  We propose four novel mathematical models, describing the microscopic
mechanisms of force generation in the cardiac muscle tissue, which are suitable
for multiscale numerical simulations of cardiac electromechanics. Such models
are based on a biophysically accurate representation of the regulatory and
contractile proteins in the sarcomeres. Our models, unlike most of the
sarcomere dynamics models that are available in the literature and that feature
a comparable richness of detail, do not require the time-consuming Monte Carlo
method for their numerical approximation. Conversely, the models that we
propose only require the solution of a system of PDEs and/or ODEs (the most
reduced of the four only involving 20 ODEs), thus entailing a significant
computational efficiency. By focusing on the two models that feature the best
trade-off between detail of description and identifiability of parameters, we
propose a pipeline to calibrate such parameters starting from experimental
measurements available in literature. Thanks to 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 correctly
predict the main features of force generation, including the steady-state
force-calcium and force-length relationships, the length-dependent prolongation
of twitches and increase of peak force, the force-velocity relationship.
Moreover, they correctly reproduce the Frank-Starling effect, when employed in
multiscale 3D numerical simulation of cardiac electromechanics.
