Model-based analysis of wrist stiffness

The analysis of the joint stiffness has valuable outcomes either for basic research in motor neuroscience, and for clinical assessment purposes:

  • Joint stiffness is actively modulated by healthy humans during tasks requiring interaction with the environment;
  • Lost of functionality derived from neurological disorder can be quantified by changes in the joint stiffness.

The stiffness of a joint is related to the stiffness of surrounding muscles, and can be described by two components: passive and active. The passive component is an intrinsic mechanical property of the muscle that depends on its passive elastic behavior. The active component instead relates to the capabilities of the muscle’s contractile elements to modulate the applied force; it is well known that the muscle stiffness is related to the force applied by the muscle by a linear relationship (i.e. Short Range Stiffness (SRS)).

Analysis of the passive component of the wrist joint stiffness

Although experimental approaches to the computation of the passive joint stiffness have been presented, the complexity and the length of the experiments limit the number of postures in which joint stiffness can be computed.

Musculoskeletal model can extend the results of human subject experiments, however since they have not been developed for joint stiffness analysis; even the simplest models can be characterized by unstable values of stiffness.

We have developed a framework to analyze passive wrist joint stiffness in MSMs and presents a procedure to minimally modify some of the muscles parameters of a MSM to obtain stable and physiologically accurate values of passive joint stiffness.

Modulation of wrist joint stiffness by active muscular co-contraction

Previous studies measured the SRS at either a joint or at a muscle level—however, the number of conditions analyzed, in terms of both joint posture and the levels of muscular co-contraction, were limited by the complexity and length of the experiments.

We have built a framework to estimate the entire set of admissible joint stiffness values for an exhaustive set of joint posture and applied torques, so that experimental data can be justified by selection over the entire range of admissible joint stiffness values.

Figure 3: Block diagram of the computational method used for the estimation of the wrist stiffness during active muscular co-contraction

Figure 4: Entire set of admissible stiffnesses for the neutral posture of the wrist

Publications on this topic

A. Zonnino, F. Sergi, “Model-based analysis of the stiffness of the wrist joint in active and passive conditions”, pre-print submitted to Bioarxiv, 2018 (Link).
A. Zonnino, F. Sergi, “Using musculoskeletal models to estimate the passive joint stiffness”, American Society of Biomechanics Conference, Boulder CO, Aug 2017 [poster presentation], pdf.
A. Zonnino, F. Sergi, “Wrist joint stiffness modulation by active muscular co-contraction: a model based approach”, Center for Biomechanical Engineering Research Annual Symposium, May 12th, 2017 [poster presentation]


[1] K. R. S. Holzbaur, W. M. Murray, and S. L. Delp, “A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control,” Ann. Biomed. Eng., vol. 33, no. 6, pp. 829–840, 2005.

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