BME 6938 Neurodynamics

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BME 6938Neurodynamics

• Instructor Dr Sachin S Talathi

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Phase of limit cycle
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Isochrons-Define phase off limit cycle
Phase of a non periodic point is taken to be the
phase of its periodic proxy
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Phase Response Curve
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Weak Coupling- Infinitesimal PRC
Linear Response Function or iPRC
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Practical Approach to Calculating iPRC

• Malkins 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)

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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 (gt30 Hz)
• Observed in attention state and is thought to be
  the learning rhythm

Excited
Relaxed
Drowsy
Deep Sleep
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Neural synchrony Mechanism for generation of
brain rhythms
Synchronous activity is large-detectable at the
electrodes on the scalp (source of EEG)
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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

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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
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Weakly coupled oscillators
Substitute
Note
where
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Two weakly coupled oscillators
represents deviation from the identical period
for each oscillator
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Analyze Simple network-Weak Coupled Oscillators
Phase Locked Solution
Stability Criteria
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Results from Weak Coupling Theory Analysis
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Spike Time Response Curves
Coupling parameters
perturbation time
Intrinsic period
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Analysis of the network using STRCs
Phase Locked Solution
Stability Criterion
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Results from analysis using STRCs