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Purpose <p>The measurement of passive muscle-tendon parameters (PMPs) is crucial for understanding and analyzing human movement. However, the common methods for measuring PMPs are inconsistent or involve invasive procedures.</p> Methods <p>We propose a novel noninvasive method for estimating PMPs using a direct collocated optimal control algorithm. The optimal control algorithm was employed to determine PMPs of a fully in silico musculoskeletal simulation, of a mechanical analogue, and of human subjects in vivo. To eliminate the confounding effects of force-velocity and active muscle contraction, a quasi-static knee flexion and ankle plantar flexion protocol was used for these evaluations.</p> Results <p>The simulation-based assessment resulted in predictions of muscle stiffness and tendon slack length with less than 3.5% error and tendon stiffness with less than 6% error. Secondly, using an analogue mechanical model of the human leg, we found maximum estimation errors in spring stiffness to be 9%. Lastly, in the in vivo validation method, we compared forward dynamic simulations of models with the predicted PMPs against experimental data. The average root mean square error (RMSE) for motion was found to be less than 0.56<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(^{\circ }\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∘</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>, while the RMSE for torque was 0.012 Nm/kg.</p> Conclusions <p>These results demonstrate the effectiveness and precision of our noninvasive method for estimating PMPs in knee flexors/extensors. This approach has the potential to provide valuable insights into the biomechanics of human movement and contribute to advancements in rehabilitation strategies, sports performance optimization, and injury prevention.</p>

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Muscle Tendon Passive Parameter Estimation Using Musculoskeletal Optimal Control

  • 期刊论文

  • 发表日期：

    2025年10月16日

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  • Sepehr Ramezani,
  • Joseph Dranetz,
  • Hwan Choi

摘要

Purpose

The measurement of passive muscle-tendon parameters (PMPs) is crucial for understanding and analyzing human movement. However, the common methods for measuring PMPs are inconsistent or involve invasive procedures.

Methods

We propose a novel noninvasive method for estimating PMPs using a direct collocated optimal control algorithm. The optimal control algorithm was employed to determine PMPs of a fully in silico musculoskeletal simulation, of a mechanical analogue, and of human subjects in vivo. To eliminate the confounding effects of force-velocity and active muscle contraction, a quasi-static knee flexion and ankle plantar flexion protocol was used for these evaluations.

Results

The simulation-based assessment resulted in predictions of muscle stiffness and tendon slack length with less than 3.5% error and tendon stiffness with less than 6% error. Secondly, using an analogue mechanical model of the human leg, we found maximum estimation errors in spring stiffness to be 9%. Lastly, in the in vivo validation method, we compared forward dynamic simulations of models with the predicted PMPs against experimental data. The average root mean square error (RMSE) for motion was found to be less than 0.56 \(^{\circ }\) ∘ , while the RMSE for torque was 0.012 Nm/kg.

Conclusions

These results demonstrate the effectiveness and precision of our noninvasive method for estimating PMPs in knee flexors/extensors. This approach has the potential to provide valuable insights into the biomechanics of human movement and contribute to advancements in rehabilitation strategies, sports performance optimization, and injury prevention.