Syndergaard Ian, Free Daniel B, Farina Dario, Charles Steven K
Mechanical Engineering, Brigham Young University, Provo, Utah, United States of America.
Bioengineering, Imperial College London, London, United Kingdom.
PLoS Comput Biol. 2025 Jun 30;21(6):e1013183. doi: 10.1371/journal.pcbi.1013183. eCollection 2025 Jun.
Both closed-loop models and multi-input multi-output (MIMO) models of the neuromusculoskeletal system of the upper limb are important for simulating and understanding motor control. Yet no large-scale linear neuromusculoskeletal models of the upper limb that are both closed-loop and MIMO have been developed. The primary difficulty in creating such models is choosing appropriate feedback parameters (such as feedback gains and delays), as such a collection of parameters is not available in the literature. The purpose of this work is to 1) present a method for developing MIMO models of short-loop afferent feedback and 2) offer estimates of average feedback parameter values and ranges based on the currently available literature. To this end, we combined measurements of feedback-related parameters available in 26 prior studies with known properties of system stability and behavior. As a result, we present estimated feedback gains and delays for a linear model of the upper limb with inputs into the 13 major superficial muscles and outputs to the 7 main joint degrees of freedom from the shoulder to the wrist. This model includes homonymous feedback mediated by Golgi tendon organs and both homonymous and heteronymous feedback mediated by muscle spindles. As a partial validation of muscle-spindle feedback gains, we compared the sign of the estimated gains to known differences in excess central delay between excitatory and inhibitory connections. The comparison proved correct in all 39 muscle pairs for which we had both estimated a feedback gain and found a measured excess central delay value in the literature. Furthermore, as a partial validation of delay times, we compared estimated delay times to measured innervation lengths. We found a strong fit for efferent delays (R = 0.88) and a moderate fit for afferent delays (R = 0.65). In addition, we demonstrate the effect of feedback on model behavior and present brief comparisons between this behavior and experimentally observed behaviors of the human upper limb with and without feedback.
上肢神经肌肉骨骼系统的闭环模型和多输入多输出（MIMO）模型对于模拟和理解运动控制都很重要。然而，尚未开发出同时具备闭环和MIMO特性的大规模上肢线性神经肌肉骨骼模型。创建此类模型的主要困难在于选择合适的反馈参数（如反馈增益和延迟），因为文献中没有这样一组参数。这项工作的目的是：1）提出一种开发短环传入反馈MIMO模型的方法；2）根据现有文献提供平均反馈参数值和范围的估计。为此，我们将26项先前研究中可用的与反馈相关的参数测量值与系统稳定性和行为的已知特性相结合。结果，我们给出了一个上肢线性模型的估计反馈增益和延迟，该模型的输入为13块主要表层肌肉，输出为从肩部到腕部的7个主要关节自由度。该模型包括由高尔基腱器官介导的同名反馈以及由肌梭介导的同名和异名反馈。作为对肌梭反馈增益的部分验证，我们将估计增益的符号与兴奋性和抑制性连接之间已知的额外中枢延迟差异进行了比较。在我们既估计了反馈增益又在文献中找到了测量的额外中枢延迟值的所有39对肌肉中，比较结果都是正确的。此外，作为对延迟时间的部分验证，我们将估计的延迟时间与测量的神经支配长度进行了比较。我们发现传出延迟拟合度很高（R = 0.88），传入延迟拟合度中等（R = 0.65）。此外，我们展示了反馈对模型行为的影响，并简要比较了这种行为与有反馈和无反馈情况下人类上肢实验观察到的行为。
