Functional Connectivity based Framework for Analysis and Visualization

Functional Connectivity based Framework for Analysis and Visualization of f. MRI data A thesis submitted toward the degree of Master of Science in Biomedical Engineering Student: Eitan Peri (email: eitanperi@gmail. com, web page: http: //eitanperi. ac. googlepages. com) Instructors: Eshel Ben Jacob, Ana Solodkin

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 2

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 3

f. MRI (functional magnetic resonance imaging) u u u Advance functional neuroimaging techniques for mapping brain activation based on BOLD (blood oxygenation level dependent) signal. Voxel - a volume element, representing a value on a regular grid in 3 D space. Time series is generated per voxel and represents the activity of this voxel. Typical f. MRI experimental designs involves repetitions of some behavioral conditions tasks such as motor activity. Most studies are focused on revealing active voxels under some behavioral conditions. èCalculate P value per voxel – Probability that voxel is a random signal (not correlated with the conditions). Functional Connectivity and Time Ordering Framework 4

f. MRI Active Voxels Analysis Block Design Experiment Rest Activate Voxels (P value map) Task One voxel’s time series Functional Connectivity and Time Ordering Framework 5

Functional Connectivity f. MRI data analysis has recently targeted the description of networks of activation rather than the mere description of regions involved in the production of the tasks. Some of these network analyses focus on “functional connectivity” u Functional connectivity = Undirected “correlations between spatially remote neurophysiological events” (Friston K. , Büchel C. ). u For f. MRI data correlation between time series of two or more voxels u Voxel a functional connectivity Voxel b èFor N voxels we get N-1 values per voxel Functional Connectivity and Time Ordering Framework 6

Functional Connectivity Challenges u Activate voxels analysis - each voxel has a single value (its P value) èCan be visualize by simply coloring activate voxels u u Functional connectivity each - voxel has many values (one value per other voxels). Defines a dynamic system. Challenges: l How to analyze? l How to visualize? Functional Connectivity and Time Ordering Framework 7

Functional Holography (FH) Analysis u Developers: Itay Baruchi, Prof. Eshel Ben Jacob. u General multivariate method for analysis of dynamic systems. u Introduces novel visualization methods that aim to capture the maximum amount of information about the functional as well as temporal relations between components of such dynamic system u Was successfully applied to some biological systems (ECo. G, EEG, cultured neural networks). Functional Connectivity and Time Ordering Framework 8

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 9

Research Objectives √Main objective: Develop an integrated framework for detection and visualization of functional connectivity as well as time ordering of brain activity from f. MRI data. √ Secondary objective: Demonstrate the framework through preliminary f. MRI data analysis. Functional Connectivity and Time Ordering Framework 10

Research Methods 1. Use the basic functional holography analysis as the framework’s outline. 2. Suit the basic analysis for f. MRI data. 3. Extend the analysis from computation and visualization point of view. 4. Implement corresponding software package. Functional Connectivity and Time Ordering Framework 11

Framework SW Requirements u User-friendly: Graphical user interface application. u Outline: Implementation of the extended functional holography method for f. MRI data. u Flexible: Interactively modification of various algorithm & display parameters by the user. u Open: Easily integration of external algorithms into the framework in the future. u Generic: Future use with different data types beyond f. MRI (EEG, ECo. G, genes, etc. ). Functional Connectivity and Time Ordering Framework 12

FH Framework Displays Functional Connectivity and Time Ordering Framework 13

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 14

Functional Holography Algorithm 0. Preprocessing: Reduces noise and artifacts before further analysis 1. Calculate correlation coefficients matrix: Generate the matrix which contains the correlation coefficients between pairs of channels. 2. Calculate correlation statistics matrix: Map the correlation coefficients matrix into [0 1] range with some statistic interpretation. 3. (optional) Calculate affinity matrix (collective normalization): Perform collective normalization of the correlation statistics matrix to construct a matrix of functional correlations named affinity matrix. 4. Dimension reduction (calculate functional space): Project the N dimensions matrix of functional correlations onto a 3 dimensions space that captures the maximal information. 5. Calculate channel specific information (color coding): Calculate channel’s specific information and assign colors that represents this information. 6. Display the Data: Display the spatial domain, correlation/affinity matrices and functional manifold. Functional Connectivity and Time Ordering Framework 15

FH 1: Calculate Correlation Coefficients Matrix Input data include time series of N channels u Calculate the symmetric correlation coefficients matrix th th u Element in the i row and j column represent the correlation between the ith and jth channel u This matrix can then be associated with an N dimensions space of correlations - simply called correlation space. u Coefficient is 1 : perfect positive correlation 0 : complete independent − 1 : perfect negative correlation Some value in between in all other cases u Our Method: Pearson Correlation which measures linear dependencies u Alternatives: Coherence, Synchronization Likelihood (SL) Connectivity and Time Ordering Framework Functional u 16

FH 1: Calculate Correlation Coefficients Matrix Pearson Correlation - measures linear dependencies. Correlation Coefficients Matrix Correlation Space N signals N dimensions space Input: Time Series -1 Functional Connectivity and Time Ordering Framework 1 17

FH 2: Calculate Correlation Statistics Matrix The purpose is to estimate the statistical significance of the correlation coefficients. Distinguish between real correlations (significant) to the ‘background’ ones (not significant) u Coefficients are then mapped into [0, 1] range. Value of 1 for significant correlation, 0 for non significant u Three basic methods are now available: 1. Linear normalization: Linear transfer which preserves difference between negative and positive correlations. 2. Absolute value normalization: Normalization by taking the absolute value of the coefficient. Eliminates the difference between negative and positive correlations. 3. Fisher’s Z transform: Convert the correlation coefficients into normal distribution. u Developing more sophisticated methods are subject to future research. We think it’s a key issue u Functional Connectivity and Time Ordering Framework 18

FH 2: Calculate Correlation Statistics Matrix Estimates correlation coefficients’ statistical significance. u Map from [-1, 1] to [0, 1] range using Absolute value normalization. u Correlation Coefficients Matrix -1 1 Functional Connectivity and Time Ordering Framework Correlation Statistics Matrix 0 1 19

Timeout: Cluster the Correlation Statistics Matrix Divide the channels into several similarity groups u Reorder the correlation matrix according to those groups u Assign a unique color to each group u Correlation Statistics Matrix Functional Connectivity and Time Ordering Framework Clustered Correlation Matrix 20

Timeout: Cluster the Correlation Statistics Matrix Clustered Correlation Matrix Functional Connectivity and Time Ordering Framework Reordered Input Time Series 21

FH 3: Calculate Affinity Matrix (Collective normalization) Motivation: go beyond two channels correlations and capture mutual or relative effects between several channels. u Idea: normalize correlation between any pair of channels according to their correlations with all other channels. u Result: new matrix of collectively normalized correlations called affinity matrix which associated with an N dimensions space called affinity space u Optional: weather to use it for f. MRI analysis is still open u Our Method: Affinity transformation which divides a coefficient by the Euclidian distance (in correlation space) between the corresponding pair of channels. u Alternatives: Meta correlation (correlation of correlation), Distances matrix u Functional Connectivity and Time Ordering Framework 22

FH 3: Affinity Transformation Go beyond two point correlations u Normalize coefficients by correlation’s Euclidian distance Clustered Correlation Matrix= Correlations. Clustered Matrix u Correlation distance with all. Affinity channels u (3, 11) Divide by Dist(3, 11) 3 11 Functional Connectivity and Time Ordering Framework N dimensions space Affinity Space 0 1 23

FH 4: Dimension Reduction - General Goal: Extract maximum significant information from N dimensions (ND ( ) affinity space. Assumption: most of the relevant information is contained in a low dimension space embedded in the larger one Main idea: 1. Define principal vectors in the ND space which are associated with the directions with maximal variations. 2. Project data onto lower dimensionality space defined by few principal vectors. Illustration of the idea from 3 -D to 1 -D u Transforms data into an N dimensions functional space. Functional Connectivity and Time Ordering Framework The Principal 1 D Vector The direction of maximal variation 3 -D 1 -D 24

FH 4: Dimension Reduction – PCA Our Method: Principal Components Analysis (PCA) u Approximates the best linear representation of the information in lower dimensionality (in terms of RMS) u Transforms data to a new coordinate system named functional space which is represented by a set of N components vectors u Channel locations are represented by a set of N scores vectors u Components vector are the eigenvectors of the original matrix. The variances explained by them are the eigenvalues. u The result components are ranked according to the level of variance in the channels positions (eigenvalues). u Project data onto functional manifold – 2 D / 3 D space defined by the 2/3 principal vectors. u u Alternatives: SVD, ICA Functional Connectivity and Time Ordering Framework 25

FH 4: Dimension Reduction (calculate functional space) Affinity Matrix ~40% explained by 3 principal dimensions Functional Connectivity and Time Ordering Framework Functional Matrix Explained Variance 26

FH 4: Dimension Reduction (calculate functional space) Functional Space Functional Connectivity and Time Ordering Framework Functional Manifold 27

FH 4: Dimension Reduction (calculate functional space) Reduced Affinity Matrix ~75% explained by 3 principal dimensions Functional Connectivity and Time Ordering Framework Functional Space Explained Variance 28

FH 4: Dimension Reduction (calculate functional space) Reduced Functional Space Functional Connectivity and Time Ordering Framework Reduced Functional Manifold 29

FH 5: Calculate Channel Specific Information 1. For each channel calculate a value that represents some type of information l info-vector : vector that contains the values of all the N channels 2. For continuous numbers only uniformly map the values into up to 64 discrete values l info-group : a group of all the channels which are assigned with the same specific discrete value 3. Assign a unique color to each info-group l color map : one set of such information (info-vector, info-groups, and colors). Functional Connectivity and Time Ordering Framework 30

FH 5: Calculate Correlation Clusters Color Map 1. Divide the channels into 3 clusters (similarity groups) u 1 2 3 Each cluster consists one info-group 2. Assign a discrete number for each cluster. 3. Assign a unique color for each cluster. Functional Connectivity and Time Ordering Framework 31

FH 5: How does it look on correlation space? Reorder correlation matrix according to those groups. u Add groups’ colors. u Reorder input time series according to clusters. u Correlation Matrix Clustered Matrix Functional Connectivity and Time Ordering Framework Reordered Input Time Series 32

FH 5: Calculate Time Ordering Color Map 1 2 3 1. Calculate time ordering rank for each channel: l A number between 0 and 1 l 0 = Early activity l 1 = Late activity 2. Map [0, 1] range into 20 discrete values u Channels assigned with the same discrete value assemble one info-group (e. g. group 17 contains channels 3 and 6) 3. Assign a color for each info-group Functional Connectivity and Time Ordering Framework 33

FH 6: Display the Functional Manifold u u Channels colors: Represent some per-channel information. The color of each channel is set according to the color of the info-group to which the channel belongs (e. g. one of the three correlation clusters in this example). Functional Manifold – All clusters Functional Manifold – Clusters 2 and 3 3 2 1 Functional Connectivity and Time Ordering Framework 34

FH 6: Display the Data - Include Time Ordering Map Color the channels according to the color of the time ordering info-group to which they belong. 20 such groups exists in this example. time 21 17 time 12 7 2 time Functional Connectivity and Time Ordering Framework 35

FH 6: Display the Data – Retrieving lost correlation information Link pairs of channels that are significantly correlated (their correlation coefficients are beyond some threshold). u Color lines according to the level of similarity between channels u Functional Manifold – Threshold= +/-0. 5 Functional Manifold – Threshold= +/-0. 1 1 -1 Functional Connectivity and Time Ordering Framework 36

FH 6: Display the Functional Manifold Connectivity diagram named functional manifold: u Channels locations: l u Channels colors: l u Represents functional information. Represent some perchannel information Channels links: l Represents pair wise correlation information Functional Connectivity and Time Ordering Framework 37

FH 6: Functional Manifold –Holographic Principle u u Simplify the complexity of a dynamic system The manifold aims to extract maximum amount of information about the dynamic system as it functions as a whole unit: Captures hidden motifs in the complex activity of a system l Reveal the existence of sub-networks l u u u The manifold can be viewed as a “holographic network”: l Hologram = ‘holo’ + ‘gram’ = ‘whole’ +‘information’ l Characteristic feature is the ‘whole in every part’ nature of the process l Small part of it gives all the functional information but less detailed Pairwise correlation information is integrated into the diagram. Various per-channel information (time ordering, correlation clusters, etc. ) is also included. Functional Connectivity and Time Ordering Framework 38

FH Algorithm - Summary 1, 2, 3 4 Calculate correlation coefficients, correlation statistics and affinity matrices 5 Calculate channel specific information Functional Connectivity and Time Ordering Framework Dimension reduction 6 Display the data 39

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 40

Experiment Description Motor task boxcar design. u One healthy subject. u Dominant-hand alternated with bi-manual movement u Task onset is signaled with an auditory command u 1 Uni Manual 24 sec 2 Rest Bi Manual 12 sec 24 sec 3 Rest Uni Manual 12 sec 24 sec 4 Rest Bi Manual 12 sec 24 sec 12 Rest Bi Manual Rest 12 sec 24 sec 12 sec 7 min 12 sec Functional Connectivity and Time Ordering Framework 41

Data Preprocessing u u Goal: remove as much artifacts and noise as possible while keeping maximum relevant information Artifacts and noise examples: 1. Head movement during acquisition period 2. Time differences between the acquisition of different slices 3. Acquisition spikes 4. Drift arise from magnet noise (e. g. parts warm up) 5. Magnetic field in-homogeneities 6. Physiological artifacts (e. g. breathing, heart pulses) Functional Connectivity and Time Ordering Framework 42

Data Preprocessing u u u Implementation: AFNI software Performed by: Prof. Ana Solodkin and E. Elinor Chen Preprocessing steps: 1. Head movement correction: – Linear weighted least square registration – First volume is the reference 2. Inter slice time shift correction – Linear interpolation 3. Despike 4. Detrending – Removes baseline, linear and quadratic trends – Implemented with multiple linear regression – Each voxel is treated independently 5. Registration with anatomy – Linear weighted least square registration Functional Connectivity and Time Ordering Framework 43

Analysis of Left M 1 (Primary Motor) Problem: Too many voxels (18, 763 for motor system…. ) u Solution: Work separately on each region u 3 D View 2 D View M 1 - has major role in controlling right hand movement u 548 voxels for current subject u Functional Connectivity and Time Ordering Framework 44

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 45

Main Display Domains Three main display domains are simultaneously shown: 1. Spatial space 2. Correlation and Affinity matrices 3. Functional manifold 1 2 3 All colors maps available in all display domains Functional Connectivity and Time Ordering Framework 46

More Displayed Information 1. 2. 3. Different time series displays Statistical plots Tables with variety of statistical measures 1 2 Functional Connectivity and Time Ordering Framework 3 47

Display 1: Spatial Space Correlation Clusters – Enlarged 3 D View u u u Channels locations: Represent their spatial location in the brain. Channels Colors: Represent some channel specific information. Channels Links: Represents pairwise correlation information. Link only pairs of channels that are significantly correlated. 1 Functional Connectivity and Time Ordering Framework 2 3 4 48

Display 1: Spatial Space - 3 D View u u Anatomy: Anatomical MRI image is registered and displayed. Correlation Clusters – 3 D View Advanced Graphics: l Scalp/face rendering. l Lightening simulation. l Semitransparent objects. Sections: Axial, sagittal, coronal u Views: 3 or 2 dimensions view u * Two hands movement Functional Connectivity and Time Ordering Framework 1 2 3 4 49

Display 1: Spatial Space - 2 D View Time Ordering – 2 D Axial View 0 Correlation Clusters – Enlarged 2 D View 1 Functional Connectivity and Time Ordering Framework 1 2 3 4 50

Display 2: Correlation & Affinity Matrices 1. Reorder correlation matrix according info-groups 2. Color matrix according info-groups Original Correlation Matrix 0 Correlation Matrix – Correlation Clusters 1 Functional Connectivity and Time Ordering Framework 1 2 3 4 51

Display 2: Correlation and Affinity Matrices Similarly, the Affinity matrix can be displayed u Do contrast enhancement using histogram equalization u Clustered Affinity Matrix Correlation Matrix – Contrast Enhancement 1 Functional Connectivity and Time Ordering Framework 2 3 4 52

Display 3: Functional Manifold u Channels locations: Represents functional information. l Set according to channel’s position in functional space èAdjacent channels are functionally related. èSystem’s general functional features are retrieved. l u Channels colors: Represent some per-channel information. l Set according to color of the corresponding info-group. l Functional Connectivity and Time Ordering Framework 3 D view 53

Display 3: Functional Manifold u Topological surface: Separate surface is drawn for each info-group. l Colored by interpolating the channels colors l u Channels links: Represent pair wise correlation information. l Link only pairs of channels that are significantly correlated (beyond threshold). l u Channels names: l Attached as text boxes. Connectivity diagram that simplify the complexity of a dynamic system and represents its functionality Functional Connectivity and Time Ordering Framework 54

Display 3: Functional Manifold Left M 1, two hands movements experiment Correlation Clusters Color Map Functional Connectivity and Time Ordering Framework Time Ordering Color Map 55

Display 3: Functional Manifold – 2 D Correlation Clusters Color Coding PC 1 Functional Connectivity and Time Ordering Framework PC 4 PC 3 PC 2 Time Ordering Color Coding PC 2 PC 3 PC = Principal Component 56

Time Series Displays 1. Channels plot: A separate plot per Channel. Plots are reordered and colored according to info-groups l Number of displayed channels is limited. 2. Channel activity image: Display all channels’ time series using an activity image in which color indicates activity strength. l Row: represents a channel; Column: represents time sample. l Rows are reordered and colored according to info-groups. 1 EEG: Channels Plots 2 f. MRI: Channels Activity Matrix l Functional Connectivity and Time Ordering Framework 57

Time Series Displays 3. Info-groups plots: A separate plot per info-group. Averaging the time series of all the info-group’s channels. 4. Principal components time series plot: Display principal components’ time series. l Averaging the time series of all the channels. l Channels are weighted according to their corresponding element in the eigenvector. l 3 f. MRI: Info-Groups Plots 4 correlation clusters 4 f. MRI: Principal Components Time series Plot 3 principal components Functional Connectivity and Time Ordering Framework 6 principal components 58

Statistical Plots 1. Correlation coefficients histogram: Histogram of the coefficients in correlation statistics matrix. 2. Functional scores histogram: Histogram of the scores vectors of 3 principal components, which represents the channel location in the functional manifold. 1 Correlation Coefficients Histogram 2 Functional Connectivity and Time Ordering Framework Functional Scores Histogram 59

Statistical Plots 3. Info-groups histogram: distribution of channels specific information which was calculated for the selected color map. 4. Functional explained variance percentage plot: presents the percent variance explained by the corresponding principal components. 3 Info-groups Histogram Time Ordering Map Correlation Clusters Functional Connectivity and Time Ordering Framework 4 Functional explained variance percentage 10 Principal Components 60

Statistics Tables u All channels statistics: Calculated on all channels together. u Per info-group statistics: Calculated separately per info-group. Spatial Space Correlation Space Functional Connectivity and Time Ordering Framework Functional Space 61

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 62

Available f. MRI Color Maps 1. Spatial location 2. P-values 3. Time ordering 4. Correlation clustering 5. Correlation grade 6. Functional clustering 7. Functional projection error Functional Connectivity and Time Ordering Framework 63

Color Map 1: Spatial Location Purpose: Distinguish between channels based on their spatial location on the brain. u Main idea: l Divide the voxels into separate spatial regions. l One info-group represents one region. u Our Method: Regions Of Interest (ROI) approach u Performed by Prof. Ana Solodkin using external tools. l 20 specific ROIs identified a priori for human motor system. l ROIs are based on the brain’s known functional neuroanatomy. l ROIs locations are identified using known anatomical landmarks. l Good reference point for multi-subject analysis. u Alternatives: Automatic methods such as: l l l Trasfering into MNI space or Talairach atlas. IBASPM - Individual Brain Atlases using Statistical Parametric Mapping. Functional Connectivity and Time Ordering Framework 64

Color Map 1: Spatial Location - RIO approach For each of the two hemispheres (left/right) we marked the following motor regions: 1. M 1: Primary motor cortex 2. S 1: Primary Somatosensory cortex 3. LPMCd: Lateral Premotor Cortex Dorsal 4. LPMCv: Lateral Premotor Cortex Ventral 5. SMA: Supplementary Motor Area 6. Pre. SMA: Pre-Supplementary Motor Area 7. CMA: Cingulate Motor Area 8. SPAR: Superior Parietal lobule and Intra-Parietal Sulcus 9. CRB: Cerebellum 10. THAL: Thalamus Functional Connectivity and Time Ordering Framework 3 D view 65

Color Map 1: Spatial Location - RIO approach 2 D view - Spatial slices u u u 20 ROIs for human motor system. ROIs are based on the known functional neuroanatomy. Good reference point for multi-subject analysis. Functional Connectivity and Time Ordering Framework 66

Color Map 1: Spatial Location - RIO approach Spatial M 1 region – 2 D view u u Can display only subset of the regions (info -groups) For example display only the left M 1 region (primary motor cortex) Functional Connectivity and Time Ordering Framework 67

Color Map 2: P-Values Purpose: Identify the extent in which the different voxels are active for the given stimulus. u Main idea: u Statistical value named P-value is calculated for each voxel. l P-value represents the probability that the channel’s time course is a random one (i. e. not correlated with the stimulus). -5 l Only channels with low values (~10 ) are considered active. l Low values are colored with red shades, high values with blue shades. l u Our Method: Performed by E. Elinor Chen using AFNI package. l Generate a model of expected hemodynamic response. l Calculate correlation coefficients using multiple linear regression. l Monte-Carlo simulation to establish significance level. l u Alternatives: Many…… Functional Connectivity and Time Ordering Framework 68

Color Map 2: P-Values – All Voxels P-Value Map – 2 D view 3 D view 1 0 Functional Connectivity and Time Ordering Framework 18, 763 voxels 69

Color Map 2: P-Values – Active Voxels P-Value Map – 2 D view 3 D view 1 0 -5, 4478 voxels Functional Connectivity and Time Ordering. Threshold=10 Framework 70

Color Map 3: Time Ordering u Purpose: Trace the time ordering of the channels’ activations. u Main idea: l l u u Calculate for each channel separately a temporal rank. Combining the results of all channels supplies the information about the global activation ordering. Our Method: Temporal Center of Mass l Regard each channel’s activity as a temporal weight function. l Temporal rank = Temporal center of mass of this function. l Calculate separately for each stimulation block. l Average results for all experiment blocks. Alternatives: Cross Correlation. Functional Connectivity and Time Ordering Framework 71

Color Map 3: Temporal Center of Mass Activity = temporal weight function u Temporal rank = Temporal center of mass u Divide into 64 infogroups u Assign color to every info-group. u Calculate separately each block u Average results Calculate Temporal Rank for one Simulation Block Design Experiment u block 1 block 2 Functional Connectivity and Time Ordering Framework block 3 block 4 block 5 block 6 72

Color Map 3: Right dominant hand movement Early activity = blue colors 6 Regions: M 1, SMA for L/R hemispheres Late activity = red colors u M 1 and S 1 regions: Left: prominent early activated areas. l Right: less prominent early activated areas. l u 21 22 23 24 25 26 27 28 SMA region: Shows more symmetric activation (early activated areas on both hemispheres) l Still, the left SMA dominates the early activation l u General: Early activity is dominated by left hemisphere Functional Connectivity and Time Ordering Framework 73

Color Map 3: Two hands movement Early activity = blue colors 6 Regions: M 1, SMA for L/R hemispheres Late activity = red colors u M 1 and S 1 regions: l u 21 22 23 24 25 26 27 28 SMA region: l u Early activity is almost symmetric (early activated areas on both hemispheres) General: Early activity is approximately symmetric Functional Connectivity and Time Ordering Framework 74

Color Map 3: Right dominant hand vs. Two hands blue = early Early activity is approximately symmetric Right Dominant Hand Early activity is dominated by left hemisphere Two Hands red = late 6 Regions: M 1, SMA for L/R hemispheres Functional Connectivity and Time Ordering Framework 75

Color Map 3: Temporal Center of Mass Correlation Matrix Order: Time Ordering Color: Time Ordering Early synchronized activity Order: Correlation Clusters Color: Time Ordering Roughly fits clusters’ division Functional Connectivity and Time Ordering Framework 76

Color Map 3: Temporal Center of Mass Functional Manifold Color: Time Ordering Smooth distribution of time ordering values (colors) Surface gradually changes colors Functional Connectivity and Time Ordering Framework 77

Color Map 4: Correlation Clustering Purpose: Identify groups of channels that share similar behavior as indicated by their activity signals. Idea: u Divided channels into groups based on their proximity in correlation space. u Each such info-group is refer to as correlation cluster. Method: Hierarchical (dendrogram) clustering u Number of clusters is explicitly defined by the user. u Based on Euclidean distance between channels. u Enables to examine clustering over a variety of scales. Functional Connectivity and Time Ordering Framework 78

Color Map 4: Correlation Clustering – Hierarchical Clustering Correlation Clustering Tree Correlation Distances Plot Distance threshold Original correlation matrix Re-ordered colored correlation matrix Functional Connectivity and Time Ordering Framework Re-ordered activity image 79

Clustering left M 1 – Old method vs. New method Old method: u Correlation matrix is reordered according to the linkage information u Do not define the exact borders between correlation clusters. Our method: u Correlation matrix reordered according to 4 specific 4 clusters. u Clusters colors are marked on the color bar located left to the matrix Old method Functional Connectivity and Time Ordering Framework New method 80

Clustering left M 1 – Right dominant hand vs. Two hands Was performed on the voxels of left M 1 region. u Similar 4 clusters on both cases but different sizes - first prominent blue cluster is larger in the two hands case. èMore voxels on left M 1 participate in the correlated activity when need to control also the right hand. u Two hands Functional Connectivity and Time Ordering Framework Right dominant hand 81

Clustering left M 1 – Right hand vs. Two hands Spatial space: u Clusters distribution on the brain is similar but not identical for both tasks. u Prominent blue cluster is very similar for both tasks on the central slices (23, 24, 25) but less similar on the border slices (21, 22, 26). u Other clusters show less consistent differences. u For both tasks the clusters are relatively continuous but higher degree of homogeneity during the two hands task. Right Dominant hand 21 22 23 24 25 26 27 Two hands 21 22 23 24 Functional Connectivity and Time Ordering Framework 82

Clustering left M 1 – Right hand vs. Two hands Spatial space: u Relatively continues clusters for both tasks. u One cluster is similar (blue) others clusters are less. Right Dominant hand Two hands 3 D view Functional Connectivity and Time Ordering Framework 83

Clustering M 1 – Right hand vs. Two hands Functional manifold: u Similar structure but different sub networks u Clustering do not divide the scattered sub-network (blue cluster) Two hands Functional Connectivity and Time Ordering Framework Dominant hand 84

Left M 1: Clustering the Trend u Purpose: Analyze the 1 st and 2 nd order trends in the data along the time series. u Method: Create data set that contains solely the trend signal: l Data set A: data on which detrending was performed. l Data set B: data on which detrending was not performed. l Subtracted the values of data set A from data set B l The result is the trend signal (B contains the trend signal and A does not) u Data: Analysis was done on the voxels of left M 1 region. u Control: l Similar analysis was done for a CSF region l This region contains liquid and has NO neural activity Functional Connectivity and Time Ordering Framework 85

Left M 1: Clustering the Trend Division into 4 explicit clusters: 1. 2. 3. 4. Re-ordered Activity Image Blue: 1 st order ascending trend Red: 1 st order descending trend Turquoise: 2 nd order trend Yellow: 2 nd order trend Clustered Correlation Matrix Clusters Time Plots Functional Connectivity and Time Ordering Framework 86

Left M 1: Clustering the Trend Spatial space: u Clusters are NOT spatially continuous 2 D View Functional Connectivity and Time Ordering Framework 3 D View 87

Left M 1: Clustering the Trend Questions: u u Does the trend represents physiological phenomena? l. Increasing trend voxels (blue cluster): -Amplify their activity as the subject repeats the same motor task -‘short term learning’ voxels? l. Decreasing trend voxels (red cluster): -Deal with non familiar task that required the subject attention. -Reduce their activity as the task become more familiar. -‘handle new scenarios’ voxels? Does the trend represents acquisition artifact (magnetic or electric trend)? Findings: u Control region (CSF) that has no neural activity showed similar results Conclusion: u We cannot tell at this stage is the trend (or part of it) represents physiological phenomena or acquisition artifact Functional Connectivity and Time Ordering Framework 88

Color Map 5: Correlation Grade Purpose: Translate some correlation related features into channel specific information. u Calculated separately for each channel (input is its correlation values vector). u 3 different types of grades are available. 1. Standard deviation (STD) of the correlation values: èSpot channels that belongs to well defined clusters. 2. Average correlation value: èEstimate how ‘functionally friendly’ each channel is (has high correlation values with many other channels). 3. Number of links (correlation values that exceed a threshold): èIsolate channels that constitute a major junction in the brain functional network. èIf statistical test is perform may be used to monitor statistically significant correlation values. u Functional Connectivity and Time Ordering Framework 89

Color Map 5: Correlation Grade - STD Correlation Matrixes: Re-ordered according to correlation clusters Color: Correlation Clusters Color: Correlation Grade - STD 3 Prominent clusters: blue turquoise yellow High Grade 1 Indistinct cluster: Low Grade red Functional Connectivity and Time Ordering Framework 90

Color Map 5: Correlation Grade - Average u Right dominant hand movement task. u Four regions - left and right M 1 and S 1 u u u Correlation matrixes/grade were calculated separately for each region: èCorrelation grade represents only withinregion correlations. Map characters: l Smooth - gradual transitions between voxels with high grades to those with low grades. l Not homogenous - differences between voxels with different grades are noticeable. Left M 1 and S 1 regions: l Have larger number of voxels with high correlation grades (blue shades): l May indicates that the activity of the voxels within those regions is more correlated èThose voxels are more synchronized in performing the same task. CMake senses since voxels on left hemisphere have to work together in controlling right hand movement. Functional Connectivity and Time Ordering Framework Average High Average Low 91

Color Map 5: Correlation Grade – Number of Links u u Right dominant hand movement task. Four regions - left and right M 1 and S 1 A single correlation matrix and corresponding grade was calculated for all voxels: èCorrelation grade represents both withinregion and inter-region correlations Monitor voxels that have big number of significant correlation links (blue shades) èBlue spatial region indicates that voxels in this region have high correlation with other voxels in this or other region. One such blue region is enlarged on the bottom: u Falls within the left M 1 region which manages the movement of the right hand è Contains many significant links between voxels (marked with lines) u u Has preferential within-region correlation (large number of links between left M 1 voxels) Has weaker inter-region correlation (no links between M 1 and S 1 voxels) High Number Low Number Functional Connectivity and Time Ordering Framework 92

Color Map 6: Functional Clustering Similarly to correlation clusters but applied on functional matrix. u Functional clusters have different features then correlation ones: u èAssist in capturing hidden collective motifs related to functional connectivity. u An automatic procedure for analyzing the functional space: l l Can use any number of dimensions (unlike visual investigation which is limited to 3 dimensions) Provide an objective measure instead of leaning on a subjective visual analysis Succeed in identify sub-networks Functional Connectivity and Time Ordering Framework 93

Color Map 6: Functional Clustering Optionally use only few principal vectors instead of entire functional matrix: ☺Those vectors usually contain most of the information. ☺Achieving similar results to clustering the entire matrix. ☺Reduced complexity (dealing with “curse of dimensionality”). Clustering first + second principal vectors PCA 2 Clustering first principal vector PCA 2 u PCA 1 Borders are determined solely by the first vector (PCA 1 axis) è Borders between the clusters are completely vertical u PCA 1 Borders are determined by combination of the first two vectors (PCA 1, PCA 2). è Borders are curve lines in the two dimensional space u Functional Connectivity and Time Ordering Framework 94

Color Map 6: Functional Clustering vs. Correlation clustering u u Divide the voxels into four clusters Perform either functional clustering (according to first 3 dimensions) or correlation clustering (according to the entire matrix) Correlation clusters è Two meaningful groups: 1. One blue cluster whose channels have scattered representation in the manifold. 2. The rest of the three clusters shrink into relatively small sphere in the functional manifold Functional clusters Succeeds to divide the ‘scattered’ channels (blue correlation cluster) into few clusters (blue, yellow, turquoise) è Each of those clusters define one subnetwork in the functional manifold. è Succeeds to keep the shrunken channels as one separate (red) cluster. è Functional Connectivity and Time Ordering Framework 95

Color Map 6: Functional Clustering vs. Correlation clustering Correlation Clusters Mixed Functional Clusters Functional clustering: u Do not distinguish between the 3 clusters - turquoise, yellow, red. u Dividing the correlation blue cluster into 3 different groups. Functional Connectivity and Time Ordering Framework 96

Color Map 6: Functional Clustering in Spatial Space 2 D Axial View 3 D View è Define clusters with many significant links between voxels from the same cluster. è Clusters has relatively continuous representation in the spatial space * Two hands movements Functional Connectivity and Time Ordering Framework 97

Color Map 7: Functional Projection Error u u Purpose: Estimate the per-channel information that was lost (error) when dimension reduction was performed. Main Idea: 1. Reconstruct the affinity matrix using only the principal vectors. 2. Calculate the error between the original and reconstructed matrices (done separately for each channel’s vector). u Our Method: Reverse Projection RMS 1. Reconstruct the affinity matrix by reverse projection - multiply principal scores vectors and inversed components vectors. 2. Calculate Root Mean Square (RMS) error between the original and reconstructed matrices. Functional Connectivity and Time Ordering Framework 98

Color Map 7: Functional Projection Error Full manifold (all channels) small error large error 0 1 Small errors only (<0. 7 = median) è Manifold’s structure is similar to the full manifold one but sparser. Large errors only (>0. 7 = median) è Manifold has only isolated channels structure is not continuous. A good method to reduce number of channels being analyzed s while preserving most of relevant functional information? Functional Connectivity and Time Ordering Framework 99

Important Open Issue Questions: Should we use the affinity transform? Affinity matrix’s manifold ~30% explained Correlation matrix’s manifold ~85% explained More variance is explained in the correlation matrix case but not necessary more relevant information… Functional Connectivity and Time Ordering Framework 100

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 101

FH Application – Main Features u u u Graphical user interface application. Implemented in Matlab. Supported input files: AFNI, Brain Voyager, Matlab. Export to output files: images (*. jpg), text, Matlab. Display: l l u Three main displays (spatial, correlation, functional). Multi purpose display (time series, statistics plots/tables). Interactive control: l l Calculate each of the analysis steps separately or performing the entire analysis. Select data being analyzed (e. g. subset of the channels) Algorithm parameters Display attributes. Functional Connectivity and Time Ordering Framework 102

FH Application – Display Domains u Three main displays: 1. Spatial space 2. Correlation and affinity matrix 3. Functional manifold u Multi purpose display: l 4 time series plots: Channels time series plot, Info-group time series, channels activity image, principal component time series. l 8 general plots: Info-groups histogram, correlation/affinity value histogram, correlation clustering tree, correlation clustering distance, functional coefficient histogram, functional explained variance percentage, functional clustering tree, functional clustering distance. l 3 statistics tables: data space statistics, correlation space statistics, functional statistics. Functional Connectivity and Time Ordering Framework 103

FH Application – Data Display Mode 1. Spatial space 2. Correlation matrix 3. Functional manifold 4. Statistical plots 5. Control panel Functional Connectivity and Time Ordering Framework 104

FH Application – Correlation Display Mode 1. Spatial space 2. Correlation matrix 3. Functional manifold 4. Time series displays 5. Control panel Functional Connectivity and Time Ordering Framework 105

FH Application – Interactive view control u Selecting the displayed color map. May be selected separately for each display domain. u Zooming and rotating of displays. u Setting correlation links threshold. u u Showing either 2 D or 3 D display of spatial space and functional manifold. Select principal components that are used as the functional manifold axes. Selecting the anatomical slices that are displayed. Other display attributes – markers size, links width, background color, etc. Functional Connectivity and Time Ordering Framework 106

FH Application – Interactive view control u Interactive marking of info-group: l l l u Interactive selection of info-groups: l l u Assign channels into groups. Remove channels from groups. Unite two different groups. Groups which are displayed. Groups on which the analysis is performed. Interactive setting of algorithm parameters l l l Type of algorithms that is used. Number of correlation clusters. Thresholds. Distance measurement method. More…. Functional Connectivity and Time Ordering Framework 107

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 108

Future Directions - Functional Connectivity Studies u u u In our research we performed preliminary f. MRI data analysis to demonstrate the framework capabilities. In the future, the framework can be a fertile ground for more comprehensive functional connectivity related studies : l Analysis of multiple data sets (e. g. different subjects, same subject under different behavioral conditions). l Comparing the different data set results using the framework objective measurements. l Perform some statistical inference. Performing functional connectivity studies on our framework can provide mutual usefulness: l l The studies may benefit from the varied functional information that can be obtained using the framework. Development of the framework may benefit from the studies (validation of the methods, highlight weakness points, etc. ) Functional Connectivity and Time Ordering Framework 109

Future Directions - Future Clinical Applications Background u Novel neurobiological approaches start emphasizing that combined actions of interacting brain elements may constitute the link between the brain activity and human mental function. u The brain’s unique structural and functional architecture enables transitions between different types of neural network expressions. u Such expressions may be at the core of brain function and describe variations in behavior when similar regions are activate. u Damage to specific brain regions results in disruption of a network via damage to regions and the connections among them. Challenges u Brain injury clinical observations show highly variable relationship between lesion location and cognitive deficit, u The basis for such variation is still poorly understood, and there is currently no framework to link brain injury to functional deficit Functional Connectivity and Time Ordering Framework 110

Future Directions - Future Clinical Applications Motivation u Changes on brain network dynamics can determine their ability to adapt to brain insult and recovery. u New analytical approaches to understand network function are essential to understand both normal and pathological operations of the human brain u Such understanding may used in various clinical applications, for example monitor or predict the patient recovery for some therapy. Proposal u Our analysis and the varied functional information provided by our framework can help in further understanding the brain functional networks and the networks dynamic u This may later be translated to developing the clinical applications described above. Functional Connectivity and Time Ordering Framework 111

Future Directions - Framework Improvements 1. Statistical interpretation of correlation coefficients: u u u Add statistical interpretation to distinguish between significant correlations and not significant one. A key issue in order to use the framework for more comprehensive f. MRI research. Suggested methods - Bartlett estimator (analytic approach) and Bootstrapping (non analytic). 2. Dealing with the large number of voxels: u u Develop methods to deal with larger number of voxels. Enable to analyze entire data set and provide information about functional connectivity of the entire brain. Functional Connectivity and Time Ordering Framework 112

Future Directions - Framework Improvements 3. Objective measurements of the functional network: u u Automatically investigate the functional space and provide additional objective measurements of the functional network. Suggested methods 1. Refer to functional space as a weighted graph and apply graph theory analysis (e. g. small world properties). 2. Define the channels who are major hubs or the group of channels who constitute the skeleton of the network. 4. Implementation of alternative algorithms: Add alternative algorithms for implementing the existing analysis steps (preserve the same input and output). u Easy to integrate into existing framework since the Functional Connectivity and Time Ordering Framework algorithms are implemented in separate functions/files. 113 u

Presentation Outline u Background u Research objectives and methods u Functional holography algorithm u Experiment description and preprocessing u Displaying the f. MRI data u Color maps and f. MRI preliminary analysis u Graphical user interface application u Future directions and applications u Summary Functional Connectivity and Time Ordering Framework 114

Summary – Main Objective √ Met main objective: Developed novel framework u u for detection of functional connectivity as well as time ordering of brain correlations based on f. MRI data. Framework outline is functional holography analysis. We significantly extended the original analysis: 1. Enhanced analysis flow: add new steps, extend some of the existing ones, and suit algorithm to f. MRI data. 2. Extended channel specific information: support seven color maps (instead of one in the past) which represent seven types of functional / temporal / spatial information. 3. Improved visualization techniques: display the color maps in the three display domains (instead of one in the past) and add new time series and statistics plots/tables. Functional Connectivity and Time Ordering Framework 115

Summary – Main Objective Implementation √ Implementation: Framework was implemented as graphical user interface application u Open source on Matlab environment. u Generic: Enable future use for different dynamic systems data sets beyond f. MRI (e. g. EEG, ECo. G, genes) u Flexible: Interactively modification of various algorithm and display parameters by the user. u Open: Easily integration of external algorithms into the framework in the future. Functional Connectivity and Time Ordering Framework 116

Summary – Secondary Objective (Data Analysis) √ Met secondary objective: Performed preliminary u u f. MRI data analysis for demonstrating the analysis and the implemented software. Data was recorded during motor experiment (hand or two hands movement). Analysis was performed to small number of motor regions (between one and six regions). √ Result: Analysis provided some promising results and showed the potential that this framework has. u Next step: Comprehensive studies are required to validate the results and provide statistical evidences. Functional Connectivity and Time Ordering Framework 117

Summary – “What the framework can do for you? ” ? What’s next? How can the introduced framework can be used? ☺The framework and the corresponding graphical user interface application can be a good tool for future research related to functional connectivity as well as the time ordering of the human brain based on various data types (f. MRI, EEG, ECo. G) Functional Connectivity and Time Ordering Framework 118

Acknowledgements Many thanks to: TAU Instructors: Prof. Eshel Ben Jacob The University of Chicago: l Prof. Ana Solodkin l E. Elinor Chen l Prof. Leo Towle Complex Biological Systems Lab: l Dror Kenett, Itay Baruchi l Itai Doron, Yael Jacob f. MRI Unit Sourasky Medical Center: l Dr. Talma Hendler University of Michigan l Dr. Oren Sagher l Functional Connectivity and Time Ordering Framework 119

Eitan Peri email: eitanperi@gmail. com web page: http: //eitanperi. ac. googlepages. com Functional Connectivity and Time Ordering Framework 120