How to model a muscle’s active force–length relation: A comparative study

摘要: Abstract The active isometric force–length relation (FLR) of mammalian skeletal muscle is one the most investigated characteristics throughout biomechanics. Numerous experiments have been conducted that reveal insights on mechanisms contraction. However, entity molecular processes yet not fully understood. Modelers thus rely a rather descriptive characterization experimental findings. Starting with well-known, piece-wise linear formulation by A. Gordon, Huxley and F. Julian in 1966, variety structurally distinguishable FLR models developed. Five decades later, original idea was taken up to derive first purely physiological formulation, based sliding filament cross-bridge theory. This derivation offers us opportunity contrast broad 19 distinct models. By comparing their ability fit data, we deduce qualitative as well quantitative acceptance criteria such symmetry, normalization, complexity, interpretability. Resultant, different comprise advantages. new model overall favorable, further exponential mathematically more robust, polynomial fourth order has best optimization properties, certain computationally cheapest. work gives detailed overview, mathematical/physiological assessment existing models, serves guideline for modelers choose proper individual requirements.