Modélisation et simulation numérique appliquées à la prédiction de l'effet des médicaments sur le système cardiovasculaire
Sara Costa Faya · HAL (Le Centre pour la Communication Scientifique Directe) · 2024
The present thesis is devoted to the mathematical modeling and the numerical simulation of the impact of drugs on cardiovascular tissue in the context of safety pharmacology. Chemical compounds can influence arterial stiffness by affecting both the active and passive components of the vessels' wall. In the first part, we develop and validate a mathematical model against experimental results obtained in the ROTSAC experimental setup (Leloup, 2019), which investigates how arterial stiffness is influenced by vasoconstrictors and vasodilators in pharmacological studies. In this experiment, aortic segments are mounted on two parallel metal hooks and stretched with an imposed dynamic load. We develop a 3D-shell model with active fibers describing the behavior of the tissue. The model parameters involved in the constitutive laws are identified using real data by means of an optimization method. The resulting model is able to reproduce the experimental data and predict the system's behavior in different settings beyond those used for parameter estimation. This enables the assessment of different scenarios concerning the impact of the molecules on the active or passive contributions of the arterial wall. In the second part, we present a more complete mathematical model for simulating the aforementioned ex vivo setup. It includes a contact mechanics model to account for the interactions between the tissue and rigid components. The main contribution of this part is the use of a 3D-shell model and a comparison of three different numerical methods (augmented Lagrangian, Nitsche and penalty) applied to contact mechanics. To the best of our knowledge, this is the first time that Nitsche's method has been used in the context of 3D-shells.Lastly, we present a comparative analysis of artificial neural networks, statistical, and mathematical modeling methods employed in in vivo studies to examine the aging effects on dogs' cardiovascular system. In particular, arterial stiffness is one of the main factors related to the cardiovascular health status. In this part, a closed-loop 0D model for the global circulation is developed. The parameters related to the arterial stiffness and the peripheral circulation resistance are identified using real telemetry data. The calibrated model is able to assess changes in the vascular system of dogs and deliver results comparable to those obtained with machine learning or statistical methods.