WORKSHOP
Connectivity Analysis
Correlation, Coherence and Causality
Albert C. Yang, M.D., Ph.D.
Beth Israel Deaconess Medical Center
Harvard Medical School, Boston, USA
• 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