Description

This folder contains OpenSim reading utilities and a script for calculating the
feasible joint stiffness for an arbitrary movement. The process is broken into
three steps:

1. Extract the symbolic representation of the muscle moment arm from the OpenSim
   model, where higher order derivatives are required for the calculation of the
   stiffness script.
2. Calculate the feasible muscle forces that satisfy the movement under study
   script.
3. Calculate the feasible joint stiffness script.

The user can navigate into the corresponding folders and inspect the source
code. The following case study us provided in the form of interactive Jupyter
notebook:

• Feasible Joint Stiffness calculates
  the feasible joint stiffness of an OpenSim model during walking

The .html file corresponding to the .ipynb notebook included in the folder
contain the pre-executed results of the demo.

Dependencies

• OpenSim: python wrappings Tested Version
• sympy: pip install sympy
• numpy: pip install numpy
• matplotlib: pip install matplotlib
• multipolyfit: pip install multipolyfit for multivariate polynomial fitting
• tqdm: pip install tqdm for progress bar
• pycddlib (pip install pycddlib) for finding the feasible muscle force set
• cython (for pycddlib)
• lrs (command line tool see /lrslib-062 folder)

Symbolic Derivation of the Muscle Moment Arm Matrix (OpenSim v4.0)

OpenSim is a framework for
modeling and simulation of musculoskeletal systems. The muscle moment arm is an
important variable for evaluating the effectiveness of a muscle to actuate a
particular joint. Calculating the muscle moment arm requires knowledge of the
muscle path and wrapping surfaces. OpenSim is restricted to evaluate the muscle
moment arm at an arbitrary configuration (e.g., with n
degrees of freedom and m muscles), lacking the information for calculating
higher order derivatives (e.g., ). Visual inspection of the polynomial
fitting is provided below.

Calculation of the Feasible Muscle Forces

The calculation of the feasible muscle forces that satisfy the movement and
physiological muscle constraints is based on the method developed in [1].

[1] D. Stanev and K. Moustakas, Modeling musculoskeletal kinematic and dynamic
redundancy using null space projection, PLoS ONE, 14(1): e0209171,
Jan. 2019, DOI: https://doi.org/10.1371/journal.pone.0209171

Calculation of the Feasible Joint Stiffness

The calculation of the feasible joint stiffness is described in more detailed
[2].

[2] D. Stanev and K. Moustakas, Stiffness Modulation of Redundant
Musculoskeletal Systems, Journal of Biomechanics}, accepted Jan. 2019

This work is
licensed under a Creative Commons Attribution
4.0 International License.