Thermal effects of a short light pulse on biological tissues. II. Light and heat fields

A set of heat conduction equations for a two-component medium simulating biological tissues were formulated. Their solutions were obtained, and the spatial distribution of light and temperature over tissue depth at different times after irradiation by a short light pulse was studied. The local absorption of light by blood vessels and the influence of this effect on the optical parameters of the medium, a more intense heating of blood as compared with its surrounding tissue, heat exchange between them, and heat transfer at the interface with different environments were accounted for. The solutions are expressed via characteristic times of the respective thermal processes to enable one to easily and vividly analyze the features of tissue heating and the influence of optical and thermal parameters on the temperature distributions of the components. The calculations are illustrated by examples.     

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.     

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.     

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.     

Fast inverse prediction of the freezing front in cryosurgery

Cryosurgery has become a well-established technique for the ablation of undesirable tissues such as tumors and cancers. The motivation for this study is to improve the efficacy and safety of this technique. This study presents an inverse heat transfer method for monitoring the motion of the freezing front from a cryoprobe. With the help of a thermocouple inserted into the layer of diseased tissue, the inverse heat transfer method estimates simultaneously the blood perfusion rate and the thermal conductivities of both frozen and unfrozen tissues. This information is then fed to the Pennes bioheat equation that: (1) calculates the time-varying temperature distribution inside the layer of tissue and (2) predicts the motion of the freezing front. The effect of the most influential parameters on the inverse predictions is investigated. These parameters are (1) the initial guesses for the unknown Levenberg-Marquardt polynomial parameters of the thermo-physical properties; (2) the temperature of the cryoprobe; (3) the heat transfer coefficient of the impinging jet of liquid nitrogen; and (4) the noise on the temperature data recorded by the thermocouple probe. Results show that the proposed inverse method is a promising alternative to ultrasound and Magnetic Resonance Imaging (MRI) for monitoring the motion of the freezing front during cryosurgery. For all the cryogenic scenarios simulated, the predictions of the inverse model remain accurate and stable.     

Theory on thermal probe arrays for the distinction between the convective and the perfusive modalities of heat transfer in living tissues

Recent suggestions for an improved model of heat transfer in living tissues emphasize the existence of a convective mode due to flowing blood in addition to, or even instead of, the perfusive mode, as proposed in Pennes' "classic" bioheat equation. In view of these suggestions, it might be beneficial to develop a technique that will enable one to distinguish between these two modes of bioheat transfer. To this end, a concept that utilizes a multiprobe array of thermistors in conjunction with a revised bioheat transfer equation has been derived to distinguish between, and to quantify the perfusive and convective contribution of blood to heat transfer in living tissues. The array consists of two or more temperature sensors one of which also serves to locally insert a short pulse of heat into the tissue prior to the temperature measurements. A theoretical analysis shows that such a concept is feasible. The construction of the system involves the selection of several important design parameters, i.e., the distance between the probes, the heating power, and the pulse duration. The choice of these parameters is based on computer simulations of the actual experiment.     

Mechanism of heat transfer in different regions of human body

The processes of heat transfer in a human body were studied with the use of a mathematical model. It has been shown that only conductive or only convective heat transfer may occur in different body areas. The rate of blood-mediated heat transfer in the presence of blood circulation is many times higher than heat transfer due to temperature gradient; therefore, the convective process prevails over the conductive process. The body core contains a variety of blood vessels, and the bulk of blood concentrates there in the norm. Hence, heat transfer in it is mainly convective. In surface tissues, where the rate of blood circulation is lower and the vasculature has certain specific features, heat transfer is mainly conductive. Hence, the core and surface tissues are absolutely different body zones in terms of heat transfer.     

Conventional and newly developed bioheat transport models in vascularized tissues: A review

Heat transfer in a biological system is a complex process and its analysis is difficult. Heterogeneous vascular architecture, blood flow in the complex network of arteries and veins, varying metabolic heat generation rates and dependence of tissue properties on its physiological condition contribute to this complexity. The understanding of heat transfer in human body is important for better insight of thermoregulatory mechanism and physiological conditions. Its understanding is also important for accurate prediction of thermal transport and temperature distribution during biomedical applications. During the last three decades, many attempts have been made by researchers to model the complex thermal behavior of the human body. These models, viz., blood perfusion, countercurrent, thermal phase-lag, porous-media, perturbation, radiation, etc. have their corresponding strengths and limitations. Along with their biomedical applications, this article reviews various contextual issues associated with these models. After brief discussion of early bioheat models, the newly developed bioheat models are discussed in detail. Dependence of these models on biological properties, viz., thermophysical and optical properties are also discussed.     

New mathematical model to estimate tissue blood perfusion, thermal contact resistance and core temperature

Analytical solutions were developed based on the Green's function method to describe heat transfer in tissue including the effects of blood perfusion. These one-dimensional transient solutions were used with a simple parameter estimation technique and experimental measurements of temperature and heat flux at the surface of simulated tissue. It was demonstrated how such surface measurements can be used during step changes in the surface thermal conditions to estimate the value of three important parameters: blood perfusion (w(b)), thermal contact resistance (R"), and core temperature of the tissue (T(core)). The new models were tested against finite-difference solutions of thermal events on the surface to show the validity of the analytical solution. Simulated data was used to demonstrate the response of the model in predicting optimal parameters from noisy temperature and heat flux measurements. Finally, the analytical model and simple parameter estimation routine were used with actual experimental data from perfusion in phantom tissue. The model was shown to provide a very good match with the data curves. This demonstrated the first time that all three of these important parameters (w(b), R", and T(core)) have simultaneously been estimated from a single set of thermal measurements at the surface of tissue.     

Prediction of temperature profiles in the human skin and subcutaneous tissues

Exact mathematical solutions in terms of confluent hypergeometric and Airy's functions are obtained to study the steady state temperature distributions in human skin and subcutaneous tissues (SST). It is assumed that the skin is exposed to an air environment and heat transfer from the skin occurs by convection, radiation and evaporation. A mathematical model of the SST, accounting for heat conduction, perfusion of the capillary beds and metabolic heat productions of the dermis and subcutaneous tissues, has been solved to obtain interface temperatures for a wide range of environmental temperatures, rates of evaporation of sweat, wind speeds and relative humidities. The solutions provide inter-relationships between interface temperatures, thermal conductivities, metabolic heat production, blood perfusion, thicknesses of various layers of SST and ambient temperature.     

Melanin Granule Models for the Processes of Laser-Induced Thermal Damage in Pigmented Retinal Tissues. I. Modeling of Laser-Induced Heating of Melanosomes and Selective Thermal Processes in Retinal Tissues

The computer modeling was applied for investigation of the processes of laser-induced tissue damage. The melanin granule models for the processes of laser-induced thermal damage and the results of computer modeling of the optical, thermophysical, and thermochemical processes during selective laser interaction with melanoprotein granules (melanosomes) in retinal pigment epithelium are presented in this paper. Physical-mathematical model and system of equations are formulated which describe thermal interaction processes for “short” laser pulses of duration t _p<10⁻⁶ s and for “ long’ pulses of duration t _p10⁻⁶ s. Results of numerical simulation of the processes give the space–time distributions of temperature and degrees of thermodenaturation of the protein molecules inside and around melanosomes and in the volume of irradiated tissues. Energy absorption, heat transfer and thermochemical (thermodenaturation, coagulation) processes occurring during the interaction of laser pulses with pigmented spherical and spheroidal granules in heterogeneous tissues are theoretically investigated. The possibility for selective interaction of short laser pulses with pigmented granules is discussed which results in the formation of denaturation microregions inside and near the pigmented granules (granular thermodenaturation) without origination of a continuous macroscopic thermodenaturation lesion in tissue. Analytical model of heating of single spherical and spheroidal granule under laser pulse is presented. Simple equations for time dependencies of particle temperature are obtained. The presented results are of essential interest for laser applications in and can be used for investigation of laser interaction with pigmented tissues in different fields of laser medicine.     

Numerical analysis of dynamic temperature in response to different levels of reactive hyperaemia in a three-dimensional image-based hand model

Vascular reactivity (VR) is considered as an effective index to predict the risk of cardiovascular events. A cost-effective alternative technique used to evaluate VR called digital thermal monitoring (DTM) is based on the response of finger temperature to vessel occlusion and reperfusion. In this work, a simulation has been developed to investigate hand temperature in response to vessel occlusion and perfusion. The simulation consists of image-based mesh generation and finite element analysis of blood flow and heat transfer in tissues. In order to reconstruct a real geometric model of human hand, a computer programme including automatic image processing for sequential MR data and mesh generation based on the transfinite interpolation method is developed. In the finite element analysis part, blood flow perfused in solid tissues is considered as fluid phase through porous media. Heat transfer in tissues is described by Pennes bioheat equation and blood perfusion rate is obtained from Darcy velocities. Capillary pressure, blood perfusion and temperature distribution of hand are obtained. The results reveal that fingertip temperature is strongly dependent on larger arterial pressure. This simulation is of potential to quantify the indices used for evaluating the VR in DTM test if it is integrated with the haemodynamic model of blood circulation in upper limb.     

Noninvasive Method for Simultaneously Measuring the Thermophysical Properties and Blood Perfusion in Cylindrically Shaped Living Tissues

An easy-to-use noninvasive method was developed to simultaneously measure the thermophysical parameters and blood perfusion in cylindrically shaped living tissues. This method is based on a two-dimensional mathematical model which requires temperature measurements at only three separate points along the axial direction on the cylinder surface. A sensitivity analysis has shown that the key thermophysical parameters, such as the thermal conductivity, volumetric heat capacity, and blood perfusion can be estimated simultaneously with high accuracy. Genetic algorithm (GA) selection, crossover, and mutation operators were developed to solve this multi-parameter optimization problem. This three-point method was validated by measuring the properties of a dynamic tissue-equivalent phantom with known thermal parameters. The method has also been applied to measure the thermophysical parameters and blood perfusion in human forearms with measured results agreeing well with the literature values.     

An Algorithm of Mathematical Modeling of Laser-Induced Indirect Thermotherapy of a Baker’s Cyst

Biophysics - Abstract—A thermophysical model of heat transfer from a liquid heated by radiation into biological tissues with a cyst of an individual picture of temperature fields, which takes...     

Numerical simulation for heat transfer in tissues during thermal therapy

In this paper, a mathematical model describing the process of heat transfer in biological tissues for different coordinate system during thermal therapy by electromagnetic radiation is studied. The boundary value problem governing this process has been solved using Galerkin’s method taking B-polynomial as basis function. The system of ordinary differential equation in unknown time variable, thus obtained, is solved by homotopy perturbation method. The effect of thermal conductivity, antenna power constant, surface temperature, and blood perfusion rate on temperature for different coordinates are discussed. It has been observed that the process is faster in spherical symmetric coordinates in comparison to axisymmetric coordinate and faster in axisymmetric in comparison to Cartesian coordinate.     

A 3D thermal model to analyze the temperature changes of digits during cold stress and predict the danger of frostbite in human fingers

The existing computational models of frostbite injury are limited to one and two dimensional schemes. In this study, a coupled thermo-fluid model is applied to simulate a finger exposed to cold weather. The spatial variability of finger-tip temperature is compared to experimental ones to validate the model. A semi-realistic 3D model for tissue and blood vessels is used to analyze the transient heat transfer through the finger. The effect of heat conduction, metabolic heat generation, heat transport by blood perfusion, heat exchange between tissues and large vessels are considered in energy balance equations. The current model was then tested in different temperatures and air speeds to predict the danger of frostbite in humans for different gloves. Two prevalent gloves which are commonly used in cold climate are considered for investigation. The endurance time and the fraction of necrotic tissues are two main factors suggested for obtaining the response of digit tissues to different environmental conditions.     

A thermal model of the human body exposed to an electromagnetic field

The human body was modeled by numerical procedures to determine the thermal response under varied electromagnetic (EM) exposures. The basic approach taken was to modify the heat transfer equations for man in air to account for thermal loading due to the energy absorbed from the EM field. The human body was represented in an EM model by a large number of small cubical cells of tissue, and the energy density was determined for each cell. This information was then analyzed by a thermal response model consisting of a series of two-dimensional transient conduction equations with internal heat generation due to metabolism, internal convective heat transfer due to blood flow, external interaction by convection and radiation, and cooling of the skin by sweating and evaporation. This model simulated the human body by a series of cylindrical segments. The local temperature at 61 discrete locations as well as the thermoregulatory responses of vasodilatation and sweating were computed for a number of EM field intensities and two frequencies, one near whole-body resonance.     

Numerical study on the thawing process of biological tissue induced by laser irradiation

Most of the laser applications in medicine and biology involve thermal effects. The laser-tissue thermal interaction has therefore received more and more attentions in recent years. However, previous works were mainly focused on the case of laser heating on normal tissues (37 degrees C or above). To date, little is known on the mechanisms of laser heating on the frozen biological tissues. Several latest experimental investigations have demonstrated that lasers have great potentials in tissue cryopreservation. But the lack of theoretical interpretation limits its further application in this area. The present paper proposes a numerical model for the thawing of biological tissues caused by laser irradiation. The Monte Carlo approach and the effective heat capacity method are, respectively, employed to simulate the light propagation and solid-liquid phase change heat transfer. The proposed model has four important features: (1) the tissue is considered as a nonideal material, in which phase transition occurs over a wide temperature range; (2) the solid phase, transition phase, and the liquid phase have different thermophysical properties; (3) the variations in optical properties due to phase-change are also taken into consideration; and (4) the light distribution is changing continually with the advancement of the thawing fronts. To this end, 15 thawing-front geometric configurations are presented for the Monte Carlo simulation. The least-squares parabola fitting technique is applied to approximate the shape of the thawing front. And then, a detailed algorithm of calculating the photon reflection/refraction behaviors at the thawing front is described. Finally, we develop a coupled light/heat transport solution procedure for the laser-induced thawing of frozen tissues. The proposed model is compared with three test problems and good agreement is obtained. The calculated results show that the light reflectance/transmittance at the tissue surface are continually changing with the progression of the thawing fronts and that lasers provide a new heating method superior to conventional heating through surface conduction because it can achieve a uniform volumetric heating. Parametric studies are performed to test the influences of the optical properties of tissue on the thawing process. The proposed model is rather general in nature and therefore can be applied to other nonbiological problems as long as the materials are absorbing and scattering media.     

中医隔物灸的传热学研究

运用有限元软件ANSYS进行数值建模模拟中医隔物灸产生的热在人体组织中的传导过程,并给出定性和定量分析。同时运用高灵敏度红外热像仪记录艾炷隔附子饼灸对生物组织热作用的过程,对比实验和计算结果验证了实验和数值模拟方法的合理性。然后建立简化的人体两维模型,得到穴位点横截面上热传导过程的两维温度分布图和热在生物组织中传播的整个过程。红外热像技术和数值建模方法为临床各种灸法的运用提供了理论和实验基础支持。