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Matematicheskoe modelirovanie, 2016, Volume 28, Number 4, Pages 125–136 (Mi mm3725)  
This article is cited in 2 scientific papers (total in 2 papers)

Numerical modeling of the cellular necrosis front localization effect during cutaneous cryosurgery

N. A. Kudryashov, K. E. Shilnikov

National Research Nuclear University “MEPhI”, Department of Applied Mathematics
Full-text PDF (2343 kB) Citations (2)
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Abstract: In this paper we consider the problem of planning and optimization of the tumor tissue destruction during cutaneous cryosurgery operations. The method of the additional heating elements mounting is proposed as an approach to control the cellular necrosis front propagation. Mathematical modeling and Pareto optimization of calculable functions is used for the effectiveness improvement of the proposed method. An explicit scheme based on the finite volume approximation of Pennes bioheat transfer model is applied together with the enthalpy method for blurred phase change computations. The flux relaxation method is used for the stability improvement of scheme.
Keywords: cryosurgery, Pennes model, Pareto solution, finite volume method, flux relaxation method.
Funding agency Grant number
Russian Science Foundation 14-11-00258
Received: 06.05.2015
English version:
Mathematical Models and Computer Simulations, 2016, Volume 8, Issue 6, Pages 680–688
DOI: https://doi.org/10.1134/S2070048216060119
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. A. Kudryashov, K. E. Shilnikov, “Numerical modeling of the cellular necrosis front localization effect during cutaneous cryosurgery”, Mat. Model., 28:4 (2016), 125–136; Math. Models Comput. Simul., 8:6 (2016), 680–688
Citation in format AMSBIB
\Bibitem{KudShi16}
\by N.~A.~Kudryashov, K.~E.~Shilnikov
\paper Numerical modeling of the cellular necrosis front localization effect during cutaneous cryosurgery
\jour Mat. Model.
\yr 2016
\vol 28
\issue 4
\pages 125--136
\mathnet{http://mi.mathnet.ru/mm3725}
\elib{https://elibrary.ru/item.asp?id=26414255}
\transl
\jour Math. Models Comput. Simul.
\yr 2016
\vol 8
\issue 6
\pages 680--688
\crossref{https://doi.org/10.1134/S2070048216060119}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84994899472}
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  • https://www.mathnet.ru/eng/mm3725
  • https://www.mathnet.ru/eng/mm/v28/i4/p125
    • This publication is cited in the following 2 articles:
    1. K E Shilnikov, M B Kochanov, “Numerical simulation of cryosurgery in biological tissue with developed circulatory system”, IOP Conf. Ser.: Mater. Sci. Eng., 657:1 (2019), 012039  crossref
    2. N. A. Kudryashov, K. E. Shilnikov, “Multiscale numerical modeling of the spherically symmetric cryosurgery problem”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012023  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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