Technical Brief

Using Torque-Angle and Torque–Velocity Models to Characterize Elbow Mechanical Function: Modeling and Applied Aspects

[+] Author and Article Information
Diane Haering

ENSAM ParisTech,
Paris F-75014, France
e-mail: diane.haering@gmail.com

Charles Pontonnier

Univ Rennes,
Rennes F-35000, France
e-mail: charles.pontonnier@ens-rennes.fr

Nicolas Bideau

Univ Rennes,
M2S, EA1274,
Rennes F-35000, France
e-mail: nicolas.bideau@univ-rennes2.fr

Guillaume Nicolas

Univ Rennes,
M2S, EA1274,
Rennes F-35000, France
e-mail: guillaume.nicolas@univ-rennes2.fr

Georges Dumont

Univ Rennes,
Rennes F-35000 France
e-mail: georges.dumont@ens-rennes.fr

1Corresponding author.

Manuscript received November 14, 2018; final manuscript received March 28, 2019; published online May 6, 2019. Assoc. Editor: Paul Rullkoetter.

J Biomech Eng 141(8), 084501 (May 06, 2019) (7 pages) Paper No: BIO-18-1495; doi: 10.1115/1.4043447 History: Received November 14, 2018; Revised March 28, 2019

Characterization of muscle mechanism through the torque-angle and torque–velocity relationships is critical for human movement evaluation and simulation. in vivo determination of these relationships through dynamometric measurements and modeling is based on physiological and mathematical aspects. However, no investigation regarding the effects of the mathematical model and the physiological parameters underneath these models was found. The purpose of the current study was to compare the capacity of various torque-angle and torque–velocity models to fit experimental dynamometric measurement of the elbow and provide meaningful mechanical and physiological information. Therefore, varying mathematical function and physiological muscle parameters from the literature were tested. While a quadratic torque-angle model seemed to increase predicted to measured elbow torque fitting, a new power-based torque–velocity parametric model gave meaningful physiological values to interpret with similar fitting results to a classical torque–velocity model. This model is of interest to extract modeling and clinical knowledge characterizing the mechanical behavior of such a joint.

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Fig. 1

Experimental setup. The participant is seated and attached to the ConTrex dynamometer in upright position with the arm along his side. The axis of the dynamometer is aligned with the epicondylitis axis with the elbow flexed at 90 deg.

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Fig. 2

Normalized torque–angle relationship as defined by the five mathematical models: normal, cosinus, and quadratic models are symmetrical; cubic and sinus-exponential are asymmetrical

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Fig. 3

Normalized torque–velocity models and constraint parameters: in the Anderson-based model (a), we find one derivative constraint at ωmax, two independent constraints at −ωmax and ω0, and two dependant constraints at ωΓ0.5 and ωΓ0.75; in our power-based model (b), we defined three derivative constraints and three independent constraints at ωmax, ωmax, and ω0, and an additional derivative constraints at ωPmax on the power-velocity relationship

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Fig. 4

Effects of torque-angle models (a) and interaction between the torque-angle and torque–velocity models (b) on average prediction errors. Shaded stars represent individuals (one shade = one subject). Black dots, blue dots and red diamonds represent the average of all individuals. Asterisks indicate significant difference between means.



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