A New Simplified Bioheat Equation for the Effect of Blood Flow on Local Average Tissue Temperature

1985 ◽  
Vol 107 (2) ◽  
pp. 131-139 ◽  
Author(s):  
S. Weinbaum ◽  
L. M. Jiji
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Blood Perfusion ◽  
Basic Mechanism ◽  
Simple Expression ◽  
Tissue Temperature ◽  
Bioheat Equation ◽  
Countercurrent Exchange

A new simplified three-dimensional bioheat equation is derived to describe the effect of blood flow on blood-tissue heat transfer. In two recent theoretical and experimental studies [1, 2] the authors have demonstrated that the so-called isotropic blood perfusion term in the existing bioheat equation is negligible because of the microvascular organization, and that the primary mechanism for blood-tissue energy exchange is incomplete countercurrent exchange in the thermally significant microvessels. The new theory to describe this basic mechanism shows that the vascularization of tissue causes it to behave as an anisotropic heat transfer medium. A remarkably simple expression is derived for the tensor conductivity of the tissue as a function of the local vascular geometry and flow velocity in the thermally significant countercurrent vessels. It is also shown that directed as opposed to isotropic blood perfusion between the countercurrent vessels can have a significant influence on heat transfer in regions where the countercurrent vessels are under 70-μm diameter. The new bioheat equation also describes this mechanism.

Formulation of a Statistical Model of Heat Transfer in Perfused Tissue

1994 ◽  
Vol 116 (4) ◽  
pp. 521-527 ◽  
Author(s):  
J. W. Baish
Keyword(s):  
Heat Transfer ◽  
Heat Transport ◽  
Drug Transport ◽  
Transfer Problem ◽  
Three Dimensional ◽  
Tissue Temperature ◽  
Statistical Interpretation ◽  
Transfer Equations ◽  
Vascular Geometry ◽  
Steady State Heat

A new model of steady-state heat transport in perfused tissue is presented. The key elements of the model are as follows: (1) a physiologically-based algorithm for simulating the geometry of a realistic vascular tree containing all thermally significant vessels in a tissue; (2) a means of solving the conjugate heat transfer problem of convection by the blood coupled to three-dimensional conduction in the extravascular tissue, and (3) a statistical interpretation of the calculated temperature field. This formulation is radically different from the widely used Pennes and Weinbaum-Jiji bio-heat transfer equations that predict a loosely defined local average tissue temperature from a local perfusion rate and a minimal representation of the vascular geometry. Instead, a probability density function for the tissue temperature is predicted, which carries information on the most probable temperature at a point and uncertainty in that temperature due to the proximity of thermally significant blood vessels. A sample implementation illustrates the dependence of the temperature distribution on the flow rate of the blood and the vascular geometry. The results show that the Pennes formulation of the bio-heat transfer equation accurately predicts the mean tissue temperature except when the arteries and veins are in closely spaced pairs. The model is useful for fundamental studies of tissue heat transport, and should extend readily to other forms of tissue transport including oxygen, nutrient, and drug transport.

Lumped Parameter Thermal Model for the Study of Vascular Reactivity in the Fingertip

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
O. Ley ◽  
C. Deshpande ◽  
B. Prapamcham ◽  
M. Naghavi
Keyword(s):  
Heat Flux ◽  
Blood Flow ◽  
Thermal Model ◽  
Vascular Reactivity ◽  
Arterial Occlusion ◽  
Blood Perfusion ◽  
Cost Effective ◽  
Venous Occlusion ◽  
Cardiovascular Complications ◽  
Tissue Temperature

Vascular reactivity (VR) denotes changes in volumetric blood flow in response to arterial occlusion. Current techniques to study VR rely on monitoring blood flow parameters and serve to predict the risk of future cardiovascular complications. Because tissue temperature is directly impacted by blood flow, a simplified thermal model was developed to study the alterations in fingertip temperature during arterial occlusion and subsequent reperfusion (hyperemia). This work shows that fingertip temperature variation during VR test can be used as a cost-effective alternative to blood perfusion monitoring. The model developed introduces a function to approximate the temporal alterations in blood volume during VR tests. Parametric studies are performed to analyze the effects of blood perfusion alterations, as well as any environmental contribution to fingertip temperature. Experiments were performed on eight healthy volunteers to study the thermal effect of 3min of arterial occlusion and subsequent reperfusion (hyperemia). Fingertip temperature and heat flux were measured at the occluded and control fingers, and the finger blood perfusion was determined using venous occlusion plethysmography (VOP). The model was able to phenomenologically reproduce the experimental measurements. Significant variability was observed in the starting fingertip temperature and heat flux measurements among subjects. Difficulty in achieving thermal equilibration was observed, which indicates the important effect of initial temperature and thermal trend (i.e., vasoconstriction, vasodilatation, and oscillations).

Model of local temperature changes in brain upon functional activation

2004 ◽  
Vol 97 (6) ◽  
pp. 2051-2055 ◽  
Author(s):  
Christopher M. Collins ◽  
Michael B. Smith ◽  
Robert Turner
Keyword(s):  
Brain Temperature ◽  
Human Subjects ◽  
Potential Temperature ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Human Head ◽  
Bioheat Equation ◽  
Three Dimensional Model ◽  
Temperature Changes ◽  
Blood Temperature

Experimental results for changes in brain temperature during functional activation show large variations. It is, therefore, desirable to develop a careful numerical model for such changes. Here, a three-dimensional model of temperature in the human head using the bioheat equation, which includes effects of metabolism, perfusion, and thermal conduction, is employed to examine potential temperature changes due to functional activation in brain. It is found that, depending on location in brain and corresponding baseline temperature relative to blood temperature, temperature may increase or decrease on activation and concomitant increases in perfusion and rate of metabolism. Changes in perfusion are generally seen to have a greater effect on temperature than are changes in metabolism, and hence active brain is predicted to approach blood temperature from its initial temperature. All calculated changes in temperature for reasonable physiological parameters have magnitudes <0.12°C and are well within the range reported in recent experimental studies involving human subjects.

On Natural Convection Heat Transfer From Three-Dimensional Bodies of Arbitrary Shape

1989 ◽  
Vol 111 (2) ◽  
pp. 363-371 ◽  
Author(s):  
A. V. Hassani ◽  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Arbitrary Shape ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Simple Expression ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Oblate Spheroids ◽  
Body Shapes

A simple expression is developed for the natural convection heat transfer from three-dimensional bodies of arbitrary shape immersed in an extensive fluid. The expression applies to both laminar and turbulent regimes and requires the calculation of purely geometric properties of the bodies. Experiments were performed with air, covering a Rayleigh number (Ra) range of from 10 to 108, on different body shapes oriented in various directions: for example, circular or square disks, a short circular cylinder of height equal to diameter and a similar cylinder but with hemispherical ends, prolate and oblate spheroids of various aspect ratio, and an “apple core” shape. Comparison between the predictions of the expression and the experimental results of this work and those gathered from several other sources ranging up to Ra = 1014 showed very good agreement, with an average rms difference of 3.5 percent for Ra < 108 and 22 percent for 108 < Ra < 1014.

scholarly journals Numerical Study of Fluid Flow and Heat Transfer Characteristics in Solid and Perforated Finned Heat Sinks Utilizing a Piezoelectric Fan

2019 ◽  
Vol 25 (7) ◽  
pp. 83-103
Author(s):  
Ayser Shamil Salman ◽  
Mohammed A. Nima
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Numerical Study ◽  
Air Flow ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Heat Sinks ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Flow Generator

Numerical study is adapted to combine between piezoelectric fan as a turbulent air flow generator and perforated finned heat sinks. A single piezoelectric fan with different tip amplitudes placed eccentrically at the duct entrance. The problem of solid and perforated finned heat sinks is solved and analyzed numerically by using Ansys 17.2 fluent, and solving three dimensional energy and Navier–Stokes equations that set with RNG based k−ε scalable wall function turbulent model. Finite volume algorithm is used to solve both phases of solid and fluid. Calculations are done for three values of piezoelectric fan amplitudes 25 mm, 30 mm, and 40 mm, respectively. Results of this numerical study are compared with previous both numerical and experimental studies and give a good agreement. Numerical solution is invoked to explain the behavior of air flow and temperature distribution for two types of circular axial and lateral perforations. For each type, all the results are compared with an identical solid finned heat sink. Perforations show a remarkable enhanced in the heat transfer characteristics. The results achieved enhancement in the heat transfer coefficient about 12% in axial perforation and 25% in the lateral perforation at the maximum fan amplitude.  

Buoyancy Effects on Human Skin Tissue Thermoregulation due to Environmental Influence

2020 ◽  
Vol 401 ◽  
pp. 107-116
Author(s):  
Lawal Hamid Adeola ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Human Skin ◽  
Environmental Influence ◽  
Saturated Porous Medium ◽  
Skin Tissue ◽  
Bioheat Equation ◽  
Biophysical Parameters ◽  
Thermal Buoyancy ◽  
The Impact

This paper theoretically examines the impact of thermal buoyancy on human skin tissue’s blood flow, heat exchange and their interaction with the surrounding environment using a two phase mathematical model that relies on continuity, momentum and energy conservation equations in continuum mechanics. The tissue blood flows and heat transfer characteristics are determined numerically based on Darcy’s Brinkman model for a saturated porous medium coupled with modified Pennes bioheat equation while analytical approach is employed to tackle the model of interacting surrounding environmental buoyancy driven air flow with heat sink. The influence of embedded biophysical parameters on the skin tissue’s blood flow rate and temperature distribution together with friction coefficient at skin tissue surface and Nusselt number are display graphically and discussed quantitatively. It is found that a boost in thermal buoyancy enhances skin tissue heat transfer and blood flow rates.

Heat Transfer Normal to Paired Arterioles and Venules Embedded in Perfused Tissue During Hyperthermia

1988 ◽  
Vol 110 (4) ◽  
pp. 277-282 ◽  
Author(s):  
C. K. Charny ◽  
R. L. Levin
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Three Dimensional ◽  
Numerical Data ◽  
Tissue Temperature ◽  
Three Dimensional Model ◽  
Sources And Sinks ◽  
The Mean ◽  
Krogh Cylinder ◽  
Subsequent Incorporation

A numerical model of the heat transer normal to an arteriole-venule pair embedded in muscle tissue has been constructed. Anatomical data describing the blood vessel size, spacing, and density have been incorporated into the model. This model computes temperatures along the vessel walls as well as the temperature throughout the tissue which comprises an infinitely long Krogh cylinder around the vessel pair. Tissue temperatures were computed in the steady-state under resting conditions, while transient calculations were made under hyperthermic conditions. Results show that for both large- (1st generation) and medium-sized (5th generation) vessel pairs, the mean tissue temperature within the tissue cylinder is not equal to the mean of the arteriole and venule blood temperatures under both steady-state and transient conditions. The numerical data were reduced so that a comparison could be made with the predictions of a simple two-dimensional superposition of line sources and sinks presented by Baish et al. [1]. This comparison reveals that the superposition model accurately describes the heat transfer effects during hyperthermia, permitting subsequent incorporation of this theory into a realistic three-dimensional model of heat transfer in a whole limb during hyperthermia.

ANALYTICAL SOLUTIONS OF NON-FOURIER PENNES AND CHEN–HOLMES EQUATIONS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250022 ◽  
Author(s):  
WEIPING ZHU ◽  
FANGBAO TIAN ◽  
PENG RAN
Keyword(s):  
Heat Transfer ◽  
Analytical Solutions ◽  
Laplace Transformation ◽  
Solution Method ◽  
Thermal Relaxation ◽  
Blood Perfusion ◽  
Good Alternative ◽  
Tissue Temperature ◽  
Particular Solution ◽  
Insight Into

The analytical solutions of non-Fourier Pennes and Chen–Holmes equations are obtained using the Laplace transformation and particular solution method in the present paper. As an application, the effects of the thermal relaxation time τ, the blood perfusion wb, and the blood flow velocity v on the biological skin and inner tissue temperature T are studied in detail. The results obtained in this study provide a good alternative method to study the bio-heat and a biophysical insight into the understanding of the heat transfer in the biotissue.

Sensitivity Analysis of One-Dimensional Heat Transfer in Tissue With Temperature-Dependent Perfusion

1997 ◽  
Vol 119 (1) ◽  
pp. 77-80 ◽  
Author(s):  
C. R. Davies ◽  
G. M. Saidel ◽  
H. Harasaki
Keyword(s):  
Heat Transfer ◽  
Sensitivity Analysis ◽  
Heated Surface ◽  
Experimental Studies ◽  
Total Artificial Heart ◽  
Tissue Temperature ◽  
Model Parameters ◽  
Temperature Dependent ◽  
One Dimensional

Design criteria for implantable, heat-generating devices such as the total artificial heart require the determination of safe thresholds for chronic heating. This involves in-vivo experiments in which tissue temperature distributions are obtained in response to known heat sources. Prior to experimental studies, simulation using a mathematical model can help optimize the design of experiments. In this paper, a theoretical analysis of heat transfer is presented that describes the dynamic, one-dimensional distribution of temperature from a heated surface. Loss of heat by perfusion is represented by temperature-independent and temperature-dependent terms that can reflect changes in local control of blood flow. Model simulations using physiologically appropriate parameter values indicate that the temperature elevation profile caused by a heated surface adjacent to tissue may extend several centimeters into the tissue. Furthermore, sensitivity analysis indicates the conditions under which temperature profiles are sensitive to changes in thermal diffusivity and perfusion parameters. This information provides the basis for estimation of model parameters in different tissues and for prediction of the thermal responses of these tissues.

Numeric Analysis of Temperature Distribution in Man using a 3D Human Model

2018 ◽  
Author(s):  
Sipho Mfolozi ◽  
Arnaud Malan ◽  
Tunde Bello-Ochende ◽  
Lorna J. Martin
Keyword(s):  
Body Temperature ◽  
Initial Conditions ◽  
Accurate Determination ◽  
Three Dimensional ◽  
Blood Perfusion ◽  
Human Model ◽  
Post Mortem ◽  
Bioheat Equation ◽  
Death Time ◽  
Analysis Scheme

AbstractPremortem three-dimensional body temperature is the basis on which post-mortem cooling commences. Thermo-numeric analysis of post-mortem cooling for death-time calculation applies pre-mortem three-dimensional body temperature as initial conditions; therefore, an accurate determination of this distribution is important. To date, such prediction is not performed. This paper presents a thermo-numeric analysis method of predicting premortem three-dimensional body temperature in man, to be applied in thermo-numeric analysis of the post-mortem interval using the finite-difference time-domain method. The method applied a Pennes BioHeat Equation modified to linearize organ metabolic and blood flow rates with temperature in a transient thermo-numeric analysis scheme to predict naked three-dimensional temperatures of an MRI-built, 3D human model having 247 segmented organs and 58 categories of material properties under chosen boundary conditions. Organ metabolic heat and blood perfusion rates appropriate for a chosen pre-mortem physical activity, and known organ physical and thermal properties, were assigned to each organ. A steady-state temperature equilibration occurred after 8400 seconds. Predicted organ temperatures were topographically inhomogeneous. Skin temperatures varied between 20.5°C and 42.5°C, liver capsule temperatures were lower than parenchymal, and rectal luminal temperature were uniform.

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