Geodesic
Models of cooling and freezing of living biological tissues with a flat ruler applicator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 30-36.

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

In this work, we construct new mathematical models of cooling and freezing of living biological tissue with a flat, long ruler applicator located on its surface. The models are two-dimensional boundary-value problems (including Stefan-type problems) and have applications in cryosurgery. The method of numerical study of these problems is based on smoothing discontinuous functions and applying locally one-dimensional difference schemes to “smoothed” problems without explicitly identifying the boundaries of the influence of cold and the boundaries of the phase transition.
Keywords: mathematical model, cryomedicine, Stefan type problem 
@article{INTO_2024_232_a2,
     author = {B. K. Buzdov},
     title = {Models of cooling and freezing of living biological tissues with a flat ruler applicator},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {30--36},
     publisher = {mathdoc},
     volume = {232},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2024_232_a2/}
}
TY  - JOUR
AU  - B. K. Buzdov
TI  - Models of cooling and freezing of living biological tissues with a flat ruler applicator
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2024
SP  - 30
EP  - 36
VL  - 232
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2024_232_a2/
LA  - ru
ID  - INTO_2024_232_a2
ER  - 
%0 Journal Article
%A B. K. Buzdov
%T Models of cooling and freezing of living biological tissues with a flat ruler applicator
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2024
%P 30-36
%V 232
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2024_232_a2/
%G ru
%F INTO_2024_232_a2
B. K. Buzdov. Models of cooling and freezing of living biological tissues with a flat ruler applicator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 30-36. http://geodesic.mathdoc.fr/item/INTO_2024_232_a2/

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

[2] Berezovskii A. A., Prostranstvennaya lokalizatsiya kriovozdeistviya na biologicheskie tkani / Preprint # 87.60, In-t matematiki AN USSR, Kiev, 1987

[3] Berezovskii A. A., Leontev Yu. V., “Matematicheskoe prognozirovanie kriovozdeistviya na biologicheskie tkani”, Kriobiologiya., 1989, no. 3, 7–13

[4] Budak B. M., Soloveva E. N., Uspenskii A. B., Zh. vychisl. mat. mat. fiz., 5 (Raznostnyi metod so sglazhivaniem koeffitsientov dlya resheniya zadachi Stefana), 828–840 | MR | Zbl

[5] Buzdov B. K., “Modelirovanie kriodestruktsii biologicheskoi tkani”, Mat. model., 23:3 (2011), 22–28 | MR

[6] Buzdov B. K., “Chislennoe issledovanie odnoi dvumernoi matematicheskoi modeli s peremennym koeffitsientom teploobmena, voznikayuschei v kriokhirurgii”, Sib. zh. industr. mat., 20:4 (2017), 22–28 | MR | Zbl

[7] Buzdov B. K., “Ob odnoi dvumernoi kraevoi zadache tipa Stefana, voznikayuschei v kriokhirurgii”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 167 (2019), 20–26 | MR

[8] Zhmakin A. I., “Fizicheskie osnovy kriobiologii”, Usp. fiz. nauk., 178:3 (2008), 243–266 | DOI

[9] Samarskii A. A., “Lokalno-odnomernye raznostnye skhemy na neravnomernykh setkakh”, Zh. vychisl. mat. mat. fiz., 3:3 (1963), 431–466

[10] Samarskii A. A., Moiseenko B. D., “Ekonomicheskaya skhema skvoznogo scheta dlya mnogomernoi zadachi Stefana”, Zh. vychisl. mat. mat. fiz., 5:5 (1965), 816–827

[11] Pennes H. H., “Analysis of tissue and arterial blood temperature in the resting human forearm”, J. Appl. Physiol., 1 (1948), 93–102 | DOI