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Technical Brief

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

[+] Author and Article Information
Diane Haering

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

Charles Pontonnier

Univ Rennes,
CNRS, INRIA, IRISA, UMR6074,
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,
CNRS, INRIA, IRISA, UMR6074,
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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References

Bosco, C. , Belli, A. , Astrua, M. , Tihanyi, J. , Pozzo, R. , Kellis, S. , Tsarpela, O. , Foti, C. , Manno, R. , and Tranquilli, C. , 1995, “ A Dynamometer for Evaluation of Dynamic Muscle Work,” Eur. J. Appl. Physiol., 70(5), pp. 379–386. [CrossRef]
Frey-Law, L. A. , Laake, A. , Avin, K. G. , Heitsman, J. , Marler, T. , and Abdel-Malek, K. , 2012, “ Knee and Elbow 3D Strength Surfaces: Peak Torque-Angle-Velocity Relationships,” J. Appl. Biomech., 28(6), pp. 726–737. [CrossRef] [PubMed]
Gülch, R. W. , 1994, “ Force-Velocity Relations in Human Skeletal Muscle,” Int. J. Sports Med., 15(S 1), pp. S2–S10. [CrossRef] [PubMed]
Cole, G. K. , Van Den Bogert, A. J. , Herzog, W. , and Gerritsen, K. G. , 1996, “ Modelling of Force Production in Skeletal Muscle Undergoing Stretch,” J. Biomech., 29(8), pp. 1091–1104. [CrossRef] [PubMed]
Rassier, D. , MacIntosh, B. , and Herzog, W. , 1999, “ Length Dependence of Active Force Production in Skeletal Muscle,” J. Appl. Physiol., 86(5), pp. 1445–1457. [CrossRef] [PubMed]
Murray, W. M. , Delp, S. L. , and Buchanan, T. S. , 1995, “ Variation of Muscle Moment Arms With Elbow and Forearm Position,” J. Biomech., 28(5), pp. 513–515525. [CrossRef] [PubMed]
Brown, I. E. , Cheng, E. J. , and Loeb, G. E. , 1999, “ Measured and Modeled Properties of Mammalian Skeletal Muscle—II: The Effects of Stimulus Frequency on Force-Length and Force-Velocity Relationships,” J. Muscle Res. Cell Motil., 20(7), pp. 627–643. [CrossRef] [PubMed]
Zajac, F. E. , 1989, “ Muscle and Tendon: Properties, Models, Scaling, and Application to Biomechanics and Motor Control,” Crit. Rev. Biomed. Eng., 17(4), pp. 359–411. [PubMed]
Chow, J. W. , Darling, W. G. , Hay, J. G. , and Andrews, J. G. , 1999, “ Determining the Force-Length-Velocity Relations of the Quadriceps Muscles—III: A Pilot Study,” J. Appl. Biomech., 15(2), pp. 200–209. [CrossRef]
van den Bogert, A. J. , Gerritsen, K. G. , and Cole, G. K. , 1998, “ Human Muscle Modelling From a User's Perspective,” J. Electromyogr. Kinesiol. Off. J. Int. Soc. Electrophysiol. Kinesiol., 8(2), pp. 119–124. [CrossRef]
Lloyd, D. G. , and Besier, T. F. , 2003, “ An EMG-Driven Musculoskeletal Model to Estimate Muscle Forces and Knee Joint Moments In Vivo,” J. Biomech., 36(6), pp. 765–776. [CrossRef] [PubMed]
Anderson, D. E. , Madigan, M. L. , and Nussbaum, M. A. , 2007, “ Maximum Voluntary Joint Torque as a Function of Joint Angle and Angular Velocity: Model Development and Application to the Lower Limb,” J. Biomech., 40(14), pp. 3105–3113. [CrossRef] [PubMed]
Hatze, H. , 1977, “ A Myocybernetic Control Model of Skeletal Muscle,” Biol. Cybern., 25(2), pp. 103–119. [CrossRef] [PubMed]
Haering, D. , Pontonnier, C. , and Dumont, G. , 2017, “ Which Mathematical Model Best Fit the Maximal Isometric Torque-Angle Relationship of the Elbow?,” Comput. Methods Biomech. Biomed. Eng., 20(Suppl. 1), pp. 101–102. [CrossRef]
Brown, I. E. , Scott, S. H. , and Loeb, G. E. , 1996, “ Mechanics of Feline Soleus—II: Design and Validation of a Mathematical Model,” J. Muscle Res. Cell Motil., 17(2), pp. 221–233. [CrossRef] [PubMed]
van Soest, A. J. , Huijing, P. A. , and Solomonow, M. , 1995, “ The Effect of Tendon on Muscle Force in Dynamic Isometric Contractions: A Simulation Study,” J. Biomech., 28(7), pp. 801–807. [CrossRef] [PubMed]
Wickiewicz, T. L. , Roy, R. R. , Powell, P. L. , Perrine, J. J. , and Edgerton, V. R. , 1984, “ Muscle Architecture and Force-Velocity Relationships in Humans,” J. Appl. Physiol., 57(2), pp. 435–443. [CrossRef]
Yeadon, M. R. , King, M. A. , and Wilson, C. , 2006, “ Modelling the Maximum Voluntary Joint Torque/Angular Velocity Relationship in Human Movement,” J. Biomech., 39(3), pp. 476–482. [CrossRef] [PubMed]
Forrester, S. E. , Yeadon, M. R. , King, M. A. , and Pain, M. T. , 2011, “ Comparing Different Approaches for Determining Joint Torque Parameters From Isovelocity Dynamometer Measurements,” J. Biomech., 44(5), pp. 955–961. [CrossRef] [PubMed]
Haering, D. , Pontonnier, C. , Bideau, N. , Nicolas, G. , and Dumont, G. , 2017, “ Task Specific Maximal Elbow Torque Model for Ergonomic Evaluation,” XXVI Congress of the International Society of Biomechanics, Brisbane, Australia, July 23–27, p. 875.
Moore, J. S. , and Garg, A. , 1995, “ The Strain Index: A Proposed Method to Analyze Jobs for Risk of Distal Upper Extremity Disorders,” Am. Ind. Hyg. Assoc. J., 56(5), pp. 443–458. [CrossRef] [PubMed]
Haff, G. G. , and Nimphius, S. , 2012, “ Training Principles for Power,” Strength Cond. J., 34(6), p. 2. [CrossRef]
Hedlund, M. , Lindström, B. , Sojka, P. , Lundström, R. , and Olsson, C.-J. , 2015, “ Pronounced Decrease in Concentric Strength Following Stroke Due to Pre-Frontally Mediated Motor Inhibition,” Physiotherapy, 101, pp. e553–e554. [CrossRef]
Muller, A. , Haering, D. , Pontonnier, C. , and Dumont, G. , 2017, “ Non-Invasive Techniques for Musculoskeletal Model Calibration,” Congrès Français de Mécanique, Lille, France, Aug.
Staron, R. S. , Hagerman, F. C. , Hikida, R. S. , Murray, T. F. , Hostler, D. P. , Crill, M. T. , Ragg, K. E. , and Toma, K. , 2000, “ Fiber Type Composition of the Vastus Lateralis Muscle of Young Men and Women,” J. Histochem. Cytochem. Off. J. Histochem. Soc., 48(5), pp. 623–629. [CrossRef]
Sopher, R. S. , Amis, A. A. , Davies, D. C. , and Jeffers, J. R. , 2017, “ The Influence of Muscle Pennation Angle and Cross-Sectional Area on Contact Forces in the Ankle Joint,” J. Strain Anal. Eng. Des., 52(1), pp. 12–23. [CrossRef] [PubMed]
Veeger, H. E. , Yu, B. , An, K. N. , and Rozendal, R. H. , 1997, “ Parameters for Modeling the Upper Extremity,” J. Biomech., 30(6), pp. 647–652. [CrossRef] [PubMed]
Croisier, J. L. , and Crielaard, J. M. , 1999, “ Exploration Isocinétique: Analyse Des Paramètres Chiffrés,” Ann. Réadapt. Médecine Phys., 42(9), pp. 538–545. [CrossRef]
Froese, E. A. , and Houston, M. E. , 1985, “ Torque-Velocity Characteristics and Muscle Fiber Type in Human Vastus Lateralis,” J. Appl. Physiol., 59(2), pp. 309–314. [CrossRef] [PubMed]
Schantz, P. , Randal Fox, E. , Hutchison, W. , Tydén, A. , and Åstrand, P. , 1983, “ Muscle Fibre Type Distribution, Muscle Cross‐Sectional Area and Maximal Voluntary Strength in Humans,” Acta Physiol., 117(2), pp. 219–226. [CrossRef]
Hill, A. V. , 1938, “ The Heat of Shortening and the Dynamic Constants of Muscle,” Proc. R. Soc. Lond. B., 126(843), pp. 136–195. [CrossRef]
Koo, T. K. , Mak, A. F. , and Hung, L. , 2002, “ In Vivo Determination of Subject-Specific Musculotendon Parameters: Applications to the Prime Elbow Flexors in Normal and Hemiparetic Subjects,” Clin. Biomech., 17(5), pp. 390–399. [CrossRef]
Gauthier, A. , Davenne, D. , Martin, A. , and Van Hoecke, J. , 2001, “ Time of Day Effects on Isometric and Isokinetic Torque Developed During Elbow Flexion in Humans,” Eur. J. Appl. Physiol., 84(3), pp. 249–252. [CrossRef] [PubMed]
Ellenbecker, T. S. , and Roetert, E. P. , 2003, “ Isokinetic Profile of Elbow Flexion and Extension Strength in Elite Junior Tennis Players,” J. Orthop. Sports Phys. Ther., 33(2), pp. 79–84. [CrossRef] [PubMed]
Boone, D. C. , and Azen, S. P. , 1979, “ Normal Range of Motion of Joints in Male Subjects,” JBJS, 61(5), pp. 756–759. [CrossRef]
Chang, Y.-W. , Su, F.-C. , Wu, H.-W. , and An, K.-N. , 1999, “ Optimum Length of Muscle Contraction,” Clin. Biomech., 14(8), pp. 537–542. [CrossRef]
Mountjoy, K. , Morin, E. , and Hashtrudi-Zaad, K. , 2010, “ Use of the Fast Orthogonal Search Method to Estimate Optimal Joint Angle for Upper Limb Hill-Muscle Models,” IEEE Trans. Biomed. Eng., 57(4), pp. 790–798. [CrossRef] [PubMed]
Hasan, Z. , and Enoka, R. , 1985, “ Isometric Torque-Angle Relationship and Movement-Related Activity,” Exp. Brain Res., 59(3), pp. 441–450. [PubMed]
Thomis, M. A. , Van Leemputte, M. , Maes, H. H. , Blimkie, C. J. R. , Claessens, A. L. , Marchal, G. , Willems, E. , Vlietinck, R. F. , and Beunen, G. P. , 1997, “ Multivariate Genetic Analysis of Maximal Isometric Muscle Force at Different Elbow Angles,” J. Appl. Physiol., 82(3), p. 959. [CrossRef] [PubMed]
Karp, J. R. , 2001, “ Muscle Fiber Types and Training,” Strength Cond. J., 23(5), p. 21. [CrossRef]
MacIntosh, B. R. , Herzog, W. , Suter, E. , Wiley, J. P. , and Sokolosky, J. , 1993, “ Human Skeletal Muscle Fibre Types and Force: Velocity Properties,” Eur. J. Appl. Physiol., 67(6), pp. 499–506. [CrossRef]
Suter, E. , Herzog, W. , Sokolosky, J. , Wiley, J. P. , and Macintosh, B. R. , 1993, “ Muscle Fiber Type Distribution as Estimated by Cybex Testing and by Muscle Biopsy,” Med. Sci. Sports Exerc., 25(3), pp. 363–370. [CrossRef] [PubMed]
Kim, C. , Gao, Q. , Kim, W. , and Kim, W. , 1994, “ Muscle Fiber Type Distribution Estimated by Non-Invasive Technique: Based on Isometric Force and Integrated Electromyography,” Clin. Sci., 87(s1), p. 107.
Toji, H. , and Kaneko, M. , 2007, “ Effects of Aging on Force, Velocity, and Power in the Elbow Flexors of Males,” J. Physiol. Anthropol., 26(6), pp. 587–592. [CrossRef] [PubMed]

Figures

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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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