180 likes | 322 Views
BME 6938 Neurodynamics. Instructor: Dr Sachin S Talathi. Phase of limit cycle. Isochrons-Define phase off limit cycle. Phase of a non periodic point is taken to be the phase of its periodic proxy. Phase Response Curve. Weak Coupling- Infinitesimal PRC. Linear Response Function or iPRC.
E N D
BME 6938Neurodynamics Instructor: Dr Sachin S Talathi
Isochrons-Define phase off limit cycle Phase of a non periodic point is taken to be the phase of its periodic proxy
Weak Coupling- Infinitesimal PRC Linear Response Function or iPRC
Practical Approach to Calculating iPRC • Malkin’s Theorem: Let the system have exponentially stable limit cycle with period T and receive infinitesimal periodic perturbation Then its phase is described by equation Where with (XPPAUTO exploits this theorem to estimate iPRC)
Brain rhythms (EEG) correlate with behavioral states • Delta (0.5-4 Hz): • Dominant rhythm in infants and stage 3 and 4 of sleep • Theta (4-8 Hz): • Normal activity in young children and represents drowsiness in adults • Alpha (8-12 Hz): • It is observed in relaxed state • Beta (12-30 Hz): • Observed in an anxious state • Gamma (>30 Hz): • Observed in attention state and is thought to be the learning rhythm Excited Relaxed Drowsy Deep Sleep
Neural synchrony: Mechanism for generation of brain rhythms Synchronous activity is large-detectable at the electrodes on the scalp (source of EEG)
Neural Synchrony and the Binding Problem • No central location in the brain where all information related to a task is centralized • How are the parallel computations in spatially segregated regions in the brain coordinated? • How are signals selected and routed from sensory structures to executive structures without confounding? • How information about relatedness of content is encoded? • Related to the problem of consciousness • Potential Answer: Neural synchrony
How does synchrony arise? Two key mechanisms. • Related to the intrinsic properties of neurons in terms their preference for input frequencies (resonance) • Related to the pattern of connectivity between neurons and the dynamic properties of intervening synapses (network and network interactions) Note: These are not mutually exclusive explanations
Weakly coupled oscillators Substitute Note where
Two weakly coupled oscillators represents deviation from the identical period for each oscillator
Analyze Simple network-Weak Coupled Oscillators Phase Locked Solution: Stability Criteria:
Spike Time Response Curves Coupling parameters perturbation time Intrinsic period
Analysis of the network using STRCs Phase Locked Solution: Stability Criterion: