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Analytical CPG model driven by limb velocity input generates accurate temporal locomotor dynamics.

Sergiy Yakovenko1,2,3,4,5, Anton Sobinov5, Valeriya Gritsenko2,3,4,5,6

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Spinal neural networks generate rhythm for vertebrate locomotion. This study simplifies central pattern generator (CPG) models, revealing limb speed as a key input for rhythmic movement control.

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Area of Science:

  • Neuroscience
  • Biophysics
  • Computational Biology

Background:

  • Vertebrate locomotion relies on spinal neural networks for rhythmic behaviors like walking and running.
  • Central pattern generator (CPG) networks are well-studied nonlinear dynamical systems underlying these movements.
  • Locomotion mechanisms involve leaky integration and resetting states to modulate limb phase based on body velocity.

Purpose of the Study:

  • To determine the minimal parameters required for a CPG model of locomotion.
  • To analytically solve a reduced CPG system for a single limb.
  • To investigate the role of reciprocal interactions in two-limb CPGs for heading control.

Main Methods:

  • Formulating the CPG network as a nonlinear dynamical system.
  • Reducing the system of equations for a single-limb CPG.
  • Applying two complementary analytical methods to solve the reduced system.
  • Analyzing the reciprocal interaction of two leaky integration processes for a two-limb CPG.

Main Results:

  • Analytical and empirical cycle durations for the reduced CPG model showed high similarity (R² = 0.99) across walking speeds.
  • The solution structure supports limb speed as the primary input domain for CPG networks.
  • Reciprocal interactions in a two-limb CPG model successfully captured experimental dynamics of heading direction control.

Conclusions:

  • The study validates a simplified CPG model, demonstrating the sufficiency of leaky integration with resetting states for rhythm generation.
  • Limb speed is confirmed as a critical input command for CPG networks, influencing swing and stance modulation.
  • Spinal neural pathways likely embed velocity or limb speed representations for rhythmic motor control.