Bme 6938 neurodynamics
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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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Bme 6938 neurodynamics

BME 6938Neurodynamics

Instructor: Dr Sachin S Talathi


Phase of limit cycle

Phase of limit cycle


Isochrons define phase off 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

Phase Response Curve


Weak coupling infinitesimal prc

Weak Coupling- Infinitesimal PRC

Linear Response Function or iPRC


Practical approach to calculating 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

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

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

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

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

Weakly coupled oscillators

Substitute

Note

where


Two weakly coupled oscillators

Two weakly coupled oscillators

represents deviation from the identical period for each oscillator


Analyze simple network weak coupled oscillators

Analyze Simple network-Weak Coupled Oscillators

Phase Locked Solution:

Stability Criteria:


Results from weak coupling theory analysis

Results from Weak Coupling Theory Analysis


Spike time response curves

Spike Time Response Curves

Coupling parameters

perturbation time

Intrinsic period


Analysis of the network using strcs

Analysis of the network using STRCs

Phase Locked Solution:

Stability Criterion:


Results from analysis using strcs

Results from analysis using STRCs


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