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

Jacobo Ayensa-Jiménez, Marina Pérez-Aliacar, Teodora Randelovic, José Antonio Sanz-Herrera, Mohamed H. Doweidar and Manuel Doblaré
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Jacobo Ayensa-Jiménez: Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain
Marina Pérez-Aliacar: Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain
Teodora Randelovic: Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50018 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
Manuel Doblaré: Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, 50018 Zaragoza, Spain

Mathematics, 2020, vol. 9, issue 1, 1-22

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.

Keywords: copulas; design of experiments; glioblastoma multiforme; mathematical modelling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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