Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, plan surgical interventions, or control realistic high-dimensional articulated prosthetic limbs. If the models are sufficiently accurate, they may embed complex relationships within the sensorimotor system. These potential benefits are limited by the challenge of implementing fast and accurate musculoskeletal computations. A typical hand muscle spans over 3 degrees of freedom (DOF), wrapping over complex geometrical constraints that change its moment arms and lead to complex posture-dependent variation in torque generation. Here, we report a method to accurately and efficiently calculate musculotendon length and moment arms across all physiological postures of the forearm muscles that actuate the hand and wrist. Then, we use this model to test the hypothesis that the functional similarities of muscle actions are embedded in muscle structure. The posture dependent muscle geometry, moment arms and lengths of modeled muscles were captured using autogenerating polynomials that expanded their optimal selection of terms using information measurements. The iterative process approximated 33 musculotendon actuators, each spanning up to 6 DOFs in an 18 DOF model of the human arm and hand, defined over the full physiological range of motion. Using these polynomials, the entire forearm anatomy could be computed in <10 μs, which is far better than what is required for real-time performance, and with low errors in moment arms (below 5%) and lengths (below 0.4%). Moreover, we demonstrate that the number of elements in these autogenerating polynomials does not increase exponentially with increasing muscle complexity of muscles; complexity increases linearly instead. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, indicating the high accuracy of approximating models. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models to describe human movement.

肌肉骨骼系统的计算模型是用于研究人体运动，量化伤害和疾病的影响，计划外科手术干预或控制现实的高维关节假肢的科学工具。如果模型足够准确，则它们可能会在感觉运动系统中嵌入复杂的关系。这些潜在的好处受到实现快速，准确的肌肉骨骼计算的挑战的限制。典型的手部肌肉跨度超过3个自由度（DOF），包裹在复杂的几何约束上，从而改变了其力矩臂并导致扭矩产生中与姿势有关的复杂变化。这里，我们报告了一种方法，可以准确有效地计算促动手和腕的前臂肌肉所有生理姿势中的肌腱长度和弯臂。然后，我们使用该模型来检验肌肉动作功能相似性嵌入肌肉结构的假设。使用自动生成的多项式来捕获与姿势有关的肌肉几何形状，弯矩臂和建模肌肉的长度，这些多项式可以使用信息测量扩展其对术语的最佳选择。迭代过程近似于33个musculotendon执行器，在整个人的生理动作范围内，每个执行器在人手臂和手的18 DOF模型中跨越多达6个DOF。使用这些多项式，可以在<10μs的时间内计算出整个前臂解剖结构，这远远优于实时性能要求，并且力矩臂（低于5％）和长度（低于0.4％）的错误率低。此外，我们证明了这些自动生成多项式中元素的数量不会随着肌肉复杂性的增加而呈指数增加；相反，复杂度线性增加。仅使用多项式项的降维会导致由具有相似功能的肌肉组成的簇，这表明近似模型的准确性很高。我们建议，这种新颖的描述肌肉骨骼生物力学的方法可能会进一步改善详细和可扩展的模型来描述人类运动的应用。我们证明，在这些自动生成的多项式中，元素的数量不会随着肌肉复杂性的增加而呈指数增长；相反，复杂度线性增加。仅使用多项式项的降维会导致由具有相似功能的肌肉组成的簇，这表明近似模型的准确性很高。我们建议，这种新颖的描述肌肉骨骼生物力学的方法可能会进一步改善详细和可扩展的模型来描述人类运动的应用。我们证明，在这些自动生成的多项式中，元素的数量不会随着肌肉复杂性的增加而呈指数增长；相反，复杂度线性增加。仅使用多项式项的降维会导致由具有相似功能的肌肉组成的簇，这表明近似模型的准确性很高。我们建议，这种新颖的描述肌肉骨骼生物力学的方法可能会进一步改善详细和可扩展的模型来描述人类运动的应用。