WORKSHOP

Connectivity Analysis

Correlation, Coherence and Causality

Albert C. Yang, M.D., Ph.D.

Beth Israel Deaconess Medical Center

Harvard Medical School, Boston, USA

cyang1@bidmc.harvard.edu

• Understand brain imaging data

• Understand correlation and coherence

• Computation tools for brain networks

• Visualization tools for neuroimaging

Objective

Neuroimaging: NIFTI Format

• https://nifti.nimh.nih.gov/

• Matlab toolbox for reading/saving NIFIT datahttps://www.mathworks.com/matlabcentral/fileexchange/8797-tools-for-nifti-and-analyze-image

Correlation Between Phased Lagged Signal

• t=0:0.01:10;

• s1=sin(2*pi*2*t);

• plot(t,s1)

• s2=sin(2*pi*2*t-pi);

• plot(t,s1,t,s2)

• corr(s1,s2)

Phase Lagged Signal

Correlation Between Noise

• t=1:1:1000;

• s1=rand(1000,1);

• s2=rand(1000,1);

• plot(t,s1,t,s2)

• corr(s1,s2)

Uncorrelated Noise

Phase Coherence

Power Spectrum of S1

• [ps,fs] = pwelch(s1,hanning(length(s1)),0,length(s1),100);

• plot(fs,ps)

Power Spectrum of S2

• [ps,fs] = pwelch(s2,hanning(length(s2)),0,length(s2),100);

• plot(fs,ps)

Spectral Phase Coherence

• Correlation between spectral power of two signals

• [ps1,fs] = pwelch(s1,hanning(length(s1)),0,length(s1),100);

• [ps2,fs] = pwelch(s2,hanning(length(s2)),0,length(s2),100);

• corr(ps1,ps2)

Computation Tools for Brain Networks

• Brain Connectivity Toolbox

• Multivariate Granger Causality Matlab Toolbox

Visualization Tools

• MRICron

• MicroGL

• BrainNet Viewer