Force-Length Relationship Modeling of Wrist and Finger Flexor Muscles

Because the hand joints possess a broad range of motion, the muscle length can vary importantly which might result in significant variations of the muscle force-generating capacities. However, facing the complexity of this musculoskeletal system, no study has examined the effect of hand muscle length change on muscle force. This study aimed to characterize the force-length relationship of muscles involved in wrist and metacarpophalangeal flexion.

Eleven participants performed two sessions: (i) one for the wrist flexor muscles and (ii) one for the finger flexor muscles. For each session, the participants performed two maximal voluntary contractions and then two progressive isometric ramps from 0% to 100% of their maximal force capacity at five different wrist/metacarpophalangeal angles. Torque, kinematic, and electromyographic data were recorded. An ultrasound scanner was used to measure the myotendinous junction displacement of flexor carpi radialis (FCR) and flexor digitorum superficialis (FDS) during isometric contractions. A three-dimensional relationship between muscle length, force, and activation level was modeled using optimization procedure.

Globally, the FCR was stronger and shorter compared with FDS. The results showed that the three-dimensional relationships fitted well the experimental data (mean R = 0.92 ± 0.07 and 0.87 ± 0.11 for FCR and FDS, respectively). Using joint angle and EMG data, this approach allows to estimate the muscle force with low estimation errors (<9% of Fmax).

This study proposes a new method to investigate the force-length relationship by combining ultrasound measurement, musculoskeletal modeling and optimization procedures. The data and relationships provide a new insight into hand biomechanics and muscle function that could be useful for designing hand tools or surgical operations.