nature protocols: doi:10.1038/nprot.2015€¦ · telemetric ecg hrv whole mount san calcium imaging...

Supplementary Figure 1

Step-by-step exposure and dissection of the SAN.

(a) Posterior view of the isolated heart with tissue that must be removed for SAN dissection. (b) Lungs, esophagus, large parts of the thymus and fat are removed to expose the central SAN region. At this stage it is already possible to dissect the SAN. Black arrow heads: vagus nerve, white arrow heads: sulcus terminalis. (c) Same heart after complete removal of excess tissue. The white dotted line indicates the cutting line for SAN dissection. The white dot indicates the area where the SAN should be gently hold with fine forceps for isolation. Other parts should not be touched to avoid damage of the central SAN region. Please note that removal of all surrounding tissue was done for demonstration purposes only and is not necessary for SAN dissection. (d) The SAN was dissected and is placed on the ventricles for demonstration. The white dot indicates the area where the SAN was grabbed with fine forceps. Th: thymus, Lu: parts of the lung, Es: esophagus, RAA: right atrial appendage, LV: left ventricle, RV: right ventricle, SAN: sinoatrial node, ST: sulcus terminalis, SVC: right superior vena cava, IVC: inferior vena cava, VN: vagus nerve, Ao: Aorta. Scale bar: 1 mm.

Nature Protocols: doi:10.1038/nprot.2015.139


Dissection of a whole mount SAN preparation of a gelatin-inflated heart.

(a) Dorsal view of the heart. All excess tissue and organs were removed. The white dotted line indicates the first cutting line along the sulcus coronarius. The second cut (yellow dotted line) is made after folding up the RAA and cutting along the sulcus coronarius up to the superior caval vein. The third cut (black dotted line) is made slightly left of the IVC along the intraatrial septum up to the SVC. The whole mount preparation is isolated completely by making a connecting cut (red dotted line) between the root of the aorta and the root of the right superior caval vein. SVC: right superior vena cava, IVC: inferior vena cava, PV: pulmonary veins, RAA: right atrial appendage, LV: left ventricle, RV: right ventricle, Ao: Aorta (b) The first incision is indicated by white arrow heads. The second and third incision cannot be seen because they lie behind the RAA and IVC, respectively. (c) The last connecting cut leads to complete isolation of the whole mount SAN preparation. (d) Heart together with whole mount SAN preparation. Scale bar: 1 mm.



Ventral view of the gelatin- inflated heart.

Black dotted line indicates optimal length of Aorta for cannulation. Ao: Aorta; LCA: left carotid artery; RCA: right carotid artery; PT: pulmonary truncus; RSA: right subclavian artery; LAA: left atrial appendage; RAA: right atrial appendage, LV: left ventricle: RV: right ventricle. Scale bar: 1 mm


1

Comprehensive Multi-level in vivo and in vitro Analysis of Heart Rate Fluctuations in

Mice by ECG Telemetry and Electrophysiology.

Fenske S., Pröbstle R., Auer F., Hassan S., Marks V., Pauza D., Biel M., Wahl-Schott C.

Supplementary Table 1 │ Development of the protocol

Mouse models with increased HRV

References In vivo SAN network Isolated SAN cells

(Fenske et al., 2013)

Telemetric ECG

HRV, TP, VLF, LF, HF

SDNN, RMSDD

Langendorff heart and Whole mount SAN microelectrode recordings

fluctuation

Current clamp

(Le Scouarnec et al., 2008)

Telemetric ECG

HRV

Whole mount SAN calcium imaging

fluctuation

Current clamp

afterdepolarizations Confocal imaging

fluctuation

(Posokhova et al., 2010)

Telemetric ECG

SDNN

Whole heart

Rgs6: HRV, TP, LF, HF

Girk4: HRV, TP, HF

Calcium imaging

fluctuation: Rgs6

(Neco et al., 2012)

Telemetric ECG

SDNN

Whole mount SAN calcium imaging

fluctuation under Isoproterenol

Calcium imaging

fluctuation under Isoproterenol

(Ecker et al., 2006)

Telemetric ECG

HRV, LF, HF

SDNN

(Joaquim et al., 2004)

Telemetric BP

HRV, LF

(Tank et al., 2004)

Telemetric BP

HRV, TP, LF, HF

(Williams et al., 2003)

Telemetric BP

HRV, TP, LF, HF

Mouse models with decreased HRV


(Hao et al., 2011) Surface ECG

HRV

Whole mount SAN microelectrode array recording

sinoatrial conduction time

AP model of murine SAN cells

frequency

(Mesirca et al., 2013)

Telemetric ECG

HRV, TP, HF

Langendorff heart

beating rate under Ach compared to WT

Current clamp

beating rate under Ach compared to WT

(Direnberger et al., 2012)

Telemetric ECG

HRV, TP, LF, HF

Embryonic heart and Whole mount SAN

(Hajiasgharzadeh et al., 2011)

Surface ECG

SDNN

Isolated atria

(Pelat et al., 2003) Telemetric BP

HRV, HF

VLF


2

Supplementary Table 1 │ Development of the protocol (continued)

Mouse models with decreased HRV


(Wickman et al., 1998)

Telemetric ECG

HRV, TP, LF, HF

(Zuberi et al., 2008)

Telemetric ECG

Gi2: HRV, HF, LF

(Uechi et al., 1998) Telemetric ECG / BP

HRV, TP, LF, HF

(Mansier et al., 1996)

Telemetric ECG

HRV, TP, LF, HF

(Pham et al., 2009) Telemetric ECG

SDNN, RMSDD

(Rokosh and Simpson, 2002)

Telemetric BP

HRV

(Gross et al., 2005) Telemetric BP

HRV, LF, HF

(Fazan et al., 2005) Indwelling BP catheter

LF

(Chen et al., 2005) Telemetric BP

HRV, LF, HF

(Sebastian et al., 2013)

Telemetric ECG

Gs: HRV, LF

Gi2: HRV, HF

(Zhang et al., 2014)

Telemetric ECG

HRV, HF under propranolol

(Corey et al., 2006) Telemetric ECG

HRV, TP, VLF, LF, HF

(Chu et al., 2002) Surface ECG

HRV

(Wu et al., 2006) Telemetric ECG

3: HRV, TP, LF, HF

(Dev et al., 2010) Surface ECG

HRV


3

Supplementary Table 2 │Animal health score sheet


4

Supplementary Method 1

Commented MATLAB script 1│Peak detection

Contents

1. Description

2. Upload data

3. Find peaks*

4. Save

*contains changeable values

1. Description Matlab script for peak detection

peak_detect (filename, sheet, range, Fs)

Input: filename : name of the file in which raw-data is stored (xls file)

Fs: sampling frequency of ECG data (in Hz)

Output: NN NN data

function [NN] = peak_detect(filename, sheet, range, Fs)

2. Upload reads data from excel file (filename, sheet, range)

ECGtrace = xlsread(filename, sheet, range);

3. Find peaks Changeable value: threshold for peak detection

Find highest peak:

Max_ecg = max(ECGtrace);

Define threshold for peak detection:

threshold = 0.2*Max_ecg;

len = length(ECGtrace);

time = 0:(1/Fs):(len-1)/Fs;

time_trace = len/Fs;

ECG_trace = ECGtrace;

ECG_trace = max(ECG_trace, threshold);

Find peaks above threshold:

[pks,locs] = findpeaks(ECG_trace);

Calculate NN:

NN = diff(locs);


5

4. Figures

figure

plot(time,ECGtrace,'k');

xlabel('time [s]');

ylabel('voltage [mV]');

hold on

plot(locs/Fs,pks,'rx');

hold on

line([0 time_trace],[threshold threshold])

legend('ECG trace','recognized heartbeats','threshold for spikes')

figure

plot(NN,'.')

ylabel('NN intervals [ms]')

xlabel('beat number')

axis([0 length(NN) 0 200])

5. Save

Save NN data:

a ='tachogram';

extI = '.xls';

res = strcat(filename, a, extI);

d = {'NN [ms]';NN};

xlswrite(res,d)


6


Commented MATLAB script 2 │Determination of the model order

Contents

1. Description

2. Upload data

3. Remove trend

4. Interpolation*

5. Model order estimation*

6. Figures


1. Description Matlab script for AR model order estimation

model_order (filename, sheet, range);

Input: array with arbitrary length containing NN intervals; data is loaded from a Microsoft Excel file

filename : name of the file in which raw-data is stored (xls file)

interpolation : 'linear' or 'spline'

function model_order(filename, sheet, range)

2. Upload data reads data from excel file (filename, sheet, range)

datNN = xlsread(filename, sheet, range);

3. Detrend removes DC component from signal;

moves data to mean = 0

data = detrend(dat,'constant');

data1 = detrend(dat1,'constant');

detrending: smoothness prior(1)

Changeable value: g (determines the cut off frequency; g cut-off f. )

length_data = length(data);

g = 40;

Mat = speye(length_data);

Mat_2 = spdiags(ones(length_data-2,1)*[1 -2 1], [0:2], length_data-2,length_data);

data = (Mat-inv(Mat+g^2*Mat_2’*Mat_2))*data;


7

4. Interpolation Linear ('linear') or cubic spline ('spline') interpolation

length of datafile:

timems = sum (datNN);

Changeable value: Step size (50ms step size results in a sampling rate of 20Hz)

number of data points for interpolation (20Hz):

step = 50; %[ms]

dataPoints = timems/step;

L =length(data);

define delta

delta = L/(dataPoints);

create vector from 1 to; step size = delta

v = 1:delta:L;

create vector from 1 to; step size = 1

ve = 1:L;

Interpolation:

valinterp_long = interp1(ve,data',v,interpolation);

reduce interpolated data to 2048 data points:

if length(valinterp_long)>= 2048

valinterp = valinterp_long(1:2048);

else

valinterp = valinterp_long;

disp('not enough data points <2048')

disp(length(valinterp))

end

5. Autoregressive model Estimate model order for autoregressive models

Reflection Coefficients to identify the order of the AR model

Changeable values: AR model

AR models: Burg’s method (arburg),

Yule-Walker method (aryule)

Covariance method (arcov)

e = zeros(120,1);

AICburg = zeros(120,1);

for p = 1:120 % tested model orders

[a,ki(p)] = arburg(valinterp,p);


8

estimated Error with Burg´s method

e(p) = ki(p);

Calculation of AIC value(2)

AICburg(p) = length(valinterp)*log(((e(p))^2))+2*p;

end

6. Figures

Figure [Partial Autocorrelation function, AIC Value]

Partial Autocorrelation

W = figure('units','normalized','outerposition',[0 0 1 1]);

subplot(2,2,1:2)

parcorr(valinterp,90)

set(gca,'FontSize',14)

AIC Value

subplot(2,2,1:2)

title('Estimation Model Orders');


plot(AICburg,'k')

7. References (1) Tarvainen, M., P. Ranta-Aho and P. Karjalainen, 2002. An advanced detrending method with

application to HRV analysis. IEEE Trans. Biomed. Eng., 49(2): 172-175.

(2) Takalo, Reijo, Heli Hytti, and Heimo Ihalainen. "Tutorial on univariate autoregressive spectral

analysis." Journal of clinical monitoring and computing19.6 (2005): 401-410.


9


Commented MATLAB script 3│HRV calculation

Contents

1. Description

2. Upload data

3. Ectopic beats*

4. Calculate time domain parameters

5. Detrend*

6. Interpolation*

7. Fast-Fourier Transformation*

8. Autoregressive model*

9. Poincare plot

10. Figures

11. Power in different frequency bands

12. Save

13. References


1. Description Matlab script for heart rate variability analysis

HRV (name,filename,sheet,range,interpolation,burg)

Input: array with arbitrary length containing NN intervals; data is loaded from a Microsoft Excel file

name : new filename with which data and figures are saved

filename : name of the file in which raw-data is stored (xls file)

interpolation : 'linear' or 'spline'

burg : model order for AR model

Settings:

Interpolation : linear interpolation or cubic spline

Order of Autoregression model : -identification via partial autocorrelation

-identification via Akaike´s Information Criterion (AIC) AIC =

N*log(std(e)^2)+2*M N: number of data points e: prediction error M: model

order Takalo et al., Tutorial on univariate autoregressive spectral analysis

(2005) J Clin Monit Comput pp.401-410

Fourier transformation:

window hamming

window_size 1024

overlap 512

Frequency bands:

VLF 0Hz - 0.4Hz

LF 0.4Hz - 1.5Hz

HF 1.5Hz - 4Hz


10

Output:

Mean (mean of the NN intervals in [ms])

SDNN (standard deviation of the NN intervals)

RMSSD (root mean square of the successive difference)

pNNx per (percentage of consecutive NN intervals that

differ more than x ms)

STV (STV: dispersion (standard deviation) of points

perpendicular to the axis of line of identity)

LTV (dispersion (standard deviation) of points

along the axis of line of identity)

TP (total power of the frequencies)

VLF (power in the very low frequency band)

LF (power in the low frequency band)

HF (power in the high frequency band)

VLFper (fraction of the very low frequency band)

LFper (fraction of the low frequency band)

HFper (fraction of the high frequency band)

function [d]=HRV(name,filename,sheet,range,interpolation,burg)

2. Upload data reads data from excel file (filename, sheet, range)

datNN= xlsread(filename,sheet, range);

3. Ectopic beats removes ectopic beats from further analysis

Changeable values: Criteria for removal of ectopic beats: (x% difference from a moving average or x*STD of a

moving window)

Length of the track:

le=numel(datNN);

datN=datNN;

Removes beats that are outside a 20% border around the moving average

window_size = 80;

mov_av=tsmovavg(datNN,'s',window_size,1);

for h = 1:le

if abs(datNN(h))< 0.80*mov_av(h) || abs(datNN(h))>1.20*mov_av(h)

datN(h)=0;

end

end


11

Removes beats that differ more than x*STD from a moving window

win = 5;

for h=win+1:le-win-1

if abs(datNN(h)-datNN(h+1))> 3*std(datNN(h-win):((h+win));

datN(h)=0;

end

end

datN = datN(datN~=0);

New data without ectopic beats in [s]:

dat=datN/1000;

Original data in [s]:

dat1=datNN/1000;

4. Calculate time domain parameters Mean, SDNN, RMSSD

Mean:

meanNN= mean(datN);

Standard deviation:

SDNN= rms(datN-mean(datN)) ;

Root mean square of the standard deviation:

rmd = zeros(length(datN)-1,1);

for j=1:(length(datN)-1)

rmd(j) = (datN(j)-datN(j+1));

end

RMSSD = rms(rmd);

Calculate pNN6ms

Length of data:

totNN= length(dat);

x=6/1000;

nnp=0;

nnm=0;

for i = 1:(totNN-1)

if (dat(i)-dat(i+1))> x

nnp = nnp +1;

end


12

if (dat(i)-dat(i+1))< - x

nnm = nnm +1;

end

end

pNNp = nnp/totNN * 100;

pNNm = nnm/totNN * 100;

pNN percentage

PNNper = (nnp+nnm)/totNN*100;

5. Detrend removes DC component from signal;

moves data to mean = 0

detrending: smoothness prior OR polynomial detrending

data=detrend(dat,'constant');

data1=detrend(dat1,'constant');

detrending: smoothness prior(1)

Changeable value: g (determines the cut off frequency; g cut-off f. )

length_data = length(data);

g = 40;

Mat = speye(length_data);

Mat_2 = spdiags(ones(length_data-2,1)*[1 -2 1], [0:2], length_data-2,length_data);

data = (Mat-inv(Mat+g^2*Mat_2’*Mat_2))*data;

detrending: polynomial detrending

Changeable value: number of tested polynomial orders (preset: orders 1-5)

[data]=poly_detrend(data);

6. Interpolation Linear ('linear') or cubic spline ('spline') interpolation

length of data file:

timems = sum (datNN);

Changeable value: Step size (50ms step size results in a sampling rate of 20Hz)

number of data points for interpolation (20Hz):

step = 50; %[ms]

dataPoints = timems/step;

L =length(data);

define delta

delta = L/(dataPoints);


13

create vector from 1 to; step size = delta

v = 1:delta:L;

create vector from 1 to; step size = 1

ve = 1:L;

Interpolation:

valinterp_long = interp1(ve,data',v,interpolation);

reduce interpolated data to 2048 data points:

if length(valinterp_long)>= 2048

valinterp = valinterp_long(1:2048);

else

valinterp=valinterp_long;

disp('not enough data points <2048')

disp(length(valinterp))

end

7. Fast-Fourier Transformation Power Spectral Density estimate via Welch's method

Length of the track:

time =(length(valinterp)*step)/1000;

Length of signal (e.g 103s):

LUN =length(valinterp);

Sampling frequency

Fs = LUN/time;

Sample time

T = 1/Fs;

Time vector for interpolated data:

tint = (0:LUN-1)*T;

N=size(valinterp);

Next power of 2 from length of y:

NFFT = 2.^nextpow2(LUN);

Time vector for real data without ectopic beats:

time_real = sum(dat)

treal= (0:L -1)*(time_real/L);


14

Time vector for real data:

treal1=(0:length(data1)-1)*(sum(dat1)/length(data1));

Power Spectral Density estimate via Welch's method

Changeable values: window, window size, overlap

Windows: Hamming window (hamming)

Hanning window (hann)

Rectangular window (rectwin)

Triangular window (triang)

Window: hamming

window_size = 1024;

overlap = 512;

[Pxx,f] = pwelch(valinterp',hamming(window_size),overlap,NFFT,Fs,'psd');

8. Autoregressive model Estimate model order for autoregressive models

Reflection coefficients to identify the order of the AR model


AR models: Burg’s method (arburg),

Yule-Walker method (aryule)

Covariance method (arcov)

e=zeros(120,1);

AICburg=zeros(120,1);

for p=1:120 % tested model orders

[a,ki(p)]=arburg(valinterp,p);

estimated Error with Burg´s method

e(p)=ki(p);

Calculation of AIC value(2)

AICburg(p)=length(valinterp)*log(((e(p))^2))+2*p;

end

Autoregressive power spectral density estimate using Burg's method


AR models: Burg’s method (pburg),

Yule-Walker method (pyulear)

Covariance method (pcov)

[PxxA,fA] = pburg(valinterp',burg,NFFT,Fs);

9. Poincaré plot

d = size (datN);

xpoi = datN(1:(d-1));

ypoi = datN(2:d);


15

q=figure('units','normalized','outerposition',[0 0 1 1]);

subplot(2,3,6)

hold on

plot (xpoi,ypoi,'ko','MarkerSize',4)

axis([200 310 200 310])

ylabel('NNn+1 (ms)')

xlabel('NNn (ms)')

title('Poincarè plot');


Calculate STV and LTV

arg1 = (xpoi/(sqrt(2))-ypoi/(sqrt(2))); % X1=(x-y)/(sqrt(2))

STVsquare = var(arg1); % variance

STV = sqrt(STVsquare); % standard deviation

arg2 = (xpoi/(sqrt(2)) + ypoi/(sqrt(2)));

LTVsquare = var(arg2);

LTV = sqrt(LTVsquare);

10. Figures

Figure 1 [Tachogram, Poincaré plot, Welch PSD]

Tachogram

figure(q)

subplot(2,3,1:3)

plot (treal1, data1, 'LineWidth', 1)

hold on

plot (tint, valinterp,'r', 'LineWidth', 1)

hold on

plot (treal, data,'k', 'LineWidth', 1)

hold off

ylabel('NN interval (s)')

xlabel('time (s)')

title('NN data');

legend('original data','interpolated data', 'data without ectopic beats')


Welch PSD

subplot(2,3,4:5)

plot (f,Pxx,'k')

axis([-0.1 5 0 max(Pxx)]);

ylabel('PSD (s^2/Hz)')

xlabel('Frequency Hz')

title('PSD Welch');


Figure 2 [Autoregressive PSD (Burg´s method)]

AR Spectrum (Burg´s method)

w=figure('units','normalized','outerposition',[0 0 1 1]);


16

subplot(2,2,4)

plot (fA,PxxA,'k')

axis([-0.1 5 0 max(Pxx)]);

ylabel('PSD (s^2/Hz)')

xlabel('Frequency Hz')

title('PSD Burg´s method');


Figure 3 [PSD Welch and Burg, Histogram]

PSD Welch and Burg

yx=figure('units','normalized','outerposition',[0 0 1 1]);

subplot(1,2,1)

plot (f,Pxx,'k','LineWidth',2)

hold on

plot (fA,PxxA,'r','LineWidth',3)

axis([-0.1 5 0 max(Pxx(96:350))]);

legend('PSD Welch', 'PSD Burg - Autoregressive method')


Histogram

subplot(1,2,2)

hist(datNN,15)

legend('NN intervals')

xlim([0.2 0.5])

Figure 4 [Tachogram (different scaling), Welch PSD (different scaling)]

Tachogram

z=figure('units','normalized','outerposition',[0 0 1 1]);


subplot(5,2,1:2)

plot (treal1,data1, 'LineWidth', 1)

hold on

plot (tint,valinterp,'r', 'LineWidth', 1)

hold on

plot (treal,data,'k', 'LineWidth', 1)

hold off


title('NN data');



set(gca,'xtick',[])

subplot(5,2,3:4)


hold on


hold on


17


hold off



ylim([-0.3 0.3])


set(gca,'xtick',[])

subplot(5,2,5:6)


hold on


hold on


hold off


xlabel('time (s)')


ylim([-0.05 0.05])


Welch PSD

subplot(5,2,7)

title('Welch PSD')

plot(f,Pxx)

xlim([0 4]);


subplot(5,2,8)

plot(f,Pxx)

axis([0 4 0 10^-3])


subplot(5,2,9)

plot(f,Pxx)

axis([0 4 0 10^-4])


subplot(5,2,10)

plot(f,Pxx)

axis([0 4 0 10^-5])



18

11. Power in different frequency bands

Length of frequency axis

nu = length(f);

Last value of f

a = f(nu);

Frequencies from 0 to 0.4 Hz: VLF

VLFl = 1; lower border for very low freq

VLFh = (nu*0.4)/a; upper border for very low freq

VLF = sum(Pxx(VLFl:VLFh)); sum of very low freq Pxx

Frequencies from 0.4 to 1.5 Hz: LF

LFl = VLFh+1; lower border

LFh = (nu*1.5)/a; upper border

LF = sum(Pxx(LFl:LFh)); sum of low freq Pxx

Frequencies from 1.5 to 4 Hz: HF

HFl = LFh+1; lower border

HFh = (nu*4)/a; upper border

HF = sum(Pxx(HFl:HFh)); sum of high freq Pxx

Calculate percentage of high and low frequency power

Total power:

TP = sum(Pxx(1:HFh));

[%] of total power

VLFper = VLF/TP*100;

LFper = LF/(TP)*100

HFper = HF/(TP)*100;

ratio=LF/HF;

Pow=figure('units','normalized','outerposition',[0 0 1 1]);

bar_Matrix=[TP VLF LF HF];

h=bar(bar_Matrix,'k');

l = cell(1,4);

l{1}='Total Power'; l{2}='VLF'; l{3}='LF'; l{4}='HF';

set(gca,'xticklabel', l)

ylabel('Power s^2/Hz')

ylim([0 0.15])



19

12. Save Write excel file with calculated values

extI = '.xls';

res = strcat(name,extI);

Save figures

a=strcat(name,filename,'_Autocorr.jpeg');

b=strcat(name,filename,'_Tachogram.jpeg');

c=strcat(name,filename,'_Histo.jpeg');

d=strcat(name,filename,'_Spectrum.jpeg');

e=strcat(name,filename,'_Power.jpeg');

hgexport(w, a, hgexport('factorystyle'), 'Format', 'jpeg');

hgexport(q, b, hgexport('factorystyle'), 'Format', 'jpeg');

hgexport(yx, c, hgexport('factorystyle'), 'Format', 'jpeg');

hgexport(z, d, hgexport('factorystyle'), 'Format', 'jpeg');

hgexport(Pow, e, hgexport('factorystyle'), 'Format', 'jpeg');

d = {'meanNN [ms]', 'SDNN','RMSSD','NN+x', 'NN-x', 'pNN+x', 'pNN-x','PNNperxms

[%]','STV', 'LTV', 'TP',...

'VLF','LF', 'HF','VLFper [%]', 'LFper [%]', 'HFper [%]'; meanNN SDNN...

RMSSD nnp nnm pNNp pNNm PNNper STV LTV TP VLF LF HF VLFper LFper HFper};

close all

xlswrite(res, d)

13. References

(3) Tarvainen, M., P. Ranta-Aho and P. Karjalainen, 2002. An advanced detrending method with

application to HRV analysis. IEEE Trans. Biomed. Eng., 49(2): 172-175.

(4) Takalo, Reijo, Heli Hytti, and Heimo Ihalainen. "Tutorial on univariate autoregressive spectral

analysis." Journal of clinical monitoring and computing19.6 (2005): 401-410.


20


Commented MATLAB script 4│Polynomial detrending

Contents

1. Description

2. Polynomial order*

3. Remove trend


1. Description Matlab script for detrending

[detrended, poly_order] = poly_detrend(data)

Input: data: data with trend

Output: detrended: detrended data

poly_order: polynomial order (which was fitted to the data and removed)

function [detrended, poly_order] = poly_detrend(data)

3. Polynomial order changeable value: highest tested order

time = 1:length(data);

highest tested order:

z = 8;

total_er = NaN(1,z);

for n = 1:z

[p,S] = polyfit(time',data,n);

[FIT, er]=polyval(p,time,S);

total_er(n) = sum(er);

warning('off','all')

end

4. Remove trend Removes trend from data

Poly = 1:z;

[a,poly_order] = min(total_er);

p_ = polyfit(time',data,poly_order);

trend = polyval(p_,time);

detrended = data-trend';


21

Supplementary Method 2 │FFT window calculation

Number of data points: N

Number of segments: x

Length of segment: l = α ∙ N

Percent overlaping: β

overlaping part of segment: s = β ∙ α ∙ N

Non overlaping part of Segment: y = (α ∙ N) - (β ∙ α ∙ N)

N = α ∙ N + (x-1) ∙ y

N = α ∙ N + (x-1) ∙ ((α ∙ N) - (β ∙ α ∙ N))

Factorise:

N = α ∙ N (1+ (x-1) - (x-1) ∙ β )

Divide by N

1 = α ∙ (1+ (x-1) - (x-1) ∙ β )

α = 1/(1+(x -1) - (x -1) ∙ β)

Number of FFT bins: N/2

N/2 = 2048/2 = 1024 FFT bins

Frequency resolution: Δf = NyF/number of bins


22

NyF/number of bins = 10Hz/1024 bins = 9.77 ∙ 10-3 Hz/bin

To calculate the length of one segment by given x and given β you first have to calculate α.

Example: x = 5 and 25% overlap (β = 0.25)

α = 1/(1+(x -1) - (x -1) ∙ β)

calculate α with the formula:

α = 1/(1+ 4 - 4 ∙ 0.25) = 1/4 = 0.25

To get the length l, multiply α with the total number of data points:

l = α ∙ N = 0.25 ∙ 2048 = 512

To get the number of overlapping data points multiply the overlap (β) with the length of one

segment:

s = β ∙ α ∙ N = 0.25 ∙ 0.25 ∙ 2048 = 128

Using the formulas specified above, the total fft points N can easily be calculated when the

desired resolution/point number, the number of windows and the overlap of the windows is

known through simple rearrangement.

Or if you have a time series of ECG, or action potentials of a limited time, the resolution of the

periodogram can be calculated when changing the numbers of windows or varying the overlap.

During the setup and validation phase of the method these considerations are important.


23

Supplementary Method 3 │Model-based autoregressive spectral analysis

Frequency domain analysis can also be performed using autoregressive (AR) modeling. The

advantage of the AR model is that its frequency resolution is higher as compared to power

spectral density estimation via the fast fourier transformation (FFT). Furthermore, the AR

model can be used for parametric estimation of the main characteristics of the power spectral

density of HRV, especially to resolve peak frequencies and to display a more normalized shape

in the power graphics. We usually calculate the frequency bands using FFT, because FFT

calculations are more accurate than autoregressive models. In graphs we also use the

autoregressive method for illustration of the main oscillatory components of HRV.

An AR model of the oscillatory components present in the stationary segments of the RR

interval time series is calculated as follows: The current RR value of the series 𝑥(𝑛) is

expressed as a linear function of previous values plus an error term 𝑒(𝑛).

𝑥(𝑛) = −𝑎(1)𝑥(𝑛 − 1) − 𝑎(2)𝑥(𝑛 − 2) − ⋯

−𝑎(𝑝)𝑥(𝑛 − 𝑝) + 𝑒(𝑛)

The equation incorporates p previous terms and represents a model of order p. It is commonly

rewritten as:

𝑥(𝑛) = − ∑ 𝑎(𝑘)𝑥(𝑛 − 𝑘) + 𝑒(𝑛)

𝑝

𝑘=1

The model parameters a(k) and x(n-k) are determined using the Levinson-Durbin recursion

to solve the Yule Walker equation or using Burg´s method. This procedure allows for the

automatic quantification of the centre frequency and power of each relevant oscillatory

component present in the time series. In Supplementary Software MATLAB script 2

parameter settings for the AR model are specified.


24

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