Approximating complex musculoskeletal biomechanics using multidimensional autogenerating polynomials
Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, and plan surgical interventions. Additionally, these models could also be used to intuitively link biological control signals and realistic high-dimensional articulated prosthetic limbs. However, implementing fast and accurate musculoskeletal computations that can be used to control a prosthetic limb in real-time is a challenging problem. As muscles typically span multiple joints, the wrapping over complex geometrical constraints changes their moment arms and length as a function of joint angle and, thus, their ability to generate joint torques. As a result of these biomechanical complexities, calculating these muscle state variables in real-time is a difficult simulation problem. Here, we report a method to accurately and efficiently calculate these variables for the forearm muscles that actuate the hand and wrist across multiple postures. 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 {micro}s, 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 the increase in complexity of muscles, increasing linearly instead. The similar structure and function of muscles are represented with specific invariant polynomial terms. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, suggesting that the polynomials themselves captured biologically relevant features of muscle structure and function. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models for the description of human movement.