# Cerebral Diagnosis

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```					  Capturing the Secret Dances in
the Brain
“Detecting current density vector coherent movement”
A problem proposed by:

Cerebral Diagnosis
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

V
o
l
t
a
g
e

time
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

Goal: to capture certain behaviour common to
groups of vectors

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

• Problem B:
– Classify the vectors that dance in unison
Problem A
Classify 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
xy   L                                  
 max x1  y1 , x2  y2 , x3  y3  n, (e.g.,n  5)

where x and y are physical coordinates of

a pair of voxels.
Problem A-Nataliya
Next step: Refinement of clusters based on orientation.
pairwise                      5
5               inner product < i, j >    2       6
2           6
1       4                            1       4
3                                      3

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
Problem B
Dance in Unison???

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

Algorithm 1
• 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
r       r                  r             r
diff i ,diff j , diffi  (Ji t2  Ji t1 ), diff j  (J j t        J j ).
t
2       1

r                diffi
Ji t                              r
        1
r                       Jjt                diffj
i         Ji t                         1

2                         i   r
j                Jjt

2



n time frames
The clustered vectors move along relatively the
tn                      
same trajectory with variation controlled by a user
defined tolerance parameter.

t1

Problem B: Nataliya
Problem B: Varvara (Clustering Using
Cosine Similarity Measure)

v
Problem B: Varvara (Clustering Using Cosine
Similarity Measure)
Input-Data

Compute Cosine for any two
consecutive times for each voxel

Test
Member of a
condition
1
cluster
Dancing in unison means
Test
Member of a
condition
cluster
m

End
Problem B: Varvara (Clustering Using
Cosine Similarity Measure)

Current Density Vectors Activity Over Time

4

.5

3

.5                                                                       1.6
1.5
2
1.4
-4
-2                                                1.3
0
1.2
2
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

```
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