Active Force Generation in Cardiac Muscle Cells: Mathematical Modeling and Numerical Simulation of the Actin-Myosin Inte
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Active Force Generation in Cardiac Muscle Cells: Mathematical Modeling and Numerical Simulation of the Actin-Myosin Interaction Francesco Regazzoni1
· Luca Dede` 1 · Alfio Quarteroni1,2
Received: 18 November 2019 / Accepted: 21 May 2020 / © The Author(s) 2020
Abstract Cardiac in silico numerical simulations are based on mathematical models describing the physical processes involved in the heart function. In this review paper, we critically survey biophysically-detailed mathematical models describing the subcellular mechanisms behind the generation of active force, that is the process by which the chemical energy of ATP (adenosine triphosphate) is transformed into mechanical work, thus making the muscle tissue contract. While presenting these models, that feature different levels of biophysical detail, we analyze the trade-off between the accuracy in the description of the subcellular mechanisms and the number of parameters that need to be estimated from experiments. Then, we focus on a generalized version of the classic Huxley model, built on the basis of models available in the literature, that is able to reproduce the main experimental characterizations associated to the time scales typical of a heartbeat—such as the force-velocity relationship and the tissue stiffness in response to small steps—featuring only four independent parameters. Finally, we show how those parameters can be calibrated starting from macroscopic measurements available from experiments. Keywords Mathematical modeling · Cardiac modeling · Active stress · Sarcomeres · Crossbridges Mathematics Subject Classification (2010) 65M22 · 65Z05
1 Introduction Cardiovascular diseases represent the worldwide leading causes of death [60], with millions of cases every year. While advancements in medical practice are continuously leading to Alfio Quarteroni (Professor Emeritus) Francesco Regazzoni
[email protected] 1
MOX - Dipartimento di Matematica, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133 Milano, Italy
2
´ Mathematics Institute, Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Av. Piccard, CH-1015 Lausanne, Switzerland
F. Regazzoni et al.
the development of new therapies and to the improvement of patients care, the role of mathematical and numerical modeling and, more generally, computational medicine, is being increasingly recognized in the context of cardiovascular research. Realistic and accurate in silico models can indeed provide valuable insights on the heart function and support clinicians for personalized treatment of patients [13, 19, 25, 27, 63, 67, 75]. The development of a mathematical and numerical model of the heart function requires integrating together models describing the different physical processes involved, at different spatial scales, in the cardiac activity. The heart is indeed a multiphysics and multiscale system, whose functions is the result of multiple processes acting in concert to accomplish its main goal, that is pumping blood throughout the body, to supply organs with oxygen and nutr
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