Temperature Distribution In Tissue Research Articles

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 200ms and fluences of 20, 40 and 60J/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.

Finite-element-based photoacoustic imaging of absolute temperature in tissue.

We describe a finite-element-based algorithm for the reconstruction of absolute temperature distribution in tissue using photoacoustic measurements. Assuming a linear temperature dependence of the Grueneisen parameter in tissue, the algorithm aims to recover the temperature-dependent acoustic speed while a heating mechanism is used. The absolute temperature over time is then calculated using the recovered temperature-dependent acoustic speed. To validate our method, photoacoustic measurements were conducted using a graphene nanosheet-containing target embedded in a 20-mm-diameter tissue-like phantom with varied heating power. The results obtained suggest that quantitatively accurate temperature images can be produced, suggesting that our method may serve as a tool to guide and monitor the temperature distribution in tissue in real time noninvasively and to improve the safety and efficacy of thermotherapy.

Thermal isotherms in PMMA and cell necrosis during total hip arthroplasty.

Polymethylmethacrylate (PMMA), also known as bone cement, is a commonly used adhesive material to fix implants in Total Hip Arthroplasty (THA). During implantation, bone cement undergoes a polymerization reaction which is an exothermic reaction and results in the release of heat to the surrounding bone tissue, which ultimately leads to thermal necrosis. Necrosis in the bony tissue results in early loosening of the implant, which causes pain and reduces the life of the implant. The main objective of the present study was to understand the thermal isotherms in PMMA and to determine the optimal cement mantle thickness to prevent cell necrosis during THA. In this study, the environment in the bony tissue during implantation was simulated by constructing 3D solid models to observe the temperature distribution in the bony tissue at different cement mantle thicknesses (1 mm, 3 mm and 5 mm), by applying the temperature conditions that exist during the surgery. Stems made with Co-Cr-Mo, 316L stainless steel and Ti6Al4V were used, which acted as heat sinks, and a thermal damage equation was used to measure the bone damage. FEA was conducted based on temperature conditions and thermal isotherms at different cement mantle thicknesses were obtained. Thermal isotherms derived with respect to distance in the bony tissue from the center of the cement mantle, and cell necrosis was determined at different mantle thicknesses. Based on the deduced results, cement mantle thickness of 1-5 mm does not cause thermal damage in the bony tissue. Considering the long term stability of the implant, cement mantle thickness range from 3 mm-5 mm was found to be optimal in THA to prevent cell necrosis.

Numerical thermal analysis of skin tissue using parabolic and hyperbolic approaches

The understanding of heat transfer in skin tissue is of utmost significance in various areas. Especially in medicine is required a precise determination of the temperature distribution for not thermally damaging healthy tissue when any region of the body is subjected to a heat treatment. The accuracy in predicting temperatures is linked to the use of adequate thermal and numerical methods. In this way, this study presents the results of a two-dimensional model to calculate transient temperature and burn injury distributions in skin tissue. Heat transfer was modeled using the Pennes' thermal model, and the mechanism of heat conduction assessed through two different approaches, classical Fourier law and non-Fourier law, characterized mathematically as parabolic and hyperbolic, respectively. The numerical solutions of the two approaches were compared to analytical solutions reported in the literature, as well as are shown various numerical results under various conditions to evaluate the differences between the two approaches to predict the temperature distribution and thermal damage.

Simultaneous estimation of controllable parameters in a living tissue during thermal therapy

During hyperthermia, controlling the temperature distribution along the tissue can cause remedial advantages. This can be obtained by proper manipulation of effective parameters in hyperthermia such as the external heat source and the heat transfer coefficient at the skin surface. In this study, these parameters are estimated simultaneously for an arbitrary temperature distribution in a skin tissue. The direct problem is solved by the fully implicit finite volume method to obtain the temperature data. This data is used as additional information to estimate the external heat source and the heat transfer coefficient at the skin surface simultaneously. Both of these parameters are considered as functions of time, and since no information exists about their functional form, the problem is classified as the function estimation approach. Conjugate gradient method is applied as an inverse method. Two test cases are considered and the effect of measurement errors is evaluated. The comparison of estimated results with measurements confirms the accuracy of this method.

Boundary prediction of bio-heat conduction in a two-dimensional multilayer tissue

The prediction and control of temperature distributions in tissue by the thermal conditions on the tissue surface is an issue that is novel to the multilayer bio-heat problem. Acceptable thermal conditions on the boundary can be obtained by using a known temperature field inside the tissue. The inverse solution to this problem was deduced from a numerical approach combined with the concept of future time. The problem with inverse bio-heat conduction is the slow heat-wave propagation speed, which makes the traversing temperature difficult to obtain. Three cases are presented in this paper to demonstrate the features and validity of the proposed method. The estimated result were compared to confirm the validity and accuracy of the proposed method.

METHOD OF FUNDAMENTAL SOLUTIONS FOR NONLINEAR SKIN BIOHEAT MODEL

In this paper, the method of fundamental solution (MFS) coupling with the dual reciprocity method (DRM) is developed to solve nonlinear steady state bioheat transfer problems. A two-dimensional nonlinear skin model with temperature-dependent blood perfusion rate is studied. Firstly, the original bioheat transfer governing equation with nonlinear term induced by temperature-dependent blood perfusion rate is linearized with the Taylor's expansion technique. Then, the linearized governing equation with specified boundary conditions is solved using a meshless approach, in which the DRM and the MFS are employed to obtain particular and homogeneous solutions, respectively. Several numerical examples involving linear, quadratic and exponential relations between temperature and blood perfusion rate are tested to verify the efficiency and accuracy of the proposed meshless model in solving nonlinear steady state bioheat transfer problems, and also the sensitivity of coefficients in the expression of temperature-dependent blood perfusion rate is analyzed for investigating the influence of blood perfusion rate to temperature distribution in skin tissues.

Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent surface heat flux in a skin tissue, which is stratified into epidermis, dermis, and subcutaneous layers, from the temperature measurements taken within the medium. Subsequently, the temperature distributions in the tissue can be calculated as well. The concept of finite heat propagation velocity is applied to the modeling of the bioheat transfer problem. The inverse solutions will be justified based on the numerical experiments in which two different heat flux distributions are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors on the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent surface heat flux can be obtained for the test cases considered in this study.

Influence of Heat Sources and Relaxation Time on Temperature Distribution in Tissues

In the present study, the temperature fluctuations in tissues based on Penne’s bio-heat transfer equation is investigated by applying the Laplace and Hankel transforms. To get the solution in a physical form, a numerical inversion technique has been applied. The temporal and spatial distribution of temperature is investigated with the effect of relaxation time and is presented graphically.

Fluid-Structure Interactions in a Tissue during Hyperthermia

A numerical investigation based on fluid-structure interaction analysis was conducted to determine the influence of pulsatile turbulent flow and heating protocol on temperature distribution and heat flux variation in blood vessel and tumor tissues receiving hyperthermia treatment. The arterial wall was modeled using the volume-averaged porous media equations. In addition, a physiological waveform was employed for the inlet velocity and exit pressure. Furthermore, the present numerical model was validated by comparing it with previously published results in the literature. Moreover, discretization of the transport equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. The results were presented for both flexible and rigid wall models and three different heating schemes were considered in this investigation; constant temperature, constant wall flux and a step-wise heat flux. The first two heating schemes were found to exhibit large temperature variation along the top and bottom surfaces of the tumor, which could influence the surrounding healthy tissues. The results of this investigation illustrate that the local heat flux variation along the bottom surface of the tumor is greater at the beginning of the cycle, where the velocity magnitude is low as compared to the peak flow condition for different heating schemes. The results of this work may enhance the current understanding of the factors that determine the effect of hyperthermia treatment on tumor tissues.

ICG-assisted blood vessel detection during stereotactic neurosurgery: Simulation study on excitation power limitations due to thermal effects in human brain tissue

Intraoperative blood vessel detection based on intraluminal indocyanin-green (ICG) would allow to minimize the risk of blood vessel perforation during stereotactic brain tumor biopsy. For a fiber-based approach compatible with clinical conditions, the maximum tolerable excitation light power was derived from simulations of the thermal heat load on the tissue. Using the simulation software LITCIT, the temperature distribution in human brain tissue was calculated as a function of time for realistic single-fiber probes (0.72mm active diameter, numerical aperture 0.35, optional focusing to 0.29mm diameter) and for the optimum ICG excitation wavelength of 785nm. The asymptotic maximum temperature in the simulated tissue region was derived for different radiant fluxes at the distal fiber end. Worst case values were assumed for all other parameters. In addition to homogeneous (normal and tumor) brain tissue with homogeneous blood perfusion, models with localized extra blood vessels incorporated ahead of the distal fiber end were investigated. If one demands that destruction of normal brain tissue must be excluded by limiting the tissue heating to 42°C, then the radiant flux at the distal fiber end must be limited to 33mW with and 43mW without focusing. When considering extra blood vessels of 0.1mm diameter incorporated into homogeneously perfused brain tissue, the tolerable radiant flux is reduced to 22mW with and 32mW without focusing. The threshold value according to legal laser safety regulations for human skin tissue is 28.5mW. For the envisaged modality of blood vessel detection, light power limits for an application-relevant fiber configuration were determined and found to be roughly consistent with present legal regulations for skin tissue.

Temperature evolution in tissues embedded with large blood vessels during photo-thermal heating

During laser-assisted photo-thermal therapy, the temperature of the heated tissue region must rise to the therapeutic value (e.g., 43°C) for complete ablation of the target cells. Large blood vessels (larger than 500 micron in diameter) at or near the irradiated tissues have a considerable impact on the transient temperature distribution in the tissue. In this study, the cooling effects of large blood vessels on temperature distribution in tissues during laser irradiation are predicted using finite element based simulation. A uniform flow is assumed at the entrance and three-dimensional conjugate heat transfer equations in the tissue region and the blood region are simultaneously solved for different vascular models. A volumetric heat source term based on Beer–Lambert law is introduced into the energy equation to account for laser heating. The heating pattern is taken to depend on the absorption and scattering coefficients of the tissue medium. Experiments are also conducted on tissue mimics in the presence and absence of simulated blood vessels to validate the numerical model. The coupled heat transfer between thermally significant blood vessels and their surrounding tissue for three different tissue-vascular networks are analyzed keeping the laser irradiation constant. A surface temperature map is obtained for different vascular models and for the bare tissue (without blood vessels). The transient temperature distribution is seen to differ according to the nature of the vascular network, blood vessel size, flow rate, laser spot size, laser power and tissue blood perfusion rate. The simulations suggest that the blood flow through large blood vessels in the vicinity of the photothermally heated tissue can lead to inefficient heating of the target.

Photoacoustic thermography of tissue

Photoacoustic (PA) techniques can measure temperature in biological tissues because PA signal amplitude is sensitive to tissue temperature. So far, temperature-measuring PA techniques have focused on sensing of temperature changes at a single position. In this work, we photoacoustically measured spatial distribution of temperature in deep tissue. By monitoring the temperature at a single position using a thermocouple, the relationship between the PA signal amplitude and the actual temperature was determined. The relationship was then used to translate a PA image into a temperature map. This study showed that it is possible to calibrate the system for the temperature range of hyperthermia using single-point measurements over a smaller temperature range. Our experimental results showed a precision of -0.8±0.4°C (mean±standard error) in temperature measurement, and a spatial resolution as fine as 1.0 mm. PA techniques can be potentially applied to monitor temperature distribution deep in tissue during hyperthermia treatment of cancer.

Transient State Finite Element Model to Analyse Thermal Variations in Peripheral Region of Human Limb undergoing Healing after Surgery

The temperature distribution in human tissues is significantly affected by the introduction of an abnormality. The study of temperature distribution in different layers of peripheral tissue is intended to contribute in the diagnosis of many disorders in various organs. In this paper, an axisymmetric one dimensional model has been developed to study transient state temperature distribution in different layers of normal and post surgery peripheral (abnormal) tissues of human limb. Taking into account the variable physiological parameters in dermal layer of peripheral region, the well known Pennes' bio heat equation is used to analyse and compare the time-dependent temperature distribution of normal and abnormal tissues using finite element technique. A computer program in MATLAB has been developed to simulate the results.

2P5-13 Ultrasonic measurement of temperature distribution of biological tissue by local heating(Poster Session)

2P5-13 Ultrasonic measurement of temperature distribution of biological tissue by local heating(Poster Session)

Influence of ambient temperature on heat transfer in the human eye during exposure to electromagnetic fields at 900 MHz

The topic of temperature increase in human tissue when exposed to EM fields, particularly those radiated to the eye, has been of interest for many years. This study presents a numerical analysis of the specific absorption rate (SAR) and the heat transfer in a heterogeneous two-dimensional human eye model exposed to TM-mode of electromagnetic (EM) fields of 900MHz at various power densities. In this study, the effects of ambient temperature and power density on the temperature distributions and fluid flow in the eye during exposure to electromagnetic fields were systematically investigated. The electric field, SAR, temperature distribution and fluid flow in various tissues in the eye during exposure to EM fields were obtained by numerical simulation of EM wave propagation and a heat transfer model. The heat transfer model was then developed based on the porous media theories. The study highlights heat transfer and fluid flow in the eye during exposure to EM fields at different ambient temperatures. This study indicated that when the eye exposed to EM fields at the frequency of 900MHz, the highest electric field intensity and SAR values at the chosen frequency was in the cornea. At the highest power density of 100mW/cm2, the absorbed EM energy is converted to heat causes a further increase of 3°C in corneal temperature in cases of hot, moderate and cold ambient temperatures. The result shows important information related to a complex interaction between ambient temperature, fluid flow and temperature distribution in the eye during exposure to electromagnetic fields. Moreover, this study also showed that the power density had a strong influence on the temperature increase and fluid flow in the eye.

Analysis of heat transport on local thermal non-equilibrium in porous liver during microwave ablation

Microwave ablation (MWA) is a process that uses the heat from microwave energy to kill cancer cells without damaging the surrounding tissue. The effectiveness of this technique is related to the temperature achieved during the process, as well as the input microwave power and heating time of treatment. The modeling of heat transport within biological tissues are key issues and have been used extensively in medical thermal therapeutic applications, for instance MWA treatment for predicting the temperature distribution during process. In this work, the interstitial MWA in porous liver by single slot microwave coaxial antenna (MCA) is carried out. A mathematical model of MWA of the porous media approach is proposed, which uses transient energy equation coupled with electromagnetic wave propagation equation to describe the temperature distribution within porous liver under local thermal non-equilibrium (LTNE) assumption. The LTNE assumption is taken into account by solving the two energy equations for tissue and blood phases. The thermal model considers the tissue with its blood vessel distribution as a porous medium and employs both the interfacial convective heat transfer and blood perfusion rate terms in the transient energy equations for both tissue and blood phases. The coupled nonlinear set of these equations is solved using the axisymmetric finite element method (FEM). The influences of blood velocities, porosities, input microwave powers and positions within the porous liver (distance from a MCA) on the tissue and blood temperature distributions have been investigated. Furthermore, the tissue and blood temperatures of LTNE model are compared with the tissue temperature of Pennes model and Klinger model. Through an accuracy comparison, the temperature results of the one-energy equation under local thermal equilibrium (LTE) model and Pennes model are compared with the experimental results from previous work in order to show the validity of the numerical results. The results show that the LTE assumption is found to be suitable for predicting the temperature distribution when the blood velocities to be 0.4cm/s and 2cm/s in all porosities, whilst, in case of blood velocities to be 3cm/s and 3.4cm/s the LTNE assumption for heat transfer analysis needs to be utilized. In addition, the LTE model is suitable for predicting a distribution of temperature when the high porosity for this model. This investigation provides the essential aspects for a fundamental understanding of heat transport within biological tissues while experiencing an applied electromagnetic field such as applications in the thermal ablation.

Temperature-Dependent Thermal Properties of ex Vivo Liver Undergoing Thermal Ablation

Thermotherapy uses a heat source that raises temperatures in the target tissue, and the temperature rise depends on the thermal properties of the tissue. Little is known about the temperature-dependent thermal properties of tissue, which prevents us from accurately predicting the temperature distribution of the target tissue undergoing thermotherapy. The present study reports the key thermal parameters (specific heat capacity, thermal conductivity and heat diffusivity) measured in ex vivo porcine liver while being heated from 20°C to 90°C and then naturally cooled down to 20°C. The study indicates that as the tissue was heated, all the thermal parameters resulted in plots with asymmetric quasi-parabolic curves with temperature, being convex downward with their minima at the turning temperature of 35–40°C. The largest change was observed for thermal conductivity, which decreased by 9.6% from its initial value (at 20°C) at the turning temperature (35°C) and rose by 45% at 90°C from its minimum (at 35°C). The minima were 3.567 mJ/(m3∙K) for specific heat capacity, 0.520 W/(m.K) for thermal conductivity and 0.141 mm2/s for thermal diffusivity. The minimum at the turning temperature was unique, and it is suggested that it be taken as a characteristic value of the thermal parameter of the tissue. On the other hand, the thermal parameters were insensitive to temperature and remained almost unchanged when the tissue cooled down, indicating that their variations with temperature were irreversible. The rate of the irreversible rise at 35°C was 18% in specific heat capacity, 40% in thermal conductivity and 38.3% in thermal diffusivity. The study indicates that the key thermal parameters of ex vivo porcine liver vary largely with temperature when heated, as described by asymmetric quasi-parabolic curves of the thermal parameters with temperature, and therefore, substantial influence on the temperature distribution of the tissue undergoing thermotherapy is expected.

Effect of convective term on temperature distribution in biological tissue

We introduce a phase imprint into the order parameter describing the influence of blood flow on the temperature distribution in the tissue described by the one-dimensional Pennes equation and then engineer the imprinted phase suitably to generate a modified Pennes equation with a gradient term (known in the theory of biological systems as convective term) which is associated with the heat convected by the flowing blood. Using the derived model, we analytically investigate temperature distribution in biological tissues subject to two different spatial heating methods. The applicability of our results is illustrated by one of typical bio-heat transfer problems which is often encountered in therapeutic treatment, cancer hyperthermia, laser surgery, thermal injury evaluation, etc. Analyzing the effect of the convective term on temperature distribution, we found that an optimum heating of a biological system can be obtained through regulating the convective term.

Numerical study of partial differential equations to estimate thermoregulation in human dermal regions for temperature dependent thermal conductivity

The paper deals with the temperature distribution in multi-layered human skin and subcutaneous tissues (SST). The model suggests the solution of parabolic heat equation together with the boundary conditions for the temperature distribution in SST by assuming the thermal conductivity as a function of temperature. The model formulation is based on singular non-linear boundary value problem and has been solved using finite difference method. The numerical results were found similar to clinical and computational results.