Using models to advance medicine: mathematical modeling of post-myocardial infarction left ventricular remodeling

The heart is an organ with a limited capacity for regeneration and repair. In this paper, a new mathematical model is presented to study the left ventricular remodeling after myocardial infarction (MI) and followed stem cell therapeutic effort. The model represents the post-MI regeneration process of cardiomyocytes under stem cell therapy with oxygen restoration. The resulting system of nonlinear ordinary differential equations (ODE) is studied numerically in order to demonstrate the functionality and performance of the new model. The optimal time of stem cell injection for various oxygen restorations is determined. Moreover, the regeneration of cardiomyocytes is successfully correlated with improved left ventricle function observed in experiments. The proposed nonlinear ODE model is able to capture the complicated biological interactions in post-MI remodeling and can serve as a platform for in silico simulation and perturbation to optimize MI stem cell therapy.

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Mathematical Modeling of Stem Cell Therapy for Left Ventricular Remodeling After Myocardial Infarction

Buyukkahraman

Chen-Charpentier

Lei

et al. 2023

J. Mech. Med. Biol.

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Sensitivity Analysis and Uncertainty of a Myocardial Infarction Model

Chen-Charpentier,

Kojouharov

2024

Mathematics

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There is uncertainty in the results of any mathematical model due to different reasons. It is important to estimate this uncertainty. Sensitivity analysis is commonly used to estimate how the changes in the input parameters affect the solutions of the model. In this paper, we discuss different ways of performing local and global sensitivity analyses and apply them to two models: an epidemic model and a new myocardial infarction model, both based on ordinary differential equations. The first model is a simple model used to explain the ideas, while the second one shows how to apply them to a model with more state variables and parameters. We find that if the parameters are not accurately known, local sensitivity analysis can be misleading and that global sensitivity methods that sample the whole parameter space, varying all the values of the parameters at the same time, are the most reliable. We also show how the sensitivity analysis results can be used to determine the uncertainty in the results of the model. We present numerical simulations.

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Using models to advance medicine: mathematical modeling of post-myocardial infarction left ventricular remodeling

Cited by 2 publications

References 40 publications

Mathematical Modeling of Stem Cell Therapy for Left Ventricular Remodeling After Myocardial Infarction

Mathematical Modeling of Stem Cell Therapy for Left Ventricular Remodeling After Myocardial Infarction

Sensitivity Analysis and Uncertainty of a Myocardial Infarction Model

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