Hierarchical modeling of force generation in cardiac muscle
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ORIGINAL PAPER
Hierarchical modeling of force generation in cardiac muscle François Kimmig1,2
· Matthieu Caruel3
Received: 22 December 2019 / Accepted: 10 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Performing physiologically relevant simulations of the beating heart in clinical context requires to develop detailed models of the microscale force generation process. These models, however, may reveal difficult to implement in practice due to their high computational costs and complex calibration. We propose a hierarchy of three interconnected muscle contraction models—from the more refined to the more simplified—that are rigorously and systematically related to each other, offering a way to select, for a specific application, the model that yields a good trade-off between physiological fidelity, computational cost and calibration complexity. The three model families are compared to the same set of experimental data to systematically assess what physiological indicators can be reproduced or not and how these indicators constrain the model parameters. Finally, we discuss the applicability of these models for heart simulation. Keywords Muscle modeling · Model reduction · Sliding filaments · Cross-bridges · Sarcomere
1 Introduction Mechanical modeling of the microscale muscle contraction mechanisms is an essential component for patient-specific physiologically relevant in silico heart simulations, with the aim of providing effective diagnoses and treatment planning tools. The effectiveness of the developed models relies primarily on their ability to reproduce the biological processes at the origin of the muscle contraction with a level of detail adapted to the investigated clinical questions. One of the most essential processes to be modeled is the conversion of the metabolic energy extracted from ATP turnover into mechanical work by Myosin II molecular motors in the presence of actin (Hill 1938; Alberts 2015; Barclay et al. 2010; Barclay 2015). In the muscle tissue, this myosin–actin interaction occurs inside elementary contractile units called sarcomeres, where the myosin motors bundle into thick filaments. The heads of the myosin motors, protruding from the thick filaments, can attach to specific actin-binding sites on the neighboring
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François Kimmig [email protected]
1
LMS, CNRS, École polytechnique, Institut Polytechnique de Paris, Paris, France
2
Inria, Inria Saclay-Ile-de-France, Palaiseau, France
3
MSME, CNRS, Université Paris-Est, Marne-la-Vallée, France
parallel actin (thin) filaments. This attachment is possible only after the actin filaments have been activated by calcium ions whose release in the cell cytosol triggers the contraction. While attached to actin, a myosin head produces force via a large conformational change—the power stroke—which induces a relative displacement between the myosin filaments and the actin filaments (∼ 10 nm at zero load) (Lymn and Taylor 1971; Huxley and Simmons 1971; Rayment et al. 1993a, b). The energy necessary to rech
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