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1
Content available The BEM-FDM model of thermal processes proceeding in the domain of the human finger
Majchrzak E., Mochnacki B., Tarasek D., Dziewoński M.
Acta of Bioengineering and Biomechanics
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2015
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Vol. 17, no. 4
85--96
EN
Purpose: The problem of the numerical modeling of thermal processes proceeding in the non-homogeneous domain of the human finger is discussed. The domain considered constitutes the assembling of soft and bone tissues and the system of supplying blood vessels (arteries and veins). The mathematical description of the process analyzed corresponds to the so-called vascular models. Methods: At the stage of numerical modeling the algorithm being the composition of the boundary element method (BEM) and the finite difference method (FDM) is applied. Results: The algorithm presented allows one to determine the steady state temperature field in the finger domain in natural convection conditions. To verify the effectiveness and exactness of the method of the problem solution, the thermal imaging measurements of the finger surface temperature have been done. Conclusions: The compatibility of numerical and experimental results (the natural convection conditions) has proved to be quite satisfactory. It is possible to use the algorithm proposed for the modeling of thermal processes proceeding in the conditions of low or high ambient temperatures and the big values of heat transfer coefficients. The impact of protective clothing on the temperature field in the domain of the finger can also be analyzed.
2
Content available remote Modeling of temperature field inside the tissue with a blood vessel using the BEM-FDM algorithm
Majchrzak E., Borowska J., Klekot J., Tarasek D.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 4
85-92
EN
The thermal interactions between the blood vessel and surrounding biological tissue are analyzed. The tissue temperature is described by the Pennes equation, while the equation determining the change of blood temperature along the blood vessel is formulated on the basis of adequate energy balance. These equations are coupled by a boundary condition given at the blood vessel wall. The problem is solved using the hybrid algorithm, this means the temperature field in biological tissue is determined by means of the boundary element method (BEM), while the blood temperature is determined by means of the finite difference method (FDM). In the final part the examples of computations are presented.
3
Content available remote Numerical analysis of heat transfer in countercurrent blood flow and biological tissue
Majchrzak E., Tarasek D.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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Vol. 10, nr 2
143-153
EN
Bioheat transfer in biological tissue is described by the Pennes equation, while the change of blood temperature along the artery and vein is described by ordinary differential equations, at the same time the countercurrent blood flow is taken into account. The coupling of these equations results from the boundary conditions given by the blood vessel walls. There are two methods used here in order to calculate the temperatures along the blood vessels and across biological tissue. To solve the Pennes equation, the Multiple Reciprocity Boundary Element Method (MRBEM) is applied. It should be pointed out that this method does not require discretisation of the interior of the domain. The second method used in this paper is the Finite Difference Method (FDM) and it is applied to calculate the temperatures along the blood vessels, and it complements the previous one. It is important to note that the diameter of an artery is smaller than of a vein, which results from the physiological characteristics of these blood vessels. In the final part of the paper, the results of the computations are shown and conclusions are formulated.
4
Content available remote Numerical modeling of heat transfer in a single blood vessel and surrounding biological tissue
Majchrzak E., Tarasek D.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2010
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Vol. 9, nr 2
145-152
EN
The thermal interactions between the single blood vessel and surrounding biological tissue are analyzed. The temperature in the tissue is described by the Pennes equation, while the equation determining the change of blood temperature along the blood vessel is formulated on the basis of adequate energy balance. These equations are coupled by boundary condition given at the blood vessel wall. There are two models considered here in terms of blood vessel types. First is the supplying vessel model and the other one is traversing vessel model. Both are distinguished in the computations. The solution of the problem has been provided by means of finite difference method.
5
Content available remote Identification of internal hole parameters on the basis of boundary temperature
Majchrzak E., Tarasek D.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2009
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Vol. 8, nr 1
147-154
EN
The Laplace equation describing temperature field in 2D domain with an internal hole of circle shape supplemented by adequate boundary conditions is considered. On the basis of known temperature at the fragment of boundary the position of circle center or its radius is identified. To solve the inverse problem discussed the least square criterion is formulated, and next the gradient method coupled with the boundary element method is applied. To determine sensitivity coefficients the shape sensitivity analysis is used. In the final part of the paper the examples of computations are shown.
6
Content available remote Shape sensitivity analysis with respect to the parameters of internal hole
Majchrzak E., Tarasek D.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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Vol. 7, nr 1
129-140
EN
The Laplace equation describing temperature field in 2D domain supplemented by adequate boundary conditions is considered. The aim of investigations is to estimate the changes of temperature due to changes of shape parameter (e.g. radius or position of internal hole). To solve the problem, the implicit differentiation method of shape sensitivity analysis coupled with the boundary element method is applied.
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