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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. Neural Eng. 8 065003), 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.

    Similar Publications

    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. Read More
    Afferent control of locomotor CPG: insights from a simple neuromechanical model.
    Ann N Y Acad Sci 2010 Jun;1198:21-34
    Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, Pennsylvania, USA.
    A simple neuromechanical model has been developed that describes a spinal central pattern generator (CPG) controlling the locomotor movement of a single-joint limb via activation of two antagonist (flexor and extensor) muscles. The limb performs rhythmic movements under control of the muscular, gravitational and ground reaction forces. Muscle afferents provide length-dependent (types Ia and II) and force-dependent (type Ib from the extensor) feedback to the CPG. Read More
    Dynamic behavior of a neural network model of locomotor control in the lamprey.
    J Neurophysiol 1996 Mar;75(3):1074-86
    Department of Zoology, University of Maryland, College Park 20742, USA.
    1. Experimental studies have shown that a central pattern generator in the spinal cord of the lamprey can produce the basic rhythm for locomotion. This pattern generator interacts with the reticular neurons forming a spinoreticulospinal loop. Read More
    Modeling the mammalian locomotor CPG: insights from mistakes and perturbations.
    Prog Brain Res 2007 ;165:235-53
    Spinal Cord Research Centre and Department of Physiology, University of Manitoba, Winnipeg, MB, R3E 3J7, Canada.
    A computational model of the mammalian spinal cord circuitry incorporating a two-level central pattern generator (CPG) with separate half-center rhythm generator (RG) and pattern formation (PF) networks is reviewed. The model consists of interacting populations of interneurons and motoneurons described in the Hodgkin-Huxley style. Locomotor rhythm generation is based on a combination of intrinsic (persistent sodium current dependent) properties of excitatory RG neurons and reciprocal inhibition between the two half-centers comprising the RG. Read More