A spasticity model based on feedback from muscle force explains muscle activity during passive stretches and gait in children with cerebral palsy

Muscle spasticity is characterized by exaggerated stretch reflexes and affects about 85% of the children with cerebral palsy. However, the mechanisms underlying spasticity and its influence on gait are not well understood. Here, we first aimed to model the response of spastic hamstrings and gastrocnemii in children with cerebral palsy to fast passive stretches. Then, we evaluated how the model applied to gait. We developed three models based on exaggerated proprioceptive feedback. The first model relied on feedback from muscle fiber length and velocity (velocity-related model), the second model relied on feedback from muscle fiber length, velocity, and acceleration (acceleration-related model), and the third model relied on feedback from muscle force and its first time derivative (force-related model). The force-related model better reproduced measured hamstrings and gastrocnemii activity during fast passive stretches (coefficients of determination (R-2): 0.73 +/- 0.10 and 0.60 +/- 0.13, respectively, and root mean square errors (RMSE): 0.034 +/- 0.031 and 0.009 +/- 0.007, respectively) than the velocity-related model (R-2: 0.46 +/- 0.15 and 0.07 +/- 0.13, and RMSE: 0.053 +/- 0.051 and 0.015 +/- 0.009), and the acceleration-related model (R-2: 0.47 +/- 0.15 and 0.09 +/- 0.14, and RMSE: 0.052 +/- 0.050 and 0.015 +/- 0.008). Additionally, the force-related model predicted hamstrings and gastrocnemii activity that better correlated with measured activity during gait (cross correlations: 0.82 +/- 0.09 and 0.85 +/- 0.06, respectively) than the activity predicted by the velocity-related model (cross correlations: 0.49 +/- 0.17 and 0.71 +/- 0.22) and the acceleration-related model (cross correlations: 0.51 +/- 0.16 and 0.67 +/- 0.20). Our results therefore suggest that force encoding in muscle spindles in combination with altered feedback gains and thresholds underlie activity of spastic muscles during passive stretches and gait. Our model of spasticity opens new perspectives for studying movement impairments due to spasticity through simulation.