Numerical simulation of dual-phase-lag bioheat transfer model during thermal therapy

Influence of different heat transfer models on therapeutic temperature prediction and heat-induced damage during magnetic hyperthermia

Magnetic hyperthermia regulates the therapeutic temperature within a specific range to damage malignant cells after exposing the magnetic nanoparticles inside tumor tissue to an alternating magnetic field. The therapeutic temperature of living tissues can be generally predicted using Pennes' bio-heat equation after ignoring both the inhomogeneity of biological structure and the microstructural responses. Although various of the bio-heat transfer models proposed in literature fix these shortages, there is still a lack of a comprehensive report on investigating the discrepancy for different models when applied in the magnetic hyperthermia context. This study compares four different bio-heat equations in terms of the therapeutic temperature distribution and the heat-induced damage situation for a proposed geometric model, which is established based on computed tomography images of a tumor bearing mouse. The therapeutic temperature is also used as an index to evaluate the effect of two key relaxation times for the phase lag behavior on bio-heat transfer. Moreover, this work evaluates the effects of two blood perfusion rates on both the treatment temperature and the cumulative equivalent heating minutes at 43 °C. Numerical analysis results reveal that relaxation times for phase-lag behavior as well as the porosity for living tissues directly affect the therapeutic temperature variation and ultimately the thermal damage for the malignant tissue during magnetic hyperthermia. The dual-phase-lag equation can be converted into Pennes' equation and simple-phase-lag equation when relaxation times meet specific conditions during the process of heat transfer. In addition, different blood perfusion rates can result in an amplitude discrepancy for treatment temperature, but this parameter does not change the characteristics of thermal propagation during therapy.

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.

Refined Dual-Phase-Lag Theory for the 1D Behavior of Skin Tissue under Ramp-Type Heating

In this article, a mathematical analysis of thermoelastic skin tissue is presented based on a refined dual-phase-lag (DPL) thermal conduction theory that considers accounting for the effect of multiple time derivatives. The thin skin tissue is regarded as having mechanically clamped surfaces that are one-dimensional. Additionally, the skin tissue undergoes ramp-type heating on its outer surface, whereas its inner surface keeps the assessed temperature from vanishing. Some of the previous generalized thermoelasticity theories were obtained from the proposed model. The distributions of temperature, displacement, dilatation, and stress are attained by applying the Laplace transform and its numerical reversal approaches. The outcomes are explicitly illustrated to examine the significant influences on the distributions of the field variables. The refined DPL bioheat conduction model in this study predicts temperature, and the findings revealed that the model is located among the existing generalized thermoelastic theories. These findings offer a more thorough understanding of how skin tissue behaves when exposed to a particular boundary condition temperature distribution.

Analysis of thermal injuries using classical Fourier and DPL models for multi-layer of skin under different boundary conditions

In this paper, the temperature distribution in the multi-layer of the skin is studied when the skin surface is subjected to most generalized boundary condition. Our skin model consists of three layers known as the epidermis, dermis, and subcutaneous layers. All layers of skin are assumed to be connected with point of interface condition and taking the barrier in between each of the two layers by symmetric flux condition and analyzing each layer separately. The classical Fourier and non-Fourier (DPL) models are extended to analyze the behavior of heat transfer in the multi-layer of the skin. The Laplace transform technique is used to derive analytical solutions for the multi-layer of skin models. The effects of the variability of different parameters such as relaxation time, layer thickness, and different types of boundary conditions on the behavior of temperature distribution in the multi-layer of skin are analyzed and discussed in detail. All the effects are shown graphically. It has been observed that during temperature distribution in the multi-layer of skin, the measurement of skin damage is less on the DPL model ([Formula: see text]) in comparison to the classical Fourier model.

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 solution of generalized DPL model using wavelet method during thermal therapy applications

In this paper, generalized dual-phase-lag (DPL) model has been studied for the numerical analysis of spatial variation of temperature within living biological tissues during thermal therapy applications. A new hybrid numerical scheme based on finite difference scheme and Chebyshev wavelet Galerkin method are used to solve the generalized DPL model with constant heat flux boundary condition. Multi-resolution and multi-scale computational property of Chebyshev wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. Our study demonstrates that due to presence of coupling factor (convection–perfusion), generalized DPL model predicts lower temperature than classical DPL and Pennes model at the tumor position. Higher values of phase lag times results in lower temperature at the tumor position. But, in case of variation of phase lag time due to temperature gradient, the nature of temperature profile also depends on the spatial coordinate. The effect of the blood temperature, porosity and interfacial convective heat transfer on temperature distribution has been investigated. It is found that larger values of porosity and interfacial convective heat transfer results in lower temperature at the tumor position. Also, both porosity and interfacial convective heat transfer are pronounced more at higher values. The whole analysis is presented in dimensionless form.

Clinical validation of a novel thermophysical bladder model designed to improve the accuracy of hyperthermia treatment planning in the pelvic region

PURPOSE

Hyperthermia treatment planning for deep locoregional hyperthermia treatment may assist in phase and amplitude steering to optimize the temperature distribution. This study aims to incorporate a physically correct description of bladder properties in treatment planning, notably the presence of convection and absence of perfusion within the bladder lumen, and to assess accuracy and clinical implications for non muscle invasive bladder cancer patients treated with locoregional hyperthermia.

METHODS

We implemented a convective thermophysical fluid model based on the Boussinesq approximation to the Navier-Stokes equations using the (finite element) OpenFOAM toolkit. A clinician delineated the bladder on CT scans obtained from 14 bladder cancer patients. We performed (1) conventional treatment planning with a perfused muscle-like solid bladder, (2) with bladder content properties without and (3) with flow dynamics. Finally, we compared temperature distributions predicted by the three models with temperature measurements obtained during treatment.

RESULTS

Much higher and more uniform bladder temperatures are predicted with physically accurate fluid modeling compared to previously employed muscle-like models. The differences reflect the homogenizing effect of convection, and the absence of perfusion. Median steady state temperatures simulated with the novel convective model (3) deviated on average -0.6 °C (-12%) from values measured during treatment, compared to -3.7 °C (-71%) and +1.5 °C (+29%) deviation for the muscle-like (1) and static (2) models, respectively. The Grashof number was 3.2 ± 1.5 × 10⁵ (mean ± SD).

CONCLUSIONS

Incorporating fluid modeling in hyperthermia treatment planning yields significantly improved predictions of the temperature distribution in the bladder lumen during hyperthermia treatment.

FRACTIONAL MODELING OF HYPERBOLIC BIOHEAT TRANSFER EQUATION DURING THERMAL THERAPY

In this paper, we have developed a fractional hyperbolic bioheat transfer (FHBHT) model by applying fractional Taylor series formula to the single-phase-lag constitutive relation. A new hybrid numerical scheme that combines the multi-resolution and multi-scale computational property of Legendre wavelets based on fractional operational matrix has been used to find the numerical solution of the present problem. This study demonstrates that FHBHT model can provide a unified approach for analyzing heat transfer within living biological tissues, as standard hyperbolic bioheat transfer (SHBHT) and Pennes models are particular cases of FHBHT model. The effect of phase lag time and order of fractional derivative on temperature distribution within living biological tissues for both SHBHT and FHBHT models have been studied and shown graphically. It has been observed that thermal signal propagates more easily with larger values of order of fractional derivative within living biological tissues. The time interval for achieving temperature range of thermal treatment for different models have been studied and compared. It is least for Pennes model, highest for FHBHT model and in between them for SHBHT model. The whole analysis is presented in dimensionless form.