Geodesic
On one model of freezing biological living tissues
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 14-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we present a new mathematical model of freezing a living biological tissue by a cryoapplicator and a method for its numerical study based on the use of local one-dimensional difference schemes. The model is a three-dimensional three-phase boundary-value Stefan-type problem and has applications in cryosurgery. A special nonlinear dependence of heat sources on the unknown temperature field allows one to take into account the spatial effect of heat localization.
Keywords: mathematical modeling, cryomedicine, cryobiology, Stefan problem. 
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B. K. Buzdov. On one model of freezing biological living tissues. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 14-18. http://geodesic.mathdoc.fr/item/INTO_2021_190_a1/

[1] Berezovskii A. A., “Odnomernaya lokalnaya zadacha Stefana ploskoparallelnoi kriodestruktsii biologicheskoi tkani”, Zadachi teploprovodnosti s podvizhnymi granitsami, In-t mat. AN USSR, Kiev, 1985, 38 | Zbl

[2] Berezovskii A. A., Leontev Yu. V., “Matematicheskoe prognozirovanie kriovozdeistviya na biologicheskie tkani”, Kriobiologiya, Naukova dumka, Kiev, 1989 | Zbl

[3] Budak B. M., Soloveva E. N., Uspenskii A. B., “Raznostnyi metod so sglazhivaniem koeffitsientov dlya resheniya zadachi Stefana”, Zh. vychisl. mat. mat. fiz., 5 (1965), 828840

[4] Buzdov B. K., “Modelirovanie kriodestruktsii biologicheskoi tkani”, Mat. model., 23:3 (2011), 2737 | MR

[5] Buzdov B. K., “Chislennoe issledovanie odnoi dvumernoi matematicheskoi modeli s peremennym koeffitsientom teploobmena, voznikayuschei v kriokhirurgii”, Sib. zh. industr. mat., 20:4 (2017), 2228 | MR

[6] Zhmakin A. I., “Fizicheskie osnovy kriobiologii”, Usp. fiz. nauk., 178:3 (2008), 243266

[7] Samarskii A. A., “Lokalno-odnomernye raznostnye skhemy na neravnomernykh setkakh”, Zh. vychisl. mat. mat. fiz., 3:3 (1963), 431466

[8] Pennes H. H., “Analysis of tissue and arterial blood temperature in the resting human forearm”, J. Appl. Physiol., 1 (1948), 93102 | DOI