Isometric Twitch Experiments & the Frank-Starling Mechanism

Isometric Twitch Experiments & the Frank-Starling Mechanism#

These examples all run the same experiment – stretch a slab of myocardial tissue to a fixed length, lock the boundaries (isometric condition), then activate it – to study how active tension depends on pre-stretch, using progressively more physiologically detailed models of active tension generation. They use a quasi-static formulation (no inertia), so no time integration scheme is required.

  • Frank-Starling Twitch (ad hoc): Reproduces the Frank-Starling mechanism with a simple, curve-fitted stretch-dependent multiplier (pulse.FrankStarlingActiveStress) applied on top of a constant activation level. Cheap and dependency-free; a good default when only the qualitative length-tension trend matters.

Cross-bridge cycling models (crossbridge)#

These replace the fitted multiplier with an actual sub-cellular force-generation model, driven by a realistic calcium transient and coupled through pulse.StabilizedActiveStress (using the model’s own active tension \(T_a\) and active stiffness \(K_a\), per [RQ21]). Length-dependent activation and, for two of the four models, a genuine force-velocity relationship, fall out of the model’s own kinetics rather than being imposed.

  • Land (2017): three-state cross-bridge cycle with curve-fitted length-dependent-activation gradients.

  • Lewalle (2024): the same cross-bridge cycle, with length dependence replaced by a mechanistic myosin OFF-state force-feedback loop.

  • RDQ18: cooperative regulatory-unit thin-filament kinetics with explicit filament overlap; no force-velocity effect.

  • RDQ20-MF: RDQ18’s regulatory-unit kinetics plus an explicit, velocity-dependent cross-bridge cycle.

  • Model Comparison: runs all four side by side under matched conditions and compares twitch shape, Frank-Starling steepness, and computational cost.

References#

[RQ21]

Francesco Regazzoni and Alfio Quarteroni. An oscillation-free fully staggered algorithm for velocity-dependent active models of cardiac mechanics. Computer Methods in Applied Mechanics and Engineering, 373:113506, 2021. doi:10.1016/j.cma.2020.113506.