Real vs. spurious interactions We located the peaks in the spectral estimation and then visualized the coherences at different frequencies and locations using the following Matlab code: clear close all load P1_connectivity_data.mat [spectra, f] = pwelch(funct_data', [], [], 2^nextpow2(4*sff), sff); d = diff(f); n = round(2/d(1)); win = hamming(n); win = win/sum(win); f30 = f(f<30); % Find peak locations [~, inds] = sort(max(spectra, [], 1)); inds = inds(end-1:end); %% figure spectra1_2Hz = conv(spectra(:,inds(1)),win,'same'); spectra15_2Hz = conv(spectra(:,14),win,'same'); semilogy(f30, spectra1_2Hz(f<30), 'linewidth', 2 ) hold on semilogy(f30, spectra15_2Hz(f<30), 'linewidth', 2 ) xlabel('frequency [Hz]'); ylabel('Spectral density'); legend('Appropriate reference','Inappropriate reference', 'Location', 'Best'); Cxy = zeros(2,1025,29); [Cxy(1,:,:), f] = mscohere(funct_data(inds(1),:)', funct_data', [], [], 2^nextpow2(4*sff), sff); [Cxy(2,:,:), f] = mscohere(funct_data(14,:)', funct_data', [], [], 2^nextpow2(4*sff), sff); % Convolve with 2 Hz window Cxy2Hz = zeros(size(Cxy)); for i=1:2 for j=1:29 Cxy2Hz(i,:,j) = conv(Cxy(i,:,j), win, 'same'); end end Cxy30 = Cxy2Hz(:,f<30,:); %% figure; plot( locations, mean(squeeze(Cxy30(1,n:end,:)), 1), 'linewidth', 2 ); axis tight; hold on plot( locations, mean(squeeze(Cxy30(2,n:end,:)), 1), 'linewidth', 2 ); axis tight; xlabel('Distance'); ylabel('Coherence'); legend('Appropriate reference','Inappropriate reference', 'Location', 'Best'); % Plot magnitude squared coherence of the two source points figure; subplot(1,2,1); surf(locations, f30(n:4:end), squeeze(Cxy30(1,n:4:end,:)),'edgealpha',0.3, 'FaceColor','interp'); xlabel('location'); ylabel('frequency'); title('Appropriate reference') subplot(1,2,2); surf(locations, f30(n:4:end), squeeze(Cxy30(2,n:4:end,:)),'edgealpha', 0.3, 'FaceColor','interp'); xlabel('location'); ylabel('frequency'); title('Inappropriate reference')

FMRI DATA ANALYSIS

SPONTANEOUS OSCILLATORY ACTIVITY Spontaneous occipital Alpha rhythm can be induced or suppressed by closing and opening one’s eyes, respectively. In Fig. [fig_spectra] we can see a clear spike in the 10 Hz area in data 1. Compared to the data set 2 no clear spikes it’s pretty safe to assume that data 1 was recorded with eyes closed and data 2 with eyes opened.

To construct the L2 MNE operator, we used the formula found in the lecture slides: $$P_{MNE}=RL^T(LRL^T + \lambda C_n)^{-1}$$ The following Matlab script was used in the simple case without depth weighting: load ex3_data.mat %% MNE L2=L*L'; snr = sqrt(n_trial); lambda = trace(L2)/(trace(Cn)*snr^2); ev = eigs(L2+lambda*Cn, rank(data1)); tol = ev(end) p_mne=L'*pinv(L2+lambda*Cn, tol); src1 = p_mne*data1; src2 = p_mne*data2; Here an identity matrix was used for the source covariance matrix. Next, to include depth weighting, we modified the source covariance matrix: %% Depth-Weighted MNE W_i = diag(sqrt(sum(L,1).^2./306)); lambda = trace(L*W_i*L')/(trace(Cn)*snr^2); ev = eigs(L*W_i*L'+lambda*Cn, rank(data1)); tol = ev(end) pw_mne=W_i*L'*pinv(L*W_i*L'+lambda*Cn,tol); srcw1 = pw_mne*data1; srcw2 = pw_mne*data2; Finally, we constructed a beamformer operator for the data: %% Beamformer N = 306; M = 5124; ev = eigs(Cd, rank(data1)); tol = ev(end) p_bf = (pinv(Cd,tol)*L)'; denominator = diag(p_bf*L); p_bf = p_bf./repmat(denominator,1, N); srcb1 = p_bf*data1; srcb2 = p_bf*data2; using the following formula from the lecture slides $$P_{BF,\theta} = ^{-1} L_\theta)^T}{L_\theta^T C_^{-1} L_\theta},$$ where Lθ is the gain vector for source point θ. We wanted to visualize the source estimates as a function of time. We achieved this with the following script: %% Plots close all vis_surface_data(srcb1(:,115), 0.1, max(srcb1(:)), anat_decim) %% close all figure(3) hold on vv = var(data1,[], 2); plot(timeaxis,data1(vv > 0.3*max(vv),:)) plot([1,1]*timeaxis(115),ylim(gca()), 'k--') plot([1,1]*timeaxis(140),ylim(gca()), 'k--') plot([1,1]*timeaxis(190),ylim(gca()), 'k--') xlabel('time [s]') axis tight %% close all figure(4) hold on vv = var(data2,[], 2); plot(timeaxis,data2(vv > 0.3*max(vv),:)) plot([1,1]*timeaxis(125),ylim(gca()), 'k--') plot([1,1]*timeaxis(190),ylim(gca()), 'k--') xlabel('time [s]') axis tight

The evoked responses were calculated over 600 ms time window, with 100 ms pre-stimulus and 500 ms post-stimulus. Evoked responses for triggers 2, 3, and 16 are visualized in Figures [fig_topo2], [fig_topo3] and [fig_topo23]. Since all sensors were planar gradiometers, the signal is strongest over the areas of the corresponding brain activity. The following Matlab script was used to calculate and visualize the pre-recorded data set: find_trgs; %Extract the positions of trigger code 2 events| trigs_2 = trgs{2}; %Compute the number of samples before and after the stimulus prestimulus = round(0.100*samplingrate); poststimulus = round(0.500*samplingrate); ave = zeros(306, prestimulus+poststimulus+1); %Compute the average response for i=1:length(trigs_2) ave = ave + data(1:306,trigs_2(i)-prestimulus:trigs_2(i)+poststimulus); end ave = ave / length(trigs_2); plotEF(taxis, ave, 'axes','on','comment', 'Trigger 2'); figure; channel0 = 'MEG 1923'; plot((1:361)/samplingrate -0.1, ave(ismember(channels, channel0),:) ) title(channel0); xlabel('time from stimulus [s]'); ylabel('Response amplitude [T/m]')} The highest response for trigger 2 is located over the visual cortex so the stimulus is most likely visual. The two peaks are also found from reference articles and . The response is greater on the left side, which means the stimulus was most likely in the right visual hemifield as can be seen from Fig. [fig_vishemi] Trigger 3 seems to correspond to an audio stimulus. Highest activation is over auditory cortex and the responses have clear peak at 100 ms, which is typical for certain audio stimuli . Based on the measurements in , the frequency of the tone is most likely over 600 Hz. Since there is activation on the left and right sides of the cortex, the stimulus is most probably heard by both ears. The last stimulus type is most likely median nerve stimulation and more precisely left median nerve stimulation since the activation is seen over the right somatosensory cortex. The response in Fig. [fig_trig23] is very similar as the one in Fig. 1. Distribution of Work - Manu wrote some of the Matlab script and contributed to the writing of the homework. - Antti M. assisted in writing the Matlab script, searched three of the papers, and initialized the report-writing platform. - Antti R. found one of the papers, wrote the basic structure of the homework, and compiled the LaTex file. - Tuomo was reassigned to the group when the assignment was already completed, although read through the assignment and checked through the neurobiological interpretation and found it to be valid