Study of the one dimensional and transient bioheat transfer equation: multi-layer solution development and applications

Theoretical estimation of the thermal damages of living tissues caused by laser irradiation in tumor thermal therapy

This article aims to provide theoretical predictions for the thermal reactions of human tissues during tumor thermotherapy when exposed to laser irradiation and an external heat source. For the construction of a theoretical study of bioheat transfer, the selection of a suitable thermal model capable of accurately predicting the required thermal responses is essential. The effect of heat production by heat treatment on a spherical multilayer tumor tissue is evaluated using this approach. Analytical solution for the non-homogenous differential equations is derived in the Laplace domain. The study examines the impact of thermal relaxation time on tissue temperature and the subsequent thermal damage. The numerical findings of thermal damage and temperatures are depicted in a graphical representation. This model explains laser treatment, physical events, metabolic support, and blood perfusion. The numerical outcomes of the recommended model are validated by comparing them to the literatures.

Development of a Coherent Model for Radiometric Core Body Temperature Sensing

This paper examines the utility of a wideband, physics-based model to determine human core body or brain temperature via microwave radiometry. Pennes's bioheat equation is applied to a six-layer human head model to generate the expected layered temperature profile during the development of a fever. The resulting temperature profile is fed into the forward electromagnetic (EM) model to determine the emitted brightness temperature at various points in time. To accurately retrieve physical temperature via radiometry, the utilized model must incorporate population variation statistics and cover a wide frequency band. The effect of human population variation on emitted brightness temperature is studied by varying the relevant thermal and EM parameters, and brightness temperature emissions are simulated from 0.1 MHz to 10 GHz. A Monte Carlo simulation combined with literature-derived statistical distributions for the thermal and EM parameters is performed to analyze population-level variation in resulting brightness temperature. Variation in thermal parameters affects the offset of the resulting brightness temperature signature, while EM parameter variation shifts the key maxima and minima of the signature. The layering of high and low permittivity layers creates these key maxima and minima via wave interference. This study is one of the first to apply a coherent model to and the first to examine the effect of population-representative variable distributions on radiometry for core temperature measurement. These results better inform the development of an on-body radiometer useful for core body temperature measurement across the human population.

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.

Multifocus Thermal Strain Imaging Using a Curved Linear Array Transducer for Identification of Lipids in Deep Tissue

Thermal strain imaging (TSI) is an ultrasound-based imaging technique intended primarily for diseases in which lipid accumulation is the main biomarker. The goal of the research described here was to successfully implement TSI on a single, commercially available curved linear array transducer for heating and imaging of organs at a deeper depth. For an effective temperature rise of the tissue over a large area, which is key to TSI performance, an innovative multifocus beamforming approach was applied. This yielded a heating area from 32 to 96 mm in the axial direction and -7 to +7 mm in the lateral direction. The pressure fields generated from simulation were in agreement with pressure fields measured with the hydrophone. TSI with safe acoustic power identified with high contrast a rubber inclusion and liposuction fat tissue embedded in a gelatin block.

In silico study of enhanced permeation and retention effect and hyperthermia of porous tumor

Nanotechnology has recently gained fame for its extensive use in biomedical applications particularly in magnetic fluid hyperthermia (MFH) of tumors. The magnetic nanoparticles (MNPs) are usually injected into the tumor either intravenously or through direct needle injection. Depending on the location of the tumor, the needle approach may not be appropriate and in the case, when the nanoflow rate is higher, it may produce cracks in the tumor. In this scenario, the intravenous approach following the enhanced permeation and retention effect (EPR) effect proves advantageous. In this paper, we have simulated the EPR effect of nanofluid flowing from blood vessels to the tumor through epithelial cells spacing and then its diffusion in the tumor interstitium using COMSOL Multiphysics. The velocity in the blood vessel and diffusion in the tumor have been simulated and analyzed using Finite Element Method (FEM) based models of Navier-Stokes equations and convection-diffusion equation. The simulation results show that the velocity and concentration are higher in the blood vessel and it decreases slowly while moving through epithelial spacing to the tumor interstitium. The heat transfer in the tumor interstitium is simulated and analyzed for temperature distribution quantitatively.

Variational finite element approach to study heat transfer in the biological tissues of premature infants

The body temperature of newborn preterm infants depends on the heat transfer between the infant and the external environment. Factors that influence the heat exchange include the temperature and humidity of the air and the temperature of surfaces in contact with and around the infant. Neonatal thermoregulation has a different pattern as they have an immature thermoregulatory system. For this purpose, mathematical models can provide detailed insights for the heat transfer processes and its applications for clinical purposes. A new multi-compartment mathematical model of the neonatal thermoregulatory system is presented. The formulation of the model is based on the Pennes' bio-heat equation with suitable boundary and initial conditions. The variational finite element method has been employed to determine heat transfer and exchange in the biological tissues of premature infants. The results obtained in this paper have shown that premature infants are unable to maintain a constant core temperature and resemble the empirically obtained results, proving the validity and feasibility of our model. AMS (2010): SUBJECT CLASSIFICATION: 92BXX, 92CXX, 92C35, 92C50, 46N60.

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.

Computational Modelling of the Bioheat Transfer Process in Human Skin Subjected to Direct Heating and/or Cooling Sources: A Systematic Review

The purpose of this systematic review is to analyze characteristics and methodologies utilized in bioheat transfer models of human skin to provide state-of-the-art knowledge on the topic. This review was conducted according to the Preferred Reporting Items for Systematic Reviews and Meta-analyses guidelines. PubMed, EMBASE and Web of Science databases were searched up to May 30th, 2019 for bioheat transfer models focusing on direct contact between skin and temperature (heat and/or cold) source. Ten studies were included. A 16-item checklist was used to assess their methodological quality. Four studies analyzed healthy skin and six included pathological conditions. All determined skin's thermal behavior, and studies including pathological conditions also analyzed burn damage. Studies did not present a wide variety of mathematical formulation, emphasizing on modelling equations of well-established models from the literature, such as the Pennes' bioheat transfer equation, and the Henriques and Moritz model to quantify skin damage. Reporting of modelling characteristics and formulation of the computational models is not standardized and there is shortage of implementation of validation procedures, hindering representative conclusions. The lack of validation procedures led to low methodological quality. However, all studies provided strategies and parameters as starting points for future developments in this research area.

Feasibility of removable balloon implant for simultaneous magnetic nanoparticle heating and HDR brachytherapy of brain tumor resection cavities

AIM

Hyperthermia (HT) has been shown to improve clinical response to radiation therapy (RT) for cancer. Synergism is dramatically enhanced if HT and RT are combined simultaneously, but appropriate technology to apply treatments together does not exist. This study investigates the feasibility of delivering HT with RT to a 5-10mm annular rim of at-risk tissue around a tumor resection cavity using a temporary thermobrachytherapy (TBT) balloon implant.

METHODS

A balloon catheter was designed to deliver radiation from High Dose Rate (HDR) brachytherapy concurrent with HT delivered by filling the balloon with magnetic nanoparticles (MNP) and immersing it in a radiofrequency magnetic field. Temperature distributions in brain around the TBT balloon were simulated with temperature dependent brain blood perfusion using numerical modeling. A magnetic induction system was constructed and used to produce rapid heating (>0.2°C/s) of MNP-filled balloons in brain tissue-equivalent phantoms by absorbing 0.5 W/ml from a 5.7 kA/m field at 133 kHz.

RESULTS

Simulated treatment plans demonstrate the ability to heat at-risk tissue around a brain tumor resection cavity between 40-48°C for 2-5cm diameter balloons. Experimental thermal dosimetry verifies the expected rapid and spherically symmetric heating of brain phantom around the MNP-filled balloon at a magnetic field strength that has proven safe in previous clinical studies.

CONCLUSIONS

These preclinical results demonstrate the feasibility of using a TBT balloon to deliver heat simultaneously with HDR brachytherapy to tumor bed around a brain tumor resection cavity, with significantly improved uniformity of heating over previous multi-catheter interstitial approaches. Considered along with results of previous clinical thermobrachytherapy trials, this new capability is expected to improve both survival and quality of life in patients with glioblastoma multiforme.

EXACT ANALYTICAL SOLUTION OF BIOHEAT EQUATION SUBJECTED TO INTENSIVE MOVING HEAT SOURCE

Presented is the analytical solution of Pennes bio-heat equation, under localized moving heat source. The thermal behavior of one-dimensional (1D) nonhomogeneous layer of biological tissue is considered with blood perfusion term and modeled under the effect of concentric moving line heat source. The procedure of the solution is Eigen function expansion. The temperature profiles are calculated for three tissues of liver, kidney, and skin. Behavior of temperature profiles are studied parametrically due to the different moving speeds. The analytical solution can be used as a verification branch for studying the practical operations such as scanning laser treatment and other numerical solutions.

Diagnosis of breast tumor using thermal tomography q-r curve

Metabolic heat, the product following the metabolism of cells, is closely related to the pathological information of living organisms, which means there are strong connections between the heat distribution and the pathological state of the living organism. The mathematical function δ is introduced in the classical Pennes bioheat transfer equation as a point heat source, and by simplifying the boundary condition, a bioheat transfer model is established. Based on the temperature distribution of the human body surface, the q−r curve of heat intensity q varying with depth r is acquired while combining the fitting method of the Lorentz curve. According to 34,977 clinical confirmed cases and the corresponding classified statistics, diagnostic criteria (for breast diseases) for judging diseases by the q−r curve are proposed. The P -value of our statistics is <0.05 , which means our classified statistics are reliable. Six typical clinical examinations are performed, and the diagnosis results are very consistent with those of B-ultrasonic images, molybdenum target x-ray, and pathological examination, which suggests that the method of diagnosing diseases with a q−r curve has very good prospects for application. It is radiation free and noninvasive to the human body.

Q-r curve of thermal tomography and its clinical application on breast tumor diagnosis

Heat is the product following the metabolism of cells, and the metabolism is closely related with the pathological information of living organism. So, there are strong ties between the heat distribution and the pathological state in living organism. In this paper, the mathematical function δ is introduced in the classical Pennes bio-heat transfer equation as the point heat source. By simplifying the boundary conditions, a novel bio-heat transfer model is established and solved in a spherical coordinate system. Based on the temperature distribution of human body surface, the information of heat source is mined layer by layer, and the corresponding q-r curve of heat intensity varying with depth is acquired combining the fitting method of Lorentz curve. According to a large number of clinical confirmed cases and statistics, the diagnostic criteria judging diseases by q-r curve are proposed. Five typical clinical practices are performed and four of the diagnosis results are very consistent with those of molybdenum target (MT) X-ray, B-ultrasonic images and pathological examination, one gives the result of early stage malignant tumor that MT X-ray and B-ultrasonic can't check out. It is a radiation-free green method with noninvasive diagnostic procedure and accurate diagnosis result.