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*