Being Comoplex is Simpler: Event Related Dynamics

Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences CentreWael El-Deredy School of Psychological Sciences

Different event-related scenarios From time to time-frequency Examples of pitfalls of current methods New methods based on complex statistics Where do we go next?

Outline

How did we get here?

Makeig et al, S

cience 2002

Event-Related Potential (ERP)

Induced Activity: Event-related synchronization and desynchronization (ERS/ERD)

AVG [ + ] =

AVG [ ] =

ERBD = ongoing EEG + Additive ERP;

ERBD = PPR (ongoing EEG); Partial Phase Resetting

Event-related scenarios

A measure of the distribution of the energy of the signal in time and frequency: STFT, Morlet Wavelet, Hilbert, Gabor, etc

Complex coefficients , whose moduli is a measure of the amplitude of the oscillations and whose argument is a measure of their phases.

arctan Im( ) Re( )ift iftx x| |iftxiftx

0 500 1000

µV

Time (ms)0 500 1000 ms

µV2

Hz

From time to time-frequency

Real

Imag Net vector

From time to time-frequency

Each point is a complex wavelet coefficient of a trial at a given frequency and time

All trials at a certain t & f form a complex cloud

Net Phase

From time to time-frequency

Event-related scenarios Change in the position of the cloud mean vector Change in the shape of the cloud Eigen structure Change in the dispersion of the cloud variance

Current measures confound changes

ITC measures the uniformity of the distribution of angles, wrt the origin - not wrt the centre of the cloud

Example confound: Mean vector & Phase1 1

1 1ITC iftL L

j iftft

i i ift

xe

L L x

Intertrial Phase Coherence

Removing Mean Activity

1 1

1 1ITC iftL L

j iftft

i i ift

xe

L L x

Example confound: Mean vector & Phase

Therefore, ITC (and its variants) are NOT a valid tests for inter-trial phase organisation

Tests on the complex cloud

Real

Imag

Complex statistics on the features of the cloud (SEPARATELY): mean vector; variance; form

Real

Imag Net vector

Variance

Tests on the complex cloudNecessary conditions

Real

Imag

For PPR: It has to survive the subtraction of the mean vector.• Significant test wrt pre-stim

Real

Imag

For additive ERP: It has to survive a T-test on the mean(compared to pre-stim)

T-complex mean (test for additive activity)*

2

( )( )1

pre preft f ft f

ft

ft

x x x xT N

1

1 L

ft ifti

x xL

Tests on the complex cloudProposed tests

L

T-complex mean (test for additive activity)*

2

( )( )1

pre preft f ft f

ft

ft

x x x xT N

2

2 2( )1

ft

preft f

ft preT NSTD

2 *

1

1 ( )( )1

L

ft ift ft ift fti

x x x xL

1

1 L

ft ifti

x xL

T-complex variance (test for induced activity)

Tests on the complex cloudProposed tests

L

L

T-Eigenvalue (test for phase similarity)• Generalised correlation

1 2 2 1 2( 15 6) log ( ) 4ft ft ft ft ftL

Tests on the complex cloudProposed tests

The eigen values of the covariance matrix (2 x L)

Mardia, Kent and Bibby Multivariate analysis, 1979.

L

T-Eigen value (test for phase similarity - bimodal)• Second trigonometric moment

22

1

1 iftL

jft

i

R eL

Tests on the complex cloudProposed tests

Mardia, Statistics of Directional Data, 1972.

L

ERP

PPR

Testing the tests: Simulations

ERP

PPR

Testing the tests

Real DataVisual spatial attention. POz

Testing the tests

Current measures (e.g. ITC) cannot distinguish between additive activity and phase resetting.

Statistical tests based on the complex time-frequency are more sensitive to changes event-related brain dynamics.

Separate tests for separate features, to avoid confounds.

Purely descriptive: No mechanistic interpretation.

Summary

What happens next? New tests based on comparing models fitted to data.

○ Neural mass models○ Non-parametric time series modeling

Non-parametric time series modeling

22

Original LIN-Surr

SW linear AR

Kernel Regression

24

Original Kernel-NFR

SW Kernel-AR

25

26

Nonstationary Kernel AR

0 01

0 0

0 01

;

ˆ ;x t

x t

t t t

N

t h htN

h ht

v f t

v K L t tf t

K L t t

x

x xx

x x

0

* * *; 1 0

ˆ ;t t t tv f t x

0

** **; 1 0

ˆ ;t t tv f t x

27

Non Stationary NW **

; , , ,kt t kv t A B C D

28

Appearance of Limit Cycle in Epilepsy

LH

RA

LH t

ra t

**

;limmax s ts

t

abs v