Biological Cybernetics

, Volume 96, Issue 3, pp 341–350

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

  • Dinant A. Kistemaker
  • Arthur J. (Knoek) Van Soest
  • Maarten F. Bobbert
Original Paper

DOI: 10.1007/s00422-006-0120-6

Cite this article as:
Kistemaker, D.A., Van Soest, A.J.. & Bobbert, M.F. Biol Cybern (2007) 96: 341. doi:10.1007/s00422-006-0120-6
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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 (Kilf). 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 Kilf, which ranged from 18 to 42 N m·rad−1, could be independently controlled. In the model, LDCS contributed substantially to Kilf (up to 25 N m·rad−1) and caused Kilf to peak at a sub-maximal level of co-contraction.

List of Symbols

Kilf

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

FCE

Force delivered by CE

FMAX

Maximum isometric force

Fisomn

FCE / FMAX

lMTC

Muscle-tendon complex length

lCE

CE length

lCE_opt

CE optimum length

lCE_rel

lCE /lCE_opt

lPE

PE length

lPE_0

PE slack length

lSE

SE length

lSE_0

SE slack length

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Dinant A. Kistemaker
    • 1
  • Arthur J. (Knoek) Van Soest
    • 1
  • Maarten F. Bobbert
    • 1
  1. 1.Institute for Fundamental and Clinical Human Movement Sciences, IFKBVrije UniversiteitAmsterdamThe Netherlands