Thermogram-based estimation of foot arterial blood flow using neural networks

The altered blood flow in the foot is an important indicator of early diabetic foot complications. However, it is challenging to measure the blood flow at the whole foot scale. This study presents an approach for estimating the foot arterial blood flow using the temperature distribution and an artificial neural network. To quantify the relationship between the blood flow and the temperature distribution, a bioheat transfer model of a voxel-meshed foot tissue with discrete blood vessels is established based on the computed tomography (CT) sequential images and the anatomical information of the vascular structure. In our model, the heat transfer from blood vessels and tissue and the inter-domain heat exchange between them are considered thoroughly, and the computed temperatures are consistent with the experimental results. Analytical data are then used to train a neural network to determine the foot arterial blood flow. The trained network is able to estimate the objective blood flow for various degrees of stenosis in multiple blood vessels with an accuracy rate of more than 90%. Compared with the Pennes bioheat transfer equation, this model fully describes intra- and inter-domain heat transfer in blood vessels and tissue, closely approximating physiological conditions. By introducing a vascular component to an inverse model, the blood flow itself, rather than blood perfusion, can be estimated, directly informing vascular health.     

Analytical analysis of the dual-phase-lag model of bioheat transfer equation during transient heating of skin tissue

Dual-phase-lag model of bioheat transfer equation is utilized in treating the transient heat transfer problems in skin tissue considering prevalent heating conditions in thermal therapy applications, namely, pulse train and periodic heat flux. Comparisons between the presented analytical results for limiting cases and previous studies display an excellent agreement. The effects of temperature gradient relaxation time on the tissue temperature, damage, and also on the blood perfusion in skin tissue are studied.     

Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing

Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.     

电磁加热条件下皮肤组织的生物热力学行为

研究目的是开发一种数学方法来计算传热过程、热引起的力学响应以及相应的疼痛等级, 从而对临床上应用的各种加热疗法之间的差别进行定量评估. 采用基于有限差分法的数值模拟方法, 基于无限大和均匀化假设, 分析了各种热疗法中皮肤组织的温度、烧伤和热应力分布. 研究发现: 充血对热损伤的影响很小, 但对皮肤的温度分布影响很大, 而这又反过来显著影响由此产生的热应力场; 对于激光加热, 光波越短则峰值温度越高, 但峰值更接近皮肤表面温度; 激光和微波加热所产生的热应力集中于表皮顶层, 因为发热量沿皮肤深度方向呈指数衰减; 薄角质层(常常被忽略)对皮肤组织的热力学响应起主导作用.      

Rewetting analysis of hot surfaces with internal heat source by the heat balance integral method

A two region conduction-controlled rewetting model of hot vertical surfaces with internal heat generation and boundary heat flux subjected to constant but different heat transfer coefficient in both wet and dry region is solved by the Heat Balance Integral Method (HBIM). The HBIM yields the temperature field and quench front temperature as a function of various model parameters such as Peclet number, Biot number and internal heat source parameter of the hot surface. Further, the critical (dry out) internal heat source parameter is obtained by setting Peclet number equal to zero, which yields the minimum internal heat source parameter to prevent the hot surface from being rewetted. Using this method, it has been possible to derive a unified relationship for a two-dimensional slab and tube with both internal heat generation and boundary heat flux. The solutions are found to be in good agreement with other analytical results reported in literature.     

Local nonsimilarity solution for the impact of the buoyancy force on heat and mass transfer in a flow over a porous wedge with a heat source in the presence of suction/injection

Combined heat and mass transfer in free, forced and mixed convection flows along a porous wedge with internal heat generation in the presence of uniform suction or injection is investigated. The boundary-layer analysis is formulated in terms of the combined thermal and solute buoyancy effect. The flow field characteristics are analyzed using the Runge-Kutta-Gill method, the shooting method, and the local nonsimilarity method. Due to the effect of the buoyancy force, power law of temperature and concentration, and suction/injection on the wall of the wedge, the flow field is locally nonsimilar. Numerical calculations up to third-order level of truncation are carried out for different values of dimensionless parameters as a special case. The effects of the buoyancy force, suction, heat generation, and variable wall temperature and concentration on the dimensionless velocity, temperature, and concentration profiles are studied. The results obtained are found to be in good agreement with previously published works.     

A rigorous derivation of the bioheat equation for local tissue heat transfer based on a volume averaging theory

A general three-dimensional bioheat equation for local tissue heat transfer has been derived with less assumptions, exploiting a volume averaging theory commonly used in fluid-saturated porous media. The volume averaged energy equations obtained for the arterial blood, venous blood and tissue were combined together to form a single energy equation in terms of the tissue temperature alone. The resulting energy equation turns out to be remarkably simple as we define the effective thermal conductivity tensor, which accounts not only for the countercurrent heat exchange mechanism but also for the thermal dispersion mechanism. The present equation for local tissue heat transfer naturally reduces to the Weinbaum-Jiji equation for the unidirectional case.     

Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet

We study the MHD flow and also heat transfer in a viscoelastic liquid over a stretching sheet in the presence of radiation. The stretching of the sheet is assumed to be proportional to the distance from the slit. Two different temperature conditions are studied, namely (i) the sheet with prescribed surface temperature (PST) and (ii) the sheet with prescribed wall heat flux (PHF). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The resulting non-linear momentum differential equation is solved exactly. The energy equation in the presence of viscous dissipation (or frictional heating), internal heat generation or absorption, and radiation is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation using a new variable and using the Rosseland approximation for the radiation. The governing differential equations are solved analytically and the effects of various parameters on velocity profiles, skin friction coefficient, temperature profile and wall heat transfer are presented graphically. The results have possible technological applications in liquid-based systems involving stretchable materials.     

Measurement of local tissue perfusion through a minimally invasive heating bead

A minimally invasive approach was proposed to measure local blood perfusion rate in living tissues, based on the well-known Pennes bioheat equation. The measuring probe consists of a heater covered with conductive epoxy and temperature sensor deposited on the probe–tissue interface. By monitoring the probe–tissue interface’s temperature response before and after employing the constant heat flux, the tissue blood perfusion rate can be obtained. A theoretical model was developed to describe the measurement system. In vivo experiments were performed on the rabbit’s thighs to validate this method. At last, uncertainties implied in the temperature measurement and voltage across the heater was evaluated. The results point out the way to improve the accuracy of the present method and its appropriate application occasion.     

Magnetic field effect on heat transfer and fluid flow characteristics of blood flow in multi-stenosis arteries

Heat and fluid flow characteristics of blood flow in multi-stenosis arteries in the presence of magnetic field is considered. A mathematical model of the multi-stenosis inside the arteries is introduced. A finite difference scheme is used to solve the governing equations in terms of vorticity-stream function along with their boundary conditions. The effect of magnetic field and the degree of stenosis on wall shear stress and Nusselt number is investigated. It was found that magnetic field modifies the flow patterns and increases the heat transfer rate. The severity of the stenosis affects the wall shear stress characteristics significantly. The magnetic field torque will increase the thermal boundary layer thickness and the temperature gradient in the streaming blood, and hence increasing the local Nusselt number     

Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk

In this paper we have studied the effects of temperature dependent fluid properties such as density, viscosity and thermal conductivity and variable Prandtl number on unsteady convective heat transfer flow over a porous rotating disk. Using similarity transformations we reduce the governing nonlinear partial differential equations for flow and heat transfer into a system of ordinary differential equations which are then solved numerically by applying Nachtsheim–Swigert shooting iteration technique along with sixth-order Runge–Kutta integration scheme. Comparison with previously published work for steady case of the problem were performed and found to be in very good agreement. The obtained numerical results show that the rate of heat transfer in a fluid of constant properties is higher than in a fluid of variable properties. The results further show that consideration of Prandtl number as constant within the boundary layer for variable fluid properties lead unrealistic results. Therefore, modeling thermal boundary layers with temperature dependent fluid properties Prandtl number must treated as variable inside the boundary layer.     

Nonsimilar solutions for free convection from a vertical plate in porous media

A nonsimilar boundary layer analysis has been presented for the free convection along a vertical plate embedded in a fluid-saturated porous medium in the presence of surface mass transfer and internal heat generation. The transformed conservation laws are solved numerically for the cases of variable wall temperature and variable wall heat flux boundary conditions. Results are presented for the details of the velocity and temperature fields as well as Nusselt number. Received on 13 December 1996     

Approximate heat transfer coefficients based on variable thermophysical properties for laminar flow over a uniformly heated flat plate

New heat transfer coefficient approximations are developed for forced laminar flow over a uniformly heated flat plate at zero incidence angle. The development is based on solving the variable property boundary layer equations using a variable property similarity transform that incorporates an adjustable similarity scaling constant. The scaling constants value is iteratively adjusted until the scaled temperature gradient-at-the-wall value is equal to the small temperature difference value. The resulting scaled profiles are nearly congruent. The congruency scaling constant is then approximated in terms of simple functions of the kinematic viscosity and the Prandlt number evaluated at the plate and free stream temperatures. The approximate scaling constants are used to form new approximations for the heat transfer coefficient. The new approximate coefficients are compared to traditional coefficients for four gases and six liquid flows covering the range 0.5 < Pr < 3,000 with large temperature differences.     

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.The study considers the effects of frictional heating(viscous dissipation) and internal heat generation or absorption.The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations.The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method.An analysis is carried out for two different cases of heating processes,namely,variable wall temperature(VWT) and variable heat flux(VHF).The effects of various physical parameters such as the magnetic parameter,the fluid-particle interaction parameter,the unsteady parameter,the Prandtl number,the Eckert number,the number density of dust particles,and the heat source/sink parameter on velocity and temperature profiles are shown in several plots.The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.     

Biothermomechanics of skin tissues

Biothermomechanics of skin is highly interdisciplinary involving bioheat transfer, burn damage, biomechanics and neurophysiology. During heating, thermally induced mechanical stress arises due to the thermal denaturation of collagen, resulting in macroscale shrinkage. Thus, the strain, stress, temperature and thermal pain/damage are highly correlated; in other words, the problem is fully coupled. The aim of this study is to develop a computational approach to examine the heat transfer process and the heat-induced mechanical response, so that the differences among the clinically applied heating modalities can be quantified. Exact solutions for temperature, thermal damage and thermal stress for a single-layer skin model were first derived for different boundary conditions. For multilayer models, numerical simulations using the finite difference method (FDM) and finite element method (FEM) were used to analyze the temperature, burn damage and thermal stress distributions in the skin tissue. The results showed that the thermomechanical behavior of skin tissue is very complex: blood perfusion has little effect on thermal damage but large influence on skin temperature distribution, which, in turn, influences significantly the resulting thermal stress field; the stratum corneum layer, although very thin, has a large effect on the thermomechanical behavior of skin, suggesting that it should be properly accounted for in the modeling of skin thermal stresses; the stress caused by non-uniform temperature distribution in the skin may also contribute to the thermal pain sensation.     

Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier

A fluid flow and heat transfer model has been developed for the reactive, porous bed of the biomass gasifier to simulate pressure drop, temperature profile in the bed and flow rates. The conservation equations, momentum equation and energy equation are used to describe fluid and heat transport in porous gasifier bed. The model accounted for drag at wall, and the effect of radial as well as axial variation in bed porosity to predict pressure drop in bed. Heat transfer has been modeled using effective thermal conductivity approach. Model predictions are validated against the experiments, while effective thermal conductivity values are tested qualitatively using models available in literature. Parametric analysis has been carried out to investigate the effect of various parameters on bed temperature profile and pressure drop through the gasifier. The temperature profile is found to be very sensitive to gas flow rate, and heat generation in oxidation zone, while high bed temperature, gas flow rate and the reduction in feedstock particle size are found to cause a marked increase in pressure drop through the gasifier. The temperatures of the down stream zones are more sensitive to any change in heat generation in the bed as compared to upstream zone. Author recommends that the size of preheating zone may be extended up to pyrolysis zone in order to enhance preheating of input air, while thermal insulation should not be less than 15 cm.     

Flow structure and wall layer control in a lower half heated upper half cooled enclosure with superimposed temperature deviations

This paper presents an investigation on the effects of superimposed temperature deviations as a control technique for the flows and mixing in lower half heated upper half cooled enclosures. Results show that the strength of the wall layer depends on the difference between the wall surface temperature and the fluid core temperature. The location of the head-on collision between a pair of upward/downward wall layers, which controls the mixing and fluid exchange between the two halves, is determined by the wall layer flow momentum strengths. Elevating/reducing the wall temperature by a superimposed temperature deviation is an effective control for the flow and mixing in such enclosures. Heat transfer analysis shows that the superimposed temperature deviations have minor effects on the total heat flow rate from the lower walls. Thus, this technique can be applied onto reactor vessels without modifying the reactor vessel configuration.     

Effect of variable viscosity on non-Darcy free or mixed convection flow on a vertical surface in a fluid saturated porous medium

This paper analyzes the variable viscosity effects on non-Darcy free or mixed convection flow on a vertical surface in a fluid saturated porous medium. The viscosity of the fluid is assumed to be a inverse linear function of temperature. Velocity and heat transfer are found to be significantly affected by the variable viscosity parameter, Ergun number, Peclet number or Rayleigh number.     

Exact Solution of the Heat Transfer Problem for a Rotating Disk under Uniform Jet Impingement

An exact solution of the heat transfer problem for a uniform air stream impinging on a rotating disk is found. By introducing self-similar radial velocity and temperature profiles, the problem is reduced to a system of ordinary differential equations which are solved numerically. The Nusselt numbers are calculated for Prandtl numbers equal to 1 and 0.71 and various ratios of the free-stream velocity to the disk rotation velocity. The limits of the flow regime in which the heat transfer is determined solely by the impact jet parameters are found. The results are compared with experimental data for the stagnation point.