The Simultaneous Model-Based Estimation of Joint, Muscle, and Tendon Stiffness is Highly Sensitive to the Tendon Force-Strain Relationship

Christopher P. Cop, Kristen L. Jakubowski, Alfred C. Schouten, Bart Koopman, Eric J. Perreault, Massimo Sartori

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<italic>Objective:</italic> Accurate estimation of stiffness across anatomical levels (i.e., joint, muscle, and tendon) <italic>in vivo</italic> has long been a challenge in biomechanics. Recent advances in electromyography (EMG)-driven musculoskeletal modeling have allowed the non-invasive estimation of stiffness during dynamic joint rotations. Nevertheless, validation has been limited to the joint level due to a lack of simultaneous <italic>in vivo</italic> experimental measurements of muscle and tendon stiffness. <italic>Methods:</italic> With a focus on the triceps surae, we employed a novel perturbation-based experimental technique informed by dynamometry and ultrasonography to derive reference stiffness at the joint, muscle, and tendon levels simultaneously. Here, we propose a new EMG-driven model-based approach that does not require external joint perturbation, nor ultrasonography, to estimate multi-level stiffness. We present a novel set of closed-form equations&#x00A0;that enables the person-specific tuning of musculoskeletal parameters dictating biological stiffness, including passive force-length relationships in modeled muscles and tendons. <italic>Results:</italic> Calibrated EMG-driven musculoskeletal models estimated the reference data with average normalized root-mean-square error <inline-formula><tex-math notation="LaTeX">$\approx$</tex-math></inline-formula>&#x00A0;20&#x00A0;&#x0025;. Moreover, only when calibrated tendons were approximately four times more compliant than typically modeled, our approach could estimate multi-level reference stiffness. <italic>Conclusion:</italic> EMG-driven musculoskeletal models can be calibrated on a larger set of reference data to provide more realistic values for the biomechanical variables across multiple anatomical levels. Moreover, the tendon models that are typically used in musculoskeletal modeling are too stiff. <italic>Significance:</italic> Calibrated musculoskeletal models informed by experimental measurements give access to an augmented range of biomechanical variables that might not be easily measured with sensors alone.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalIEEE transactions on biomedical engineering
Publication statusPublished - 13 Oct 2023


  • Biomechanics
  • Electromyography
  • Impedance
  • Joint stiffness
  • Mathematical models
  • Muscle stiffness
  • Muscles
  • Musculoskeletal modeling
  • Perturbation methods
  • Tendon stiffness
  • Tendons


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