Journal: PLOS Computational Biology

Article Title: A simulation framework to determine optimal strength training and musculoskeletal geometry for sprinting and distance running

doi: 10.1371/journal.pcbi.1011410

Figure Lengend Snippet: Our differentiable musculoskeletal simulator generates the derivatives of the state variables given the state variables (muscle activations a m , torque actuator activations a T , tendon forces F t , generalized positions q and velocities q ˙ ) and the decision variables (skeleton segment scaling factors p s , muscle volume scaling factors p V m u s c l e , muscle excitations e m , torque actuator excitations e T ). This is achieved by evaluating a set of dynamics equations: activation dynamics, torque actuator dynamics, muscle dynamics, and skeleton dynamics. Evaluating muscle and skeleton dynamics depends on the outputs of musculoskeletal geometry computations (i.e., muscle-tendon lengths l mt and velocities l ˙ m t and muscle moment-arm matrices R ) and on the scaled muscle parameters ( p m , scaled ). Since the scaling of the skeleton and muscle volumes are decision variables, we formulated musculoskeletal geometry computation, muscle parameter scaling and skeleton dynamics as a differentiable function of these decision variables. The dotted boxes indicate the parts of the simulator where we turned non-differentiable computation used in OpenSim and Falisse et al. into differentiable computation. Tendon forces are mapped to joint muscle torques ( τ m ) by the moment-arm matrix ( R ). Torque actuator activations are scaled to torque actuator torques ( τ T ) by a scaling factor of 150 . A contact function ( f contact ) based on the Hunt-Crossley contact model gives the generalized forces resulting from contact ( f c ).

Article Snippet: Our musculoskeletal simulator is novel since it is differentiable with respect to body-segment dimensions and the inertial properties of a model. We achieved this by (1) formulating the skeleton dynamics to be differentiable with respect to the geometries and inertial properties of the bodies and (2) approximating the computation of muscle wrapping with neural networks, using the musculoskeletal geometry of OpenSim [ ] to train the networks.

Techniques: Activation Assay