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. - PowerPoint PPT Presentation

Transcript of BME 6938 Neurodynamics

  • BME 6938NeurodynamicsInstructor: Dr Sachin S Talathi

  • Phase of limit cycle

  • Isochrons-Define phase off limit cyclePhase of a non periodic point is taken to be the phase of its periodic proxy

  • Phase Response Curve

  • Weak Coupling- Infinitesimal PRCLinear Response Function or iPRC

  • Practical Approach to Calculating iPRCMalkins Theorem:Let the system have exponentially stable limit cycle with period T and receive infinitesimal periodic perturbation Then its phase is described by equationWhere with

    (XPPAUTO exploits this theorem to estimate iPRC)

  • Brain rhythms (EEG) correlate with behavioral statesDelta (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

    Deep SleepDrowsyRelaxedExcited

  • Neural synchrony: Mechanism for generation of brain rhythmsSynchronous activity is large-detectable at the electrodes on the scalp (source of EEG)

  • Neural Synchrony and the Binding ProblemNo 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 oscillatorsSubstitutewhereNote

  • Two weakly coupled oscillatorsrepresents deviation from the identical period for each oscillator

  • Analyze Simple network-Weak Coupled OscillatorsStability Criteria:Phase Locked Solution:

  • Results from Weak Coupling Theory Analysis

  • Spike Time Response Curvesperturbation timeIntrinsic periodCoupling parameters

  • Analysis of the network using STRCsPhase Locked Solution:Stability Criterion:

  • Results from analysis using STRCs

    Evidence exist that neurons can have frequency preference that enable them to either generate spontaneous membrane potential oscillations or respond bet to inputs within a narrow frequency window*