Extracting Appropriate Mathematical Expressions Defining Moment Arm Relationships Using Symbolic Regression

Estimating tendon excursion-joint angle relationships that define moment arm variations is a critical part of biomechanical modeling. The conventional approach has been to assume a specific mathematical form for these relationships and use experimental data to regress the parameters of these assumed mathematical functions. In contrast, here we propose a novel method that uses symbolic regression to simultaneously determine both the appropriate topology, i.e. the form of the mathematical expression, and the parameter values that best fit the experimental data. We demonstrate this method with synthetic data generated using a known model of the human index finger. Cross validation with realistic noise levels shows that this method can extract the correct form and parameter values for nonlinear tendon excursion-joint angle relationships even in the presence of noise.