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Force–Length Relationship Modeling of Wrist and Finger Flexor Muscles


Medicine & Science in Sports & Exercise: November 2018 - Volume 50 - Issue 11 - p 2311–2321
doi: 10.1249/MSS.0000000000001690

Introduction 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.

Methods 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.

Results Globally, the FCR was stronger and shorter compared with FDS. The results showed that the three-dimensional relationships fitted well the experimental data (mean R2 = 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).

Conclusions 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.

1Institute of Movement Sciences, Aix-Marseille University, CNRS, ISM, Marseille, FRANCE; and

2Department of Movement, Sciences, Decathlon Sports Lab, Villeneuve d’Ascq, FRANCE

Address for correspondence: Laurent Vigouroux, Ph.D., Aix-Marseille University, Institute of Movement Sciences, CNRS UMR 7287, 13288 Marseille, France; E-mail:

Submitted for publication December 2017.

Accepted for publication June 2018.

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© 2018 American College of Sports Medicine