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Matematicheskaya Biologiya i Bioinformatika, 2016, Volume 11, Issue 2, Pages 426–444
DOI: https://doi.org/10/17537/2016.11.426
(Mi mbb271)
 

This article is cited in 8 scientific papers (total in 8 papers)

Intellectual Analisys of Data

Numerical algorithms for diffusion coefficient identification in problems of tissue engineering

A. V. Penenkoabc, S. N. Nikolaevdc, S. Golushkodb, A. V. Romashenkodc, I. A. Kirilovae

a Institute of computational mathematics and mathematical Geophysics of Siberian branch of Russian Academy of Sciences (ICM&MG SB RAS)
b Novosibirsk State University
c Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
d Institute of Computational Technologies, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
e Новосибирский научно-исследовательский институт травматологии и ортопедии им. Я.Л. Цивьяна, Новосибирск, Россия
References:
Abstract: Identification algorithms of diffusion coefficients in a specimen with tomographic images of the solution penetration dynamics are considered. With the sensitivity operator, built on the basis of adjoint equations for diffusion process model, the corresponding coefficient inverse problem is reduced to the quasilinear operator equation which is then solved by the Newton-type method with successive evaluation of r-pseudo inverse operators of increasing dimensionality. The efficiency of the constructed algorithm is tested in numerical experiments. For comparison, a gradient-based algorithm for the inverse problem solution is considered.
Key words: inverse coefficient problem, sensitivity operator, Newton-type algorithm, r-pseudoinverse operator, magnetic resonance imaging, diffusion coefficient.
Funding agency Grant number
Russian Foundation for Basic Research 15-29-04875_офи_м
Received 25.11.2016, Published 22.12.2016
Document Type: Article
UDC: 57.087
Language: Russian
Citation: A. V. Penenko, S. N. Nikolaev, S. Golushko, A. V. Romashenko, I. A. Kirilova, “Numerical algorithms for diffusion coefficient identification in problems of tissue engineering”, Mat. Biolog. Bioinform., 11:2 (2016), 426–444
Citation in format AMSBIB
\Bibitem{PenNikGol16}
\by A.~V.~Penenko, S.~N.~Nikolaev, S.~Golushko, A.~V.~Romashenko, I.~A.~Kirilova
\paper Numerical algorithms for diffusion coefficient identification in problems of tissue engineering
\jour Mat. Biolog. Bioinform.
\yr 2016
\vol 11
\issue 2
\pages 426--444
\mathnet{http://mi.mathnet.ru/mbb271}
\crossref{https://doi.org/10/17537/2016.11.426}
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  • https://www.mathnet.ru/eng/mbb271
  • https://www.mathnet.ru/eng/mbb/v11/i2/p426
  • This publication is cited in the following 8 articles:
    1. A. Penenko, V. Penenko, E. Tsvetova, A. Gochakov, E. Pyanova, V. Konopleva, “Sensitivity operator framework for analyzing heterogeneous air quality monitoring systems”, Atmosphere, 12:12 (2021), 1697  crossref  isi
    2. A. V. Penenko, Zh. S. Mukatova, A. B. Salimova, “Numerical study of the coefficient identification algorithm based on ensembles of adjoint problem solutions for a production-destruction model”, Int. J. Nonlinear Sci. Numer. Simul., 22:5 (2021), 581–592  crossref  mathscinet  zmath  isi
    3. Penenko A., “Convergence Analysis of the Adjoint Ensemble Method in Inverse Source Problems For Advection-Diffusion-Reaction Models With Image-Type Measurements”, Inverse Probl. Imaging, 14:5 (2020), 757–782  crossref  mathscinet  zmath  isi  scopus
    4. Penenko A.V., Salimova A.B., “Source Identification For the Smoluchowski Equation Using An Ensemble of Adjoint Equation Solutions”, Numer. Anal. Appl., 13:2 (2020), 152–164  crossref  mathscinet  isi  scopus
    5. V. V. Penenko, A. V. Penenko, E. A. Tsvetova, A. V. Gochakov, “Methods for studying the sensitivity of air quality models and inverse problems of geophysical hydrothermodynamics”, J. Appl. Mech. Tech. Phys., 60:2 (2019), 392–399  crossref  mathscinet  zmath  isi  scopus
    6. A. Penenko, U. Zubairova, Zh. Mukatova, S. Nikolaev, “Numerical algorithm for morphogen synthesis region identi<overline>cation with indirect image-type measurement data”, J. Bioinform. Comput. Biol., 17:1, SI (2019), 1940002  crossref  isi  scopus
    7. A. Penenko, Zh. Mukatova, A. Salimova, “Numerical solution of the coefficient inverse problem for a production-destruction model with various adjoint ensemble designs”, 2019 15Th International Asian School-Seminar Optimization Problems of Complex Systems (Opcs 2019), IEEE, 2019, 135–139  crossref  isi
    8. A. V. Penenko, “A Newton-Kantorovich Method in Inverse Source Problems For Production-Destruction Models With Time Series-Type Measurement Data”, Numer. Anal. Appl., 12:1 (2019), 51–69  mathnet  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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