A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: I. Rhythm generation

Abstract

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 systems 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 to comment on why stronger feedback leads to faster oscillations. Linking these transitions to structure 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.

A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: II. Phase asymmetry

“…This phase begins when the limb trajectory crosses from below to above the q -axis and is terminated when RG - F turns on. As described in [13], Section 3.3, we can define a curve in the limb phase plane such that when the limb trajectory hits this curve, the extensor component of the CPG becomes inactive and the flexor component activates. This definition can be made because the transition within the CPG occurs through an escape of In - F from its silent phase, causing it to shut down RG - E and In - E and hence allowing RG - F to activate.…”

“…Importantly, the resulting speed increase occurs through a decrease in the duration of the stance phase, when the limb is in contact with the ground, and is independent of the swing phase, when the limb moves without ground contact [11, 12]. This asymmetric response contrasts with fictive locomotion results, which can involve either a dominance of the flexor or extensor phase or neither [6], and indeed, the speed of model oscillations when feedback is removed changes symmetrically, with equal changes in extensor and flexor components with changes in drive [10, 7, 13]. A major goal of this paper is to analyze how the feedback components of the closed-loop neuromechanical model lead to an asymmetric frequency response.…”

“…In the companion article to this one, we investigated the mechanisms underlying oscillatory behavior within the model CPG both in the presence and in the absence of feedback [13]. Without feedback, a slow-fast decomposition analysis revealed that the intrinsic structure of a set of rhythm generator ( RG ) neurons within the CPG allows oscillations to occur through RG escape for a sufficiently large supra-spinal drive.…”

Muscle Spindles and Locomotor Control-An Unrecognized Falls Determinant?

“…Spardy et al [44] has further shown how muscle afferent feedback allows oscillations to the central pattern generator structures to occur at a wider range of drive values than the range over which oscillations occur without feedback. They specifically noted stronger feedback led to faster oscillations and argued that this implied it may be possible to restore locomotion even if the supra-spinal drive to the stimulation was applied to brainstem mesencephalic locomotor region in decerebrate animals.…”

Morphology and the gradient of a symmetric potential predict gait transitions of dogs

“…The rules that describe these dynamics are thought to remain unchanged under certain manipulations, a property termed a symmetry [6–18]. An example is left–right interchange, or bilateral symmetry.…”