness of solutions to this system of PDEs (see Efendiev et al. Adv Appl Math Sci 29(1):231-246, 2020). In the current work, we take the next natural step of studying the long-time dynamics of solutions to this model, in the case where the external forcing is quasi-periodic. In this case, we are able to prove the existence of uniform attractors to the corresponding evolutionary processes generated by our model and to estimate the Hausdorff dimension of the attractors, in terms of the physical parameters of the system.

Towards real-time finite-strain anisotropic thermo-visco-elastodynamic analysis of soft tissues for thermal ablative therapy

BACKGROUND AND OBJECTIVES

Accurate and efficient prediction of soft tissue temperatures is essential to computer-assisted treatment systems for thermal ablation. It can be used to predict tissue temperatures and ablation volumes for personalised treatment planning and image-guided intervention. Numerically, it requires full nonlinear modelling of the coupled computational bioheat transfer and biomechanics, and efficient solution procedures; however, existing studies considered the bioheat analysis alone or the coupled linear analysis, without the fully coupled nonlinear analysis.

METHODS

We present a coupled thermo-visco-hyperelastic finite element algorithm, based on finite-strain thermoelasticity and total Lagrangian explicit dynamics. It considers the coupled nonlinear analysis of (i) bioheat transfer under soft tissue deformations and (ii) soft tissue deformations due to thermal expansion/shrinkage. The presented method accounts for anisotropic, finite-strain, temperature-dependent, thermal, and viscoelastic behaviours of soft tissues, and it is implemented using GPU acceleration for real-time computation.

RESULTS

The presented method can achieve thermo-visco-elastodynamic analysis of anisotropic soft tissues undergoing large deformations with high computational speeds in tetrahedral and hexahedral finite element meshes for surgical simulation of thermal ablation. We also demonstrate the translational benefits of the presented method for clinical applications using a simulation of thermal ablation in the liver.

CONCLUSION

The key advantage of the presented method is that it enables full nonlinear modelling of the anisotropic, finite-strain, temperature-dependent, thermal, and viscoelastic behaviours of soft tissues, instead of linear elastic, linear viscoelastic, and thermal-only modelling in the existing methods. It also provides high computational speeds for computer-assisted treatment systems towards enabling the operator to simulate thermal ablation accurately and visualise tissue temperatures and ablation zones immediately.

The interplay of blood flow and temperature in regional hyperthermia: a mathematical approach

In recent decades, hyperthermia has been used to raise oxygenation levels in tumours undergoing other therapeutic modalities, of which radiotherapy is the most prominent one. It has been hypothesized that oxygenation increases would come from improved blood flow associated with vasodilation. However, no test has determined whether this is a relevant assumption or other mechanisms might be acting. Additionally, since hyperthermia and radiotherapy are not usually co-administered, the crucial question arises as to how temperature and perfusion in tumours will change during and after hyperthermia. Overall, it would seem necessary to find a research framework that clarifies the current knowledge, delimits the scope of the different effects and guides future research. Here, we propose a simple mathematical model to account for temperature and perfusion dynamics in brain tumours subjected to regional hyperthermia. Our results indicate that tumours in well-perfused organs like the brain might only reach therapeutic temperatures if their vasculature is highly disrupted. Furthermore, the characteristic times of return to normal temperature levels are markedly shorter than those required to deliver adjuvant radiotherapy. According to this, a mechanistic coupling of perfusion and temperature would not explain any major oxygenation boost in brain tumours immediately after hyperthermia.

Thermal impact of replacing constant voltage by low-frequency sine wave voltage in RF ablation computer modeling

BACKGROUND AND OBJECTIVES

A constant voltage (DC voltage) is usually used in radiofrequency ablation (RFA) computer models to mimic the radiofrequency voltage. However, in some cases a low frequency sine wave voltage (AC voltage) may be used instead. Our objective was to assess the thermal impact of replacing DC voltage by low-frequency AC voltage in RFA computer modeling.

METHODS

A 2D model was used consisting of an ablation electrode placed perpendicular to the tissue fragment. The Finite Element method was used to solve a coupled electric-thermal problem. Quasi-static electrical approximation was implemented in two ways (both with equivalent electrical power): (1) by a constant voltage of 25 V in the ablation electrode (DC voltage), and (2) applying a sine waveform with peak amplitude of 25√2 V (AC voltage). The frequency of the sine signal (f_AC) varied from 0.5 Hz to 50 Hz.

RESULTS

Sine wave thermal oscillations (at twice the f_AC frequency) were observed in the case of AC voltage, in addition to the temperature obtained by DC voltage. The amplitude of the oscillations: (1) increased with temperature, remaining more or less constant after 30 s; (2) was of up to ±3 °C for very low f_AC values (0.5 Hz); and (3) was reduced at higher f_AC values and with distance from the electrode (almost negligible for distances > 5 mm). The evolution of maximum lesion depth and width were almost identical with both DC and AC.

CONCLUSIONS

Although reducing f_AC reduces the computation time, thermal oscillations appear at points near the electrode, which suggests that a minimum value of f_AC should be used. Replacing DC voltage by low-frequency AC voltage does not appear to have an impact on the lesion depth.

Thermal field and tissue damage analysis of moving laser in cancer thermal therapy

In this paper, a closed-form analytical solution of hyperbolic Pennes bioheat equation is obtained for spatial evolution of temperature distributions during moving laser thermotherapy of the skin and kidney tissues. The three-dimensional cubic homogeneous perfused biological tissue is adopted as a media and the Gaussian distributed function in surface and exponentially distributed in depth is used for modeling of laser moving heat source. The solution procedure is Eigen value method which leads to a closed form solution. The effect of moving velocity, perfusion rate, laser intensity, absorption and scattering coefficients, and thermal relaxation time on temperature profiles and tissue thermal damage are investigated. Results are illustrated that the moving velocity and the perfusion rate of the tissues are the main important parameters in produced temperatures under moving heat source. The higher perfusion rate of kidney compared with skin may lead to lower induced temperature amplitude in moving path of laser due to the convective role of the perfusion term. Furthermore, the analytical solution can be a powerful tool for analysis and optimization of practical treatment in the clinical setting and laser procedure therapeutic applications and can be used for verification of other numerical heating models.

A Study on Non-Linear DPL Model for Describing Heat Transfer in Skin Tissue during Hyperthermia Treatment

The article studies the simulation-based mathematical modeling of bioheat transfer under the Dirichlet boundary condition. We used complex non-linear dual-phase-lag bioheat transfer (DPLBHT) for analyzing the temperature distribution in skin tissues during hyperthermia treatment of infected cells. The perfusion term, metabolic heat source, and external heat source were the three parts of the volumetric heat source that were used in the model. The non-linear DPLBHT model predicted a more accurate temperature within skin tissues. The finite element Runge–Kutta (4,5) (FERK (4,5)) method, which was based on two techniques, finite difference and Runge–Kutta (4,5), was applied for calculating the result in the case of our typical non-linear problem. The paper studies and presents the non-dimensional unit. Thermal damage of normal tissue was observed near zero during hyperthermia treatment. The effects of the non-dimensional time, non-dimensional space coordinate, location parameter, regional parameter, relaxation and thermalization time, metabolic heat source, associated metabolic heat source parameter, perfusion rate, associated perfusion heat source parameter, and external heat source coefficient on the dimensionless temperature profile were studied in detail during the hyperthermia treatment process.

Characterization of Thermal Damage Due to Two-Temperature High-Order Thermal Lagging in a Three-Dimensional Biological Tissue Subjected to a Rectangular Laser Pulse

The use of lasers and thermal transfers on the skin is fundamental in medical and clinical treatments. In this paper, we constructed and applied bioheat transfer equations in the context of a two-temperature heat conduction model in order to discuss the three-dimensional variation in the temperature of laser-irradiated biological tissue. The amount of thermal damage in the tissue was calculated using the Arrhenius integral. Mathematical difficulties were encountered in applying the equations. As a result, the Laplace and Fourier transform technique was employed, and solutions for the conductive temperature and dynamical temperature were obtained in the Fourier transform domain.

Thermal ablation of biological tissues in disease treatment: A review of computational models and future directions

Percutaneous thermal ablation has proven to be an effective modality for treating both benign and malignant tumours in various tissues. Among these modalities, radiofrequency ablation (RFA) is the most promising and widely adopted approach that has been extensively studied in the past decades. Microwave ablation (MWA) is a newly emerging modality that is gaining rapid momentum due to its capability of inducing rapid heating and attaining larger ablation volumes, and its lesser susceptibility to the heat sink effects as compared to RFA. Although the goal of both these therapies is to attain cell death in the target tissue by virtue of heating above 50°C, their underlying mechanism of action and principles greatly differs. Computational modelling is a powerful tool for studying the effect of electromagnetic interactions within the biological tissues and predicting the treatment outcomes during thermal ablative therapies. Such a priori estimation can assist the clinical practitioners during treatment planning with the goal of attaining successful tumour destruction and preservation of the surrounding healthy tissue and critical structures. This review provides current state-of-the-art developments and associated challenges in the computational modelling of thermal ablative techniques, viz., RFA and MWA, as well as touch upon several promising avenues in the modelling of laser ablation, nanoparticles assisted magnetic hyperthermia and non-invasive RFA. The application of RFA in pain relief has been extensively reviewed from modelling point of view. Additionally, future directions have also been provided to improve these models for their successful translation and integration into the hospital work flow.

Fast computation of soft tissue thermal response under deformation based on fast explicit dynamics finite element algorithm for surgical simulation

BACKGROUND AND OBJECTIVES

During thermal heating surgical procedures such as electrosurgery, thermal ablative treatment and hyperthermia, soft tissue deformation due to surgical tool-tissue interaction and patient movement can affect the distribution of thermal energy induced. Soft tissue temperature must be obtained from the deformed tissue for precise delivery of thermal energy. However, the classical Pennes bio-heat transfer model can handle only the static non-moving state of tissue. In addition, in order to enable a surgeon to visualise the simulated results immediately, the solution procedure must be suitable for real-time thermal applications.

METHODS

This paper presents a formulation of bio-heat transfer under the effect of soft tissue deformation for fast or near real-time tissue temperature prediction, based on fast explicit dynamics finite element algorithm (FED-FEM) for transient heat transfer. The proposed thermal analysis under deformation is achieved by transformation of the unknown deformed tissue state to the known initial static state via a mapping function. The appropriateness and effectiveness of the proposed formulation are evaluated on a realistic virtual human liver model with blood vessels to demonstrate a clinically relevant scenario of thermal ablation of hepatic cancer.

RESULTS

For numerical accuracy, the proposed formulation can achieve a typical 10^-3 level of normalised relative error at nodes and between 10^-4 and 10^-5 level of total errors for the simulation, by comparing solutions against the commercial finite element analysis package. For computation time, the proposed formulation under tissue deformation with anisotropic temperature-dependent properties consumes 2.518 × 10^-4 ms for one element thermal loads computation, compared to 2.237 × 10^-4 ms for the formulation without deformation which is 0.89 times of the former. Comparisons with three other formulations for isotropic and temperature-independent properties are also presented.

CONCLUSIONS

Compared to conventional methods focusing on numerical accuracy, convergence and stability, the proposed formulation focuses on computational performance for fast tissue thermal analysis. Compared to the classical Pennes model that handles only the static state of tissue, the proposed formulation can achieve fast thermal analysis on deformed states of tissue and can be applied in addition to tissue deformable models for non-linear heating analysis at even large deformation of soft tissue, leading to great translational potential in dynamic tissue temperature analysis and thermal dosimetry computation for computer-integrated medical education and personalised treatment.

Estimation of Time-Course Core Temperature and Water Loss in Realistic Adult and Child Models with Urban Micrometeorology Prediction

Ambient conditions may change rapidly and notably over time in urban areas. Conventional indices, such as the heat index and wet bulb globe temperature, are useful only in stationary ambient conditions. To estimate the risks of heat-related illness, human thermophysiological responses should be followed for ambient conditions in the time domain. We develop a computational method for estimating the time course of core temperature and water loss by combining micrometeorology and human thermal response. We firstly utilize an urban micrometeorology prediction to reproduce the environment surrounding walkers. The temperature elevations and sweating in a standard adult and child are then estimated for meteorological conditions. With the integrated computational method, we estimate the body temperature and thermophysiological responses for an adult and child walking along a street with two routes (sunny and shaded) in Tokyo on 7 August 2015. The difference in the core temperature elevation in the adult between the two routes was 0.11 °C, suggesting the necessity for a micrometeorology simulation. The differences in the computed body core temperatures and water loss of the adult and child were notable, and were mainly characterized by the surface area-to-mass ratio. The computational techniques will be useful for the selection of actions to manage the risk of heat-related illness and for thermal comfort.

Assessing structural and functional response of murine vasculature to acute β-adrenergic stimulation in vivo during hypothermic and hyperthermic conditions

Background: Because of the importance of adrenoreceptors in regulating the cardiovascular (CV) system and the role of the CV system in thermoregulation, understanding the response to these two stressors is of interest. The purpose of this study was to assess changes of arterial geometry and function in vivo during thermal and β-adrenergic stress induced in mice and quantified by MRI.Methods: Male mice were anesthetized and imaged at 7 T. Anatomical and functional data were acquired from the neck (carotid artery), torso (suprarenal and infrarenal aorta and iliac artery) and periphery (femoral artery). Intravenous dobutamine (tail vein catheter, 40 µg/kg/min, 0.12 mL/h) was used as β-adrenergic stressor. Baseline and dobutamine data were acquired at minimally hypothermic (35 °C) and minimally hyperthermic (38 °C) core temperatures. Cross-sectional vessel area and maximum cyclic strain were measured across the cardiac cycle.Results: Vascular response varied by location and by core temperature. For minimally hypothermic conditions (35 °C), average, maximum and minimum areas decreased with dobutamine only at the suprarenal aorta (avg: -17.9%, max: -13.5%, min: -21.4%). For minimally hyperthermic conditions (38 °C), vessel areas decreased between baseline and dobutamine at the carotid (avg: -19.6%, max: -15.5%, min: -19.3%) and suprarenal aorta (avg: -24.2%, max: -17.4%, min: -17.3%); whereas, only the minimum vessel area decreased for the iliac artery (min: -14.4%). Maximum cyclic strain increased between baseline and dobutamine at the iliac artery for both conditions and at the suprarenal aorta at hyperthermic conditions.Conclusions: At hypothermic conditions, the vessel area response to dobutamine is diminished compared to hyperthermic conditions where the vessel area response mimics normothermic dobutamine conditions. The varied response emphasizes the need to monitor and control body temperature during medical conditions or treatments that may be accompanied by hypothermia, especially when vasoactive agents are used.

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

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

Numerical modelling of skin tumour tissue with temperature-dependent properties for dynamic thermography

Dynamic thermography has been clinically proven to be a valuable diagnostic technique for skin tumour detection as well as for other medical applications, and shows many advantages over static thermography. Numerical modelling of heat transfer phenomena in biological tissue during dynamic thermography can aid the technique by improving process parameters or by estimating unknown tissue parameters based on measurement data. This paper presents a new non-linear numerical model of multilayer skin tissue containing a skin tumour together with thermoregulation response of the tissue during the cooling-rewarming process of dynamic thermography. The thermoregulation response is modelled by temperature-dependent blood perfusion rate and metabolic heat generation. The aim is to describe bioheat transfer more realistically. The model is based on the Pennes bioheat equation and solved numerically using a subdomain BEM approach treating the problem as axisymmetrical. The paper includes computational tests for Clark II and Clark IV tumours, comparing the models using constant and temperature-dependent properties which showed noticeable differences and highlighted the importance of using a local thermoregulation model. Results also show the advantage of using dynamic thermography for skin tumour screening and detection at an early stage. One of the contributions of this paper is a complete sensitivity analysis of 56 model parameters based on the gradient of the surface temperature difference between tumour and healthy skin. The analysis shows that size of the tumour, blood perfusion rate, thermoregulation coefficient of the tumour, body core temperature and density and specific heat of the skin layers in which the tumour is embedded are important for modelling the problem, and so have to be determined more accurately to reflect realistic skin response of the investigated tissue, while metabolic heat generation and its thermoregulation are not.

Relationship between metabolic rate and blood perfusion under Fanger thermal comfort conditions

The one-dimensional steady Pennes (bioheat) equation was applied to analyze heat conduction inside a combined layer of human muscle and fat, under Fanger thermal comfort conditions. The bioheat equation was solved subject to two boundary conditions at the skin surface: a prescribed skin temperature satisfying the Fanger comfort criterion, and a prescribed heat flux obtained from the overall energy balance for the system. In addition to a fixed body core temperature, an adiabatic condition was imposed as an auxiliary condition at the core of the body, and a pair of equations were derived, relating the blood perfusion and the volumetric heat generation rate for a given activity level and environmental conditions. By solving the two equations, we determined the functional dependence of blood perfusion and metabolic heat generation on the human activity level. For convenience, we presented simple explicit expressions for the key relations, with the aid of asymptotic analyses. Additional results include the temperature distribution inside the muscle layer, and the effects of muscle and fat layer thickness on the heat transfer processes.

Systematic Derivation of Safety Limits for Time-Varying 5G Radiofrequency Exposure Based on Analytical Models and Thermal Dose

Extreme broadband wireless devices operating above 10 GHz may transmit data in bursts of a few milliseconds to seconds. Even though the time- and area-averaged power density values remain within the acceptable safety limits for continuous exposure, these bursts may lead to short temperature spikes in the skin of exposed people. In this paper, a novel analytical approach to pulsed heating is developed and applied to assess the peak-to-average temperature ratio as a function of the pulse fraction α (relative to the averaging time [INCREMENT]T; it corresponds to the inverse of the peak-to-average ratio). This has been analyzed for two different perfusion-related thermal time constants (τ1 = 100 s and 500 s) corresponding to plane-wave and localized exposures. To allow for peak temperatures that considerably exceed the 1 K increase, the CEM43 tissue damage model, with an experimental-data-based damage threshold for human skin of 600 min, is used to allow large temperature oscillations that remain below the level at which tissue damage occurs. To stay consistent with the current safety guidelines, safety factors of 10 for occupational exposure and 50 for the general public were applied. The model assumptions and limitations (e.g., employed thermal and tissue damage models, homogeneous skin, consideration of localized exposure by a modified time constant) are discussed in detail. The results demonstrate that the maximum averaging time, based on the assumption of a thermal time constant of 100 s, is 240 s if the maximum local temperature increase for continuous-wave exposure is limited to 1 K and α ≥ 0.1. For a very low peak-to-average ratio of 100 (α ≥ 0.01), it decreases to only 30 s. The results also show that the peak-to-average ratio of 1,000 tolerated by the International Council on Non-Ionizing Radiation Protection guidelines may lead to permanent tissue damage after even short exposures, highlighting the importance of revisiting existing exposure guidelines.

Cross-sectional areas of deep/core veins are smaller at lower core body temperatures

The cardiovascular system plays a crucial role in thermoregulation. Deep core veins, due to their large size and role in returning blood to the heart, are an important part of this system. The response of veins to increasing core temperature has not been adequately studied in vivo. Our objective was to noninvasively quantify in C57BL/6 mice the response of artery-vein pairs to increases in body temperature. Adult male mice were anesthetized and underwent magnetic resonance imaging. Data were acquired from three colocalized vessel pairs (the neck [carotid/jugular], torso [aorta/inferior vena cava (IVC)], periphery [femoral artery/vein]) at core temperatures of 35, 36, 37, and 38°C. Cross-sectional area increased with increasing temperature for all vessels, excluding the carotid. Average area of the jugular, aorta, femoral artery, and vein linearly increased with temperature (0.10, 0.017, 0.017, and 0.027 mm2 /°C, respectively; P < 0.05). On average, the IVC has the largest venous response for area (18.2%/°C, vs. jugular 9.0 and femoral 10.9%/°C). Increases in core temperature from 35 to 38 °C resulted in an increase in contact length between the aorta/IVC of 29.3% (P = 0.007) and between the femoral artery/vein of 28.0% (P = 0.03). Previously unidentified increases in the IVC area due to increasing core temperature are biologically important because they may affect conductive and convective heat transfer. Vascular response to temperature varied based on location and vessel type. Leveraging noninvasive methodology to quantify vascular responses to temperature could be combined with bioheat modeling to improve understanding of thermoregulation.

Cross-sectional area of the murine aorta linearly increases with increasing core body temperature

PURPOSE

The cardiovascular (CV) system plays a vital role in thermoregulation. To date, the response of core vasculature to increasing core temperature has not been adequately studied in vivo. Our objective was to non-invasively quantify the arterial response in murine models due to increases in body temperature, with a focus on core vessels of the torso and investigate whether responses were dependent on sex or age.

METHODS

Male and female, adult and aged mice were anaesthetised and underwent magnetic resonance imaging (MRI). Data were acquired from the circle of Willis (CoW), heart, infrarenal aorta and peripheral arteries at core temperatures of 35, 36, 37 and 38 °C (±0.2 °C).

RESULTS

Vessels in the CoW did not change. Ejection fraction decreased and cardiac output (CO) increased with increasing temperature in adult female mice. Cross-sectional area of the aorta increased significantly and linearly with temperature for all groups, but at a diminished rate for aged animals (p < 0.01; male and female: adult, 0.019 and 0.024 mm²/°C; aged, 0.017 and 0.011 mm²/°C). Aged male mice had a diminished response in the periphery (% increase in femoral artery area from 35 to 38 °C, male and female: adult, 67 and 65%; aged, 0.1 and 57%).

CONCLUSION

Previously unidentified increases in aortic area due to increasing core temperature are biologically important because they may affect conductive and convective heat transfer. Leveraging non-invasive methodology to quantify sex and age dependent vascular responses due to increasing core temperature could be combined with bioheat modelling in order to improve understanding of thermoregulation.

A Novel Nanoparticle Mediated Selective Inner Retinal Photocoagulation for Diseases of the Inner Retina

A novel nanoparticle mediated methodology for laser photocoagulation of the inner retina to achieve tissue selective treatment is presented.

METHODS

Transport of 527, 577, and 810 nm laser, heat deposition, and eventual thermal damage in vitreous, retina, RPE, choroid, and sclera were modeled using Bouguer-Beer-Lambert law of absorption and solved numerically using the finite volume method. Nanoparticles were designed using Mie theory of scattering. Performance of the new photocoagulation strategy using gold nanospheres and gold-silica nanoshells was compared with that of conventional methods without nanoparticles. For experimental validation, vitreous cavity of ex vivo porcine eyes was infused with gold nanospheres. After ~6 h of nanoparticle diffusion, the porcine retina was irradiated with a green laser and imaged simultaneously using a spectral domain optical coherence tomography (Spectralis SD-OCT, Heidelberg Engineering).

RESULTS

Our computational model predicted a significant spatial shift in the peak temperature from RPE to the inner retinal region when infused with nanoparticles. Arrhenius thermal damage in the mid-retinal location was achieved in ~14 ms for 527 nm laser thereby reducing the irradiation duration by ~30 ms compared with the treatment without nanoparticles. In ex vivo porcine eyes infused with gold nanospheres, SD-OCT retinal images revealed a lower thermal damage and expansion at RPE due to laser photocoagulation.

CONCLUSION

Nanoparticle infused laser photocoagulation strategy provided a selective inner retinal thermal damage with significant decrease in laser power and laser exposure time.

SIGNIFICANCE

The proposed treatment strategy shows possibilities for an efficient and highly selective inner retinal laser treatment.

New Frontiers for Applications of Thermal Infrared Imaging Devices: Computational Psychopshysiology in the Neurosciences

Thermal infrared imaging has been proposed, and is now used, as a tool for the non-contact and non-invasive computational assessment of human autonomic nervous activity and psychophysiological states. Thanks to a new generation of high sensitivity infrared thermal detectors and the development of computational models of the autonomic control of the facial cutaneous temperature, several autonomic variables can be computed through thermal infrared imaging, including localized blood perfusion rate, cardiac pulse rate, breath rate, sudomotor and stress responses. In fact, all of these parameters impact on the control of the cutaneous temperature. The physiological information obtained through this approach, could then be used to infer about a variety of psychophysiological or emotional states, as proved by the increasing number of psychophysiology or neurosciences studies that use thermal infrared imaging. This paper presents a review of the principal achievements of thermal infrared imaging in computational psychophysiology, focusing on the capability of the technique for providing ubiquitous and unwired monitoring of psychophysiological activity and affective states. It also presents a summary on the modern, up-to-date infrared sensors technology.

Characterizing human skin blood flow regulation in response to different local skin temperature perturbations

Small nerve fibers regulate local skin blood flow in response to local thermal perturbations. Small nerve fiber function is difficult to assess with classical neurophysiological tests. In this study, a vasomotor response model in combination with a heating protocol was developed to quantitatively characterize the control mechanism of small nerve fibers in regulating skin blood flow in response to local thermal perturbation. The skin of healthy subjects' hand dorsum (n=8) was heated to 42°C with an infrared lamp, and then naturally cooled down. The distance between the lamp and the hand was set to three different levels in order to change the irradiation intensity on the skin and implement three different skin temperature rise rates (0.03°C/s, 0.02°C/s and 0.01°C/s). A laser Doppler imager (LDI) and a thermographic video camera recorded the temporal profile of the skin blood flow and the skin temperature, respectively. The relationship between the skin blood flow and the skin temperature was characterized by a vasomotor response model. The model fitted the skin blood flow response well with a variance accounted for (VAF) between 78% and 99%. The model parameters suggested a similar mechanism for the skin blood flow regulation with the thermal perturbations at 0.03°C/s and 0.02°C/s. But there was an accelerated skin vasoconstriction after a slow heating (0.01°C/s) (p-value<0.05). An attenuation of the skin vasodilation was also observed in four out of the seven subjects during the slow heating (0.01°C/s). Our method provides a promising way to quantitatively assess the function of small nerve fibers non-invasively and non-contact.

Thermal Response of Human Skin to Microwave Energy: A Critical Review

This is a review/modeling study of heating of tissue by microwave energy in the frequency range from 3 GHz through the millimeter frequency range (30-300 GHz). The literature was reviewed to identify studies that reported RF-induced increases in skin temperature. A simple thermal model, based on a simplified form of Pennes' bioheat equation (BHTE), was developed, using parameter values taken from the literature with no further adjustment. The predictions of the model were in excellent agreement with available data. A parametric analysis of the model shows that there are two heating regimes with different dominant mechanisms of heat transfer. For small irradiated areas (less than about 0.5-1 cm in radius) the temperature increase at the skin surface is chiefly limited by conduction of heat into deeper tissue layers, while for larger irradiated areas, the steady-state temperature increase is limited by convective cooling by blood perfusion. The results support the use of this simple thermal model to aid in the development and evaluation of RF safety limits at frequencies above 3 GHz and for millimeter waves, particularly when the irradiated area of skin is small. However, very limited thermal response data are available, particularly for exposures lasting more than a few minutes to areas of skin larger than 1-2 cm in diameter. The paper concludes with comments about possible uses and limitations of thermal modeling for setting exposure limits in the considered frequency range.