Modeling of temperature field inside the tissue with a blood vessel using the BEM-FDM algorithm

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

Abstrakty

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.

Słowa kluczowe

EN

biological tissue; blood vessel; thermal interactions; heat transfer

PL

tkanka biologiczna; naczynia krwionośne; interakcje termiczne; przepływ ciepła

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2012
• Tom: Vol. 11, nr 4
• Strony: 85--92
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Majchrzak E.

autor

Borowska J.

autor

Klekot J.

autor

Tarasek D.

• Institute of Computational Mechanics and Engineering, Silesian University of Technology Gliwice, Poland,

Bibliografia

• [1] Chato J., Heat transfer to blood vessels, Journal of Biomechanical Engineering 1980, 5, 102, 110-118.
• [2] Huang H.W., Chan C.L., Roemer R.B., Analytical solutions of Pennes bio-heat transfer equation with a blood vessel, Journal of Biomechanical Engineering 1994, 116, 208-212.
• [3] Shivastava D., Roemer R.B., Readressing the issue of thermally significant blood vessels using a countercurrent vessel network, Journal of Biomechanical Engineering 2006, 128, 210-216.
• [4] 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.
• [5] Majchrzak E., Mochnacki B., Analysis of bio-heat transfer in the system of blood vesselbiological tissue, Kluwer Academic Publishers 2001, 201-211.
• [6] Brebbia C.A., Telles J.C.F., Wrobel L.C., Boundary Element Techniques, Springer-Verlag, Berlin, New York 1984.
• [7] Majchrzak E., Metoda elementów brzegowych w przepływie ciepła, Wyd. Pol. Częstochowskiej, Częstochowa 2001.
• [8] Klekot J., Boundary element method for elliptic equation - determination of fundamental solution, Scientific Research of the Institute of Mathematics and Computer Science 2010, 1(9), 61-70.
• [9] Borowska J., Klekot J., Deternination of fundamental solution for diffusion equation in cylindrical co-ordinate system with temperature-dependent source term, Scientific Research of the Institute of Mathematics and Computer Science 2012, 2(11), 15-24.
• [10] Polyanin A.D., Manzhirov A.V., Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press 2007.
• [11] Majchrzak E., Tarasek D., Numerical modelling of heat transfer in a single blood vessel and surrounding biological tissue, Scientific Research of the Institute of Mathematics and Computer Science 2010, 2(9), 145-152.
• [12] Majchrzak E., Modelowanie i analiza zjawisk termicznych, Część IV, [in:] Mechanika techniczna, Tom XII: Biomechanika, ed. R. Będziński, IPPT PAN, Warszawa 2011, 223-361.