Normalized Isometry Index as a bounded force-velocity metric for assessing mechanical stimulus in isometric and low-velocity muscle contractions

Quasi-isometric high intensity training was proven to induce hypertrophy and type II to type I muscle fiber shift. While advances in musculoskeletal modeling enable detailed muscle force estimation, a stable metric for quantifying mechanical stimulus under isometric and low-velocity conditions remains lacking. The question arises weather a stable, bounded force-velocity metric can be formulated to accurately quantify mechanical stimulus under isometric and low-velocity conditions in musculoskeletal modeling. The proposed index was mathematically and empirically evaluated to determine its structural validity and physiological relevance. Optimization of the velocity attenuation coefficient was grounded in literature describing contraction-velocity-dependent muscle fiber adaptations, ensuring physiological plausibility. Redundancy was tested with the use of exemplary experimental data derived from musculoskeletal modeling. Analytical assessment confirmed monotonicity with respect to force, boundedness across the velocity domain, numerical stability, and a coherent force-velocity interaction structure. Correlation analyses demonstrated significant yet non-redundant associations with the component variables, supporting construct validity. Isometry Index avoided singularities at low velocities and provided a stable, interpretable representation of force-velocity behavior under both isometric and quasi-isometric conditions. The index was verified to provide a stable, interpretable, and physiologically grounded unitless scalar measure of force-velocity interactions in near-isometric conditions.