Computational study on 2D three-phase lag bioheat model during cryosurgery using RBF meshfree method.

Biological tissue has a multidimensional and non-homogeneous inner structure by nature. The temperature distribution and freezing front locations in biological tissue are crucial to optimizing the damage to tissue during cryosurgery. There is a need for a good mathematical model and effective simulation techniques to predict the effectiveness of the therapy. The present study concerns the numerical study of phase change phenomena during cryosurgery using the three-phase lag (TPL) bioheat model in arbitrary soft tissue domains, i.e., circular (Γ1), ameba-like (Γ2), and multiconnected (Γ3). We employ the effective heat capacity formulation to solve the nonlinear governing equation. The Gaussian radial basis function and Crank-Nicolson finite difference approximation are applied for spatial and time derivatives, respectively. Using the present algorithm, we study the impact of phase lag (τv) due to thermal displacement involved in the TPL model on phase change interface position and thermal distribution in all three domains. The obtained results may be beneficial in the field of oncology.

Temperature Dynamics in Rat Brains Exposed to Near-Field Waveguide Outputs at 2.8 GHz.

Biological effects in the microwave band of the radiofrequency (RF) spectrum are thermally mediated. For acute high-power microwave exposures, these effects will depend on transient time-temperature histories within the tissue. In this article, we summarize the transient temperature response of rats exposed to RF energy emanating from an open-ended rectangular waveguide. These exposures produced specific absorption rates of approximately 36 and 203 W/kg in the whole body and brain, respectively. We then use the experimentally measured thermal data to infer the baseline perfusion rate in the brain and modify a custom thermal modeling tool based upon these findings. Finally, we compare multi-physics simulations of rat brain temperature against empirical measurements in both live and euthanized subjects and find close agreement between model and experimentation. This research revealed that baseline brain perfusion rates in rat subjects could be larger than previously assumed in the RF thermal modeling literature, and plays a significant role in the transient thermal response to high-power microwave exposures. © 2021 Bioelectromagnetics Society.

Review of Thermal and Physiological Properties of Human Breast Tissue.

Electromagnetic thermal therapies for cancer treatment, such as microwave hyperthermia, aim to heat up a targeted tumour site to temperatures within 40 and 44 °C. Computational simulations used to investigate such heating systems employ the Pennes' bioheat equation to model the heat exchange within the tissue, which accounts for several tissue properties: density, specific heat capacity, thermal conductivity, metabolic heat generation rate, and blood perfusion rate. We present a review of these thermal and physiological properties relevant for hyperthermia treatments of breast including fibroglandular breast, fatty breast, and breast tumours. The data included in this review were obtained from both experimental measurement studies and estimated properties of human breast tissues. The latter were used in computational studies of breast thermal treatments. The measurement methods, where available, are discussed together with the estimations and approximations considered for values where measurements were unavailable. The review concludes that measurement data for the thermal and physiological properties of breast and tumour tissue are limited. Fibroglandular and fatty breast tissue properties are often approximated from those of generic muscle or fat tissue. Tumour tissue properties are mostly obtained from approximating equations or assumed to be the same as those of glandular tissue. We also present a set of reliable data, which can be used for more accurate modelling and simulation studies to better treat breast cancer using thermal therapies.

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.

Human thermophysiological models: Quantification of uncertainty in the output quantities of the passive system due to uncertainties in the control equations of the active system via the Monte Carlo method.

Uncertainty propagation analysis in the Fiala thermophysiological model is performed by the Monte Carlo Method. The uncertainties of the output quantities of the passive system, due to imported uncertainties in the coefficients of the control equations of the active system, caused by the variation of the experimental data, are computed. The developed and implemented in-house code is accordingly validated. The effect of the input uncertainties, in each of the four main responses (shivering, vasodilatation, vasoconstriction, sweating) of the active system, is separately examined by simulating the human exposure from neutral conditions to cold and hot environments. It is predicted that the maximum output uncertainties of the response mechanisms may be of the same order of magnitude as the imported ones, while the corresponding maximum uncertainties in core and skin temperatures always remain less than 2%. The maximum absolute deviations of the rectal (core) temperatures from their estimated mean values may be up to 0.72 °C and 0.22 °C, due to input uncertainties in shivering and sweating respectively, while the corresponding deviations due to uncertainties in vasomotion processes are negligible. The deviations, particularly the ones due to shivering, are significant, since differences of a few tenths of a degree may have large impact in human health. The maximum absolute deviations of the skin temperatures are 0.42 °C in the hands due to uncertainties in shivering and 0.69 °C in the feet due to uncertainties in vasodilatation. These deviations are less significant than the core ones, but they may still affect human thermal sensation and comfort. The present analysis provides a better insight in the dynamic response of the model and indicates which response mechanism needs to be further investigated by more accurate estimates in order to improve model reliability. It can be also applied in other human thermophysiological models.

In vivo magnetic nanoparticle hyperthermia: a review on preclinical studies, low-field nano-heaters, noninvasive thermometry and computer simulations for treatment planning.

Magnetic nanoparticle hyperthermia (MNH) is a promising nanotechnology-based cancer thermal therapy that has been approved for clinical use, together with radiation therapy, for treating brain tumors. Almost ten years after approval, few new clinical applications had appeared, perhaps because it cannot benefit from the gold standard noninvasive MRI thermometry technique, since static magnetic fields inhibit heat generation. This might limit its clinical use, in particular as a single therapeutic modality. In this article, we review the in vivo MNH preclinical studies, discussing results of the last two decades with emphasis on safety as a clinical criteria, the need for low-field nano-heaters and noninvasive thermal dosimetry, and the state of the art of computational modeling for treatment planning using MNH. Limitations to more effective clinical use are discussed, together with suggestions for future directions, such as the development of ultrasound-based, computed tomography-based or magnetic nanoparticle-based thermometry to achieve greater impact on clinical translation of MNH.

Temperature-controlled power modulation compensates for heterogeneous nanoparticle distributions: a computational optimization analysis for magnetic hyperthermia.

PURPOSE: To study, with computational models, the utility of power modulation to reduce tissue temperature heterogeneity for variable nanoparticle distributions in magnetic nanoparticle hyperthermia. METHODS: Tumour and surrounding tissue were modeled by elliptical two- and three-dimensional computational phantoms having six different nanoparticle distributions. Nanoparticles were modeled as point heat sources having amplitude-dependent loss power. The total number of nanoparticles was fixed, and their spatial distribution and heat output were varied. Heat transfer was computed by solving the Pennes' bioheat equation using finite element methods (FEM) with temperature-dependent blood perfusion. Local temperature was regulated using a proportional-integral-derivative (PID) controller. Tissue temperature, thermal dose and tissue damage were calculated. The required minimum thermal dose delivered to the tumor was kept constant, and heating power was adjusted for comparison of both the heating methods. RESULTS: Modulated power heating produced lower and more homogeneous temperature distributions than did constant power heating for all studied nanoparticle distributions. For a concentrated nanoparticle distribution, located off-center within the tumor, the maximum temperatures inside the tumor were 16% lower for modulated power heating when compared to constant power heating. This resulted in less damage to surrounding normal tissue. Modulated power heating reached target thermal doses up to nine-fold more rapidly when compared to constant power heating. CONCLUSIONS: Controlling the temperature at the tumor-healthy tissue boundary by modulating the heating power of magnetic nanoparticles demonstrably compensates for a variable nanoparticle distribution to deliver effective treatment.

An analytical study on the fractional transient heating within the skin tissue during the thermal therapy.

In the present paper, the bioheat equation under fractional derivatives is used to study the thermal damage within the skin tissue during the thermal therapy. Basically, the analytical solutions in the Laplace domain are easily obtainable. The influences of the fractional derivative and moving heat source velocity on the temperature of skin tissues and the thermal injuries are precisely investigated. The outcomes show that the fractional bioheat model are reduced to the hyperbolic and parabolic bioheat models when the fractional order parameter is equal to one and the relaxation time is close to zero respectively. The thermal injuries to the tissue are assessed by the denatured protein range using the formulation of Arrhenius. The numerical outcomes of thermal injuries and temperatures are graphically introduced. In conclusion, a parametric analysis is devoted to the identification of an appropriate procedure for selecting important design variables to reach effective heating in hyperthermia treatment.

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.

Temperature elevation in the human brain and skin with thermoregulation during exposure to RF energy.

BACKGROUND: Two international guidelines/standards for human protection from electromagnetic fields define the specific absorption rate (SAR) averaged over 10 g of tissue as a metric for protection against localized radio frequency field exposure due to portable devices operating below 3-10 GHz. Temperature elevation is suggested to be a dominant effect for exposure at frequencies higher than 100 kHz. No previous studies have evaluated temperature elevation in the human head for local exposure considering thermoregulation. This study aims to discuss the temperature elevation in a human head model considering vasodilation, to discuss the conservativeness of the current limit. METHODS: This study computes the temperature elevations in an anatomical human head model exposed to radiation from a dipole antenna and truncated plane waves at 300 MHz-10GHz. The SARs in the human model are first computed using a finite-difference time-domain method. The temperature elevation is calculated by solving the bioheat transfer equation by considering the thermoregulation that simulates the vasodilation. RESULTS: The maximum temperature elevation in the brain appeared around its periphery. At exposures with higher intensity, the temperature elevation became larger and reached around 40 °C at the peak SAR of 100 W/kg, and became lower at higher frequencies. The temperature elevation in the brain at the current limit of 10 W/kg is at most 0.93 °C. The effect of vasodilation became notable for tissue temperature elevations higher than 1-2 °C and for an SAR of 10 W/kg. The temperature at the periphery was below the basal brain temperature (37 °C). CONCLUSIONS: The temperature elevation under the current guideline for occupational exposure is within the ranges of brain temperature variability for environmental changes in daily life. The effect of vasodilation is significant, especially at higher frequencies where skin temperature elevation is dominant.

Numerical and Experimental Evaluation of High-Intensity Focused Ultrasound-Induced Lesions in Liver Tissue Ex Vivo.

OBJECTIVES: Recent advances in the field of acoustics and piezoelectric and ultrasound transducers have led to new approaches to the diagnosis and treatment of certain diseases. One method of treatment with ultrasonic waves is high-intensity focused ultrasound (HIFU) treatment, which is a thermal therapeutic method used to treat malignant tumors. Although a variety of treatment-planning strategies using ultrasonic waves have been investigated, little clinical success has been achieved. Computational modeling is a powerful tool for predicting device performance. METHODS: The heating induced by a concave transducer with operating powers of 85 and 135 W was studied, and the experimental results presented in this article verify its applicability. Numerical simulations of the nonlinear acoustic field were performed by using the Westervelt and Khokhlov-Zabolotskaya-Kuznetsov equations. Heat transfer was measured for the 2 operational powers, and the results were compared with ex vivo experimental results. In addition, thermal dose contours for both the simulation and experimental results were calculated to investigate the ablated area. RESULTS: Good agreement was found between the experimental and numerical results. The results show that the average temperature deviations calculated at the focal point were 12.8% and 4.3% for transducer powers of 85 and 135 W, respectively. CONCLUSIONS: This study provides guidance to HIFU practitioners in determining lesion size and identifying nonlinear effects that should be considered in HIFU procedures.

Numerical study to establish relationship between coagulation volume and target tip temperature during temperature-controlled radiofrequency ablation.

The present study aims at proposing a relationship between the coagulation volume and the target tip temperature in different tissues (viz., liver, lung, kidney, and breast) during temperature-controlled radiofrequency ablation (RFA). A 20-min RFA has been modelled using commercially available monopolar multi-tine electrode subjected to different target tip temperatures that varied from 70°C to 100°C with an increment of 10°C. A closed-loop feedback proportional-integral-derivative (PID) controller has been employed within the finite element model to perform temperature-controlled RFA. The coagulation necrosis has been attained by solving the coupled electric field distribution, the Pennes bioheat and the first-order Arrhenius rate equations within the three-dimensional finite element model of different tissues. The computational study considers temperature-dependent electrical and thermal conductivities along with the non-linear piecewise model of blood perfusion. The comparison between coagulation volume obtained from the numerical and in vitro experimental studies has been done to evaluate the aptness of the numerical models. In the present study, a total of 20 numerical simulations have been performed along with 12 experiments on tissue-mimicking phantom gel using RFA device. The study revealed a strong dependence of the coagulation volume on the pre-set target tip temperature and ablation time during RFA application. Further, the effect of target tip temperature on the applied input voltage has been studied in different tissues. Based on the results attained from the numerical study, statistical correlations between the coagulation volume and treatment time have been developed at different target tip temperatures for each tissue.

Parameters sensitivity assessment and heat source localization using infrared imaging techniques.

BACKGROUND: At present, infrared (IR) imaging is used both as a non-invasive and a non-ionizing technology. Using an IR camera, it is possible to measure body surface temperature in order to detect tumors and malignant cells. Tumors have a high amount of vasculature and an enhanced metabolism rate, which may result in an increase in body surface temperature by several degrees above its normal level. METHODS: Using thermograms, it is possible to assess various tumor parameters, such as depth, intensity, and radius. Also, by solving for Penne's bioheat equation, it is possible to develop the analytical method to solve for inverse heat conduction problem (IHCP). RESULTS: In the present study, these parameters were optimized using artificial neural networks in order to localize the heat source in the medium (i.e. female breast) more accurately. CONCLUSION: Eventually, a new formula was derived from Penne's bioheat equation to estimate the depth and radius of the embedded heat source. Moreover, by analyzing the data, errors of the parameters could be estimated.

Temperature-controlled radiofrequency ablation of different tissues using two-compartment models.

PURPOSE: This study aims to analyse the efficacy of temperature-controlled radiofrequency ablation (RFA) in different tissues. MATERIALS AND METHODS: A three-dimensional, 12 cm cubical model representing the healthy tissue has been studied in which spherical tumour of 2.5 cm has been embedded. Different body sites considered in the study are liver, kidney, lung and breast. The thermo-electric analysis has been performed to estimate the temperature distribution and ablation volume. A programmable temperature-controlled RFA has been employed by incorporating the closed-loop feedback PID controller. The model fidelity and integrity have been evaluated by comparing the numerical results with the experimental in vitro results obtained during RFA of polyacrylamide tissue-mimicking phantom gel. RESULTS: The results revealed that significant variations persist among the input voltage requirements and the temperature distributions within different tissues of interest. The highest ablation volume has been produced in hypovascular lungs whereas least ablation volume has been produced in kidney being a highly perfused tissue. The variation in optimal treatment time for complete necrosis of tumour along with quantification of damage to the surrounding healthy tissue has also been reported. CONCLUSIONS: The results show that the surrounding tissue environment significantly affects the ablation volume produced during RFA. The optimal treatment time for complete tumour ablation can play a critical role in minimising the damage to the surrounding healthy tissue and ensuring safe and risk free application of RFA. The obtained results emphasise the need for developing organ-specific clinical protocols and systems during RFA of tumour.

A parametric study of thermal therapy of skin tissue.

A thermal therapy for cancer in skin tissue is numerically investigated using three bioheat conduction models, namely Pennes, thermal wave and dual-phase lag models. A laser is applied at the surface of the skin for cancer ablation, and the temperature and thermal damage distributions are predicted using the three bioheat models and two different modeling approaches of the laser effect. The first one is a prescribed surface heat flux, in which the tissue is assumed to be highly absorbent, while the second approach is a volumetric heat source, which is reasonable if the scattering and absorption skin effects are of similar magnitude. The finite volume method is applied to solve the governing bioheat equation. A parametric study is carried out to ascertain the effects of the thermophysical properties of the cancer on the thermal damage. The temperature distributions predicted by the three models exhibit significant differences, even though the temperature distributions are similar when the laser is turned off. The type of bioheat model has more influence on the predicted thermal damage than the type of modeling approach used for the laser. The phase lags of heat flux and temperature gradient have an important influence on the results, as well as the thermal conductivity of the cancer. In contrast, the uncertainty in the specific heat and blood perfusion rate has a minor influence on the thermal damage.

Estimation of optical properties of neuroendocrine pancreas tumor with double-integrating-sphere system and inverse Monte Carlo model.

The investigation of laser-tissue interaction is crucial for diagnostics and therapeutics. In particular, the estimation of tissue optical properties allows developing predictive models for defining organ-specific treatment planning tool. With regard to laser ablation (LA), optical properties are among the main responsible for the therapy efficacy, as they globally affect the heating process of the tissue, due to its capability to absorb and scatter laser energy. The recent introduction of LA for pancreatic tumor treatment in clinical studies has fostered the need to assess the laser-pancreas interaction and hence to find its optical properties in the wavelength of interest. This work aims at estimating optical properties (i.e., absorption, µ a , scattering, µ s , anisotropy, g, coefficients) of neuroendocrine pancreas tumor at 1064 nm. Experiments were performed using two popular sample storage methods; the optical properties of frozen and paraffin-embedded neuroendocrine tumor of the pancreas are estimated by employing a double-integrating-sphere system and inverse Monte Carlo algorithm. Results show that paraffin-embedded tissue is characterized by absorption and scattering coefficients significantly higher than frozen samples (µ a of 56 cm(-1) vs 0.9 cm(-1), µ s of 539 cm(-1) vs 130 cm(-1), respectively). Simulations show that such different optical features strongly influence the pancreas temperature distribution during LA. This result may affect the prediction of therapeutic outcome. Therefore, the choice of the appropriate preparation technique of samples for optical property estimation is crucial for the performances of the mathematical models which predict LA thermal outcome on the tissue and lead the selection of optimal LA settings.

Thermal analysis of induced damage to the healthy cell during RFA of breast tumor.

Effective pre-clinical computational modeling strategies have been demonstrated in this article to enable risk free clinical application of radiofrequency ablation (RFA) of breast tumor. The present study (a) determines various optimal regulating parameters required for RFA of tumor and (b) introduces an essential clinical monitoring scheme to minimize the extent of damage to the healthy cell during RFA of tumor. The therapeutic capabilities offered by RFA of breast tumor, viz., the rise in local temperature and induced thermal damage have been predicted by integrating the bioheat transfer model, the electric field distribution model and the thermal damage model. The mathematical model has been validated with the experimental results available in the literature. The results revealed that, the effective damage of tumor volume sparing healthy tissue essentially depends on the voltage, the exposure time, the local heat distribution, the tumor stage and the electrode geometric configuration. It has been confirmed that, the assessment of damage front can accurately determine the extent of damage as compared to the thermal front. The study further evaluates the damaged healthy and tumor volumes due to RFA of different stages of breast cancer. The assessment of cell survival and damage fractions discloses the propensity of reappearance/healing of tumor cells after treatment.

Accurate 3D temperature dosimetry during hyperthermia therapy by combining invasive measurements and patient-specific simulations.

PURPOSE: Dosimetry during deep local hyperthermia treatments in the head and neck currently relies on a limited number of invasively placed temperature sensors. The purpose of this study was to assess the feasibility of 3D dosimetry based on patient-specific temperature simulations and sensory feedback. MATERIALS AND METHODS: The study includes 10 patients with invasive thermometry applied in at least two treatments. Based on their invasive thermometry, we optimised patient-group thermal conductivity and perfusion values for muscle, fat and tumour using a 'leave-one-out' approach. Next, we compared the accuracy of the predicted temperature (ΔT) and the hyperthermia treatment quality (ΔT50) of the optimisations based on the patient-group properties to those based on patient-specific properties, which were optimised using previous treatment measurements. As a robustness check, and to enable comparisons with previous studies, we optimised the parameters not only for an applicator efficiency factor of 40%, but also for 100% efficiency. RESULTS: The accuracy of the predicted temperature (ΔT) improved significantly using patient-specific tissue properties, i.e. 1.0 °C (inter-quartile range (IQR) 0.8 °C) compared to 1.3 °C (IQR 0.7 °C) for patient-group averaged tissue properties for 100% applicator efficiency. A similar accuracy was found for optimisations using an applicator efficiency factor of 40%, indicating the robustness of the optimisation method. Moreover, in eight patients with repeated measurements in the target region, ΔT50 significantly improved, i.e. ΔT50 reduced from 0.9 °C (IQR 0.8 °C) to 0.4 °C (IQR 0.5 °C) using an applicator efficiency factor of 40%. CONCLUSION: This study shows that patient-specific temperature simulations combined with tissue property reconstruction from sensory data provides accurate minimally invasive 3D dosimetry during hyperthermia treatments: T50 in sessions without invasive measurements can be predicted with a median accuracy of 0.4 °C.

A comparative study of thermal effects of 3 types of laser in eye: 3D simulation with bioheat equation.

The application of laser in ophthalmology and eye surgery is so widespread that hardly can anyone deny its importance. On the other hand, since the human eye is an organ susceptible to external factors such as heat waves, laser radiation rapidly increases the temperature of the eye and therefore the study of temperature distribution inside the eye under laser irradiation is crucial; but the use of experimental and invasive methods for measuring the temperature inside the eye is typically high-risk and hazardous. In this paper, using the three-dimensional finite element method, the distribution of heat transfer inside the eye under transient condition was studied through three different lasers named Nd:Yag, Nd:Yap and ArF. Considering the metabolic heat and blood perfusion rate in various regions of the eye, numerical solution of space-time dependant Pennes bioheat transfer equation has been applied in this study. Lambert-Beer's law has been used to model the absorption of laser energy inside the eye tissues. It should also be mentioned that the effect of the ambient temperature, tear evaporation rate, laser power and the pupil diameter on the temperature distribution have been studied. Also, temperature distribution inside the eye after applying each laser and temperature variations of six optional regions as functions of time have been investigated. The results show that these radiations cause temperature rise in various regions, which will in turn causes serious damages to the eye tissues. Investigating the temperature distribution inside the eye under the laser irradiation can be a useful tool to study and predict the thermal effects of laser radiation on the human eye and evaluate the risk involved in performing laser surgery.

Simulation of radiofrequency ablation in real human anatomy.

PURPOSE: The objective of the current work was to simulate radiofrequency ablation treatment in computational models with realistic human anatomy, in order to investigate the effect of realistic geometry in the treatment outcome. MATERIALS AND METHODS: The body sites considered in the study were liver, lung and kidney. One numerical model for each body site was obtained from Duke, member of the IT'IS Virtual Family. A spherical tumour was embedded in each model and a single electrode was inserted into the tumour. The same excitation voltage was used in all cases to underline the differences in the resulting temperature rise, due to different anatomy at each body site investigated. The same numerical calculations were performed for a two-compartment model of the tissue geometry, as well as with the use of an analytical approximation for a single tissue compartment. RESULTS: Radiofrequency ablation (RFA) therapy appears efficient for tumours in liver and lung, but less efficient in kidney. Moreover, the time evolution of temperature for a realistic geometry differs from that for a two-compartment model, but even more for an infinite homogenous tissue model. However, it appears that the most critical parameters of computational models for RFA treatment planning are tissue properties rather than tissue geometry. CONCLUSIONS: Computational simulations of realistic anatomy models show that the conventional technique of a single electrode inside the tumour volume requires a careful choice of both the excitation voltage and treatment time in order to achieve effective treatment, since the ablation zone differs considerably for various body sites.