Accuracy of experimentally estimated muscle properties: Evaluation and improvement using a newly developed toolbox

Abstract The mechanical behaviour of a muscle-tendon complex depends on properties such as the force-length relationships, the force-velocity relationship, and the excitation dynamics. Quick-release and step-ramp experiments are commonly used to estimate these properties. The accuracy of these methods is unclear, as the actual values of these properties are unknown in experiments on real muscle. We conducted a modelling study using a Hill-type muscle-tendon complex model with literature-derived parameter values and simulated quick-release, step-ramp, and isometric experiments. From the simulated experiments, we assessed how accurately the model’s parameter values could be retrieved. Using a method traditionally used in literature, the series elastic element stiffness was underestimated by ~35%, due to the incorrect assumption that muscle fibres do not shorten during quick releases. Consequently, this yielded an overestimation of the excitation dynamics activation time constants of ~20%. We developed an improved method that accounted for muscle fibre length shortening during quick releases. Using our improved method, all parameter values closely matched their actual values. A sensitivity analysis showed that the most critical parameters were robust to perturbations in experimental data. Lastly, we compared Hill-type MTC model predictions against in situ data from three rat m. gastrocnemius medialis muscles. Predictions based on parameters from the improved method showed closer agreement than those based on the traditional method — both for quick-release, step-ramp, and isometric experiments, as well as for independent stretch-shortening cycles. In conclusion, the improved method enables more accurate estimates of muscle-tendon complex properties, addressing limitations of the traditionally used method. Competing Interest Statement The authors have declared no competing interest. Footnotes Access the code and full analysis notebook at https://edwinreuvers.github.io/publications/acc-mp-estimation/ Glossary - a - Hill constant - b - Hill constant - Minimal scale factor of b (i.e., the minimal value of bscale) - bshape - Determines the steepness of the relation between bscale and q - Fasymp - Oblique asymptote of the eccentric part of the CE force-velocity relationship - Maximum isometric CE force - kPEE - Scales the PEE stiffness - kSEE - Scales the SEE stiffness - CE length at which CE can produce maximal isometric force - PEE slack length - SEE slack length - ras - Slope of the slanted asymptote of the eccentric part of the CE force-velocity relationship - rslope - Ratio between the eccentric and concentric derivatives of - w - Determines the width of the CE force-length relationship - aact - Determines the steepness of the relation between γ and q - bact,1 - Determines together with bact,1 and bact,3 the pCa2+ level at which q = 0.5 - bact,2 - Determines together with bact,2 and bact,3 the pCa2+ level at which q = 0.5 - bact,3 - Determines together with bact,1 and bact,2 the pCa2+ level at which q = 0.5 - kCa - Relates γ to the actual Ca2+ concentration - γ0 - Minimal value of γ - q0 - Minimal value q - τact - Activation time constant of the calcium dynamics - τdeact - Deactivation time constant of the calcium dynamics