# Visualizing joint force–velocity properties in musculoskeletal models

## TL;DR

This paper introduces a new visualization method to better understand how muscles and joints work together during movement.

## Contribution

The novel joint-FV visualization provides a compact way to communicate joint dynamics in musculoskeletal models.

## Key findings

- Shoulder, elbow, and wrist joints show near circular trajectories in joint-FV space when muscle forces dominate.
- Co-contraction increases the slope of joint-FV curves, providing damping and stability against perturbations.
- Joint-FV visualizations reveal how intrinsic muscle properties influence movement dynamics.

## Abstract

Musculoskeletal modelling opens windows into how muscle properties interact with neural control to govern movement. Although musculoskeletal models produce vast computational data, they lack a visual language that compactly communicates how joint dynamics relate to time-varying muscle activation, force and length change. We developed a novel representation of joint-level force–velocity (joint-FV) properties, which shows how agonist and antagonist muscles contribute to the overall joint state and its trajectory throughout a movement. Using a model of human goal-directed reaching, we used joint-FV visualizations to discern the salient joint dynamic features across joints and between different reach targets. Regardless of target, we found that the shoulder, elbow and wrist joints traversed a near circular trajectory through joint-FV space when muscle forces were dominant, but trajectories were more complex when joint-interaction forces dominated (i.e. cross-joint forces due to Coriolis, Euler and centrifugal effects). Additionally, we found that co-contraction steepens the slope of the instantaneous joint-FV curve, causing damping, which helps stabilize against small perturbations. We therefore propose that our joint-FV visualization can be used to explain the intricate features seen in musculoskeletal simulation data to reveal how intrinsic muscle properties govern the behaviour of dynamical systems.