WORKSHOP Connectivity Analysis Correlation, Coherence and ... · WORKSHOP Connectivity Analysis Correlation, Coherence and Causality Albert C. Yang, M.D., Ph.D. Beth Israel Deaconess

WORKSHOP

Connectivity Analysis

Correlation, Coherence and Causality

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

Beth Israel Deaconess Medical Center

Harvard Medical School, Boston, USA

[email protected]

• 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