Automated muscle path calibration with gradient-specified optimization based on moment arm

Abstract

AbstractMuscle path calibration is a fundamental step in musculoskeletal modeling, as it determines moment arm and hence the kinetic characteristics of the muscle. However, this task can be laborious, where a large number of path-related parameters must be tuned to match a high-dimensional moment arm–joint angle relation. Here, the process of parameter tuning is formulated as a least-squares problem with a moment arm–based cost function, and this optimization problem is solved with its gradient specified. To derive the gradient analytically, the cost function is first smoothed into a differentiable form by replacing the conditional statements and indifferentiable components with soft functions, and then dissembled into the product of multiple modules, whose gradients are easier to derive in separation. For calibration and validation, a 12-DoF 42-muscle shoulder–arm model is utilized to generate artificial data, and the optimization is configured with non-strict preconditions and constraints. With the specified gradient, the calibration of 42 muscles is completed in 3.7 min, and the validation error is on average 0.12 mm for 182 moment arms. The performance is further compared with two other optimization methods in four conditions. Our method offers a once-and-for-all solution to calibrating the classic obstacle-set path, and the concept employed in gradient derivation is applicable to many other cost functions.Author summaryMuscle path modeling is more than just routing a cable that visually represents the muscle, but rather it defines how moment arms vary with different joint configurations. The muscle moment arm is the factor that translates muscle force into joint moment, and this property has a huge impact on the accuracy of musculoskeletal simulation. However, it is not easy to calibrate muscle path based on moment arm, because each path is configured by various parameters while the relations between moment arm and both the parameters and joint configuration are complicated. Here, we tackle this challenge in the simple fashion of optimization, but with an emphasis on the gradient; when specified in its analytical form, optimization speed and accuracy will be greatly improved. We explain in detail how to differentiate the enormous cost function and how our optimization is configured, then we demonstrate the performance of this method by fast and accurate replication of muscle paths from a state-of-the-art shoulder–arm model. As long as the muscle is represented as a cable wrapping around obstacles, our method could free the trouble of path calibration, both for developing generic models and for customizing subject-specific models.