A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment

The success of hyperthermia in the treatment of cancer depends on the precise prediction and control of temperature. It was absolutely a necessity for hyperthermia treatment planning to understand the temperature distribution within living biological tissues. In this paper, dual-phase-lag model of bio-heat transfer has been studied using Gaussian distribution source term under most generalized boundary condition during hyperthermia treatment. An approximate analytical solution of the present problem has been done by Finite element wavelet Galerkin method which uses Legendre wavelet as a basis function. Multi-resolution analysis of Legendre wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. The whole analysis is presented in dimensionless form. The dual-phase-lag model of bio-heat transfer has compared with Pennes and Thermal wave model of bio-heat transfer and it has been found that large differences in the temperature at the hyperthermia position and time to achieve the hyperthermia temperature exist, when we increase the value of τ_T. Particular cases when surface subjected to boundary condition of 1st, 2nd and 3rd kind are discussed in detail. The use of dual-phase-lag model of bio-heat transfer and finite element wavelet Galerkin method as a solution method helps in precise prediction of temperature. Gaussian distribution source term helps in control of temperature during hyperthermia treatment. So, it makes this study more useful for clinical applications.     

Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy

In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy.     

Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating

An analytical solution to the Pennes bioheat transfer equation in three-dimensional geometry with practical hyperthermia boundary conditions and random heating was obtained in this paper. Uncertainties for the predicted temperatures of tissues due to approximate parameters were studied based on analyzing one-dimensional heat transfer in the biological bodies subject to a spatially decay heating. Contributions from each of the thermal parameters such as heat conductivity, blood perfusion rate, and metabolic rate of the tissues, the scattering coefficient and the surface power flux of the heating apparatus were compared and the uncertainty limit for temperature distribution in this case was estimated. The results are useful in a variety of clinical hyperthermia and biological thermal parameter measurement.     

Three-dimensional model on thermal response of skin subject to laser heating

A three-dimensional (3D) multilayer model based on the skin physical structure is developed to investigate the transient thermal response of human skin subject to laser heating. The temperature distribution of the skin is modeled by the bioheat transfer equation, and the influence of laser heating is expressed as a source term where the strength of the source is a product of a Gaussian shaped incident irradiance, an exponentially shaped axial attenuation, and a time function. The water evaporation and diffusion is included in the model by adding two terms regarding the heat loss due to the evaporation and diffusion, where the rate of water evaporation is determined based on the theory of laminar boundary layer. Cryogen spray cooling (CSC) in laser therapy is studied, as well as its effect on the skin thermal response. The time-dependent equation is discretized using the finite difference method with the Crank–Nicholson scheme and the stability of the numerical method is analyzed. The large sparse linear system resulted from discretizing the governing partial differential equation is solved by a GMRES solver and the expected simulation results are obtained.     

Three-dimensional model on thermal response of skin subject to laser heating

A three-dimensional (3D) multilayer model based on the skin physical structure is developed to investigate the transient thermal response of human skin subject to laser heating. The temperature distribution of the skin is modeled by the bioheat transfer equation, and the influence of laser heating is expressed as a source term where the strength of the source is a product of a Gaussian shaped incident irradiance, an exponentially shaped axial attenuation, and a time function. The water evaporation and diffusion is included in the model by adding two terms regarding the heat loss due to the evaporation and diffusion, where the rate of water evaporation is determined based on the theory of laminar boundary layer. Cryogen spray cooling (CSC) in laser therapy is studied, as well as its effect on the skin thermal response. The time-dependent equation is discretized using the finite difference method with the Crank-Nicholson scheme and the stability of the numerical method is analyzed. The large sparse linear system resulted from discretizing the governing partial differential equation is solved by a GMRES solver and the expected simulation results are obtained.     

Transient bioheat simulation of the laser-tissue interaction in human skin using hybrid finite element formulation

This paper presents a hybrid finite element model for describing quantitatively the thermal responses of skin tissue under laser irradiation. The model is based on the boundary integral-based finite element method and the Pennes bioheat transfer equation. In this study, temporal discretization of the bioheat system is first performed and leads to the well-known modified Helmholtz equation. A radial basis function approach and the boundary integral based finite element method are employed to obtain particular and homogeneous solutions of the laser-tissue interaction problem. In the boundary integral based finite element formulation, two independent fields are assumed: intra-element field and frame field. The intra-element field is approximated through a linear combination of fundamental solutions at a number of source points outside the element domain. The frame temperature field is expressed in terms of nodal temperature and the corresponding shape function. Numerical examples are considered to verify and assess the proposed numerical model. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature and to identify the degree of burn injury due to laser heating.     

Nano-assisted radiofrequency ablation of clinically extracted irregularly-shaped liver tumors

Radiofrequency ablation (RFA) for liver tumors is a minimally invasive procedure that uses electrical energy and heat to destroy cancer cells. One of the critical factors that impedes its successful outcome is the use of inappropriate radiofrequency levels that will not completely destroy the target tumor tissues, resulting in therapy failure. Additionally, the surrounding healthy tissues may suffer from serious damage due to excessive ablation. To address these challenges, this work proposes the employment of injected nanoparticles to thermally promote the ablation efficacy of conventional RFA. A three-dimensional finite difference analysis is employed to simulate the RFA treatment. Based on the data acquired from measured experiments, the simulation results have demonstrated close agreement with experimental data with a maximum discrepancy of within ±8.7%. Several types of nanoparticles were selected to evaluate their influences on liver tissue's thermal and electrical properties. We analysed the effects of nanoparticles on liver RFA via a tumor rending process incorporating several clinically-extracted tumor profiles and vascular systems. Simulations were conducted to explore the temperature difference responses between conventional RFA treatment and one with the inclusion of assisted nanoparticles on several irregularly-shaped tumors. Results have indicated that applying selected nanoparticles with high thermal conductivity and electrical conductivity on the targeted tissue zone promotes heating rate while sustaining a similar ablation zone that experiences lower maximum temperature when compared with the conventional RFA treatment. In sum, incorporating thermally-enhancing nanoparticles promotes heat transfer during the RFA treatment, resulting in improved ablation efficiency.     

Temperature and burn injury prediction of human skin exposed to microwaves: a model analysis

A one-dimensional multi-layer model is presented to characterize skin temperature rises and burn processes resulting from skin exposure to microwaves. Temperature variations and damage function analyses in the skin tissue exposed to microwaves were predicted depending on blood perfusion rate, thermal conductivity, power density, and exposure time. Thermal wave model was applied and the bio-heat transfer equation was solved using the finite difference time domain method. The thermal wave model of bio-heat transfer predicts a lower temperature rise than a model that uses Pennes’ equation. When approaching steady state, the solutions overlaps with that obtained using the Pennes’ equation. The results obtained may help to analyze the consequences of short-time high-power MW exposures in biological tissues.     

A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments

The genesis of the present research paper is to develop a revised exact analytical solution of thermal profile of 1-D Pennes’ bioheat equation (PBHE) for living tissues influenced in thermal therapeutic treatments. In order to illustrate the temperature distribution in living tissue both Fourier and non-Fourier model of 1-D PBHE has been solved by ‘Separation of variables’ technique. Till date most of the research works have been carried out with the constant initial steady temperature of tissue which is not at all relevant for the biological body due to its nonhomogeneous living cells. There should be a temperature variation in the body before the therapeutic treatment. Therefore, a coupled heat transfer in skin surface before therapeutic heating must be taken account for establishment of exact temperature propagation. This approach has not yet been considered in any research work. In this work, an initial condition for solving governing differential equation of heat conduction in biological tissues has been represented as a function of spatial coordinate. In a few research work, initial temperature distribution with PBHE has been coupled in such a way that it eliminates metabolic heat generation. The study has been devoted to establish the comparison of thermal profile between present approach and published theoretical approach for particular initial and boundary conditions inflicted in this investigation. It has been studied that maximum temperature difference of existing approach for Fourier temperature distribution is 19.6% while in case of non-Fourier, it is 52.8%. We have validated our present analysis with experimental results and it has been observed that the temperature response based on the spatial dependent variable initial condition matches more accurately than other approaches.     

Radio-frequency ablation in a realistic reconstructed hepatic tissue

This study uses a reconstructed vascular geometry to evaluate the thermal response of tissue during a three-dimensional radiofrequency (rf) tumor ablation. MRI images of a sectioned liver tissue containing arterial vessels are processed and converted into a finite-element mesh. A rf heat source in the form of a spherically symmetric Gaussian distribution, fit from a previously computed profile, is employed. Convective cooling within large blood vessels is treated using direct physical modeling of the heat and momentum transfer within the vessel. Calculations of temperature rise and thermal dose are performed for transient rf procedures in cases where the tumor is located at three different locations near the bifurcation point of a reconstructed artery. Results demonstrate a significant dependence of tissue temperature profile on the reconstructed vasculature and the tumor location. Heat convection through the arteries reduced the steady-state temperature rise, relative to the no-flow case, by up to 70% in the targeted volume. Blood flow also reduced the thermal dose value, which quantifies the extent of cell damage, from approximately 3600 min, for the no-flow condition, to 10 min for basal flow (13.8 cms). Reduction of thermal dose below the threshold value of 240 min indicates ablation procedures that may inadequately elevate the temperature in some regions, thereby permitting possible tumor recursion. These variations are caused by vasculature tortuosity that are patient specific and can be captured only by the reconstruction of the realistic geometry.     

An inverse problem in estimating the laser irradiance and thermal damage in laser-irradiated biological tissue with a dual-phase-lag model

The aim of this study is to solve an inverse heat conduction problem to estimate the unknown time-dependent laser irradiance and thermal damage in laser-irradiated biological tissue from the temperature measurements taken within the tissue. The dual-phase-lag model is considered in the formulation of heat conduction equation. The inverse algorithm used in the study is based on the conjugate gradient method and the discrepancy principle. The effect of measurement errors and measurement locations on the estimation accuracy is also investigated. Two different examples of laser irradiance are discussed. Results show that the unknown laser irradiance and thermal damage can be predicted precisely by using the present approach for the test cases considered in this study.     

FDTD analysis of a noninvasive hyperthermia system for brain tumors

ABSTRACT: BACKGROUND: Hyperthermia is considered one of the new therapeutic modalities for cancer treatment and is based on the difference in thermal sensitivity between healthy tissues and tumors. During hyperthermia treatment, the temperature of the tumor is raised to 40--4[DEGREE SIGN]C for a definite period resulting in the destruction of cancer cells. This paper investigates design, modeling and simulation of a new non-invasive hyperthermia applicator system capable of effectively heating deep seated as well as superficial brain tumors using inexpensive, simple, and easy to fabricate components without harming surrounding healthy brain tissues. METHODS: The proposed hyperthermia applicator system is composed of an air filled partial half ellipsoidal chamber, a patch antenna, and a head model with an embedded tumor at an arbitrary location. The irradiating antenna is placed at one of the foci of the hyperthermia chamber while the center of the brain tumor is placed at the other focus. The finite difference time domain (FDTD) method is used to compute both the SAR patterns and the temperature distribution in three different head models due to two different patch antennas at a frequency of 915 MHz. RESULTS: The obtained results suggest that by using the proposed noninvasive hyperthermia system it is feasible to achieve sufficient and focused energy deposition and temperature rise to therapeutic values in deep seated as well as superficial brain tumors without harming surrounding healthy tissue. CONCLUSIONS: The proposed noninvasive hyperthermia system proved suitable for raising the temperature in tumors embedded in the brain to therapeutic values by carefully selecting the systems components. The operator of the system only needs to place the center of the brain tumor at a pre-specified location and excite the antenna at a single frequency of 915 MHz. Our study may provide a basis for a clinical applicator prototype capable of heating brain tumors.     

Heat transfer analysis of skin during thermal therapy using thermal wave equation

Specifying exact geometry of vessel network and its effect on temperature distribution in living tissues is one of the most complicated problems of the bioheat field. In this paper, the effects of blood vessels on temperature distribution in a skin tissue subjected to various thermal therapy conditions are investigated. Present model consists of counter-current multilevel vessel network embedded in a three-dimensional triple-layered skin structure. Branching angles of vessels are calculated using the physiological principle of minimum work. Length and diameter ratios are specified using length doubling rule and Cube law, respectively. By solving continuity, momentum and energy equations for blood flow and Pennes and modified Pennes bioheat equations for the tissue, temperature distributions in the tissue are measured. Effects of considering modified Pennes bioheat equation are investigated, comprehensively. It is also observed that blood has an impressive role in temperature distribution of the tissue, especially at high temperatures. The effects of different parameters such as boundary conditions, relaxation time, thermal properties of skin, metabolism and pulse heat flux on temperature distribution are investigated. Tremendous effect of boundary condition type at the lower boundary is noted. It seems that neither insulation nor constant temperature at this boundary can completely describe the real physical phenomena. It is expected that real temperature at the lower levels is somewhat between two predicted values. The effect of temperature on the thermal properties of skin tissue is considered. It is shown that considering temperature dependent values for thermal conductivity is important in the temperature distribution estimation of skin tissue; however, the effect of temperature dependent values for specific heat capacity is negligible. It is seen that considering modified Pennes equation in processes with high heat flux during low times is significant.     

MicroCT image based simulation to design heating protocols in magnetic nanoparticle hyperthermia for cancer treatment

ObjectivesThe objective is to design heating protocols to completely damage PC3 tumors after a single magnetic nanoparticle hyperthermia session with minimal collateral thermal damage, based on microCT image generated tumor and mouse models.MethodsTumor geometries and volumetric heat generation rate distributions that are generated from microCT scans in our previous study are imported into COMSOL 4.3® multiphysics for heat transfer simulations and heating protocol design using the Arrhenius damage model. Then, parametric studies are performed to evaluate how significantly the infusion rate affects the protocol design and its resulted collateral thermal damage.ResultsThe simulated temperature field in the generated tumor geometry and volumetric heat generation rate distribution are reasonable and correlates well with the amount of the total thermal energy deposited into the tumors. The time needed for complete thermal damage is determined to be approximately 12 min or 25 min if one uses the Arrhenius integral Ω equal to 1 or 4 as the damage threshold, when the infusion rate is 3 μL/min. The heating time increases 26% or 91% in the higher infusion rate groups of 4 or 5 μL/min, respectively. Collateral thermal damage to the surrounding tissue is also assessed. Although the two larger infusion rate groups can still cause thermal damage to the entire tumor, the collateral thermal damage would have exceeded the design criterion of 5%, while the assessment criterion is acceptable only in the infusion rate group of 3 μL/min. Based on the results of this study, we identify an injection strategy and heating protocols to be implemented in future animal experiments to evaluate treatment efficacy for model validation.     

Heat transfer simulation using energy conservative dissipative particle dynamics

Dissipative particle dynamics with energy conservation (eDPD) was used to investigate conduction heat transfer in two dimensions under steady-state condition. Various types of boundary condition were implemented to the conduction domain. Besides, 2D conduction with internal heat generation was studied and the heat generation term was used to measure the thermal conductivity and diffusivity of the eDPD system. The boundary conditions used include both the Neumann and Dirichlet boundary conditions. The Neumann boundary condition was applied via adiabatic surfaces and surfaces exposed to convection heat transfer. The DPD simulations were compared to analytical solutions and finite-difference techniques. It was found that DPD appropriately predicts the temperature distribution in the conduction regime. Details of boundary condition implementation and thermal diffusivity measurement are also described in this paper.     

Investigation of thermal distribution for pulsed laser radiation in cancer treatment with nanoparticle-mediated hyperthermia

In this paper, we have simulated the efficacy of gold/gold sulfide (GGS) nanoshells in NIR laser hyperthermia to achieve effective targeting for tumor photothermal therapy. The problem statement takes into account the heat transfer with the blood perfusion through capillaries, and pulsed laser irradiation during the hyperthermia. Although previous researchers have used short laser pulses (nanosecond and less), in order to prevent heat leakage to the neighbor tissues, we have examined the effect of millisecond pulses, as the extent of the target volume to which hyperthermia is induced is usually larger and also the lasers with this specification are more available. A tumor with surrounding tissue was simulated in COMSOL software (a finite element analysis, solver and simulation software) and also in a phantom made of agarose and intralipid. The tumor was irradiated by 10, 20 and 30 laser pulses with durations of 15, 50 and 200 ms and fluences of 20, 40 and 60 J/cm². Experimental tests performed on a phantom prove the ability of the applied numerical model to capture the temperature distribution in the target tissue. We have shown that our simulation permits prediction of treatment outcome from computation of thermal distribution within the tumor during laser hyperthermia using GGS nanoshells and millisecond pulsed laser irradiation. The advantage of this simulation is its simplicity as well as its accuracy. Although, to develop the model completely for a given organ and application, all the parameters should be estimated based on a real vasculature of the organ, physiological conditions, and expected variation in those physiological conditions for that application in the organ.     

An Energy Analysis of Extracellular Hyperthermia

The classical hyperthermia effect is based on well‐focused energy absorption targeting the malignant tissue. The treatment temperature has been considered as the main technical parameter. There are discussions about the mechanism and control of the process because of some doubts about the micro‐mechanisms. The main idea of the extracellular hyperthermia is to heat up the targeted tissue by means of electric field, keeping the energy absorption in the extracellular liquid. This produces a temperature gradient and connected heat flow through the cell membrane, which initializes numerous nonequilibrium thermal microprocesses to destroy the cell membrane. Furthermore, before the heat shock activates the intracellular heat shock protein (HSP) mechanisms, thecell membrane has been already compromised, therefore the HSP synthesis in the cells starts secondarily only after the membrane damage. The process could explain why the nonuniform and basically unsatisfactorily high temperature locoregional hyperthermia could be effective.     

Predicting effects of blood flow rate and size of vessels in a vasculature on hyperthermia treatments using computer simulation

Background

Pennes Bio Heat Transfer Equation (PBHTE) has been widely used to approximate the overall temperature distribution in tissue using a perfusion parameter term in the equation during hyperthermia treatment. In the similar modeling, effective thermal conductivity (K_eff) model uses thermal conductivity as a parameter to predict temperatures. However the equations do not describe the thermal contribution of blood vessels. A countercurrent vascular network model which represents a more fundamental approach to modeling temperatures in tissue than do the generally used approximate equations such as the Pennes BHTE or effective thermal conductivity equations was presented in 1996. This type of model is capable of calculating the blood temperature in vessels and describing a vasculature in the tissue regions.

Methods

In this paper, a countercurrent blood vessel network (CBVN) model for calculating tissue temperatures has been developed for studying hyperthermia cancer treatment. We use a systematic approach to reveal the impact of a vasculature of blood vessels against a single vessel which most studies have presented. A vasculature illustrates branching vessels at the periphery of the tumor volume. The general trends present in this vascular model are similar to those shown for physiological systems in Green and Whitmore. The 3-D temperature distributions are obtained by solving the conduction equation in the tissue and the convective energy equation with specified Nusselt number in the vessels.

Results

This paper investigates effects of size of blood vessels in the CBVN model on total absorbed power in the treated region and blood flow rates (or perfusion rate) in the CBVN on temperature distributions during hyperthermia cancer treatment. Also, the same optimized power distribution during hyperthermia treatment is used to illustrate the differences between PBHTE and CBVN models. K_eff (effective thermal conductivity model) delivers the same difference as compared to the CBVN model. The optimization used here is adjusting power based on the local temperature in the treated region in an attempt to reach the ideal therapeutic temperature of 43°C. The scheme can be used (or adapted) in a non-invasive power supply application such as high-intensity focused ultrasound (HIFU). Results show that, for low perfusion rates in CBVN model vessels, impacts on tissue temperature becomes insignificant. Uniform temperature in the treated region is obtained.

Conclusion

Therefore, any method that could decrease or prevent blood flow rates into the tumorous region is recommended as a pre-process to hyperthermia cancer treatment. Second, the size of vessels in vasculatures does not significantly affect on total power consumption during hyperthermia therapy when the total blood flow rate is constant. It is about 0.8% decreasing in total optimized absorbed power in the heated region as γ (the ratio of diameters of successive vessel generations) increases from 0.6 to 0.7, or from 0.7 to 0.8, or from 0.8 to 0.9. Last, in hyperthermia treatments, when the heated region consists of thermally significant vessels, much of absorbed power is required to heat the region and (provided that finer spatial power deposition exists) to heat vessels which could lead to higher blood temperatures than tissue temperatures when modeled them using PBHTE.     

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.