week 4 - the kuramoto oscillator model

Question 1

What are uses of the connectome

Answer 1

Providing structural information that can be implemented as part of large scale computational models

Provide an important tool for mechanistic modelling and interpretation of human functional brain data

Question 2

What creates oscillation in the brain? Give examples

Answer 2

Synchronized neuron firing

E.g alpha waves, gamma waves

Question 3

What is the communication through coherence hypothesis?

Answer 3

Synchronisation is key for communication between brain regions

Coherehence between the osscilation in the sending group and the recieving group is also essential for communication between brain regions

When the oscillations are synchronised between brain regions, there is a window of opportunity for communication. This is so the message can reach the destination when it’s in its most excitable state

Question 4

What is the general idea behind the kuramoto oscilation

Answer 4

structural connectome + model = simulated activity

This can then be paired with empirical recordings of activity

This comparison can be used by any analytical method for time series data, e.g static or dynamic connectivity or graph theory

Question 5

Describe the kuramotor oscillator model equation

Answer 5

(Print equation)

model terms:
phase of node(i) (fraction of the cycle at any point in time)
rate of change (how much does the phase change in a small increment of time
Frequency (how many cycles does the oscillatory node make for a time point )
k = coupling parameter - relative importance of the frequency vs. the interactions
interactions = the influence of the oscillators on each other (interactions between oscilattors depend on the Sin of the phase difference between them

n external noise

D = relative delays between oscillators

Tau = average length/velocity - scales all delays

Question 6

what happens if K is high

Answer 6

research and look into this

Question 7

explain the interactions explained by Sin 0

Answer 7

research this it’s important

pi radians = 180 degrees

Question 8

What happens when you add Cij and how does it relate to connectome

Answer 8

A parameter is added that varies the relative coupling of oscillators. Allows you to bring in extra oscillators, that influence each other in different levels

You can try and edit Cij so the matrix of Cij is equal to a structural connectome

Question 9

what is the difference between k and c?

Answer 9

C = how strongly is a pair of oscillators coupled

K = essentially scales all of this matrix up or down

so K applies to all coupling, but C refers to the relative coupling between oscillators

K allows you to tune the model to a point that it might behave in an interesting way

Question 10

Kuramoto model assumptions

Answer 10

• Coupling is week
• Oscillators are nearly identical
• interactions depend sinusoidally on the relationsip between oscillators

Question 11

What is the kuramoto order parameter (Rt)

Answer 11

The average vector between oscillators

describe how this changes as the oscillators become more synchronisedd

Question 12

What is syncrony?

Answer 12

The average order parameter over time

Question 13

What is metastability?

Answer 13

The standard deviation over time of the order parameter

Question 14

How did varying k change the properties in cabral et al’s study

Answer 14

At low coupling K, the system showed low synchrony and metastability

At high coupling K, the system should high coupling and low metastabiltiy

At mid level couplign K, the synchronisation was variable and the metastability was high

At the point that the model best matched empirical data, subsets of nodes were synchronised. So there was synchoronisation within large network modules, but not between them