The Bleed Off Perfusion Term in the Weinbaum-Jiji Bioheat Equation

1992 ◽  
Vol 114 (4) ◽  
pp. 539-542 ◽  
Author(s):  
S. Weinbaum ◽  
L. M. Jiji ◽  
D. E. Lemons
Keyword(s):  
Energy Equation ◽  
Source Term ◽  
Venous Return ◽  
Effective Conductivity ◽  
Blood Perfusion ◽  
Tissue Temperature ◽  
Bioheat Equation ◽  
Countercurrent System ◽  
Thermal Equilibration ◽  
Arteries And Veins

The microvascular organization and thermal equilibration of the primary and secondary arteries and veins that comprise the bleed off circulation to the muscle fibers from the parent countercurrent supply artery and veins are analyzed. The blood perfusion heat source term in the tissue energy equation is shown to be related to this vascular organization and to undergo a fundamental change in behavior as one proceeds from the more peripheral tissue, where the perfusion term is proportional to the Ta - Tv difference in the parent supply vessels, to the deeper tissue layers where the bleed off vessels themselves form a branching countercurrent system for each muscle tissue cylinder and the venous return temperature can vary between the local tissue temperature and Ta. The consequences of this change in behavior are examined for the Weinbaum-Jiji bioheat equation and a modified expression for the effective conductivity of perfused tissue is derived for countercurrent bleed off exchange.

A New Fundamental Bioheat Equation for Muscle Tissue: Part I—Blood Perfusion Term

1997 ◽  
Vol 119 (3) ◽  
pp. 278-288 ◽  
Author(s):  
S. Weinbaum ◽  
L. X. Xu ◽  
L. Zhu ◽  
A. Ekpene
Keyword(s):  
Heat Transfer ◽  
Muscle Tissue ◽  
Source Term ◽  
Venous Return ◽  
Blood Perfusion ◽  
Efficiency Coefficient ◽  
Bioheat Equation ◽  
Or Efficiency ◽  
Cross Sectional ◽  
Transfer Unit

A new model for muscle tissue heat transfer has been developed using Myrhage and Eriksson’s [23] description of a muscle tissue cylinder surrounding secondary (s) vessels as the basic heat transfer unit. This model provides a rational theory for the venous return temperature for the perfusion source term in a modified Pennes bioheat equation, and greatly simplifies the anatomical description of the microvascular architecture required in the Weinbaum-Jiji bioheat equation. An easy-to-use closed-form analytic expression has been derived for the difference between the inlet artery and venous return temperatures using a model for the countercurrent heat exchange in the individual muscle tissue cylinders. The perfusion source term calculated from this model is found to be similar in form to the Pennes’s source term except that there is a correction factor or efficiency coefficient multiplying the Pennes term, which rigorously accounts for the thermal equilibration of the returning vein. This coefficient is a function of the vascular cross-sectional geometry of the muscle tissue cylinder, but independent of the Peclet number in contrast to the recent results in Brinck and Werner [8]. The value of this coefficient varies between 0.6 and 0.7 for most muscle tissues. In part II of this study a theory will be presented for determining the local arterial supply temperature at the inlet to the muscle tissue cylinder.

A New Fundamental Bioheat Equation for Muscle Tissue—Part II: Temperature of SAV Vessels

2001 ◽  
Vol 124 (1) ◽  
pp. 121-132 ◽  
Author(s):  
Liang Zhu ◽  
Lisa X. Xu ◽  
Qinghong He ◽  
Sheldon Weinbaum
Keyword(s):  
Source Term ◽  
Vascular Anatomy ◽  
Blood Perfusion ◽  
Surrounding Tissue ◽  
Inlet Temperature ◽  
Bioheat Equation ◽  
Temperature Variations ◽  
Relative Contribution ◽  
Branching Patterns ◽  
Vascular Branching

In this study, a new theoretical framework was developed to investigate temperature variations along countercurrent SAV blood vessels from 300 to 1000 μm diameter in skeletal muscle. Vessels of this size lie outside the range of validity of the Weinbaum-Jiji bioheat equation and, heretofore, have been treated using discrete numerical methods. A new tissue cylinder surrounding these vessel pairs is defined based on vascular anatomy, Murray’s law, and the assumption of uniform perfusion. The thermal interaction between the blood vessel pair and surrounding tissue is investigated for two vascular branching patterns, pure branching and pure perfusion. It is shown that temperature variations along these large vessel pairs strongly depend on the branching pattern and the local blood perfusion rate. The arterial supply temperature in different vessel generations was evaluated to estimate the arterial inlet temperature in the modified perfusion source term for the s vessels in Part I of this study. In addition, results from the current research enable one to explore the relative contribution of the SAV vessels and the s vessels to the overall thermal equilibration between blood and tissue.

A Combined Macro and Microvascular Model for Whole Limb Heat Transfer

1988 ◽  
Vol 110 (4) ◽  
pp. 259-268 ◽  
Author(s):  
W. J. Song ◽  
S. Weinbaum ◽  
L. M. Jiji ◽  
D. Lemons
Keyword(s):  
Heat Transfer ◽  
Venous Return ◽  
Prototype Model ◽  
Bioheat Equation ◽  
Cross Sectional ◽  
Surface Temperature Distribution ◽  
Wide Range ◽  
Cutaneous Tissue ◽  
Axial Variation ◽  
Arteries And Veins

A new prototype model for whole limb heat transfer is proposed wherein the countercurrent heat exchange from the large central arteries and veins in the core of the limb is coupled to microvascular models for the surrounding muscle and the cutaneous tissue layers. The local microvascular temperature field in the muscle tissue is described by the bioheat equation of Weinbaum and Jiji [1]. The new model allows for an arbitrary axial variation of cross-sectional area and blood distribution between the muscle and cutaneous tissue, accounts for the blood flow to and heat loss from the hand and treats the venous return temperature and surface temperature distribution as unknowns that are determined as part of the solution to the overall boundary value problem. Representative solutions are presented for a wide range of environmental conditions for a limb in both the resting state and during exercise.

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.

scholarly journals Prediction human skin temperature in comfort level

2019 ◽  
Vol 1 (3) ◽  
pp. 1-4
Author(s):  
Zaina Norhallis Zainol ◽  
Masine Md. Tap ◽  
Haslinda Mohamed Kamar
Keyword(s):  
Thermal Comfort ◽  
Skin Temperature ◽  
Human Skin ◽  
Blood Perfusion ◽  
Comfort Level ◽  
Working Environment ◽  
Percentage Error ◽  
Bioheat Equation ◽  
Acceptable Error ◽  
Human Arm

Thermal comfort is the human subject perceive satisfaction to the work environment. The thermal comfort need to be achieve towards productive working environment. The comfort level of the subject is affected by the human skin temperature. To assess the skin temperature with the sorrounding by conducting human experiment in the climatic chamber. It is rigorous and complex experiment.This study was developed to predict human skin temperature in comfort level with the finite element method and the bioheat equation. The bioheat equation is a consideration of metabolic heat generation and the blood perfusion to solve heat transfer of the living tissue. It is to determine the skin temperature focussing at the human arm. From the study, it is found that the predicted skin temperature value were in well agreement with the experimental results. The percentage error insignificant with acceptable error of 1.05%.

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).

A Non-Source Term Methodology in Simulation of Solidification

2002 ◽  
Author(s):  
Yumin Xiao ◽  
R. S. Amano ◽  
E. K. Lee ◽  
Youn-Suk Choi ◽  
Jianhui Xie
Keyword(s):  
Energy Equation ◽  
Source Term ◽  
Flow Problem ◽  
Pure Metal ◽  
Published Data ◽  
Test Cases ◽  
Discrete Form ◽  
Metal Solidification ◽  
Wide Range ◽  
Solidification Processes

In this paper a non-source term method is developed to solve the energy equation. In this new method the discrete form of the energy equation remains the same and no extra source term is introduced. The mushy-zone is treated as a porous media during solidification. This method is incorporated into the existing finite volume based CFD code. Test cases analyzed in this paper include solidification of pure metal, pure metal solidification with natural convection due to the buoyancy, and binary alloy mushy flow problem with variable Cp. The calculated results are in good agreements with available published data. This method can be applied to simulate a wide range of melting/solidification processes.

Integration of jugular venous return and circle of Willis in a theoretical human model of selective brain cooling

2007 ◽  
Vol 103 (5) ◽  
pp. 1837-1847 ◽  
Author(s):  
Matthew A. Neimark ◽  
Angelos-Aristeidis Konstas ◽  
Andrew F. Laine ◽  
John Pile-Spellman
Keyword(s):  
Venous Return ◽  
Mild Hypothermia ◽  
Brain Temperature ◽  
Circle Of Willis ◽  
Human Model ◽  
Anterior Communicating Artery ◽  
Moderate Hypothermia ◽  
Brain Cooling ◽  
Bioheat Equation ◽  
Selective Brain Cooling

A three-dimensional mathematical model was developed to examine the induction of selective brain cooling (SBC) in the human brain by intracarotid cold (2.8°C) saline infusion (ICSI) at 30 ml/min. The Pennes bioheat equation was used to propagate brain temperature. The effect of cooled jugular venous return was investigated, along with the effect of the circle of Willis (CoW) on the intracerebral temperature distribution. The complete CoW, missing A1 variant (mA1), and fetal P1 variant (fP1) were simulated. ICSI induced moderate hypothermia (defined as 32–34°C) in the internal carotid artery (ICA) territory within 5 min. Incorporation of the complete CoW resulted in a similar level of hypothermia in the ICA territory. In addition, the anterior communicating artery and ipsilateral posterior communicating artery distributed cool blood to the contralateral anterior and ipsilateral posterior territories, respectively, imparting mild hypothermia (35 and 35.5°C respectively). The mA1 and fP1 variants allowed for sufficient cooling of the middle cerebral territory (30–32°C). The simulations suggest that ICSI is feasible and may be the fastest method of inducing hypothermia. Moreover, the effect of convective heat transfer via the complete CoW and its variants underlies the important role of CoW anatomy in intracerebral temperature distributions during SBC.

Sign in / Sign up

Export Citation Format

Share Document