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EDR_Estimation.m
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% EDR_Estimation() - estimates a surrogate of the respiratory signal from
% single-lead ECG data using 8 different methods found
% in the literature (HRV, AM1, AM2, QRS-AM, ENV, PCA, kPCA and EMD)
% Usage:
% >> EDR = EDR_Estimation(dataset, filters_ecg, filters_resp, clean_peaks, plt, nb_plts)
%
% Inputs:
% dataset - input data structure with the following mandatory fields:
% 1) data -> EEG signal (each row represent an EEG channel)
% 2) ecg -> ECG signal (row vector)
% 3) srate [double] -> sampling rate
% 4) Kp -> R peak annotations
% filters_ecg - low and high cutoff values of the band-pass filtering of ECG data {[ low_cutoff high_cutoff ]}
% filters_resp - low and high cutoff values of the hypothesized respiratory signal
% (typically 0.2-04 Hz) {[ low_cutoff high_cutoff ]}
% clean_peaks - 1/0 = do/do not perform additional steps for false
% positive and false negative R peaks based on beat morphology
% plt - 1/0 = do/don't display the results
% nb_plts - number of subplots within each plot for displaying the IMFs obtained from the EMD
%
% Outputs:
% EDR [cell] - respiratory signals estimated using all different methods
% (.name -> name of the method, .signal -> the respiratory trace)
%
% Author: Rodolfo Abreu, ISR/IST, Universidade de Lisboa, 2016
function EDR = EDR_Estimation(dataset, filters_ecg, filters_resp, clean_peaks, plt, nb_plts)
fs = dataset.srate; R = dataset.Kp;
m_R = (min(diff(R)) / dataset.srate) * 1000;
m_R_smp = mean(diff(R)); % average R-to-R peak interval
% ECG filtering
ecg = eegfilt(dataset.ecg, fs, filters_ecg(1), 0);
ecg = eegfilt(ecg, fs, 0, filters_ecg(2));
% ECG baseline removal
medfilt_200 = 0.2 * fs; medfilt_600 = 0.6 * fs;
ecg_200ms = medfilt1(ecg, medfilt_200);
ecg_baseline = medfilt1(ecg_200ms, medfilt_600);
ecg_rm_baseline = ecg - ecg_baseline;
lim_inf_ms = -100;
if m_R < 4 * abs(lim_inf_ms)
lim_sup_ms = lim_inf_ms + (4 * abs(lim_inf_ms));
else
lim_sup_ms = lim_inf_ms + m_R;
end
L_Resp = length(ecg);
% EDR from the ECG envelope using the Hilbert transform
ecg_env = abs(hilbert(ecg(R)));
EDR_Env = spline(R, ecg_env, 1:L_Resp);
EDR_Env = lowpass_filter(EDR_Env, 0.5, fs);
% EDR from RR peak differences
HRV = diff(R);
EDR_HRV = spline(R(1:end-1), HRV, 1:L_Resp);
EDR_HRV = lowpass_filter(EDR_HRV, 0.5, fs);
% EDR from R peaks amplitude (R - S waves)
S = zeros(1, length(R));
win_80ms = 0.08 * fs;
for i = 1:length(R)
W = ecg(R(i):R(i) + win_80ms);
[ ~, m ] = min(W);
S(i) = R(i) + m;
end
RAmp = R - S;
EDR_RAmp = spline(R, RAmp, 1:L_Resp);
EDR_RAmp = lowpass_filter(EDR_RAmp, 0.5, fs);
% EDR from R peak amplitudes after baseline removal
EDR_RAmp_rm = spline(R, ecg_rm_baseline(R), 1:L_Resp);
EDR_RAmp_rm = lowpass_filter(EDR_RAmp_rm, 0.5, fs);
% EDR from QRS area after baseline removal
win_100ms = 0.1 * fs;
if R(1) - ceil(win_100ms / 2) < 0, R(1) = []; end
if R(end) + ceil(win_100ms / 2) > length(ecg), R(end) = []; end
QRS = zeros(1, length(R));
for i = 1:length(R)
W = ecg_rm_baseline(R(i) - ceil(win_100ms / 2):R(i) + ceil(win_100ms / 2));
QRS(i) = sum(abs(W));
end
EDR_QRS = spline(R, QRS, 1:L_Resp);
EDR_QRS = lowpass_filter(EDR_QRS, 0.5, fs);
% ERD FROM PCA - FEATURES
if R(1) - ceil(m_R_smp * 0.5) < 0, R(1) = []; end
if R(end) + win_80ms > length(ecg), R(end) = []; end
R_80ms_m = R - ceil(m_R_smp * 0.5); R_80ms_M = R + win_80ms;
R_Tw_m = R_80ms_M; R_Tw_M = R_80ms_m(2:end);
m_RTw = ceil(mean(R_Tw_M - R_Tw_m(1:end - 1)));
R_Tw_M = horzcat(R_Tw_M, R_Tw_M(end) + m_RTw);
win_RTw = median(R_Tw_M - R_Tw_m); R_Tw_M = R_Tw_m + win_RTw;
if R(1) - ceil((m_R_smp * 0.9) / 2) < 0, R(1) = []; end
if R(end) + ceil((m_R_smp * 0.9) / 2) > length(ecg), R(end) = []; end
R_QRS_m = R - ceil(win_100ms / 2); R_QRS_M = R + ceil(win_100ms / 2);
R_WB_m = R - ceil((m_R_smp * 0.9) / 2); R_WB_M = R + ceil((m_R_smp * 0.9) / 2);
l_QRS = length(R_QRS_m(1):R_QRS_M(1)); QRS_complex = zeros(l_QRS, length(R));
l_WB = length(R_WB_m(1):R_WB_M(1)); WB = zeros(l_WB, length(R));
l_Twave = win_RTw + 1; Twave = zeros(l_Twave, length(R));
for i = 1:length(R)
QRS_complex(:, i) = ecg(R_QRS_m(i):R_QRS_M(i)); % QRS complexes
WB(:, i) = ecg(R_WB_m(i):R_WB_M(i)); % whole ECG beats
Twave(:, i) = ecg(R_Tw_m(i):R_Tw_M(i)); % T wave
end
cov_QRS = cov(QRS_complex); cov_WB = cov(WB); cov_Twave = cov(Twave);
[ coeff_QRS, ~, ~ ] = pcacov(cov_QRS);
[ coeff_WB, ~, ~ ] = pcacov(cov_WB);
[ coeff_Twave, ~, ~ ] = pcacov(cov_Twave);
nb_pcs = 3;
EDR_PCA_QRS = zeros(nb_pcs, L_Resp);
EDR_PCA_WB = zeros(nb_pcs, L_Resp);
EDR_PCA_Twave = zeros(nb_pcs, L_Resp);
for i = 1:nb_pcs
EDR_PCA_QRS(i, :) = lowpass_filter(spline(R, coeff_QRS(:, i), 1:L_Resp), 0.5, fs);
EDR_PCA_WB(i, :) = lowpass_filter(spline(R, coeff_WB(:, i), 1:L_Resp), 0.5, fs);
EDR_PCA_Twave(i, :) = lowpass_filter(spline(R, coeff_Twave(:, i), 1:L_Resp), 0.5, fs);
end
% ERD FROM KERNEL PCA - FEATURES
% Polynomial Kernel
pk = [ 2 3 ];
% Gaussian Kernel
sig_QRS = l_QRS .* mean(var(QRS_complex));
sig_QRS_range = linspace(sig_QRS / 100, sig_QRS * 100, 1000);
sig_WB = l_WB .* mean(var(WB));
sig_WB_range = linspace(sig_WB / 100, sig_WB * 100, 1000);
sig_Twave = l_Twave .* mean(var(Twave));
sig_Twave_range = linspace(sig_Twave / 100, sig_Twave * 100, 1000);
% Estimation of the number of dimensions
dim_QRS = round(intrinsic_dim(cov_QRS, 'MLE'));
dim_WB = round(intrinsic_dim(cov_WB, 'MLE'));
dim_Twave = round(intrinsic_dim(cov_Twave, 'MLE'));
% Kernel PCA
[ mapped_QRS_p2, ~ ] = compute_mapping(cov_QRS, 'KernelPCA', dim_QRS, 'poly', 1, pk(1));
[ mapped_QRS_p3, ~ ] = compute_mapping(cov_QRS, 'KernelPCA', dim_QRS, 'poly', 1, pk(2));
[ mapped_WB_p2, ~ ] = compute_mapping(cov_WB, 'KernelPCA', dim_WB, 'poly', 1, pk(1));
[ mapped_WB_p3, ~ ] = compute_mapping(cov_WB, 'KernelPCA', dim_WB, 'poly', 1, pk(2));
[ mapped_Twave_p2, ~ ] = compute_mapping(cov_Twave, 'KernelPCA', dim_Twave, 'poly', 1, pk(1));
[ mapped_Twave_p3, ~ ] = compute_mapping(cov_Twave, 'KernelPCA', dim_Twave, 'poly', 1, pk(2));
E_QRS = zeros(1, length(sig_QRS_range));
E_WB = zeros(1, length(sig_WB_range));
E_Twave = zeros(1, length(sig_Twave_range));
dEig_QRS = zeros(1, length(sig_QRS_range));
dEig_WB = zeros(1, length(sig_WB_range));
dEig_Twave = zeros(1, length(sig_Twave_range));
% Standard Deviation - Serial
for i = 1:length(sig_QRS_range)
[ E_qrs, E_wb, E_twave, dEig_qrs, dEig_wb, dEig_twave ] = ...
kPCA_aux(cov_QRS, dim_QRS, sig_QRS_range(i), cov_WB, dim_WB, ...
sig_WB_range(i), cov_Twave, dim_Twave, sig_Twave_range(i));
E_QRS(i) = E_qrs; E_WB(i) = E_wb; E_Twave(i) = E_twave;
dEig_QRS(i) = dEig_qrs; dEig_WB(i) = dEig_wb; dEig_Twave(i) = dEig_twave;
end
% Maximizing Entropy
[ ~, M_QRS ] = max(E_QRS); [ ~, M_WB ] = max(E_WB); [ ~, M_Twave ] = max(E_Twave);
% Maximizing the difference between eigenvalues
[ ~, m_QRS ] = max(dEig_QRS); [ ~, m_WB ] = max(dEig_WB); [ ~, m_Twave ] = max(dEig_Twave);
sig = [ M_QRS, M_WB, M_Twave, m_QRS, m_WB, m_Twave ];
% Kernel PCA with a Gaussian kernel that maximizes the Entropy
[ mapped_QRS_gE, ~ ] = compute_mapping...
(cov_QRS, 'KernelPCA', dim_QRS, 'gauss', sig(1));
[ mapped_WB_gE, ~ ] = compute_mapping...
(cov_WB, 'KernelPCA', dim_WB, 'gauss', sig(2));
[ mapped_Twave_gE, ~ ] = compute_mapping...
(cov_Twave, 'KernelPCA', dim_Twave, 'gauss', sig(3));
% Kernel PCA with a Gaussian kernel that maximizes the Differences between eigenvalues
[ mapped_QRS_gDEig, ~ ] = compute_mapping...
(cov_QRS, 'KernelPCA', dim_QRS, 'gauss', sig(4));
[ mapped_WB_gDEig, ~ ] = compute_mapping...
(cov_WB, 'KernelPCA', dim_WB, 'gauss', sig(5));
[ mapped_Twave_gDEig, ~ ] = compute_mapping...
(cov_Twave, 'KernelPCA', dim_Twave, 'gauss', sig(6));
EDR_kPCA_QRS_p2 = zeros(dim_QRS, L_Resp); EDR_kPCA_QRS_p3 = zeros(dim_QRS, L_Resp);
EDR_kPCA_QRS_gE = zeros(dim_QRS, L_Resp); EDR_kPCA_QRS_gDEig = zeros(dim_QRS, L_Resp);
EDR_kPCA_WB_p2 = zeros(dim_WB, L_Resp); EDR_kPCA_WB_p3 = zeros(dim_WB, L_Resp);
EDR_kPCA_WB_gE = zeros(dim_WB, L_Resp); EDR_kPCA_WB_gDEig = zeros(dim_WB, L_Resp);
EDR_kPCA_Twave_p2 = zeros(dim_Twave, L_Resp); EDR_kPCA_Twave_p3 = zeros(dim_Twave, L_Resp);
EDR_kPCA_Twave_gE = zeros(dim_Twave, L_Resp); EDR_kPCA_Twave_gDEig = zeros(dim_Twave, L_Resp);
for i = 1:dim_QRS
EDR_kPCA_QRS_p2(i, :) = lowpass_filter(spline(R, mapped_QRS_p2(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_QRS_p3(i, :) = lowpass_filter(spline(R, mapped_QRS_p3(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_QRS_gE(i, :) = lowpass_filter(spline(R, mapped_QRS_gE(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_QRS_gDEig(i, :) = lowpass_filter(spline(R, mapped_QRS_gDEig(:, i), 1:L_Resp), 0.5, fs);
end
for i = 1:dim_WB
EDR_kPCA_WB_p2(i, :) = lowpass_filter(spline(R, mapped_WB_p2(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_WB_p3(i, :) = lowpass_filter(spline(R, mapped_WB_p3(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_WB_gE(i, :) = lowpass_filter(spline(R, mapped_WB_gE(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_WB_gDEig(i, :) = lowpass_filter(spline(R, mapped_WB_gDEig(:, i), 1:L_Resp), 0.5, fs);
end
for i = 1:dim_Twave
EDR_kPCA_Twave_p2(i, :) = lowpass_filter(spline(R, mapped_Twave_p2(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_Twave_p3(i, :) = lowpass_filter(spline(R, mapped_Twave_p3(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_Twave_gE(i, :) = lowpass_filter(spline(R, mapped_Twave_gE(:, i), 1:L_Resp), 0.5, fs);
EDR_kPCA_Twave_gDEig(i, :) = lowpass_filter(spline(R, mapped_Twave_gDEig(:, i), 1:L_Resp), 0.5, fs);
end
% EDR FROM EMPIRICAL MODE DECOMPOSITION (EMD)
IMF = EMD(ecg, 50, 50, 1);
selected_IMF = IMF_selection(IMF, filters_resp, plt, nb_plts);
EDR_EMD = IMF(:, selected_IMF)';
methods = { 'Env', 'HRV', 'RAmp', 'RAmp_rm', 'QRS', 'PCA_QRS', 'PCA_WB', ...
'PCA_Twave', 'kPCA_QRS_p2', 'kPCA_QRS_p3', 'kPCA_QRS_gE', 'kPCA_QRS_gDEig', ...
'kPCA_WB_p2', 'kPCA_WB_p3', 'kPCA_WB_gE', 'kPCA_WB_gDEig', 'kPCA_Twave_p2', ...
'kPCA_Twave_p3', 'kPCA_Twave_gE', 'kPCA_Twave_gDEig', 'EMD' };
EDR(1).name = 'Env'; EDR(1).signal = EDR_Env;
EDR(2).name = 'HRV'; EDR(2).signal = EDR_HRV;
EDR(3).name = 'RAmp'; EDR(3).signal = EDR_RAmp;
EDR(4).name = 'RAmp_rm'; EDR(4).signal = EDR_RAmp_rm;
EDR(5).name = 'QRS'; EDR(5).signal = EDR_QRS;
EDR(6).name = 'PCA_QRS'; EDR(6).signal = EDR_PCA_QRS;
EDR(7).name = 'PCA_WB'; EDR(7).signal = EDR_PCA_WB;
EDR(8).name = 'PCA_Twave'; EDR(8).signal = EDR_PCA_Twave;
EDR(9).name = 'kPCA_QRS_p2'; EDR(9).signal = EDR_kPCA_QRS_p2;
EDR(10).name = 'kPCA_QRS_p3'; EDR(10).signal = EDR_kPCA_QRS_p3;
EDR(11).name = 'kPCA_QRS_gE'; EDR(11).signal = EDR_kPCA_QRS_gE;
EDR(12).name = 'kPCA_QRS_gDEig'; EDR(12).signal = EDR_kPCA_QRS_gDEig;
EDR(13).name = 'kPCA_WB_p2'; EDR(13).signal = EDR_kPCA_WB_p2;
EDR(14).name = 'kPCA_WB_p3'; EDR(14).signal = EDR_kPCA_WB_p3;
EDR(15).name = 'kPCA_WB_gE'; EDR(15).signal = EDR_kPCA_WB_gE;
EDR(16).name = 'kPCA_WB_gDEig'; EDR(16).signal = EDR_kPCA_WB_gDEig;
EDR(17).name = 'kPCA_Twave_p2'; EDR(17).signal = EDR_kPCA_Twave_p2;
EDR(18).name = 'kPCA_Twave_p3'; EDR(18).signal = EDR_kPCA_Twave_p3;
EDR(19).name = 'kPCA_Twave_gE'; EDR(19).signal = EDR_kPCA_Twave_gE;
EDR(20).name = 'kPCA_Twave_gDEig'; EDR(20).signal = EDR_kPCA_Twave_gDEig;
EDR(21).name = 'EMD'; EDR(21).signal = EDR_EMD;
if plt
% Clean R peaks
if clean_peaks
ecg_norm = ecg ./ max(ecg);
figure, plot(ecg_norm), hold on, plot(R_copy, C_WB, '-ro');
plot([ 1 length(ecg) ], [ threshold threshold ], 'k');
end
% Window tests
R_80ms = R + win_80ms;
R_50ms_m = R - ceil(win_100ms / 2); R_50ms_M = R + ceil(win_100ms / 2);
figure('Name', 'ECG_f'), hold on, plot(ecg)
plot(R, ecg(R), 'ro', 'MarkerFaceColor', 'r')
axis('tight'),
line([ R_50ms_m; R_50ms_m ], [ min(ecg) max(ecg) ], 'Color', 'g');
line([ R_50ms_M; R_50ms_M ], [ min(ecg) max(ecg) ], 'Color', 'g');
% line([ R_WB; R_WB ], [ min(ecg) max(ecg) ], 'Color', 'k');
hold off
% R_WB = R + m_R;
R_WB_m = R - ceil((m_R_smp * 0.9) / 2); R_WB_M = R + ceil((m_R_smp * 0.9) / 2);
figure('Name', 'ECG_f'), hold on, plot(ecg)
plot(R, ecg(R), 'ro', 'MarkerFaceColor', 'r')
axis('tight'),
line([ R_WB_m; R_WB_m ], [ min(ecg) max(ecg) ], 'Color', 'k');
line([ R_WB_M; R_WB_M ], [ min(ecg) max(ecg) ], 'Color', 'k');
hold off
win_70ms = 0.07 * fs;
R_80ms_m = R - ceil(m_R_smp * 0.55); R_80ms_M = R + win_80ms;
R_Tw_m = R_80ms_M; R_Tw_M = R_80ms_m(2:end);
m_RTw = ceil(mean(R_Tw_M - R_Tw_m(1:end - 1)));
R_Tw_M = horzcat(R_Tw_M, R_Tw_M(end) + m_RTw);
figure('Name', 'ECG_f'), hold on, plot(ecg)
plot(R, ecg(R), 'ro', 'MarkerFaceColor', 'r')
axis('tight'),
line([ R_Tw_m; R_Tw_m ], [ min(ecg) max(ecg) ], 'Color', 'g');
line([ R_Tw_M; R_Tw_M ], [ min(ecg) max(ecg) ], 'Color', 'g');
hold off
figure('Name', 'ECG_f'), hold on, plot(ecg)
plot(R, ecg(R), 'ro', 'MarkerFaceColor', 'r')
plot(S, ecg(S), 'ko', 'MarkerFaceColor', 'k')
line([ R_80ms; R_80ms ], [ min(ecg) max(ecg) ], 'Color', 'g');
axis('tight')
hold off
end