Active contraction of cardiac cells: a reduced model for sarcomere dynamics with cooperative interactions

48/2017

Active contraction of cardiac cells: a reduced model for sarcomere dynamics with cooperative interactions

Wednesday 30th August 2017

Regazzoni, F.; Dedè, L.; Quarteroni, A.

We propose a reduced ODE model for the mechanical activation of cardiac myofilaments, which is based on explicit spatial representation of nearest-neighbour interactions. Our model is derived from the cooperative Markov Chain model of Washio et al. 2012, under the assumption of conditional independence of specific sets of events. This physically motivated assumption allows to drastically reduce the number of degrees of freedom, thus resulting in a significantly large computational saving. Indeed, the original Markov Chain model involves a huge number of degrees of freedom (order of 10^21) and is solved by means of the Monte Carlo method, which notoriously reaches statistical convergence in a slow fashion. With our reduced model, instead, numerical simulations can be carried out by solving a system of ODEs, reducing the computational time by more than 10000 times. Moreover, the reduced model is accurate with respect to the original Markov Chain model. We show that the reduced model is capable of reproducing physiological steady-state force-calcium and force-length relationships with the observed asymmetry in apparent cooperativity near the calcium level producing half activation. Finally, we also report good qualitative and quantitative agreement with experimental measurements under dynamic conditions.

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Biomechanics and Modeling in Mechanobiology (2018) 17, pp 1663-1686