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.     

Dual phase lag bio-heat transfer during cryosurgery of lung cancer: Comparison of three heat transfer models

The Pennes bio-heat model is based on Fourier's law of heat conduction, which assumed that a thermal signal propagate with infinite speed. This gives contradiction in physical situation. Also, the hyperbolic bio-heat model considers the micro scale response in time, but it does not explain the micro scale response in space. Therefore, to consider the thermal behaviour which is not captured by the Fourier's law and to take into account the microstructural effect in space, a dual phase lag (DPL) bio-heat conduction model would be advantageous. In this paper, a two dimensional DPL model is proposed to study the phase change heat transfer process during cryosurgery of lung cancer. The governing equations are solved numerically by enthalpy based finite difference method. The non-ideal behaviour of tissue and heat source terms, metabolism and blood perfusion are also considered. This study is made to examine the effects of phase lags in heat flux and temperature gradient on interface positions and temperature distribution during freezing process. A comparative study of DPL, parabolic and hyperbolic conduction models is thoroughly investigated. It is found that the phase lags of temperature gradient and heat flux have significant effect on interface positions and temperature distribution.     

Comparative evaluation of hyperthermia heating modalities. I. Numerical analysis of thermal dosimetry bracketing cases

A method for comparing the relative abilities of different hyperthermia heating modalities to properly heat tumors has been developed using solutions of the bio-heat transfer equation. A single measure, the range of absorbed powers that gives acceptable tissue temperature distributions, is used to characterize the ability of a given heating technique to heat a given tumor. An acceptable tissue temperature distribution is one for which (a) the temperatures in the coolest regions of the tumor are above a minimum therapeutic value, (b) the temperatures in the hottest regions of the tumor do not exceed a maximum clinically acceptable value, and (c) the normal tissue temperatures do not exceed maximum clinically acceptable levels. This measure can be interpreted directly in clinical terms as the range of power settings on the power indicator of a heating device for which acceptable tumor heatings will occur. This paper describes the basis of the method and investigates the role of tumor blood perfusion patterns in determining the size of the acceptable power range. Three tumor perfusion patterns are investigated: uniform tumor perfusion, a concentric annulli perfusion model in which the tumor consists of a necrotic core surrounded by two concentric layers of increased perfusion, and a random perfusion distribution model. The results show that, in general, the uniform and annular perfusion models serve as bracketing case patterns. That is, they give acceptable power range values that are upper and lower limits of the acceptable power ranges obtained for the random perfusion patterns. The method is applied to heating patterns that simulate those obtained from a variety of different available heating techniques, and it is found to be valid for all cases studied. The role of normal tissue limiting conditions is also investigated.     

Coupled field analysis of heat flow in the near field of a microwave applicator for tumor ablation

Microwave tumor ablation (MTA) offers a new approach for the treatment of hepatic neoplastic disease. Reliable and accurate information regarding the heat distribution inside biological tissue subjected to microwave thermal ablation is important for the efficient design of microwave applicators and for optimizing experiments, which aim to assess the effects of therapeutic treatments. Currently there are a variety of computational methods based on different vascular structures in tissue, which aim to model heat distribution during ablation. This paper presents results obtained from two such computational models for temperature distributions produced by a clinical 2.45 GHz MTA applicator immersed in unperfused ex vivo bovine liver, and compares them with measured results from a corresponding ex vivo experiment. The computational methods used to model the temperature distribution in tissue caused by the insertion of a 5.6 mm diameter "wandlike" microwave applicator are the Green's function method and the finite element method (FEM), both of which provide solutions of the heat diffusion partial differential equation. The results obtained from the coupled field simulations are shown to be in good agreement with a simplified analysis based on the bio-heat equation and with ex vivo measurements of the heat distribution produced by the clinical MTA applicator.     

On the solution of the non-linear bio-heat equation

With reference to microwave localized hyperthermia, a non-linear model of the thermal behavior of living tissues, where local thermoregulating convective and conducting effects due to blood flow are taken into account, has been assumed. The non-linear operator equation for the space and time temperature distribution, which describes local energy balance (bio-heat equation), has been linearized and solved by using a variant of the Newton iterative method. Numerical calculations for plane stratified structures simulating living bodies, irradiated by plane electromagnetic waves, have been carried out.     

Numerical study of the effect of ultrasound frequency on temperature distribution in layered tissue

The high intensity focused ultrasound (HIFU) technology can produce therapeutic benefits in deep-seated tissues of interest, selectively and noninvasively. In order to control the treatment process, it is important to recognize the heat generation in biological tissue and the parameters that have an effect on temperature rising. This study investigates the influence of frequency and source intensity on temperature distribution during high-intensity focused ultrasound (HIFU). A nonlinear full wave equation model is simulated to compute the pressure field. Additionally, the absorbed coefficient of tissue is added to the nonlinear equations to simulate accurately the wave propagation in tissue with high absorbed coefficient. In addition, temperature distribution was solved by the Pennes bio-heat equation. Conclusively, frequencies in the range of 1–1.5 MHz are prescribed to have maximum heat absorption in the focal region.     

Simulation and investigation of quantum dot effects as internal heat-generator source in breast tumor site

The Pennes bio-heat transfer equation, which introduces the exchange magnitude of heat transfer between tissue and blood, is often used to solve the temperature distribution for thermal imaging and sensing. Near-infrared light has the ability to be used as a non-invasive means of diagnostic imaging within the woman's breast. Due to the diffusive nature of light in different tissue, computational model-based methods are required for functional imaging within the breast. In this article, the time-dependent bio-heat transfer is solved by a numerical method. In our model, the heat generation source (intrinsic and extrinsic) involves laser, metabolism, and quantum dot that the metabolism and heat generated by QDs are considered as intrinsic. We supposed the injected quantum dots would target the tumor site by a passive targeting process and then by interaction of laser radiation and quantum dot, the photoluminescence of quantum dot is converted to heat in the tumor site. The extra generated heat can impact on the extracted heat profile. One of the important applications of this research has led to a sensitivity improvement of the imaging system, which is potentially useful in the diagnosis and detection of breast cancer.     

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.     

3D in silico study of magnetic fluid hyperthermia of breast tumor using Fe3O4 magnetic nanoparticles

Modeling and simulation of the temperature distribution, the mass concentration, and the heat transfer in the breast tissue are hot issues in magnetic fluid hyperthermia treatment of cancer. The breast tissue can be visualized as a porous matrix with saturated blood. In this paper, 3D in silico study of breast cancer hyperthermia using magnetic nanoparticles (MNPs) is conducted. The 3D FEM models are incorporated to investigate the infusion and backflow of nanofluid in the breast tumor, the diffusion of nanofluid, temperature distribution during the treatment, and prediction of the fraction of tumor necrosis while dealing with the thermal therapy. All the hyperthermia procedures are simulated and analyzed on COMSOL Multiphysics. The sensitivity of frequency and amplitude of the applied magnetic field (AMF) is investigated on the heating effect of the tumor. The mesh dependent solution of Penne's bioheat model is also analyzed. The simulated results demonstrate successful breast cancer treatment using MNPs with minimum side effects. Validation of current simulations results with experimental studies existing in literature advocates the success of our therapy. The increase in the amplitude and frequency of the AMF increases of the temperature in the tumor. The variation of mesh from coarser to finer increased the temperature through small fractions. We have also simulated the magnetic induction problem where the magnetic field is generated by current-carrying coil conductors induce heat in nearby breast tumors due to excitation of MNPs by magnetic flux. This research will aid treatment protocols and real-time clinical breast cancer treatments.     

Cancer theranostics: the rise of targeted magnetic nanoparticles

Interest in utilizing magnetic nanoparticles (MNP) for biomedical applications has increased considerably over the past two decades. This excitement has been driven in large part by the success of MNPs as contrast agents in magnetic resonance imaging. The recent investigative trend with respect to cancer has continued down a diagnostic path, but has also turned toward concurrent therapy, giving rise to the distinction of MNPs as potential "theranostics". Here we review both the key technical principles of MNPs and ongoing advancement toward a cancer theranostic MNP. Recent progress in diagnostics, hyperthermia treatments, and drug delivery are all considered. We conclude by identifying current barriers to clinical translation of MNPs and offer considerations for their future development.     

Numerical investigation of thermal response of laser-irradiated biological tissue phantoms embedded with gold nanoshells

The work presented in this paper focuses on numerically investigating the thermal response of gold nanoshells-embedded biological tissue phantoms with potential applications into photo-thermal therapy wherein the interest is in destroying the cancerous cells with minimum damage to the surrounding healthy cells. The tissue phantom has been irradiated with a pico-second laser. Radiative transfer equation (RTE) has been employed to model the light-tissue interaction using discrete ordinate method (DOM). For determining the temperature distribution inside the tissue phantom, the RTE has been solved in combination with a generalized non-Fourier heat conduction model namely the dual phase lag bio-heat transfer model. The numerical code comprising the coupled RTE-bio-heat transfer equation, developed as a part of the current work, has been benchmarked against the experimental as well as the numerical results available in the literature. It has been demonstrated that the temperature of the optical inhomogeneity inside the biological tissue phantom embedded with gold nanoshells is relatively higher than that of the baseline case (no nanoshells) for the same laser power and operation time. The study clearly underlines the impact of nanoshell concentration and its size on the thermal response of the biological tissue sample. The comparative study concerned with the size and concentration of nanoshells showed that 60 nm nanoshells with concentration of 5×10¹⁵ mm⁻³ result into the temperature levels that are optimum for the irreversible destruction of cancer infected cells in the context of photo-thermal therapy. To the best of the knowledge of the authors, the present study is one of the first attempts to quantify the influence of gold nanoshells on the temperature distributions inside the biological tissue phantoms upon laser irradiation using the dual phase lag heat conduction model.     

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.     

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.     

内热源影响下的均质组织表面温度分布研究

现有的医用红外热像技术几乎都采自体表,为了提高诊断准确性,必须进一步确定体表温度分布与体内热源间的关系。基于人体内部传热机制和人体与环境的传热机制,推导出稳态下均质（各向同性）组织的表面温度分布与内部球状热源之间的关系,通过模拟计算可验证结论的准确性。     

Analytical prediction of sub–surface thermal history in translucent tissue phantoms during plasmonic photo–thermotherapy (PPTT)

Knowledge of thermal history and/or distribution in biological tissues during laser based hyperthermia is essential to achieve necrosis of tumour/carcinoma cells. A semi–analytical model to predict sub–surface thermal distribution in translucent, soft, tissue mimics has been proposed. The model can accurately predict the spatio–temporal temperature variations along depth and the anomalous thermal behaviour in such media, viz. occurrence of sub-surface temperature peaks. Based on optical and thermal properties, the augmented temperature and shift of the peak positions in case of gold nanostructure mediated tissue phantom hyperthermia can be predicted. Employing inverse approach, the absorption coefficient of nano-graphene infused tissue mimics is determined from the peak temperature and found to provide appreciably accurate predictions along depth. Furthermore, a simplistic, dimensionally consistent correlation to theoretically determine the position of the peak in such media is proposed and found to be consistent with experiments and computations. The model shows promise in predicting thermal distribution induced by lasers in tissues and deduction of therapeutic hyperthermia parameters, thereby assisting clinical procedures by providing a priori estimates.     

铁磁热籽加温治疗肿瘤的研究

热疗治疗肿瘤是应用各种致热源的热效应,将肿瘤加热至有效治疗温度范围并维持一定时间,以杀灭肿瘤细胞的一种方法。本文探讨了用于加温治疗肿瘤的铁磁热籽在治疗时的加热原理和自控温机制。与目前几种加温方式和测温方式的相比,得出铁磁热籽在肿瘤治疗中利用感应加温有效的克服了其它加温方式的缺点,并且利用居里点效应实现了自控温。因此,有着诱人的前景。     

Insulin-like 3 expression and fibrosis induction after intra-testicular injection of magnetic nanoparticles in rat testis and the ameliorative role of Echinacea purpurea extract

The World Health Organization has approved magnetic nanoparticles (MNP) for use as a contrast agent for magnetic resonance imaging or tumor hyperthermia treatment. MNP are toxic over time after intra-testicular injection. A clear strategy to ameliorate the toxic side effects of MNP in normal tissues after medical application has not yet been developed. We used an extract of Echinacea purpurea (EP) as a natural source of antioxidant and free radical scavenging product for detoxification of MNP in testicular tissues. MNP localization in the interstitial area of testicular tissue reduced the expression of insulin-like factor 3 (INSL3) proteins as well as serum testosterone levels. Further, MNP caused accumulation of both collagen and elastin in the interstitial area and increased the thickness of the tunica albuginea. Injection of MNP during administration of EP extract for short periods slightly reduced the toxic side effects of MNP. After extended exposure to EP extract, INSL3 expression and testosterone returned to near control levels. Also, collagen and elastin accumulation caused by MNP was reduced after extended exposure to EP extract. We believe that the ameliorative effect of EP extract is due to its antioxidant properties.     

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.     

A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach

Hyperthermia is a process that uses heat from the spatial heat source to kill cancerous cells without damaging the surrounding healthy tissues. Efficacy of hyperthermia technique is related to achieve temperature at the infected cells during the treatment process. A mathematical model on heat transfer in multilayer tissues in finite domain is proposed to predict the control temperature profile at hyperthermia position. The treatment technique uses dual-phase-lag model of heat transfer in multilayer tissues with modified Gaussian distribution heat source subjected to the most generalized boundary condition and interface at the adjacent layers. The complete dual-phase-lag model of bioheat transfer is solved using finite element Legendre wavelet Galerkin approach. The present solution has been verified with exact solution in a specific case and provides a good accuracy. The effect of the variability of different parameters such as lagging times, external heat source, metabolic heat source and the most generalized boundary condition on temperature profile in multilayer tissues is analyzed and also discussed the effective approach of hyperthermia treatment. Furthermore, we studied the modified thermal damage model with regeneration of healthy tissues as well. For viewpoint of thermal damage, the least thermal damage has been observed in boundary condition of second kind. The article concludes with a discussion of better opportunities for future clinical application of hyperthermia treatment.