Numerical analysis of heat transfer in countercurrent blood flow and biological tissue

• Autorzy: Majchrzak E. , Tarasek D.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

numerical analysis; biological tissue; heat transfer

PL

analiza numeryczna; tkanka biologiczna; wymiana ciepła

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2011
• Tom: Vol. 10, nr 2
• Strony: 143--153
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Majchrzak E.

autor

Tarasek D.

• Silesian University of Technology, Gliwice, Poland,

Bibliografia

• [1] Pennes H.H., Analysis of tissue and arterial blood temperatures in the resting human forearm, Journal of Applied Physiology 1948, 1, 93-122.
• [2] Majchrzak E., Modelowanie i analiza zjawisk termicznych, Część IV, [w:] Mechanika Techniczna, Tom XII: Biomechanika, ed. R. Będziński, IPPT PAN, Warszawa 2011, 223-361.
• [3] Majchrzak E., Mochnacki B., Numerical model of heat transfer between blood vessel and biological tissue, Computer Assisted Mechanics and Engineering Sciences 1999, 6, 439-447.
• [4] Majchrzak E., Mochnacki B., Numerical modeling of heat transfer between blood vessels (artery and vein) and biological tissue, IV European Conference on Computational Mechanics, Paris 2010, 16-21 May.
• [5] Paruch M., Majchrzak E., Identification of tumor region parameters using evolutionary algorithm and multiple reciprocity boundary element method, Engineering Applications of Artificial Intelligence 2007, 20, 647-655.
• [6] Paruch M., Dziewoński M., Kokot G., Temperature determination in the tissue with a tumor using MRBEM and FEM, Scientific Research of the Institute of Mathematics and Computer Science 2005, 1(4), 195-203.
• [7] Mochnacki B., Lara-Dziembek S., Weighted residual method as a tool of FDM algorithm construction, Scientific Research of the Institute of Mathematics and Computer Science 2010, 1(10), 147-155.
• [8] Brinck H., Werner J., Estimation of the thermal effect of the blood flow in a branching countercurrent network using three dimensional vascular model, Journal of Biomechanical Engineering 1994, 116, 324-330.