Analysis of the parametric correlation in mathematical modeling of In vitro glioblastoma evolution using copulas
|Author/s||Ayensa Jiménez, Jacobo
Pérez Aliacar, Marina
Sanz Herrera, José Antonio
Doweidar, Mohamed Hamdy
Doblaré Castellano, Manuel
|Department||Universidad de Sevilla. Departamento de Mecánica de Medios Continuos y Teoría de Estructuras|
|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, ...
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.
|Funding agencies||Ministerio de Economía y Competitividad (MINECO). España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
Ministerio de Ciencia e Innovación (MICIN). España
|Project ID.||PGC2018-097257- B-C31
|Citation||Ayensa Jiménez, J., Pérez Aliacar, M., Randelovic, T., Sanz Herrera, J.A., Doweidar, M.H. y Doblaré Castellano, M. (2021). Analysis of the parametric correlation in mathematical modeling of In vitro glioblastoma evolution using copulas. Mathematics, 9 (27), 1-22.|