Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator

1990 ◽  
Vol 64 (3) ◽  
pp. 862-871 ◽  
Author(s):  
T. L. Williams ◽  
K. A. Sigvardt ◽  
N. Kopell ◽  
G. B. Ermentrout ◽  
M. P. Remler
Keyword(s):  
Central Pattern Generator ◽  
Coupled Oscillators ◽  
Nonlinear Oscillators ◽  
Pattern Generator ◽  
Fictive Locomotion ◽  
Frequency Range ◽  
Intersegmental Coordination ◽  
Coupled Nonlinear Oscillators ◽  
Phase Lags ◽  
A Chain

1. This paper reports the results of an investigation of the basic mechanisms underlying intersegmental coordination in lamprey locomotion, by the use of a combined mathematical and biological approach. 2. Mathematically, the lamprey central pattern generator (CPG) is described as a chain of coupled nonlinear oscillators; experimentally, entrainment of fictive locomotion by imposed movement has been investigated. Interpretation of the results in the context of the theory has allowed conclusions to be drawn about the nature of ascending and descending coupling in the lamprey spinal CPG. 3. Theory predicts and data show that 1) the greater the number of oscillators in the chain, the smaller is the entrainment frequency range and 2) it is possible to entrain both above and below the rest frequency at one end but only above or below at the other end. 4. In the context of the experimental results, the theory indicates the following: 1) ascending coupling sets the intersegmental phase lags, whereas descending coupling changes the frequency of the coupled oscillators; 2) there are differences in the ascending and descending coupling other than strength; and it also suggests that 3) coupling slows down the oscillators.

Frequency Clustering in a Chain of Weakly Coupled Oscillators

1997 ◽  
Vol 52 (8-9) ◽  
pp. 578-580 ◽  
Author(s):  
Thomas Kirner ◽  
Otto E. Rössler
Keyword(s):  
Numerical Simulation ◽  
Small Intestine ◽  
Coupled Oscillators ◽  
Nonlinear Oscillators ◽  
Conduction System ◽  
Linear Parameter ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators ◽  
A Chain ◽  
Frequency Gradient

Abstract A numerical simulation of a chain of diffusively coupled nonlinear oscillators with a linear parameter gradient exhibits clusters of frequencies. The intention was to investigate the frequency-gradient in the stimulus conduction system of the heart. The phenomenon generalizes earlier findings on “frequency plateaus” described in the 1960's by Nicholas Diamant as a model of small-intestine transport. This “waxing and waining” phenomenon is a version of chaos. Thus, subtle chaos in the heart and waxing and waining type chaos in the intestine may be related.

Biologically inspired motion synthesis method of two-legged robot with compliant feet

Robotica ◽  
2011 ◽  
Vol 29 (7) ◽  
pp. 1049-1057 ◽  
Author(s):  
Teresa Zielinska ◽  
Andrzej Chmielniak
Keyword(s):  
Central Pattern Generator ◽  
Coupled Oscillators ◽  
Synthesis Method ◽  
Pattern Generator ◽  
Experimental Results ◽  
Human Gait ◽  
Legged Robot ◽  
Biologically Inspired ◽  
Reference Pattern ◽  
Periodic Signals

SUMMARYThis work presents biologically inspired method of gait generation. It uses the reference to the periodic signals generated by biological central pattern generator. The coupled oscillators with correction functions are used to produce leg joint trajectories. The human gait is the reference pattern. The features of generated gait are compared to the human walk. The spring-loaded foot design is presented together with experimental results.

Effects of local oscillator frequency on intersegmental coordination in the lamprey locomotor CPG: theory and experiment

1996 ◽  
Vol 76 (6) ◽  
pp. 4094-4103 ◽  
Author(s):  
K. A. Sigvardt ◽  
T. L. Williams
Keyword(s):  
Coupled Oscillators ◽  
Intact Animal ◽  
Local Oscillator ◽  
Ventral Root ◽  
Phase Lag ◽  
Intersegmental Coordination ◽  
Glutamate Concentration ◽  
Phase Lags ◽  
Theory And Experiment

1. Experiments have been performed on in vitro preparations of lamprey spinal cord bathed in D-glutamate, which induces a pattern of activity recorded from ventral roots that is similar to that seen in the intact animal during swimming. The frequency of fictive swimming increases with increasing D-glutamate concentration, but intersegmental phase lag remains unaffected. 2. The effects on intersegmental phase lags of unequal activation of the rostral and caudal halves of a preparation were determined. Unequal activation was produced by placing a diffusion barrier in the middle of the chamber and perfusing the two halves with different concentrations of D-glutamate. 3. Within the rostral compartment, the phase lag increased from control when the rostral D-glutamate concentration was higher than the caudal concentration, and decreased from control when it was lower. By contrast, the phase lags within the caudal compartment did not depend on the ratio of D-glutamate concentration between the two compartments. 4. The frequency of the ventral root activity during differential activation was not significantly different from that of control experiments that had the same concentration as in the rostral compartment. 5. The results are discussed within the context of the mathematical analysis of chains of coupled oscillators by Kopell and Ermentrout and other current theories about the mechanisms of intersegmental coordination in the lamprey.

Detailed Model of Intersegmental Coordination in the Timing Network of the Leech Heartbeat Central Pattern Generator

2004 ◽  
Vol 91 (2) ◽  
pp. 958-977 ◽  
Author(s):  
Sami H. Jezzini ◽  
Andrew A. V. Hill ◽  
Pavlo Kuzyk ◽  
Ronald L. Calabrese
Keyword(s):  
Central Pattern Generator ◽  
Pattern Generator ◽  
Living System ◽  
Cycle Period ◽  
Intersegmental Coordination ◽  
Experimental Conditions ◽  
Detailed Model ◽  
Distributed Structure ◽  
Synaptic Interactions ◽  
Oscillatory Neuronal Networks

To address the general problem of intersegmental coordination of oscillatory neuronal networks, we have studied the leech heartbeat central pattern generator. The core of this pattern generator is a timing network that consists of two segmental oscillators, each of which comprises two identified, reciprocally inhibitory oscillator interneurons. Intersegmental coordination between the segmental oscillators is mediated by synaptic interactions between the oscillator interneurons and identified coordinating interneurons. The small number of neurons (8) and the distributed structure of the timing network have made the experimental analysis of the segmental oscillators as discrete, independent units possible. On the basis of this experimental work, we have made conductance-based models to explore how intersegmental phase and cycle period are determined. We show that although a previous simple model, which ignored many details of the living system, replicated some essential features of the living system, the incorporation of specific cellular and network properties is necessary to capture the behavior of the system seen under different experimental conditions. For example, spike frequency adaptation in the coordinating interneurons and details of asymmetries in intersegmental connectivity are necessary for replicating driving experiments in which one segmental oscillator was injected with periodic current pulses to entrain the activity of the entire network. Nevertheless, the basic mechanisms of phase and period control demonstrated here appear to be very general and could be used by other networks that produce coordinated segmental motor outflow.

Extent and Role of Multisegmental Coupling in the Lamprey Spinal Locomotor Pattern Generator

2000 ◽  
Vol 83 (1) ◽  
pp. 465-476 ◽  
Author(s):  
William L. Miller ◽  
Karen A. Sigvardt
Keyword(s):  
Spinal Cord ◽  
Pattern Generator ◽  
Synaptic Activity ◽  
System Level ◽  
Oscillatory Activity ◽  
Stable Phase ◽  
Phase Lag ◽  
Intersegmental Coordination ◽  
Cycle Frequency ◽  
Phase Lags

Timing of oscillatory activity along the longitudinal body axis is critical for locomotion in the lamprey and other elongated animals. In the lamprey spinal locomotor central pattern generator (CPG), intersegmental coordination is thought to arise from the pattern of extensive connections made by propriospinal interneurons. However, the mechanisms responsible for intersegmental coordination remain unknown, in large part because of the difficulty in obtaining quantitative information on these multisegmental fibers. System-level experiments were performed on isolated 50-segment preparations of spinal cord of adult silver lampreys, Ichthyomyzon unicuspis, to determine the dependence of CPG performance on multisegmental coupling. Coupling was manipulated through use of an experiment chamber with movable partitions, which allowed separate application of solution to rostral, middle, and caudal regions of the spinal cord preparation. During control trials, fictive locomotion, induced by bath application ofd-glutamate in all three regions, was recorded extracellularly from ventral roots. Local synaptic activity in a variable number of middle segments was subsequently blocked with a low-Ca2+, high-Mn2+ saline solution in the middle compartment, whereas conduction in axons spanning the middle segments was unaffected. Spectral analysis was used to assess the effects of blocking propriospinal coupling on intersegmental phase lag, rhythm frequency, correlation, and variability. Significant correlation and a stable phase lag between the rostral and caudal regions of the spinal cord preparation were maintained during block of as many as 16 and sometimes 20 intervening segments. However, the mean value of this rostrocaudal phase decreased with increasing number of blocked segments from the control value of approximately 1% per segment. By contrast, phase lags within the rostral and caudal end regions remained unaffected. The cycle frequency in the rostral and caudal regions decreased with the number of blocked middle segments and tended to diverge when a large number of middle segments was blocked. The variability in cycle frequency and intersegmental phase both increased with increasing number of blocked segments. In addition, a number of differences were noted in the properties of the motor output of the rostral and caudal regions of the spinal cord. The results indicate that the maximal functional length of propriospinal coupling fibers is at least 16–20 segments in I. unicuspis, whereas intersegmental phase lags are controlled at a local level and are not dependent on extended multisegmental coupling. Other possible roles for multisegmental coupling are discussed.

Deletions of Rhythmic Motoneuron Activity During Fictive Locomotion and Scratch Provide Clues to the Organization of the Mammalian Central Pattern Generator

2005 ◽  
Vol 94 (2) ◽  
pp. 1120-1132 ◽  
Author(s):  
Myriam Lafreniere-Roula ◽  
David A. McCrea
Keyword(s):  
Central Pattern Generator ◽  
Rhythmic Activity ◽  
Pattern Generator ◽  
Cycle Period ◽  
Fictive Locomotion ◽  
Integer Multiple ◽  
Extensor Motoneuron ◽  
Complete Failure ◽  
Motoneuron Activity ◽  
Decerebrate Cats

We examined the features of spontaneous deletions of bursts of motoneuron activity that can occur within otherwise rhythmic alternating flexor and extensor activity during fictive locomotion and scratch in adult decerebrate cats. Deletions of activity were observed both in hindlimb flexor and extensor motoneuron pools during brain stem–stimulation-evoked fictive locomotion but only in extensors during fictive scratch. Paired intracellular motoneuron recordings showed that deletions reduced the depolarization of homonymous motoneurons in qualitatively similar ways. Differences occurred in the extent to which activity in synergist motoneuron pools operating at other joints within the limb was reduced during deletions. The timing of the rhythmic activity that followed a deletion was often at an integer multiple of the preexisting locomotor or scratch cycle period. This maintenance of cycle period was also seen during deletions in which there was a complete failure of motoneuron depolarization. The activity of antagonist motoneurons was usually sustained during deletions with some rhythmic modulation at intervals of the preexisting cycle period. We discuss an organization of the central pattern generator for locomotion and scratch that functions as a single rhythm generator with separate and multiple pattern formation modules for controlling the hyper- and depolarization of subsets of motoneurons within the limb.

Rhythmic activity of feline dorsal and ventral spinocerebellar tract neurons during fictive motor actions

2013 ◽  
Vol 109 (2) ◽  
pp. 375-388 ◽  
Author(s):  
Brent Fedirchuk ◽  
Katinka Stecina ◽  
Kasper Kyhl Kristensen ◽  
Mengliang Zhang ◽  
Claire F. Meehan ◽  
...  
Keyword(s):  
Central Pattern Generator ◽  
Sensory Input ◽  
Rhythmic Activity ◽  
Pattern Generator ◽  
Afferent Feedback ◽  
Fictive Locomotion ◽  
Decerebrate Cat ◽  
Motor Behaviors ◽  
Spinocerebellar Tract ◽  
Motor Actions

Neurons of the dorsal spinocerebellar tracts (DSCT) have been described to be rhythmically active during walking on a treadmill in decerebrate cats, but this activity ceased following deafferentation of the hindlimb. This observation supported the hypothesis that DSCT neurons primarily relay the activity of hindlimb afferents during locomotion, but lack input from the spinal central pattern generator. The ventral spinocerebellar tract (VSCT) neurons, on the other hand, were found to be active during actual locomotion (on a treadmill) even after deafferentation, as well as during fictive locomotion (without phasic afferent feedback). In this study, we compared the activity of DSCT and VSCT neurons during fictive rhythmic motor behaviors. We used decerebrate cat preparations in which fictive motor tasks can be evoked while the animal is paralyzed and there is no rhythmic sensory input from hindlimb nerves. Spinocerebellar tract cells with cell bodies located in the lumbar segments were identified by electrophysiological techniques and examined by extra- and intracellular microelectrode recordings. During fictive locomotion, 57/81 DSCT and 30/30 VSCT neurons showed phasic, cycle-related activity. During fictive scratch, 19/29 DSCT neurons showed activity related to the scratch cycle. We provide evidence for the first time that locomotor and scratch drive potentials are present not only in VSCT, but also in the majority of DSCT neurons. These results demonstrate that both spinocerebellar tracts receive input from the central pattern generator circuitry, often sufficient to elicit firing in the absence of sensory input.

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