Geodesic
Numerical simulation of cryosurgeries and optimization of probe placement
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1611-1622 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Numerical simulation and optimization of cryosurgeries are considered. The Stefan problem that describes thermal processes running in the course of surgery is solved numerically. The finite volume method and enthalpy approach are used. The problem of optimization of the probe positions is solved to improve the surgery efficiency. The optimization problem is solved using nonparametric multiple criteria optimization techniques. 
@article{ZVMMF_2015_55_9_a15,
     author = {N. A. Kudryashov and K. E. Shilnikov},
     title = {Numerical simulation of cryosurgeries and optimization of probe placement},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1611--1622},
     year = {2015},
     volume = {55},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a15/}
}
TY  - JOUR
AU  - N. A. Kudryashov
AU  - K. E. Shilnikov
TI  - Numerical simulation of cryosurgeries and optimization of probe placement
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1611
EP  - 1622
VL  - 55
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a15/
LA  - ru
ID  - ZVMMF_2015_55_9_a15
ER  - 
%0 Journal Article
%A N. A. Kudryashov
%A K. E. Shilnikov
%T Numerical simulation of cryosurgeries and optimization of probe placement
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1611-1622
%V 55
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a15/
%G ru
%F ZVMMF_2015_55_9_a15
N. A. Kudryashov; K. E. Shilnikov. Numerical simulation of cryosurgeries and optimization of probe placement. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1611-1622. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a15/

[1] Jemal A., Tiwari R. C., Murray T. et al., “Cancer statistics”, CA Cancer J. Clin., 54 (2004), 8–29 | DOI

[2] Sakr W. A., Grignon D. J., Crissman J. D. et al., “High grade prostatic intraepithelial neoplasia (HGPIN) and prostatic adenocarcinoma between the ages of 20–69: an autopsy study of 249 cases”, In Vivo, 1994, no. 8, 439–443

[3] Tsyganov D. I., Kriomeditsina, protsessy i apparaty, Sains-press, M., 2011

[4] Cooper I. S., “Cryobiology as viewed by the surgeon”, Cryobiology, 1964, no. 1, 44–54 | DOI

[5] Smith D. J., Fahssi W. M., Swanlund D. J., Bischof J. C., “A parametric study of freezing injury in AT-1 rat prostate tumor cells”, Cryobiology, 39 (1999), 13–28 | DOI

[6] Wan R., Liu Z., Muldrew K., Rewcastle J., “A Finite Element Model for Ice Ball Evolution in a Multi-probe Cryosurgery”, Comp. Meth. Biomechanics and Biomedical Eng., 6:3 (2003), 197–208 | DOI

[7] Deljou S. H., Haghipour S., Bayat A., “Intelligent planning for cryoprobe placement during cryosurgery”, Life Sc. Journal, 10, Special Issue 3 (2013), 552–557

[8] Kudryashov N. A., Shilnikov K. E., “O raschete protsessov kriovozdeistviya na oblast tela s uchetom vliyaniya konvektsii krovi”, Vestn. Natsionalnogo Issledovatelskogo Yadernogo Universiteta “MIFI”, 3:3 (2014), 329–335 | Zbl

[9] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Izd. 2-e, Gostekhizdat, M., 1953

[10] Samarskii A. A., “Uravneniya parabolicheskogo tipa s razryvnymi koeffitsientami i raznostnye metody i resheniya”, Tr. Vsesoyuzn. soveschaniya po differents. uravneniyam (Erevan, noyabr 1958), Izd-vo AN ArmSSR, Erevan, 1960, 148–160

[11] Samarskii A. A., Moiseenko B. D., “Ekonomichnaya skhema skvoznogo scheta dlya mnogomernoi zadachi Stefana”, Zh. vychisl. matem. i matem. fiz., 5:5 (1965), 816–827 | MR

[12] Shilnikov E. V., “Modelirovanie techenii vyazkogo gaza na osnove KGD sistemy uravnenii na neortogonalnykh indeksnykh setkakh”, Preprinty IPM im. M. V. Keldysha, 2014, 033, 20 pp. http://library.keldysh.ru/preprint.asp?id=2014-33

[13] Stadler W., “A Survey of multicriteria optimization, or the vector maximum problem”, J. Optimizat. Theory and Applicat., 29 (1979), 1–52 | DOI | MR | Zbl

[14] Stadler W., Applications of multicriteria optimization in engineering and the sciences (A Survey), Multiple Criteria Decision Making Past Decade and Future Trends, ed. M. Zeleny, JAI Press, Greenwich, Connecticut, 1984

[15] Steuer R. E., Multicriteria optimization: theory, computation and application, John Wiley and Sons (WIE), New York, 1985 | MR