Capturing the Secret Dances in the Brain

Capturing the Secret Dances in the Brain

“Detecting current density vector coherent movement”

Cerebral Diagnosis

A problem proposed by:

The Brain

•The most complex organ

•85 % Water

•100 billion nerve cells

•Signal speed may reach upto 429 km/hr

Neuronal Communication

• Neurons communicate using electrical and chemical signals

• Ions allow these signals to form

Brain Imaging Techniques

EEG MEG fMRI

Electroencephalogram

•Electrodes on scalp measure these voltages

•An EEG outputs the voltage and the locations

EEG of a Vertex wave from Stage I sleep

time

Voltage

Inverse Problem Solving using eLoreta

• The EEG collects the amplitudes• Inverse Problem Solving allows the computation of

an electrical field vector• Output is current density vectors at voxels

Problems

• Problem A:– Classify the vectors according to orientations and

spatial positions

• Problem B:– Classify the vectors that dance in unison

Goal: to capture certain behaviour common to groups of vectors

Problem AClassify the vectors according to orientations and spatial positions

Input: Top 5% of Activity

Normalize the data onto a unit sphere

Classification

Output: Clusters

Classification

• Initialization: Statistical algorithm to group into 4 clusters as suggested by the data.

• Refinement: Partition each cluster into subsets of spatially related voxels via

where x and y are physical coordinates of a pair of voxels.

x yL max x1 y1 , x2 y2 , x3 y3 n, (e.g.,n 5)

Problem A-NataliyaNext step: Refinement of clusters based on orientation. pairwise inner product < i, j >

12

3

4

56

25

6

3

1 4

Separation criterion: inner product >tol (e.g., tol=0.8).

Problem A-Two Layer Classification

• First, classify the voxels in connected spatial neighborhoods

• Second, refine each neighborhood according to orientations

Problem A-Two Layer Classification

Problem B• Classify the vectors that dance in unison

Dance in Unison???

Problem B

Doing the same thing at the same time?Doing different things at the same dance?

Algorithm 1

Problem B

• Spatial proximity, similar orientation, similar velocity

• Same two-layer classification algorithm!

• Critera for refining spatial clusters : orientation, velocity

Problem B-First Layer Results

Problem B-Second Layer Result Part I

Problem B-Second Layer Result Part II

Problem B: SVD Clustering

Problem B: Dominique

Problem B: Yousef

Problem B: Yousef

Problem B

ii

j

r J i t1

r J j t2

r J j t1

r J i t2

diff i ,diff j , diff i (r J i t2

r J i t1

), diff j (r J j t2

r J j t1

).

diffi

diffj

t1

tn

n time framesThe clustered vectors move along relatively the same trajectory with variation controlled by a user defined tolerance parameter.

Problem B: Nataliya

Problem B: Varvara (Clustering Using Cosine Similarity Measure)

v

Member of a

cluster

End

Compute Cosine for any two consecutive times for each voxel

Input-Data

Test condition

1

Test condition

m

Member of a cluster

Problem B: Varvara (Clustering Using Cosine Similarity Measure)

Dancing in unison means

-4

-2

0

2

4 1.1

1.2

1.3

1.4

1.5

1.6

2

2.5

3

3.5

4

Elevation Theta

Current Density Vectors Activity Over Time

Azimuth Phi

Mag

nitu

de r

Problem B: Varvara (Clustering Using Cosine Similarity Measure)

Conclusions:• In this project we tried to observe whether or not

any pattern exists in the CDVs data at a fixed time, and over a time interval.

• During this very short period of time we were able to solve the two problems in more than one way.

• Data whose magnitudes are more that 95% of the maximum magnitudes in the given range were observed.

• Next step: validation with other random data, refine models that already work