Abstract
In the past decades, several efforts have been dedicated to the construction of mathematical models describing the complex dynamics of sarcomeres. However, because of the intrinsic complexity of the phenomenon of force generation, huge computational costs are often associated with the numerical approximation of such models. For this reason, biophysically detailed models are typically not suitable in many-query settings (such as sensitivity analysis) and for multiscale numerical simulations. This lead to the development of phenomenological models, which are computationally convenient, but which are not derived from physics first principles. In this talk we present two novel biophysically detailed models for active force generation, which explicitly describe the fundamental ingredients of the force generation apparatus, yet featuring a tractable computational cost.
The proposed models are based on a biophysically accurate representation of the regulatory and contractile proteins in the sarcomeres and on some physically motivated assumptions, aimed at neglecting second-order interactions among the proteins, while focusing on the first-order ones. In this manner, the variables describing the stochastic processes associated with the states of the proteins can be partially decoupled, thus leading to a significant reduction in the number of equations. We obtain in this manner two models (according to the undertaken assumptions), consisting of systems of ODEs. Remarkably, these models do not require the time-consuming Monte Carlo method for their numerical approximation, unlike most of the sarcomere dynamics models that are available in the literature and that feature a comparable richness of detail. We propose a pipeline to calibrate the parameters of our models starting from measurements directly available from experiments. In virtue of this pipeline, we calibrate these models for room-temperature rat and for body-temperature human cells.
We show, by means of numerical simulations, that the proposed models faithfully reproduce the main features of force generation, including the steady-state cooperative force-calcium and force-length relationships, the length-dependency of the apparent calcium sensitivity, the kinetics of activation of relaxation, the length-dependent prolongation of twitches and increase of peak force, the force-velocity relationship. Finally, we show the results of multiscale numerical simulations of a human left ventricle electromechanics, based on the proposed models. We show that our models correctly predict the increased stroke volume following a raise in the preload (Frank-Starling law), whose microscopic source lies in the length-dependent mechanisms of force generation. 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.
References
- F. Regazzoni, L. Dede', A. Quarteroni. Biophysically detailed mathematical models of multiscale cardiac active mechanics. PLOS Computational Biology (2020) 16(10), e1008294 https://doi.org/10.1371/journal.pcbi.1008294
- F. Regazzoni, L. Dede', A. Quarteroni. Active contraction of cardiac cells: a reduced model for sarcomere dynamics with cooperative interactions. Biomechanics and Modeling in Mechanobiology (2018) 17, 1663--1686 https://doi.org/10.1007/s10237-018-1049-0
- F. Regazzoni, L. Dede', A. Quarteroni. Machine learning of multiscale active force generation models for the efficient simulation of cardiac electromechanics. Computer Methods in Applied Mechanics and Engineering (2020) 370, 113268 https://doi.org/10.1016/j.cma.2020.113268