IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2020i1p27-d467799.html
   My bibliography  Save this article

Analysis of the Parametric Correlation in Mathematical Modeling of In Vitro Glioblastoma Evolution Using Copulas

Author

Listed:
  • Jacobo Ayensa-Jiménez

    (Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain
    Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, Spain)

  • Marina Pérez-Aliacar

    (Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain
    Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, Spain)

  • Teodora Randelovic

    (Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, Spain
    Aragón Institute of Health Research (IIS Aragón), 50009 Zaragoza, Spain)

  • José Antonio Sanz-Herrera

    (Department of Mechanics of Continuous Media and Theory of Structures, School of Engineering, University of Seville, 41092 Sevilla, Spain)

  • Mohamed H. Doweidar

    (Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain
    Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, Spain
    Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 50018 Zaragoza, Spain)

  • Manuel Doblaré

    (Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain
    Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 Zaragoza, Spain
    Aragón Institute of Health Research (IIS Aragón), 50009 Zaragoza, Spain
    Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 50018 Zaragoza, Spain)

Abstract

Modeling and simulation are essential tools for better understanding complex biological processes, such as cancer evolution. However, the resulting mathematical models are often highly non-linear and include many parameters, which, in many cases, are difficult to estimate and present strong correlations. Therefore, a proper parametric analysis is mandatory. Following a previous work in which we modeled the in vitro evolution of Glioblastoma Multiforme (GBM) under hypoxic conditions, we analyze and solve here the problem found of parametric correlation. With this aim, we develop a methodology based on copulas to approximate the multidimensional probability density function of the correlated parameters. Once the model is defined, we analyze the experimental setting to optimize the utility of each configuration in terms of gathered information. We prove that experimental configurations with oxygen gradient and high cell concentration have the highest utility when we want to separate correlated effects in our experimental design. We demonstrate that copulas are an adequate tool to analyze highly-correlated multiparametric mathematical models such as those appearing in Biology, with the added value of providing key information for the optimal design of experiments, reducing time and cost in in vivo and in vitro experimental campaigns, like those required in microfluidic models of GBM evolution.

Suggested Citation

  • Jacobo Ayensa-Jiménez & Marina Pérez-Aliacar & Teodora Randelovic & José Antonio Sanz-Herrera & Mohamed H. Doweidar & Manuel Doblaré, 2020. "Analysis of the Parametric Correlation in Mathematical Modeling of In Vitro Glioblastoma Evolution Using Copulas," Mathematics, MDPI, vol. 9(1), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:27-:d:467799
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/1/27/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/1/27/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hiroaki Kitano, 2002. "Computational systems biology," Nature, Nature, vol. 420(6912), pages 206-210, November.
    2. Eric K. Sackmann & Anna L. Fulton & David J. Beebe, 2014. "The present and future role of microfluidics in biomedical research," Nature, Nature, vol. 507(7491), pages 181-189, March.
    3. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    4. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    5. Fan, Yanqin, 1997. "Goodness-of-Fit Tests for a Multivariate Distribution by the Empirical Characteristic Function," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 36-63, July.
    6. Erika Spissu & Abdul Pinjari & Ram Pendyala & Chandra Bhat, 2009. "A copula-based joint multinomial discrete–continuous model of vehicle type choice and miles of travel," Transportation, Springer, vol. 36(4), pages 403-422, July.
    7. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Desislava Chetalova & Marcel Wollschlager & Rudi Schafer, 2015. "Dependence structure of market states," Papers 1503.09004, arXiv.org, revised Jul 2015.
    2. Zhu, Wenjun & Wang, Chou-Wen & Tan, Ken Seng, 2016. "Structure and estimation of Lévy subordinated hierarchical Archimedean copulas (LSHAC): Theory and empirical tests," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 20-36.
    3. de Carvalho, Pablo Jose Campos & Gupta, Aparna, 2018. "A network approach to unravel asset price comovement using minimal dependence structure," Journal of Banking & Finance, Elsevier, vol. 91(C), pages 119-132.
    4. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
    5. Mokni, Khaled & Mansouri, Faysal, 2017. "Conditional dependence between international stock markets: A long memory GARCH-copula model approach," Journal of Multinational Financial Management, Elsevier, vol. 42, pages 116-131.
    6. Heni Boubaker & Nadia Sghaier, 2015. "On the Dynamic Dependence between US and other Developed Stock Markets: An Extreme-value Time-varying Copula Approach," Bankers, Markets & Investors, ESKA Publishing, issue 136-137, pages 80-93, May-June.
    7. Pablo Jose Campos de Carvalho & Aparna Gupta, 2018. "Multivariate Jump Diffusion Model with Markovian Contagion," Working Papers Series 482, Central Bank of Brazil, Research Department.
    8. Bilbao-Terol, Amelia & Arenas-Parra, Mar & Cañal-Fernández, Verónica, 2016. "A model based on Copula Theory for sustainable and social responsible investments," Revista de Contabilidad - Spanish Accounting Review, Elsevier, vol. 19(1), pages 55-76.
    9. Paulo Horta & Carlos Mendes & Isabel Vieira, 2010. "Contagion effects of the subprime crisis in the European NYSE Euronext markets," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 9(2), pages 115-140, August.
    10. Heni Boubaker & Nadia Sghaier, 2014. "On the dynamic dependence between US and other developed stock markets: An extreme-value time-varying copula approach," Working Papers 2014-281, Department of Research, Ipag Business School.
    11. Heni Boubaker & Nadia Sghaier, 2014. "On the dynamic dependence between US and other developed stock markets: An extreme," Working Papers 2014-94, Department of Research, Ipag Business School.
    12. Chun-Pin Hsu & Chin-Wen Huang & Wan-Jiun Chiou, 2012. "Effectiveness of copula-extreme value theory in estimating value-at-risk: empirical evidence from Asian emerging markets," Review of Quantitative Finance and Accounting, Springer, vol. 39(4), pages 447-468, November.
    13. Baur, Dirk G., 2013. "The structure and degree of dependence: A quantile regression approach," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 786-798.
    14. Chin Man Chui & Jian Yang, 2012. "Extreme Correlation of Stock and Bond Futures Markets: International Evidence," The Financial Review, Eastern Finance Association, vol. 47(3), pages 565-587, August.
    15. Manner, Hans & Alavi Fard, Farzad & Pourkhanali, Armin & Tafakori, Laleh, 2019. "Forecasting the joint distribution of Australian electricity prices using dynamic vine copulae," Energy Economics, Elsevier, vol. 78(C), pages 143-164.
    16. Tarik Bahraoui & Nikolai Kolev, 2021. "New Measure of the Bivariate Asymmetry," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 421-448, February.
    17. Berger, Theo, 2016. "On the isolated impact of copulas on risk measurement: Asimulation study," Economic Modelling, Elsevier, vol. 58(C), pages 475-481.
    18. repec:ipg:wpaper:2014-094 is not listed on IDEAS
    19. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    20. Pushpa Narayan Rathie & Luan Carlos de Sena Monteiro Ozelim & Bernardo Borba de Andrade, 2021. "Portfolio Management of Copula-Dependent Assets Based on P ( Y < X ) Reliability Models: Revisiting Frank Copula and Dagum Distributions," Stats, MDPI, vol. 4(4), pages 1-24, December.
    21. Tian, Maoxi & El Khoury, Rim & Alshater, Muneer M., 2023. "The nonlinear and negative tail dependence and risk spillovers between foreign exchange and stock markets in emerging economies," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 82(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:27-:d:467799. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.