A three filament mechanistic model of musculotendon force and impedance

Matthew Millard, David W. Franklin, Walter Herzog

Abstract: The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. Across short-range perturbations the active response of muscle is well captured by a stiff spring in parallel with a light damper, a response that originates from crossbridges. The force response of muscle to longer stretches is better represented by an compliant spring that can fix its end when activated. Experimental work has made it clear that the stiffness and damping (impedance) of muscle to short-range perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model can emulate these mechanical properties. In this work, we present the visoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, the forces developed during long active stretches, as well as the classic force-velocity and force-length characteristics of muscle. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model while still retaining the ability to replicate the force-velocity and force-length properties of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the phase response of the model to low-frequency perturbations, and a mechanism to support passive force enhancement.

External IDs:doi:10.7554/elife.88344.1