The award consists of a money price and a plenary lecture at the VPH2021 Summer School held in Barcelona (and online) from 7 to 11th of June 2021.
Here the full details of the winner thesis:
Mathematical Modeling and Machine Learning for the Numerical Simulation of Cardiac Electromechanics
Computer-based numerical simulations of the heart, also known as in silico cardiac models, are increasingly assuming a recognized role in the context of computational medicine and cardiology. However, the intrinsic multiscale nature of the cardiac activity, for which energy is consumed at the microscale by subcellular mechanisms to produce work at the macroscale for the whole organ, risks to harm the exploitation of computational medicine for the heart, as it raises a challenging trade-off between accuracy of the models and computational efficiency of numerical simulations. In this thesis we develop a mathematical and numerical multiscale model of cardiac electromechanics, oriented towards large-scale simulations, wherein the mechanisms of active force generation are described by means of new biophysically motivated models. In these subcellular models, we explicitly represent only the most relevant interactions among the proteins involved in the force generation process, while we neglect secondary interactions, but still leading to accurate results — that we validate against experimental data — obtained with a drastic reduction of computational cost with respect to the models currently available in literature. The physiological goodness of the response of these models makes their use promising for studying the pharmacological action in the context of pathologies altering contractile capacity at cellular level, and for studying the organ-level effects of cellular-level alterations and the corresponding feedbacks.
As it is crucial to multiscale electromechanical modeling, we establish the link between the variables describing force generation at the microscale and those describing the strain and the stress of the tissue at the macroscale. This allows to couple, in a mathematically sound manner, the subcellular models proposed in this thesis — characterized by a stochastic behavior — with models for cardiac electrophysiology and for passive and active mechanics — based on a deterministic formalism — written as systems of Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs).
In this thesis we also combine the proposed subcellular models with a newly developed Machine Learning algorithm, in order to speedup their numerical resolution in the multiscale electromechanical model. Specifically, a reduced model based on Artificial Neural Networks (ANNs) is trained from a collection of simulations generated by means of biophysically detailed force generation models. In this manner, the computationally demanding training phase can be performed offline, with the advantage of a huge speedup when the trained ANN-based model is exploited in replacement of the high-fidelity model used to generate the training data. Overall, our multiscale model for cardiac electromechanics achieves an excellent balance between accuracy of the models, their rigorousness and computational efficiency in large-scale simulations.
Francesco Regazzoni got his PhD in 2020 at Politecnico di Milano, under the supervision of Prof. Alfio Quarteroni. He has been a visiting scholar at Inria Saclay Île-De-France and Pennsylvania State University. He is currently Junior Assistant Professor in Numerical Analysis at Politecnico di Milano. His research interests cover the mathematical modeling and numerical approximation of multiscale problems, in particular related to cardiovascular modeling. His research also focuses on combining Machine Learning with numerical analysis and reduced order modeling.