METHOD OF FUNDAMENTAL SOLUTIONS FOR NONLINEAR SKIN BIOHEAT MODEL

2014 ◽  
Vol 14 (04) ◽  
pp. 1450060 ◽  
Author(s):  
ZE-WEI ZHANG ◽  
HUI WANG ◽  
QING-HUA QIN
Keyword(s):  
Steady State ◽  
Governing Equation ◽  
Blood Perfusion ◽  
Bioheat Transfer ◽  
Method Of Fundamental Solutions ◽  
Linear Quadratic ◽  
Temperature Dependent ◽  
Perfusion Rate ◽  
Blood Perfusion Rate ◽  
Transfer Problems

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 Tissue Blood Perfusion Rate from Diffusible Indicator Measurements: A Sensitivity Analysis

1980 ◽  
Vol 102 (3) ◽  
pp. 258-264 ◽  
Author(s):  
A. Shitzer ◽  
R. C. Eberhart ◽  
J. Eisenfeld
Keyword(s):  
Sensitivity Analysis ◽  
Material Balance ◽  
Blood Perfusion ◽  
Tissue Perfusion ◽  
Optimal Time ◽  
Perfusion Rate ◽  
Experimental Conditions ◽  
Rate Analysis ◽  
Sensor Position ◽  
Blood Perfusion Rate

Recording the washout of indicator (for example, heat, radio-labeled dissolved gas, etc.) transiently introduced into tissue allows the estimation of tissue blood perfusion rate. Analysis of the washout data requires a material balance which appropriately accounts for all transport mechanisms and sources and sinks of the given indicator. From that balance one may perform a sensitivity analysis which specifies the susceptibility of the perfusion estimate to experimental errors in any of the pertinent parameters and variables. The sensitivity analysis is based on the normalized partial derivatives of tissue indicator concentration with respect to the experimental variables. The results indicate that the estimation of the tissue blood perfusion rate is highly sensitive to errors in the concentration of the diffusible indicator which dominate, by two orders of magnitude or more, the errors attributed to other parameters. For typical experimental conditions, the errors in the perfusion estimate due to the various parameters are shown to vary considerably, according to the sensor position and time of measurement. Based on this type of analysis, one may specify optimal temporal and spatial domains for the parameter estimation in order to minimize error propagation. The optimal time domains are shown to differ from those used in typical indicator washout analyses for estimating tissue perfusion rate.

Thermography as a Means of Blood Perfusion Measurement

1979 ◽  
Vol 101 (4) ◽  
pp. 246-249 ◽  
Author(s):  
J. E. Francis ◽  
R. Roggli ◽  
T. J. Love ◽  
C. P. Robinson
Keyword(s):  
Blood Flow ◽  
Skin Temperature ◽  
Strain Gage ◽  
Infrared Camera ◽  
Blood Perfusion ◽  
The Body ◽  
Perfusion Rate ◽  
Perfusion Measurement ◽  
Blood Perfusion Rate ◽  
Human Forearm

The scanning infrared camera has been used to verify an analytical model relating blood perfusion rate to skin temperature. The blood perfusion rates were measured with both the mercury strain gage and the volume plethysmograph on the human forearm. Thermograms were taken of the forearm and temperature measured using an optical densitometer. Comparison of the volume plethysmograph with the strain gage, and the thermograms with the strain gage indicate thermography to be a useful means of measuring blood flow. Thermography has the advantages of being noninvasive and can be used to measure blood perfusion in parts of the body not easily monitored with occlusive techniques.

Effects of laser acupuncture on blood perfusion rate

2006 ◽  
Author(s):  
Xian-ju Wang ◽  
Chang-chun Zeng ◽  
Han-ping Liu ◽  
Song-hao Liu ◽  
Liang-gang Liu
Keyword(s):  
Blood Perfusion ◽  
Laser Acupuncture ◽  
Perfusion Rate ◽  
Blood Perfusion Rate

scholarly journals A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
R. M. S. Gama ◽  
R. Pazetto
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Robin Boundary Conditions ◽  
Temperature Dependent ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Transfer Problems ◽  
Robin Boundary ◽  
Temperature Dependent Thermal Conductivity

This work presents an useful tool for constructing the solution of steady-state heat transfer problems, with temperature-dependent thermal conductivity, by means of the solution of Poisson equations. Specifically, it will be presented a procedure for constructing the solution of a nonlinear second-order partial differential equation, subjected to Robin boundary conditions, by means of a sequence whose elements are obtained from the solution of very simple linear partial differential equations, also subjected to Robin boundary conditions. In addition, an a priori upper bound estimate for the solution is presented too. Some examples, involving temperature-dependent thermal conductivity, are presented, illustrating the use of numerical approximations.

Thermal Pulse Decay Method for Simultaneous Measurement of Local Thermal Conductivity and Blood Perfusion: A Theoretical Analysis

1986 ◽  
Vol 108 (3) ◽  
pp. 208-214 ◽  
Author(s):  
H. Arkin ◽  
K. R. Holmes ◽  
M. M. Chen ◽  
W. G. Bottje
Keyword(s):  
Thermal Conductivity ◽  
Blood Flow ◽  
Theoretical Analysis ◽  
Simultaneous Measurement ◽  
Blood Perfusion ◽  
Perfusion Rate ◽  
Tissue Conductivity ◽  
Thermal Pulse ◽  
Measurement Protocol ◽  
Blood Perfusion Rate

Presented here is a theoretical analysis of the recently developed thermal pulse decay (TPD) method for a simultaneous measurement of local tissue conductivity and blood perfusion rate. The paper describes the theoretical model upon which the TPD method is based and details its capabilities and limitations. The theoretical aspects that affected the development of the measurement protocol are also discussed. The performance of the method is demonstrated with an experimental example which compares the measurements of local kidney blood perfusion rates made using the TPD method with the total renal blood flow obtained coincidentally using a blood flowmeter, in an anesthetized dog.

Prediction of skin burn injury. Part 2: Parametric and sensitivity analysis

2002 ◽  
Vol 216 (3) ◽  
pp. 171-183 ◽  
Author(s):  
E Y-K Ng ◽  
L T Chua
Keyword(s):  
Thermal Conductivity ◽  
Sensitivity Analysis ◽  
Burn Injury ◽  
Convective Heat Transfer Coefficient ◽  
Blood Perfusion ◽  
Tissue Temperature ◽  
Two Dimensional ◽  
Perfusion Rate ◽  
Injury Threshold ◽  
Blood Perfusion Rate

Part 2 of this paper presents an analysis of variance (ANOVA) for investigating the precedence of the various parameters, and the effects of varying these parameters, in assessment of burn injury resulting from the exposure of skin surface to heat sources. A one-dimensional model based on the finite difference method (FDM), as implemented in a spreadsheet software application, is applied to the assessment of burn injury. Henriques' theory of skin burns is used for determining the spatial and temporal extent of tissue damage. The ranks of the effects of various factors were obtained. It was found that the highest ranked factor is the initial tissue temperature followed by the thermal conductivity of the epidermal layer. The effect of blood perfusion rate is ranked much below the combinations of other factors. The results from the present numerical experiment agree well with the results obtained by Palla. Sensitivity analysis of the critical exposure levels was also carried out and results are discussed. In this study, the effects of the various parameters on injury threshold were investigated. Again, the results indicate that the four parameters: thermal conductivity of the epidermis and dermis, convective heat transfer coefficient and initial tissue temperature, have a pronounced influence on assessing the burn injury threshold. It was also found that fat thermal conductivity and blood perfusion rate have no obvious effect on injury threshold. A two-dimensional analysis was further conducted to determine the sensitivity of the predicted injury to the values of frequency factor, P, and apparent activation energy, Δ E, used in the models. Part 1 of this study details the development of the computer models based on the one- and two-dimensional bioheat equations.

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