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 Voltage time 7

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 Input: Top 5% of Activity 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 where x and y are physical coordinates of a pair of voxels.

Problem A-Nataliya Next step: Refinement of clusters based on orientation. pairwise inner product < i, j > 5 5 2 6 2 6 4 1 4 1 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 The proposed distance that determines current density vectors dancing in unison is the inner product of normalized differences diffi diffj i j n time frames The 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)

Problem B: Varvara (Clustering Using Cosine Similarity Measure) Member of a cluster End Compute Cosine for any two consecutive times for each voxel Input-Data Test condition 1 Test condition m Dancing in unison means  

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