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    A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: I. Rhythm generation.
    J Neural Eng 2011 Dec 4;8(6):065003. Epub 2011 Nov 4.
    Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
    Locomotion in mammals is controlled by a spinal central pattern generator (CPG) coupled to a biomechanical limb system, with afferent feedback to the spinal circuits and CPG closing the control loop. We have considered a simplified model of this system, in which the CPG establishes a rhythm when a supra-spinal activating drive is present and afferent signals from a single-joint limb feed back to affect CPG operation. Using dynamical system methods, in a series of two papers we analyze the mechanisms by which this model produces oscillations, and the characteristics of these oscillations, in the closed- and open-loop regimes. In this first paper, we analyze the phase transition mechanisms operating within the CPG and use the results to explain how afferent feedback allows oscillations to occur at a wider range of drive values to the CPG than the range over which oscillations occur in the CPG without feedback, and then to comment on why stronger feedback leads to faster oscillations. Linking these transitions to structures in the phase plane associated with the limb segment clarifies how increased weights of afferent feedback to the CPG can restore locomotion after removal of supra-spinal drive to simulate spinal cord injury.

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    A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: II. Phase asymmetry.
    J Neural Eng 2011 Dec 4;8(6):065004. Epub 2011 Nov 4.
    Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
    In this paper 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 (Spardy et al 2011 J. Read More
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    Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, Pennsylvania, USA.
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    Spinal Cord Research Centre and Department of Physiology, University of Manitoba, Winnipeg, MB, R3E 3J7, Canada.
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    Modelling spinal circuitry involved in locomotor pattern generation: insights from the effects of afferent stimulation.
    J Physiol 2006 Dec 28;577(Pt 2):641-58. Epub 2006 Sep 28.
    Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA 19129, USA.
    A computational model of the mammalian spinal cord circuitry incorporating a two-level central pattern generator (CPG) with separate half-centre rhythm generator (RG) and pattern formation (PF) networks has been developed from observations obtained during fictive locomotion in decerebrate cats. Sensory afferents have been incorporated in the model to study the effects of afferent stimulation on locomotor phase switching and step cycle period and on the firing patterns of flexor and extensor motoneurones. Here we show that this CPG structure can be integrated with reflex circuits to reproduce the reorganization of group I reflex pathways occurring during locomotion. Read More