Stiffness modulation of redundant musculoskeletal systems

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[![DOI](https://zenodo.org/badge/157207358.svg)](https://zenodo.org/badge/latestdoi/157207358)

`git lfs install`

`git lfs clone https://github.com/mitkof6/musculoskeletal-redundancy.git`

Description

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This project contains the source code related to the following publication:

Dimitar Stanev and Konstantinos Moustakas, Stiffness Modulation of

Redundant Musculoskeletal Systems, Journal of Biomechanics, vol. 85,

pp. 101-107, Mar. 2019, DOI:

https://doi.org/10.1016/j.jbiomech.2019.01.017

This work presents a framework for computing the limbs' stiffness using inverse

methods that account for the musculoskeletal redundancy effects. The

musculoskeletal task, joint and muscle stiffness are regulated by the central

nervous system towards improving stability and interaction with the environment

during movement. Many pathological conditions, such as Parkinson's disease,

result in increased rigidity due to elevated muscle tone in antagonist muscle

pairs, therefore the stiffness is an important quantity that can provide

valuable information during the analysis phase. Musculoskeletal redundancy poses

significant challenges in obtaining accurate stiffness results without

introducing critical modeling assumptions. Currently, model-based estimation of

stiffness relies on some objective criterion to deal with muscle redundancy,

which, however, cannot be assumed to hold in every context. To alleviate this

source of error, our approach explores the entire space of possible solutions

that satisfy the action and the physiological muscle constraints. Using the

notion of null space, the proposed framework rigorously accounts for the effect

of muscle redundancy in the computation of the feasible stiffness

characteristics. To confirm this, comprehensive case studies on hand movement

and gait are provided, where the feasible endpoint and joint stiffness is

evaluated. Notably, this process enables the estimation of stiffness

distribution over the range of motion and aids in further investigation of

factors affecting the capacity of the system to modulate its stiffness. Such

knowledge can significantly improve modeling by providing a holistic overview of

dynamic quantities related to the human musculoskeletal system, despite its

inherent redundancy.

Repository Overview

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- arm_model: simulation of simple arm model and feasible task stiffness

- feasible_joint_stiffness: calculation of the feasible joint stiffness loads,

  by accounting for musculoskeletal redundancy effects

- docker: a self contained docker setup file, which installs all dependencies

  related to the developed algorithms

Demos

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The user can navigate into the corresponding folders and inspect the source

code. The following case studies are provided in the form of interactive Jupyter

notebooks:

- [Arm Model](arm_model/model.ipynb) presents a case study using muscle space

  projection to study the response of segmental level reflexes

<!-- - [Muscle Space Projection](arm_model/muscle_space_projection.ipynb) -->

<!--   demonstrates muscle space projection in the context of segmental level -->

<!--   (reflex) modeling -->

- [Feasible Muscle Forces](arm_model/feasible_muscle_forces.ipynb) uses

  task space projection to simulate a simple hand movement, where the feasible

  muscle forces that satisfy this task are calculated and analyzed

- [Feasible Task Stiffness](arm_model/feasible_task_stiffness.ipynb) calculates

  the feasible task stiffness of the simple arm model for an arbitrary movement

- [Feasible Joint Stiffness](feasible_joint_stiffness/feasible_joint_stiffness.ipynb) calculates

  the feasible joint stiffness of an OpenSim model during walking

The .html files corresponding to the .ipynb notebooks included in the folders

contain the pre-executed results of the demos.

<a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img

alt="Creative Commons License" style="border-width:0"

src="https://i.creativecommons.org/l/by/4.0/88x31.png" /></a><br />This work is

licensed under a <a rel="license"

href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution

4.0 International License</a>.