Geodesic
Modelling of the cryodestruction of biological tissue
Matematičeskoe modelirovanie, Tome 23 (2011) no. 3, pp. 27-37.

Voir la notice de l'article provenant de la source Math-Net.Ru

In article new statements of two-dimensional Stefan's type boundary problems with the nonlinear sources, arising in cryosurgery are considered. The effective method of their full research for cases of long cylindrical form of a surface cooling a biological tissue of cryoinstruments is offered. Some results of the account on the computer are resulted.
Keywords: the Stefan's type problem, cryosurgery, space localization of heat, locally one-dimensional method. 
@article{MM_2011_23_3_a2,
     author = {B. K. Buzdov},
     title = {Modelling of the cryodestruction of biological tissue},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {27--37},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_3_a2/}
}
TY  - JOUR
AU  - B. K. Buzdov
TI  - Modelling of the cryodestruction of biological tissue
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 27
EP  - 37
VL  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_3_a2/
LA  - ru
ID  - MM_2011_23_3_a2
ER  - 
%0 Journal Article
%A B. K. Buzdov
%T Modelling of the cryodestruction of biological tissue
%J Matematičeskoe modelirovanie
%D 2011
%P 27-37
%V 23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_3_a2/
%G ru
%F MM_2011_23_3_a2
B. K. Buzdov. Modelling of the cryodestruction of biological tissue. Matematičeskoe modelirovanie, Tome 23 (2011) no. 3, pp. 27-37. http://geodesic.mathdoc.fr/item/MM_2011_23_3_a2/

[1] Baissalo R., Sandison G. A., Donnelly B. J., Saliken J. C., McKinnon J. G., Muldrew K., Rewcastle J. C., “A semi–empirical treatment planning model for optimization of multiprobe cryosurgery”, Phys. Med. Biol., 45 (2000), 1085–1098 | DOI

[2] Rossi M. R., Rabin Y., “Experimental verification of numerical simulations of cryosurgery with application to computerized planning”, Phys. Med. Biol., 52 (2007), 4553–4567 | DOI

[3] Rabin Y., Shitzer A., “Numerical solution of the multidimensional freezing problem during cryosurgery”, ASME J. Biomech. Eng., 120:1 (1998), 32–37 | DOI

[4] Berezovskii A. A., “Dvumernye matematicheskie modeli kriodestruktsii biotkani”, Matematicheskoe modelirovanie fizicheskikh protsessov, Sb. nauch. tr. in-t matematiki AN USSR, Kiev, 1989

[5] Mitropolskii Yu. A., Berezovskii A. A., “Zadachi Stefana s predelnym statsionarnym sostoyaniem v spetselektrometallurgii, kriokhirurgii i fizike morya”, Mat. fizika i nelinein. mekhanika, 1987, no. 7, 50–60

[6] Berezovskii A. A., “Odnomernaya lokalnaya zadacha Stefana ploskoparallelnoi kriodestruktsii biologicheskoi tkani”, Zadachi teploprovodnosti s podvizhnymi granitsami, In-t matematiki AN USSR, Kiev, 1985, 3–8 | MR

[7] Berezovskii A. A., Zhuraev K. O., Yurtin I. I., “Nestatsionarnye zadachi sfericheski-simmetrichnoi gipotermii biotkani”, Zadachi Stefana so svobodnymi granitsami, In-t matematiki AN USSR preprint, 27, Kiev, 1990, 9–20 | MR

[8] Berezovskii A. A., Leontev Yu. V., “Matematicheskoe prognozirovanie kriovozdeistviya na biologicheskie tkani”, Kriobiologiya, 3, Naukova dumka, Kiev, 1989, 7–13

[9] Budak B. M., Soloveva E. N., Uspenskii A. B., “Raznostnyi metod so sglazhivaniem koeffitsientov dlya resheniya zadachi Stefana”, ZhVM i MF, 5:5 (1965), 828–840 | MR | Zbl

[10] Samarskii A. A., Moiseenko B. D., “Ekonomichnaya skhema skvoznogo scheta dlya mnogomernoi zadachi Stefana”, ZhVM i MF, 5:5 (1965), 816–827 | MR | Zbl

[11] Budak B. M., Vasilev F. P., Uspenskii A. B., “Raznostnye metody resheniya nekotorykh kraevykh zadach tipa Stefana”, Chislennye metody v gazovoi dinamike, 4, Izd-vo MGU, M., 1965, 139–183 | MR

[12] Buzdov B. K., “O skhodimosti metoda kvazilinearizatsii v nelineinykh kraevykh zadachakh”, Nelineinye kraevye zadachi matematicheskoi fiziki i ikh prilozheniya, Institut matematiki AN Ukrainy, Kiev, 1993

[13] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989 | MR