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 11/8/2018

Contents Intrudoction Neurobiology of CPGs Neurobiological models of CPG Why CPG? Why not CPG? 11/8/2018

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 11/8/2018

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 11/8/2018

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 11/8/2018

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) 11/8/2018

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) 11/8/2018

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) 11/8/2018

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 11/8/2018

Neurobiological models of CPGs Different levels: Biophysical models Connectionist models Oscillator models Neuromechanical models 11/8/2018

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) 11/8/2018

Biophysical models: Hellgren et al., 1992 11/8/2018

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 11/8/2018

Connectionist models: Buchanan, 1992 11/8/2018

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: 11/8/2018

Oscillator models 11/8/2018

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) 11/8/2018

Oscillator models: Collins and Richmond (1994) 11/8/2018

Oscillator models: Collins and Richmond (1994) 11/8/2018

Oscillator models: Collins and Richmond (1994) Results 11/8/2018

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 11/8/2018

Neuromechanical models: Taga et al., 1991 11/8/2018

Neuromechanical models: Taga et al., 1991 11/8/2018

Neuromechanical models: Taga et al., 1991 11/8/2018

Neuromechanical models: Taga et al., 1991 11/8/2018

Neuromechanical models: Taga et al., 1991 11/8/2018

Neuromechanical models: Taga et al., 1991 11/8/2018

Neuromechanical models: Taga et al., 1991 11/8/2018

CPG-based Biped Locomotion 11/8/2018

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 11/8/2018

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. 11/8/2018

Thank you for your time. 11/8/2018