Download 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
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
•Delta (0.5-4 Hz):
Dominant rhythm in infants
and stage 3 and 4 of sleep
Excited
•Theta (4-8 Hz):
Normal activity in young
children and represents
drowsiness in adults
•Alpha (8-12 Hz):
It is observed in relaxed state
Relaxed
•Beta (12-30 Hz):
Observed in an anxious state
Drowsy
•Gamma (>30 Hz):
Observed in attention state
and is thought to be the
learning rhythm
Deep Sleep
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

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?
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
Substitute
Note
where
Two weakly coupled oscillators
represents deviation from the identical period for each oscillator
Analyze Simple network-Weak Coupled
Oscillators
d A
  A  H 
dt
d B
 B
dt
 
d
   H 
dt
 


 
Phase Locked Solution: H  *  
dH  
Stability Criteria:
0
d  *


Results from Weak Coupling Theory
Analysis
Spike Time Response Curves
perturbation time
Coupling parameters
T j  T0
 j t,T0 , E I ,gs, R , D  
T0
Intrinsic period

Analysis of the network using STRCs


 n 1   n  TB  TA 1  1 n   2  n 
Phase Locked Solution: 1  1

Stability Criterion: 0 
 *   2  * 
d  x 
2
dx x  *
  x   x    x

1
2
TB
TA
Results from analysis using STRCs