Journal article
A dynamical systems analysis of afferent control in a neuromechanical model of locomotion. II. Phase asymmetry
Journal of neural engineering, v 8(6), pp 065004-065004
Dec 2011
PMID: 22058275
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We analyze a closed loop neuromechanical model of locomotor rhythm generation. The model is composed of a spinal central pattern generator (CPG) and a single-joint limb, with CPG outputs projecting via motoneurons to muscles that control the limb and afferent signals from the muscles feeding back to the CPG. In a preceding companion paper, we analyzed how the model generates oscillations in the presence or absence of feedback, identified curves in a phase plane associated with the limb that signify where feedback levels induce phase transitions within the CPG, and explained how increasing feedback strength restores oscillations in a model representation of spinal cord injury; from these steps, we derived insights about features of locomotor rhythms in several scenarios and made predictions about rhythm responses to various perturbations. In this paper, we exploit our analytical observations to construct a reduced model that retains important characteristics from the original system. We prove the existence of an oscillatory solution to the reduced model using a novel version of a Melnikov function, adapted for discontinuous systems and also comment on the uniqueness and stability of this solution. Our analysis yields a deeper understanding of how the model must be tuned to generate oscillations and how the details of the limb dynamics shape overall model behavior. In particular, we explain how, due to the feedback signals in the model, changes in the strength of a tonic supra-spinal drive to the CPG yield asymmetric alterations in the durations of different locomotor phases, despite symmetry within the CPG itself.
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Details
- Title
- A dynamical systems analysis of afferent control in a neuromechanical model of locomotion. II. Phase asymmetry
- Creators
- Lucy E Spardy - Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USASergey N Markin - Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA 19104, USANatalia A Shevtsova - Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA 19104, USABoris I Prilutsky - Center for Human Movement Studies, School of Applied Physiology, Georgia Institute of Technology, Atlanta, Georgia 30332, USAIlya A Rybak - Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA 19104, USAJonathan E Rubin - Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
- Publication Details
- Journal of neural engineering, v 8(6), pp 065004-065004
- Publisher
- Institute of Physics (IOP)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Neurobiology and Anatomy
- Web of Science ID
- WOS:000297684400006
- Scopus ID
- 2-s2.0-81855221577
- Other Identifier
- 991014878406604721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Engineering, Biomedical
- Neurosciences