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

Journal: Procedia IUTAM

Article Title: OpenSim: a musculoskeletal modeling and simulation framework for in silico investigations and exchange

doi: 10.1016/j.piutam.2011.04.021

Figure Lengend Snippet: A canonical block-diagram of the dynamical musculoskeletal system. Inputs are muscle excitation or more generally actuator controls, and the outputs are trajectories for generalized coordinates, q, and speeds, u, as well as muscle states, z, as a function of time, t. The primary sources of system dynamics are musculotendinous actuators and the skeletal multibody dynamics. Controllers may also introduce dynamics to simulate signal transmission delay and other physiological behaviours.

Article Snippet: Objectives The primary objective of the OpenSim software is to enable the individual investigator to develop subject-specific musculoskeletal simulations and establish the desired mix between model complexity, accuracy, and performance that are appropriate for his/her study of human, animal, or robot movement.

Techniques: Blocking Assay, Introduce, Transmission Assay