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BME 6938 Neurodynamics

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.

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BME 6938 Neurodynamics

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  1. BME 6938Neurodynamics Instructor: Dr Sachin S Talathi

  2. Phase of limit cycle

  3. Isochrons-Define phase off limit cycle Phase of a non periodic point is taken to be the phase of its periodic proxy

  4. Phase Response Curve

  5. Weak Coupling- Infinitesimal PRC Linear Response Function or iPRC

  6. 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)

  7. 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

  8. Neural synchrony: Mechanism for generation of brain rhythms Synchronous activity is large-detectable at the electrodes on the scalp (source of EEG)

  9. 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

  10. 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

  11. Weakly coupled oscillators Substitute Note where

  12. Two weakly coupled oscillators represents deviation from the identical period for each oscillator

  13. Analyze Simple network-Weak Coupled Oscillators Phase Locked Solution: Stability Criteria:

  14. Results from Weak Coupling Theory Analysis

  15. Spike Time Response Curves Coupling parameters perturbation time Intrinsic period

  16. Analysis of the network using STRCs Phase Locked Solution: Stability Criterion:

  17. Results from analysis using STRCs

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