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Matematicheskaya Biologiya i Bioinformatika, 2018, Volume 13, Issue 2, Pages 376–391
DOI: https://doi.org/10.17537/2018.13.376
(Mi mbb343)
 

This article is cited in 9 scientific papers (total in 9 papers)

Mathematical Modeling

Markov chain Monte Carlo parameter estimation of the ODE compartmental cell growth model

T. Luzyaninaa, G. Bocharovb

a Institute of Mathematical Problems of Biology RAS – The Branch of Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Pushchino, Russian Federation
b Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation
References:
Abstract: We use a Markov chain Monte Carlo (MCMC) method to quantify uncertainty in parameters of the heterogeneous linear compartmental model of cell population growth, described by a system of ordinary differential equations. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set specifies the following characteristics of the kinetics of human T lymphocyte proliferation assay in vitro: the total number of live cells and dead but not disintegrated cells and the number of cells divided j times. Our goal is to compare results of the MCMC analysis of the uncertainty in the best-fit parameter estimates with the ones obtained earlier, using the variance-covariance approach, the profile-likelihood based approach and the bootstrap technique. We show that the computed posterior probability density functions are Gaussian for most of the model parameters and they are close to Gaussian ones for other parameters except one. We present posterior uncertainty limits for the model solution and new observations.
Key words: cell population dynamics, Markov chain Monte Carlo analysis, CFSE assay, heterogenous compartmental model, parameter estimation, uncertainty.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00636_а
This work was supported by the Russian Foundation for Basic Research (Grant number 17-01-00636) to G.B.
Received 14.09.2018, Published 03.10.2018
Document Type: Article
UDC: 519.245:577.27
Language: English
Citation: T. Luzyanina, G. Bocharov, “Markov chain Monte Carlo parameter estimation of the ODE compartmental cell growth model”, Mat. Biolog. Bioinform., 13:2 (2018), 376–391
Citation in format AMSBIB
\Bibitem{LuzBoc18}
\by T.~Luzyanina, G.~Bocharov
\paper Markov chain Monte Carlo parameter estimation of the ODE compartmental cell growth model
\jour Mat. Biolog. Bioinform.
\yr 2018
\vol 13
\issue 2
\pages 376--391
\mathnet{http://mi.mathnet.ru/mbb343}
\crossref{https://doi.org/10.17537/2018.13.376}
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  • This publication is cited in the following 9 articles:
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    2. Yikai Liu, Ruozheng Wu, Aimin Yang, “Research on Medical Problems Based on Mathematical Models”, Mathematics, 11:13 (2023), 2842  crossref
    3. Kernel Prieto, M. Victoria Chávez–Hernández, Jhoana P. Romero–Leiton, Jeffrey Shaman, “On mobility trends analysis of COVID–19 dissemination in Mexico City”, PLoS ONE, 17:2 (2022), e0263367  crossref
    4. Giulia Belluccini, Martín López-García, Grant Lythe, Carmen Molina-París, “Counting generations in birth and death processes with competing Erlang and exponential waiting times”, Sci Rep, 12:1 (2022)  crossref
    5. Kernel Prieto, Simone Lolli, “Current forecast of COVID-19 in Mexico: A Bayesian and machine learning approaches”, PLoS ONE, 17:1 (2022), e0259958  crossref
    6. Jhoana P. Romero-Leiton, Kernel Prieto, Daniela Reyes-Gonzalez, Ayari Fuentes-Hernandez, “Optimal control and Bayes inference applied to complex microbial communities”, MBE, 19:7 (2022), 6860  crossref
    7. K. Prieto, J. P. Romero-Leiton, “Current forecast of HIV/AIDS using Bayesian inference”, Nat. Resour. Model., 34:4, SI (2021), e12332  crossref  mathscinet  isi
    8. E. Ibarguen-Mondragon, Kernel-Prieto, S. Patricia Hidalgo-Bonilla, “A model on bacterial resistance considering a generalized law of mass action for plasmid replication”, J. Biol. Syst., 29:02 (2021), 375–412  crossref  mathscinet  zmath  isi
    9. Eisenkolb I., Jensch A., Eisenkolb K., Kramer A., Buchholz P.C.F., Pleiss J., Spiess A., Radde N.E., “Modeling of Biocatalytic Reactions: a Workflow For Model Calibration, Selection, and Validation Using Bayesian Statistics”, AICHE J., 66:4 (2020), e16866  crossref  isi  scopus
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