Each gauss point within a finite element is treated as a representative half-sarcomere. The half-sarcomere is modeled via an embedded Python version of MyoSim. MyoSim models half-sarcomeres with cross-bridge distribution techniques. In this implementation, MyoSim uses information about half-sarcomere length and intracellular calcium concentration [Ca²⁺] to calculate the active stress generated by a representative half-sarcomere. This stress is then scaled according to the density of half-sarcomeres in tissue and assigned to the local fiber direction.

Cross-bridge Kinetics

MyoSim accepts user-defined kinetic schemes. Included in the repository are the 3-state w/SRX¹ and 4-state w/SRX.

3-State w/SRX

This kinetic scheme is explained in detail in the footnoted manuscript, along with the fluxes. Briefly, myosin heads are assumed to occupy one of three states: a super-relaxed, detached state (SRX), a disordered-relaxed detached state (DRX), and an attached, post-powerstroke state (FG). Binding sites on the thin filament are either OFF or ON, and once ON they are either BOUND or UNBOUND. Binding sites are activated in the presence of intracellular calcium and are coupled to the thick filament through the J₃ flux. Together, the fluxes describe a system of ordinary differential equations to be solved at every timestep that yields the relative population in each of the states. From here, the populations in any attached state (cross-bridges) are modeled as linear springs. Note, the FG state is discretized over the working domain of a cross-bridge, with x=0 denoting an attachment to a binding site directly across from the myosin head.

4-State w/SRX

The 4 state kinetic scheme is utilized in a manuscript in preparation for submission. It includes the state from the “3-state w/SRX” scheme with the addition of a weakly bound, pre-powerstroke state. One of the results of the inclusion of this state is a viscosity given by the cross-bridges. Cross-bridges in this state only produce a net force when the population is displaced. A schematic of this kinetic scheme is shown below:

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