1. Central Pattern Generators Neurobiology and Modeling
Amir Kabir University of Technology Faculty of Biomedical Engineering
Neuromuscular Control Systems
A Presentation on
By: M. A. Sharifi K.
Instructor: Prof. F. Towhidkhah
February 2013
Central Pattern Generators Neurobiology and Modeling
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2. Contents Intrudoction Neurobiology of CPGs
Neurobiological models of CPG
Why CPG?
Why not CPG?
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3. Introduction
Animals’ ability to efficiently move in complex environments
The effect of this property in shaping animal’s morphologies and central nervous systems
Central pattern generators (CPGs)
Neural circuits
Producing rhythmic patterns of neural activity
Without receiving rhythmic inputs
Central: sensory feedback (from the peripheral nervous system) not needed
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4. Neurobiology of CPGs
Two different explanations for the creation of the rhythms underlying locomotion
C.S. Sherrington: chain of reflexes based on sensory feedback
T.G. Brown: centrally neural networks without input from the periphery
Half-center model: a conceptual model proposed T.G. Brown (Brown, 1914)
Two populations of neurons mutually coupled with inhibitory connections producing alternating rhythmic activity
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5. Neurobiology of CPGs
Experimental evidence for central rhythms generators
Fictive locomotion in lamprey (Cohen & Wallen, 1980; Grillner, 1985)
Fictive locomotion in salamander (Delvolvé, Branchereau, Dubuc, & Cabelguen, 1999)
Fictive locomotion in frog embryos (Soffe & Roberts, 1982)
Fictive locomotion: the spinal cord, extracted and isolated from the body, can produce patterns of activity very similar to intact locomotion activated by simple electrical or chemical stimulation
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6. Neurobiology of CPGs
Grillner’s proposition: CPGs as coupled unit-burst elements with at least one unit per degree of freedom (Grillner, 1985)
CPGs as distributed networks made of multiple coupled oscillatory centers
Experimental evidence:
Lamprey spinal cords have approx 100 segments
Small sections (1–2 segments) capable of producing rhythmic activity
The same observed in salamanders (Delvolvé et al., 1999)
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7. Neurobiology of CPGs
Sensory feedback: not needed, but shaping the rhythmic patterns
Keeping CPGs and body movements coordinated
Experimental evidence
Induced CPG activity by mechanically moving the tail of the lamprey (frequency-locked behavior (McClellan & Jang, 1993)
Induce walking gait in a decerebrated cat by a mechanically driven treadmill (Rossignol, 2000)
Phase-dependent reflexes: different effects depending on the timing within a locomotor cycle
CPGs and reflex pathways often share interneurons (Pearson, 1995)
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8. Neurobiology of CPGs Simple signals to induce activity in CPGs
Mesencephalic Locomotor Region (MLR):
Specific region in the brain stem
Has descending pathways to the spinal cord via the reticular formations
Electrical stimulation of MLR induces locomotor behavior (Grillner, Georgopoulos, & Jordan, 1997)
Level of stimulation modulates the speed of locomotion: low level stimulation for slow (low frequency) movements, and high-level stimulation for faster (higher frequency) movements
Stimulation induces automatic gait transition:
In a decerebrated cat: increasing the stimulation leads to switches from walk to trot to gallop (Shik, Severin, & Orlovsky, 1966)
In a decerebrated salamander: increasing the stimulation leads to a switch from walk to swimming (Cabelguen, Bourcier-Lucas, & Dubuc, 2003)
In a lamprey: applying an asymmetric stimulation between the left and right MLRs leads to turning (Sirota, Viana Di Prisco, & Dubuc, 2000)
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9. Neurobiology of CPGs To summarize:
The spinal CPGs produce the basic rhythmic patterns
The higher-level centers (the motor cortex, cerebellum, and basal ganglia) modulate these patterns
Interesting features of this distributed organization
Reduces time delays in the motor control loop (rhythms are coordinated with mechanical movements using short feedback loops through the spinal cord)
Reduces the dimensionality of the descending control signals (Indeed the control signals in general do not need to specify muscle activity but only modulate CPG activity)
Therefore, reduces the necessary bandwidth between the higher-level centers and the spinal cord
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10. Neurobiological models of CPGs
Different levels:
Biophysical models
Connectionist models
Oscillator models
Neuromechanical models
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11. Biophysical models
Constructed based on the Hodgkin–Huxley type of neuron models
Mostly, investigate the problem of rhythmogenesis (generation of rhythmic activity, in small neural circuits) (Traven et al., 1993)
Sometimes, investigate the pacemaker properties of single neurons
Mostly, concentrate on the detailed dynamics of small circuits
Sometimes, address the dynamics of larger populations of neurons
E.g. The generation of travelling waves in the complete lamprey swimming CPG (Hellgren et al., 1992)
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12. Biophysical models: Hellgren et al., 1992
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13. Connectionist models Use simplified neuron models
Leaky-integrator neurons
Integrate-and-fire neurons
Investigate generation of rhythmic activity by network properties
e.g. half-center networks
Investigate synchronization of different oscillatory neural circuits via interneuron connections
e.g. for intra- or inter-limb coordination
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14. Connectionist models: Buchanan, 1992
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15. Oscillator models
Based on mathematical models of coupled nonlinear oscillators to study population dynamics
An oscillator represents the activity of a complete oscillatory center (instead of a single neuron or a small circuit)
Cohen, Holmes, & Rand, 1982:
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16. Oscillator models
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17. Oscillator models
Purpose: to study how inter-oscillator couplings and differences of intrinsic frequencies affect the synchronization and the phase lags within a population of oscillatory centers
Motivation: the dynamics of populations of oscillatory centers depend mainly on the type and topology of couplings rather than on the local mechanisms of rhythm generation
Collins and Richmond (1994): obtaining the same gait transitions in a given network topology with three different types of oscillators (van der Pol, Stein, and FitzHugh–Nagumo)
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18. Oscillator models: Collins and Richmond (1994)
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19. Oscillator models: Collins and Richmond (1994)
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20. Oscillator models: Collins and Richmond (1994)
Results
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21. Neuromechanical models
Addition of a biomechanical model of the body (and its interaction with the environment)
To study the effect of sensory feedback on the CPG activity
Important phenomena such as mechanical entrainment can be studied
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22. Neuromechanical models: Taga et al., 1991
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23. Neuromechanical models: Taga et al., 1991
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24. Neuromechanical models: Taga et al., 1991
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25. Neuromechanical models: Taga et al., 1991
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26. Neuromechanical models: Taga et al., 1991
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27. Neuromechanical models: Taga et al., 1991
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28. Neuromechanical models: Taga et al., 1991
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29. CPG-based Biped Locomotion
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30. Why CPG?
Five interesting properties of CPGs from engineering point of view
Exhibiting limit cycle behavior
Well suited for distributed implementation
A few control parameters
Ideally suited to integrate sensory feedback signals
Offering a good substrate for learning and optimization algorithms
producing stable rhythmic patterns, the system rapidly returns to its normal rhythmic behavior after transient perturbations of the state variables, robustness against perturbations.
interesting for modular robots, i.e. see snake robot
for instance the speed and direction or even the type of gait, reduces the dimensionality of the control problem such that higher-level controllers (or learning algorithms) do not need to directly produce multidimensional motor commands
which can be added as coupling terms in the differential equations, provides the opportunity to obtain mutual entrainment between the CPG and the mechanical body
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31. Why not CPG CPG-based approaches disadvantages/challenges:
A sound design methodology is yet missing for designing CPGs to solve a particular locomotor problem
A solid theoretical foundation for describing CPGs is yet missing
It is very difficult to prove the stability of the complete CPG-robot system.
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32. Thank you for your time.
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