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A model of open-loop control of equilibrium position and stiffness of the human elbow joint

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Abstract

According to the equilibrium point theory, the control of posture and movement involves the setting of equilibrium joint positions (EP) and the independent modulation of stiffness. One model of EP control, the α-model, posits that stable EPs and stiffness are set open-loop, i.e. without the aid of feedback. The purpose of the present study was to explore for the elbow joint the range over which stable EPs can be set open-loop and to investigate the effect of co-contraction on intrinsic low-frequency elbow joint stiffness (K ilf). For this purpose, a model of the upper and lower arm was constructed, equipped with Hill-type muscles. At a constant neural input, the isometric force of the contractile element of the muscles depended on both the myofilamentary overlap and the effect of sarcomere length on the sensitivity of myofilaments to [Ca2+] (LDCS). The musculoskeletal model, for which the parameters were chosen carefully on the basis of physiological literature, captured the salient isometric properties of the muscles spanning the elbow joint. It was found that stable open-loop EPs could be achieved over the whole range of motion of the elbow joint and that K ilf, which ranged from 18 to 42 N m·rad−1, could be independently controlled. In the model, LDCS contributed substantially to K ilf (up to 25 N m·rad−1) and caused K ilf to peak at a sub-maximal level of co-contraction.

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Abbreviations

K ilf :

Intrinsic low-frequency joint stiffness

MEF:

Mono-articular elbow flexor

BE:

Bi-articular elbow extensor

STIM:

Muscle stimulation

q :

Active state

φe :

Elbow angle

φe :

Shoulder angle

CE:

Contractile element

SE:

Series elastic element

PE:

Parallel elastic element

F CE :

Force delivered by CE

F MAX :

Maximum isometric force

F isomn :

F CE / F MAX

l MTC :

Muscle-tendon complex length

l CE :

CE length

l CE_opt :

CE optimum length

l CE_rel :

l CE /l CE_opt

l PE :

PE length

l PE_0 :

PE slack length

l SE :

SE length

l SE_0 :

SE slack length

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Authors and Affiliations

  1. Institute for Fundamental and Clinical Human Movement Sciences, IFKB, Vrije Universiteit, Van der Boechorststraat 9, 1081 BT, Amsterdam, The Netherlands

    Dinant A. Kistemaker, Arthur J. (Knoek) Van Soest & Maarten F. Bobbert

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  1. Dinant A. Kistemaker
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  2. Arthur J. (Knoek) Van Soest
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  3. Maarten F. Bobbert
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Correspondence to Dinant A. Kistemaker.

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Kistemaker, D.A., Van Soest, A.J.(. & Bobbert, M.F. A model of open-loop control of equilibrium position and stiffness of the human elbow joint. Biol Cybern 96, 341–350 (2007). https://doi.org/10.1007/s00422-006-0120-6

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  • DOI: https://doi.org/10.1007/s00422-006-0120-6

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