diff --git a/.DS_Store b/.DS_Store deleted file mode 100644 index 487def8..0000000 Binary files a/.DS_Store and /dev/null differ diff --git a/ExampleCode.m b/ExampleCode.m old mode 100644 new mode 100755 index e7b0897..de550f3 --- a/ExampleCode.m +++ b/ExampleCode.m @@ -1,139 +1,90 @@ % Note: the following simulations use a GLM-based method to simulate V_low -% and V_high, and the p-values are the analytical p-values from the +% and V_high, and the p-values are the empirical bootstrapped p-values from the % manuscript %% Signal with neither PAC nor AAC -[XX,P,Vlo,Vhi,t] = simfun(0,0,'GLM','theoretical','none',.05); -figure(1) -plot(t,Vlo + .08,t,Vhi,'LineWidth',2); axis off -hold on; -[pks, ipks] = findpeaks(Vlo); -for i = 1:length(ipks) - ind = ipks(i); - plot([t(ind),t(ind)],[Vlo(ind)+.07,Vlo(ind)+.09],'r','LineWidth',2) -end -plot([8,8.1],[-.04,-.04],'k','LineWidth',2) -legend('V_{low}','V_{high}') -axis off -set(gca,'FontSize',13) -str = strcat({'R_PAC is '},{num2str(XX.rpac)},{' with p-value '},{num2str(P.rpac)}); disp(str); -str = strcat({'R_AAC is '},{num2str(XX.raac)},{' with p-value '},{num2str(P.raac)}); disp(str); -str = strcat({'R_CFC is '},{num2str(XX.rcfc)},{' with p-value '},{num2str(P.rcfc)}); disp(str); -xlim([8,10]) +[XX] = simfun(0,0,'pink','none','none','none',.05); +d = 5; +XX.ampAXIS = XX.ampAXIS(1:d:end); +XX.phi0 = XX.phi0(1:d:end); +XX.PAC = XX.Phi_low(1:d:end,1:d:end); XX.AAC = XX.A_low(1:d:end,1:d:end); XX.CFC = XX.Phi_low_A_low(1:d:end,1:d:end); -figure(2) -surf(XX.ampAXIS,XX.phi0,XX.PAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[35, 106, 185]/255); -hold on; -surf(XX.ampAXIS,XX.phi0,XX.AAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[214, 26, 70]/255); +surf(XX.ampAXIS,XX.phi0,XX.PAC,'FaceAlpha',.8,'FaceColor',[35, 106, 185]/255); hold on; -surf(XX.ampAXIS,XX.phi0,XX.CFC,'EdgeColor','none','FaceAlpha',.9,'FaceColor',[253, 220, 34]/255); - +surf(XX.ampAXIS,XX.phi0,XX.AAC,'FaceAlpha',.8,'FaceColor',[214, 26, 70]/255); +surf(XX.ampAXIS,XX.phi0,XX.CFC,'FaceAlpha',.9,'FaceColor',[253, 220, 34]/255); xlim([min(XX.ampAXIS),max(XX.ampAXIS)]); ylim([min(XX.phi0),max(XX.phi0)]) xlabel('A_{low}'); ylabel('\Phi_{low}'); zlabel('A_{high}') -legend('PAC','AAC','CFC') +legend('\phi_{low}','A_{low}','\phi_{low},A_{low}') set(gca,'FontSize',13) +set(gca,'YTick',-pi:pi:pi) +set(gca,'YTickLabel',{'-\pi','0','\pi'}) +set(gca,'Ydir','reverse') grid off -zlim([.008,.02]) +zlim([.002,.02]) %% Signal with PAC -[XX,P,Vlo,Vhi,t] = simfun(1,0,'GLM','theoretical','none',.05); -figure(1) -plot(t,Vlo + .08,t,Vhi,'LineWidth',2); axis off -hold on; -[pks, ipks] = findpeaks(Vlo); -for i = 1:length(ipks) - ind = ipks(i); - plot([t(ind),t(ind)],[Vlo(ind)+.07,Vlo(ind)+.09],'r','LineWidth',2) -end -plot([8,8.1],[-.04,-.04],'k','LineWidth',2) -legend('V_{low}','V_{high}') -axis off -set(gca,'FontSize',13) -str = strcat({'R_PAC is '},{num2str(XX.rpac)},{' with p-value '},{num2str(P.rpac)}); disp(str); -str = strcat({'R_AAC is '},{num2str(XX.raac)},{' with p-value '},{num2str(P.raac)}); disp(str); -str = strcat({'R_CFC is '},{num2str(XX.rcfc)},{' with p-value '},{num2str(P.rcfc)}); disp(str); -xlim([8,10]) +[XX] = simfun(1,0,'pink','none','none','none',.05); +d = 5; +XX.ampAXIS = XX.ampAXIS(1:d:end); +XX.phi0 = XX.phi0(1:d:end); +XX.PAC = XX.Phi_low(1:d:end,1:d:end); XX.AAC = XX.A_low(1:d:end,1:d:end); XX.CFC = XX.Phi_low_A_low(1:d:end,1:d:end); -figure(2) -surf(XX.ampAXIS,XX.phi0,XX.PAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[35, 106, 185]/255); -hold on; -surf(XX.ampAXIS,XX.phi0,XX.AAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[214, 26, 70]/255); +surf(XX.ampAXIS,XX.phi0,XX.PAC,'FaceAlpha',.8,'FaceColor',[35, 106, 185]/255); hold on; -surf(XX.ampAXIS,XX.phi0,XX.CFC,'EdgeColor','none','FaceAlpha',.9,'FaceColor',[253, 220, 34]/255); - +surf(XX.ampAXIS,XX.phi0,XX.AAC,'FaceAlpha',.8,'FaceColor',[214, 26, 70]/255); +surf(XX.ampAXIS,XX.phi0,XX.CFC,'FaceAlpha',.9,'FaceColor',[253, 220, 34]/255); xlim([min(XX.ampAXIS),max(XX.ampAXIS)]); ylim([min(XX.phi0),max(XX.phi0)]) xlabel('A_{low}'); ylabel('\Phi_{low}'); zlabel('A_{high}') -legend('PAC','AAC','CFC') +legend('\phi_{low}','A_{low}','\phi_{low},A_{low}') set(gca,'FontSize',13) +set(gca,'YTick',-pi:pi:pi) +set(gca,'YTickLabel',{'-\pi','0','\pi'}) +set(gca,'Ydir','reverse') grid off -zlim([.008,.02]) - +zlim([.002,.01]) %% Signal with AAC -[XX,P,Vlo,Vhi,t] = simfun(0,1,'GLM','theoretical','none',.05); -figure(1) -plot(t,Vlo + .08,t,Vhi,'LineWidth',2); axis off -hold on; -[pks, ipks] = findpeaks(Vlo); -for i = 1:length(ipks) - ind = ipks(i); - plot([t(ind),t(ind)],[Vlo(ind)+.07,Vlo(ind)+.09],'r','LineWidth',2) -end -plot([8,8.1],[-.04,-.04],'k','LineWidth',2) -legend('V_{low}','V_{high}') -axis off -set(gca,'FontSize',13) -str = strcat({'R_PAC is '},{num2str(XX.rpac)},{' with p-value '},{num2str(P.rpac)}); disp(str); -str = strcat({'R_AAC is '},{num2str(XX.raac)},{' with p-value '},{num2str(P.raac)}); disp(str); -str = strcat({'R_CFC is '},{num2str(XX.rcfc)},{' with p-value '},{num2str(P.rcfc)}); disp(str); -xlim([8,10]) +[XX] = simfun(0,1,'pink','none','none','none',.05); +d = 5; +XX.ampAXIS = XX.ampAXIS(1:d:end); +XX.phi0 = XX.phi0(1:d:end); +XX.PAC = XX.Phi_low(1:d:end,1:d:end); XX.AAC = XX.A_low(1:d:end,1:d:end); XX.CFC = XX.Phi_low_A_low(1:d:end,1:d:end); -figure(2) -surf(XX.ampAXIS,XX.phi0,XX.PAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[35, 106, 185]/255); +surf(XX.ampAXIS,XX.phi0,XX.PAC,'FaceAlpha',.8,'FaceColor',[35, 106, 185]/255); hold on; -surf(XX.ampAXIS,XX.phi0,XX.AAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[214, 26, 70]/255); -hold on; -surf(XX.ampAXIS,XX.phi0,XX.CFC,'EdgeColor','none','FaceAlpha',.9,'FaceColor',[253, 220, 34]/255); - +surf(XX.ampAXIS,XX.phi0,XX.AAC,'FaceAlpha',.8,'FaceColor',[214, 26, 70]/255); +surf(XX.ampAXIS,XX.phi0,XX.CFC,'FaceAlpha',.9,'FaceColor',[253, 220, 34]/255); xlim([min(XX.ampAXIS),max(XX.ampAXIS)]); ylim([min(XX.phi0),max(XX.phi0)]) xlabel('A_{low}'); ylabel('\Phi_{low}'); zlabel('A_{high}') -legend('PAC','AAC','CFC') +legend('\phi_{low}','A_{low}','\phi_{low},A_{low}') set(gca,'FontSize',13) +set(gca,'YTick',-pi:pi:pi) +set(gca,'YTickLabel',{'-\pi','0','\pi'}) +set(gca,'Ydir','reverse') grid off -zlim([.008,.02]) +zlim([.002,.01]) %% Signal with PAC and AAC -[XX,P,Vlo,Vhi,t] = simfun(1,1,'GLM','theoretical','none',.05); -figure(1) -plot(t,Vlo + .08,t,Vhi,'LineWidth',2); axis off -hold on; -[pks, ipks] = findpeaks(Vlo); -for i = 1:length(ipks) - ind = ipks(i); - plot([t(ind),t(ind)],[Vlo(ind)+.07,Vlo(ind)+.09],'r','LineWidth',2) -end -plot([8,8.1],[-.04,-.04],'k','LineWidth',2) -legend('V_{low}','V_{high}') -axis off -set(gca,'FontSize',13) -str = strcat({'R_PAC is '},{num2str(XX.rpac)},{' with p-value '},{num2str(P.rpac)}); disp(str); -str = strcat({'R_AAC is '},{num2str(XX.raac)},{' with p-value '},{num2str(P.raac)}); disp(str); -str = strcat({'R_CFC is '},{num2str(XX.rcfc)},{' with p-value '},{num2str(P.rcfc)}); disp(str); -xlim([8,10]) +[XX] = simfun(1,1,'pink','none','none','none',.05); +d = 5; +XX.ampAXIS = XX.ampAXIS(1:d:end); +XX.phi0 = XX.phi0(1:d:end); +XX.PAC = XX.Phi_low(1:d:end,1:d:end); XX.AAC = XX.A_low(1:d:end,1:d:end); XX.CFC = XX.Phi_low_A_low(1:d:end,1:d:end); -figure(2) -surf(XX.ampAXIS,XX.phi0,XX.PAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[35, 106, 185]/255); +surf(XX.ampAXIS,XX.phi0,XX.PAC,'FaceAlpha',.8,'FaceColor',[35, 106, 185]/255); hold on; -surf(XX.ampAXIS,XX.phi0,XX.AAC,'EdgeColor','none','FaceAlpha',.8,'FaceColor',[214, 26, 70]/255); -hold on; -surf(XX.ampAXIS,XX.phi0,XX.CFC,'EdgeColor','none','FaceAlpha',.9,'FaceColor',[253, 220, 34]/255); - +surf(XX.ampAXIS,XX.phi0,XX.AAC,'FaceAlpha',.8,'FaceColor',[214, 26, 70]/255); +surf(XX.ampAXIS,XX.phi0,XX.CFC,'FaceAlpha',.9,'FaceColor',[253, 220, 34]/255); xlim([min(XX.ampAXIS),max(XX.ampAXIS)]); ylim([min(XX.phi0),max(XX.phi0)]) xlabel('A_{low}'); ylabel('\Phi_{low}'); zlabel('A_{high}') -legend('PAC','AAC','CFC') +legend('\phi_{low}','A_{low}','\phi_{low},A_{low}') set(gca,'FontSize',13) +set(gca,'YTick',-pi:pi:pi) +set(gca,'YTickLabel',{'-\pi','0','\pi'}) +set(gca,'Ydir','reverse') grid off -zlim([.008,.02]) \ No newline at end of file +zlim([.002,.013]) \ No newline at end of file diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..f288702 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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But first, please read +. diff --git a/Patient_Data.mat b/Patient_Data.mat old mode 100644 new mode 100755 diff --git a/README.md b/README.md index c90a8a2..8dac6af 100644 --- a/README.md +++ b/README.md @@ -1,16 +1,20 @@ # GLM-CFC -A GLM based approach to measure CFC +A GLM based approach to assess CFC. -Code to measure cross-frequency coupling between two signals as described in this manuscript: [A statistical modeling framework to assess cross-frequency coupling while accounting for confounding effects] +Code to measure cross-frequency coupling between two signals as described in this manuscript: -simfun: code to simulate signals V_low, V_high, with induced cross-frequency coupling and measure output statistics R_PAC, R_AAC, and R_CFC, along with confidence intervals and p-values +[A statistical framework to assess cross-frequency coupling while accounting for confounding analysis effects](https://www.biorxiv.org/content/10.1101/519470v2), J. Nadalin, L-E Martinet, E. Blackwood, M-S Lo, A. S. Widge, S. S. Cash, U. T. Eden, M. A. Kramer, 2019. -glmfun: code to evaluate coupling statistics R_PAC, R_AAC, and R_CFC, along with confidence intervals and p-values, between two signals +`ExampleCode.m`: Run the cells in this file to produce example voltage traces and surfaces in (Phi_low, A_low, A_high)-space (as in Figure 4 of the manuscript). Four simulations are present: (i) no CFC, (ii) PAC only, (iii) AAC only, and (iv) both PAC and AAC. -ExampleCode: run to get example voltage traces and surfaces in Phi_low, A_low, A_high space (as in Figure 4). Four simulations are present: one with no CFC, one with PAC, one with AAC, and one with both PAC and AAC +`simfun.m`: Code to simulate signals V_low, V_high, with induced cross-frequency coupling and measure output statistics R_PAC and R_AAC along with confidence intervals and p-values. -glmfun_with_indicator: an example of how to update glmfun to test for effect of condition (e.g. pre and post stimuli) on coupling +`glmfun.m`: Code to evaluate the coupling statistics R_PAC and R_AAC, along with confidence intervals and p-values, between two signals. -The human data from figures 9 and 10 can be found in Patient_Data, and the rat data from figure 11 can be found at https://github.com/tne-lab/cl-example-data +`glmfun_with_indicator.m`: Cn example of how to update glmfun to test for effect of condition (e.g. pre and post stimuli) on coupling -Any questions/comments please direct to Jessica Nadalin (jnadalin@bu.edu) +The voltage traces for the human data can be found in `Patient_Data.mat`, and the rodent data can be found at https://github.com/tne-lab/cl-example-data + +The [Chaotic System Toolbox](https://www.mathworks.com/matlabcentral/fileexchange/1597-chaotic-systems-toolbox) is required to generate surrogate data. + +Any questions/comments please direct to Jessica Nadalin (jnadalin@bu.edu) or Mark Kramer (mak@bu.edu) \ No newline at end of file diff --git a/glmfun.m b/glmfun.m old mode 100644 new mode 100755 index 4a1912f..2bfda8e --- a/glmfun.m +++ b/glmfun.m @@ -1,25 +1,23 @@ -function [XX,P] = glmfun(Vlo, Vhi,pval,ci,varargin) +function [XX,P] = glmfun(Vlo, Vhi,pval,ci,AIC,varargin) %INPUTS: % Vlo: Low frequency signal % Vhi: High frequency signal -% nCtlPts: number of control points, for spline phase % pval: 'theoretical' gives analytic p-values for R % 'empirical' gives bootstrapped p-values for R % ci: 'ci' gives confidence intervals, 'none' gives no confidence intervals +% AIC: 'AIC' computes number of control points for spline +% phase via AIC minimization % varargin: optionally, include the parameter q indicating which quantiles % of AmpLo you'd like to fit over %OUTPUTS: -% XX.rpac: R_PAC value, confidence intervals XX.rPAC_CI -% XX.raac: R_AAC value, confidence intervals XX.rAAC_CI -% XX.rcfc: R_CFC value, confidence intervals XX.rCFC_CI -% XX.null: 3D surface for null model in Phi_low, A_low, A_high space -% XX.PAC: 3D surface for PAC model in Phi_low, A_low, A_high space -% XX.AAC: 3D surface for AAC model in Phi_low, A_low, A_high space -% XX.CFC: 3D surface for CFC model in Phi_low, A_low, A_high space -% P.rpac: p-value for RPAC statistic -% P.raac: p-value for RAAC statistic -% P.rcfc: p-value for RCFC statistic +% XX.rpac: R_PAC value, confidence intervals XX.rPAC_CI +% XX.raac: R_AAC value, confidence intervals XX.rAAC_CI +% XX.Phi_low: 3D surface for Phi_low model in Phi_low, A_low, A_high space +% XX.A_low: 3D surface for A_low model in Phi_low, A_low, A_high space +% XX.Phi_low_A_low: 3D surface for Phi_low,A_low model in Phi_low, A_low, A_high space +% P.rpac: p-value for RPAC statistic +% P.raac: p-value for RAAC statistic nCtlPts = 10; @@ -28,23 +26,49 @@ amp = abs(hilbert(Vhi)); ampLO = abs(hilbert(Vlo)); + if exist('AIC','var') && strcmp(AIC, 'AIC') + + Y = amp'; + CtlPts = (4:1:30); + %Compute the AIC. + AIC1 = zeros(size(CtlPts)); + for k=1:length(CtlPts) %for each suggested # knots + nCtlPts = CtlPts(k); + X1 = spline_phase0(phi',nCtlPts);%low frequency phase + [~, dev1, ~] = glmfit(X1, Y, 'gamma', 'link', 'log', 'constant', 'off'); %Phi_low model + AIC1(k) = dev1 + 2*nCtlPts; %compute AIC + end + %Select the # control points from AIC, and plot the AIC. + [~, imn1] = min(AIC1); + nCtlPts1 = CtlPts(imn1); + + figure(1); clf(); + plot(CtlPts, AIC1, 'k', 'LineWidth',2) + hold on + plot([nCtlPts1, nCtlPts1], [min(AIC1) max(AIC1)], 'r', 'LineWidth', 2) + hold off + axis tight + xlabel('# control points') + ylabel('AIC') + set(gca,'FontSize',13) + fprintf(['Suggested number of control points is ' num2str(nCtlPts1) '\n']) + nCtlPts = nCtlPts1; + end + %Define variables for GLM procedure. Y = amp'; %high frequency amplitude X1 = spline_phase0(phi',nCtlPts); %low frequency phase X2 = [ones(size(Y)),ampLO']; %low frequency amplitude X3 = [X1,ampLO',sin(phi').*ampLO',cos(phi').*ampLO']; %low frequency phase, low frequency amplitude, interaction terms - XC = ones(size(Y)); %ones (null) %Perform GLM. [b1, dev1, stats1] = glmfit(X1, Y, 'gamma', 'link', 'log', 'constant', 'off'); %PAC [b2, dev2, stats2] = glmfit(X2, Y, 'gamma','link','log','constant','off'); %AAC [b3, dev3, stats3] = glmfit(X3, Y, 'gamma','link','log','constant','off'); %CFC - [bC, dev0, statsC] = glmfit(XC, Y, 'gamma', 'link', 'log', 'constant', 'off'); %null %Chi^2 test between nested models (theoretical p-values) - chi0 = 1-chi2cdf(dev0-dev3,12); - chi1 = 1-chi2cdf(dev1-dev3,3); %Between PAC and PACAAC Model, if low AAC is present - chi2 = 1-chi2cdf(dev2-dev3,11); %Between AAC and PACAAC Model, if low PAC is present + chi1 = 1-chi2cdf(dev1-dev3,3); %Between Phi_low and Phi_low,A_low Model, if low AAC is present + chi2 = 1-chi2cdf(dev2-dev3,11); %Between A_low and Phi_low,A_low Model, if low PAC is present %create 3d model surfaces phi0 = linspace(-pi,pi,100); @@ -54,45 +78,39 @@ ind = find(ampLO>quantile(ampLO,q) & ampLOXX.rpac)))/length(M.rpac); P.raac = max(.5,length(find(M.raac>XX.raac)))/length(M.raac); - P.rcfc = max(.5,length(find(M.rcfc>XX.rcfc)))/length(M.rcfc); elseif exist('pval','var') && strcmp(pval, 'theoretical') P.rpac = chi2; %use theoretical p-values P.raac = chi1; - P.rcfc = chi0; else P = 'No p-values output'; end @@ -103,43 +121,56 @@ Amax = max(ampSORT); Amin = min(ampSORT); stepsize = (Amax-Amin)/99; X2eval = Amin:stepsize:Amax; %evaluate on all amplitudes X2eval = [ones(size(phi0))',X2eval']; - %Determine CI for the measure RPAC. - M = 10000; - bMC = b1*ones(1,M) + sqrtm(stats1.covb)*normrnd(0,1,nCtlPts,M); - splineMC = glmval(bMC,X0,'log',stats1,'constant', 'off'); - mx = zeros(M,1); - for k=1:M - mx(k) = max(abs(1-splineMC(:,k)./splineC)); - end - r_CI = quantile(mx, [0.025, 0.975]); - XX.rpac_ci = r_CI; - - %and for rAAC - M = 10000; - bMC = b2*ones(1,M) + sqrtm(stats2.covb)*normrnd(0,1,2,M); - splineMC = glmval(bMC,X2eval,'log',stats2,'constant', 'off'); - mx = zeros(M,1); - for k=1:M - mx(k) = max(abs(1-splineMC(:,k)./splineC)); - end - r2_CI = quantile(mx, [0.025, 0.975]); - XX.raac_ci = r2_CI; - - %and for rCFC - M = 10000; - [m,~] = max(abs(1-XX3./XXC)); %find point of maximum distance between null, CFC models - [~,j] = max(m); %j ampLO, I(j) phiLO - bMC = b3*ones(1,M) + sqrtm(stats3.covb)*normrnd(0,1,nCtlPts+3,M); - Y1 = spline_phase0(phi0',nCtlPts); %model 1, function of phiLo - Y2 = [Y1,ampAXIS(j)*ones(size(phi0))']; %model 2, function of phiLo, ampLo - Y3 = [Y2,ampAXIS(j)*sin(phi0'),ampAXIS(j)*cos(phi0')]; - splineMC = glmval(bMC,Y3,'log',stats3,'constant', 'off'); - mx = zeros(M,1); - for k=1:M - mx(k) = max(abs(1-splineMC(:,k)./splineC)); - end - r3_CI = quantile(mx, [0.025, 0.975]); - XX.rcfc_ci = r3_CI; + + [m] = max(abs(1-Xtemp'./XX3)); %find point of maximum distance between A_low and Phi_low,A_low models + [~,j] = max(m); %j ampLO index + [m2] = max(abs(1-Xtemp'./XX3),[],2); + [~,j2] = max(m2); %j2 phiLO index + phiLOW = phi0(j2); + M = 10000; + bMC = b3*ones(1,M) + sqrtm(stats3.covb)*normrnd(0,1,nCtlPts+3,M); + %Phi_low,A_low model at fixed Phi_low + Y_phi = spline_phase0(phiLOW*ones(size(phi0)),nCtlPts); %Phi_low model + AmpLOW = [Amin:stepsize:Amax]'; + Y_phi = [Y_phi,AmpLOW]; %A_low model + Y_phi = [Y_phi,AmpLOW*sin(phiLOW'),AmpLOW*cos(phiLOW')]; + spline_phi = glmval(bMC,Y_phi,'log',stats3,'constant', 'off'); %Phi_low,A_low model, constant in phi_low dim + %Phi_low,A_low model at fixed A_low + Y_a = spline_phase0(phi0',nCtlPts); %Phi_low model + Y_a = [Y_a,ampAXIS(j)*ones(size(phi0))']; %A_low model + Y_a = [Y_a,ampAXIS(j)*sin(phi0'),ampAXIS(j)*cos(phi0')]; + spline_a = glmval(bMC,Y_a,'log',stats3,'constant','off'); %Phi_low,A_low model, constant in A_low dimension + %A_low model at fixed A_low + bMC = b2*ones(1,M) + sqrtm(stats2.covb)*normrnd(0,1,2,M); + X2eval_fixed_A = [ones(size(phi0))',ones(size(phi0))'*ampAXIS(j)]; + splineMC = glmval(bMC,X2eval_fixed_A,'log',stats2,'constant', 'off'); + splineAAC_a = splineMC; + %A_low model at fixed Phi_low + M = 10000; + bMC = b2*ones(1,M) + sqrtm(stats2.covb)*normrnd(0,1,2,M); + splineMC = glmval(bMC,X2eval,'log',stats2,'constant', 'off'); + splineAAC_phi = splineMC; + %Phi_low model at fixed A_low + M = 10000; + bMC = b1*ones(1,M) + sqrtm(stats1.covb)*normrnd(0,1,nCtlPts,M); + splinePAC_a = glmval(bMC,X0,'log',stats1,'constant', 'off'); + %Phi_low model at fixed Phi_low + X0_eval_fixed_Phi = spline_phase0(phiLOW*ones(size(phi0)),nCtlPts); + bMC = b1*ones(1,M) + sqrtm(stats1.covb)*normrnd(0,1,nCtlPts,M); + splinePAC_phi = glmval(bMC,X0_eval_fixed_Phi,'log',stats1,'constant', 'off'); + + mx_pac = zeros(M,1); mx_aac = zeros(M,1); + for k = 1:M + m_a = max(abs(1-splineAAC_a(:,k)./spline_a(:,k))); %fixed A + m_phi = max(abs(1-splineAAC_phi(:,k)./spline_phi(:,k))); %fixed Phi + mx_pac(k) = max(m_a,m_phi); + + m_a = max(abs(1-splinePAC_a(:,k)./spline_a(:,k))); %fixed A + m_phi = max(abs(1-splinePAC_phi(:,k)./spline_phi(:,k))); %fixed Phi + mx_aac(k) = max(m_a,m_phi); + end + XX.rpac_ci = quantile(mx_pac,[0.025,0.975]); + XX.raac_ci = quantile(mx_aac,[0.025,0.975]); end end @@ -147,16 +178,15 @@ % Bootstrapped p-values function M = minvals(Vlo,Vhi) K = 100; - RPAC = zeros(1,K); RCFC = zeros(1,K); RAAC = zeros(1,K); + RPAC = zeros(1,K); RAAC = zeros(1,K); N = zeros(1,K); L = zeros(1,K); for i = 1:K Vhi_prime = AAFT(Vhi,1); - [XX] = glmfun(Vlo,Vhi_prime','none'); %compute R statistics between Vhi and shifted Vlo + [XX] = glmfun(Vlo,Vhi_prime','none','none','none',.05); %compute R statistics between Vhi and shifted Vlo RPAC(i) = XX.rpac; - RCFC(i) = XX.rcfc; RAAC(i) = XX.raac; end - M.rpac = RPAC; M.rcfc = RCFC; M.raac = RAAC; M.shiftN = N; M.shiftL = L; + M.rpac = RPAC;M.raac = RAAC; end % Generate a design matrix X (n by nCtlPts) for a phase signal (n by 1) diff --git a/simfun.m b/simfun.m old mode 100644 new mode 100755 index 93cff38..fc0b8f6 --- a/simfun.m +++ b/simfun.m @@ -1,4 +1,4 @@ -function [XX,P,Vlo,Vhi,t] = simfun(pac_mod,aac_mod,sim_method,pval,ci,varargin) +function [XX,P,Vlo,Vhi,t] = simfun(pac_mod,aac_mod,sim_method,pval,ci,AIC,varargin) %INPUTS: % pac_mod: Intensity of PAC (I_PAC in paper) % aac_mod: Intensity of AAC (I_AAC in paper) @@ -8,23 +8,22 @@ % 'empirical' gives bootstrapped p-values for R % ci: 'ci' gives confidence intervals for R % 'none' gives no confidence intervals (faster) +% AIC: 'AIC' computes number of control points for spline +% phase via AIC minimization % varargin: optionally, include the parameter q indicating which quantiles % of AmpLo you'd like to fit over % %OUTPUTS: -% XX.rpac: R_PAC value, confidence intervals XX.rPAC_CI -% XX.raac: R_AAC value, confidence intervals XX.rAAC_CI -% XX.rcfc: R_CFC value, confidence intervals XX.rCFC_CI -% XX.null: 3D surface for null model in Phi_low, A_low, A_high space -% XX.PAC: 3D surface for PAC model in Phi_low, A_low, A_high space -% XX.AAC: 3D surface for AAC model in Phi_low, A_low, A_high space -% XX.CFC: 3D surface for CFC model in Phi_low, A_low, A_high space -% P.rpac: p-value for RPAC statistic -% P.raac: p-value for RAAC statistic -% P.rcfc: p-value for RCFC statistic -% Vlo: simulated low-frequency signal -% Vhi: simulated high-frequency signal -% t: time +% XX.rpac: R_PAC value, confidence intervals XX.rPAC_CI +% XX.raac: R_AAC value, confidence intervals XX.rAAC_CI +% XX.Phi_low: 3D surface for Phi_low model in Phi_low, A_low, A_high space +% XX.A_low: 3D surface for A_low model in Phi_low, A_low, A_high space +% XX.Phi_low_A_low: 3D surface for Phi_low,A_low model in Phi_low, A_low, A_high space +% P.rpac: p-value for RPAC statistic +% P.raac: p-value for RAAC statistic +% Vlo: simulated low-frequency signal +% Vhi: simulated high-frequency signal +% t: time dt = 0.002; Fs = 1/dt; fNQ = Fs/2; % Simulated time series parameters. N = 20/dt+4000; % # steps to simulate, making the duration 20s @@ -77,16 +76,41 @@ end s = s/max(s); % Normalize so it falls between 0 and 1 -if exist('sim_method','var') && strcmp(sim_method, 'GLM') - Ahi = (1+pac_mod*s)'; % Define Ahi. - Vhi = (0.01* Ahi .* cos(angle(hilbert(Vhi'))))';% ... and use PhiHi to get Vhi. -elseif exist('sim_method','var') && strcmp(sim_method, 'pink') - Vhi = Vhi.*(1+pac_mod*s); % Modulate high freq activity by modulation envelope. +if exist('sim_method','var') + + switch sim_method + + case 'GLM' + Ahi = (1+pac_mod*s)'; % Define Ahi. + Vhi = (0.01* Ahi .* cos(angle(hilbert(Vhi'))))';% ... and use PhiHi to get Vhi. + Vhi = Vhi.*(1+aac_mod*AmpLo/max(AmpLo)); + + case 'pink' + Vhi = Vhi.*(1+pac_mod*s); % Modulate high freq activity by modulation envelope. + Vhi = Vhi.*(1+aac_mod*AmpLo/max(AmpLo)); + + case 'spiking' % Add a spiking model. + N = 20/dt; % # steps to simulate, making the duration 20s + t = (1:N)*dt; % Time axis. + Alo = 1+(sin(2*pi*t*0.1)+1)/2; % Slow modulation of low frequency envelope. + Philo = pi*sawtooth(2*pi*t*4); % Low frequency phase is periodic (4 Hz). + Vlo = Alo.*cos(Philo); + + Philo_star = pi + Alo*pi; % Target phase depends on low frequency envelope. + sigma = 0.01; + lambda = 1/sqrt(2*pi*sigma) * exp( -(1+sawtooth(Philo - Philo_star,1/2)).^2 / (2*sigma^2) ); + lambda = (0.001+0.3*lambda/max(lambda)); + Vhi = 1*binornd(1,lambda); % When low freq phase is near target phase, produce a spike. + + Vlo =(Vlo)+0.1*randn(size(Vlo)); % Define Vlo and Vhi directly for this sim. + Vhi =(Vhi)+0.1*randn(size(Vlo)); + end + else return end -Vhi = Vhi.*(1+aac_mod*AmpLo/max(AmpLo)); +if exist('sim_method','var') && ~strcmp(sim_method, 'spiking') Vpink2 = make_pink_noise(1,N,dt); % Create additional pink noise signal noise_level = 0.01; @@ -116,11 +140,13 @@ filtwts = firls(filtorder,f,m); % get FIR filter coefficients Vhi = filtfilt(filtwts,1,V1); % Define high freq band activity. +end + if isempty(varargin) - [XX,P] = glmfun(Vlo, Vhi, pval,ci); + [XX,P] = glmfun(Vlo, Vhi, pval,ci,AIC); else q = varargin{1}; - [XX,P] = glmfun(Vlo, Vhi, pval,ci,q); + [XX,P] = glmfun(Vlo, Vhi, pval,ci,AIC,q); end end