Electrocardiogram – parametrization of waves

Introduction

Electrophysiological process in the health heart generates ECG signals, that reflects the summation of

action potentials in individual hearth structures dependent on a heart cycle. The cycle starts by the

atriums depolarization (P-wave), ventricles depolarization (QRS complex) and repolarization ventricles

(T-wave). Although signal waveform variability is relatively high between individual persons, the time-

dependent sequence of the waves, their polarity and amplitudes are strictly defined, that reflects the

heart condition. A valid interpretation of ECG can be carried out only by the experienced cardiologist,

however, the modern ECG system allows automatic parametrization and classification of the

waveforms to time-saving. The parametrization is fixed to the strongest R-peaks detection; subsequent

measuring of weak waves is performed between two cycles called R-R interval. Professional ECG

systems contain algorithm, which combines signals from all 12 leads for robust parametrisation also

pathological ECG. The main goal of this exercise is the basic measuring of normal ECG in the II. lead.

Aims:

1. Record ECG (I. and II. leads) 30 seconds in relax 2. Detect all R-peaks 3. Detect P, Q, S, T maximum in each R-R interval 4. Use triangle-detector to find the onset of P, Q, T waves and end of P, Q, S(J), T 5. Implement the function with outputs of the onsets, maxima, ends of waves 6. Automatically parametrise ECG signal:

intervals P, PQ (PR), Q, QRS, QT

amplitudes of maxima P, R, T, and ST segment 7. Compute electrical heart-axes using (I, aVf) leads for P, R, T waves 8. Show (I, II, III, aVR, aVL, aVF) leads in normalised grid and results of automatic parametrisation 9. Compare automatic and manual measurement of ECG

Recording of ECG: I. lead:

- white (-): right hand

- red (+): left hand - black (ref): right leg

II. lead:

- white (-): right hand

- red (+): left leg - black (ref): right leg

Thirty seconds ECG is recorded in sit, without talking, in a relaxed position, with normal breathing. Minimize the induction loop to minimize main hum noise. Note: You can use the first 30 seconds of signals from the previous exercise. Data structure: fs=500 Hz

1. column … lead I [mV] 2. column … lead II [mV]

Useful functions:

butter, freqz, zplane, impulse, function, filtfilt, compass, gca, pbaspect, set, get

Help:

1) Detection of R-peaks: R-peak (R) is a fast transient <100 ms, which

contains frequency components >10 Hz in comparison to slower

waves. Using of high-pass filter highlight the energetic QRS

complex to determine sections with local maxima.

data=load('ECG_test_500Hz_v3.txt'); fs=500; % Hz data=data(1:30*fs,:); % 30s

t=linspace(0,(size(data,1)-1)/fs,size(data,1))';

II=data(:,2);

% Implement:

1) Band-pass filter 0,5-40 Hz

...

fII=filtfilt(bbp,abp,II);

2) Differentiate the signal. Compensate the shortening

by inserting the sample before signal (note. check

the transfer function of filter b=[-1 1], a=1).

dII=diff([fII(1); fII]);

3) Square differentiated signals and smooth it by the

moving average (MA) filter of 50ms window (envelope)

...

envelope=filtfilt(bMA,aMA,dII^.2);

4) Threshold the envelope (e.g. 10% of maximum) and

detect the onset and end of sections

th=0.1*max(envelope); % 10% of max. envelope

R_suspect=envelope>th; start=find(diff([0;R_suspect])>0); % 0+diff, >0 stop=find(diff([R_suspect;0])<0); % diff+0, <0

5) Find local maxima in QRS

for i=1:length(start) seg=fII(start(i):stop(i)); % ECG 0,5-40 Hz [~,pos]=max(seg); % index of maximum Rm(i)=start(i)+pos-1; % index after segment start end

2) Detect P, Q, S, T waves in each R-R interval. Implement of triangle-detector function and use it

to detect onsets and ends of the waves. Encapsulate the final function for all waves

parametrisation. Use it in a future exercise. 1) Make the triangle-detectro function (triangle_detector.m)

function [bx_max,S]=triangle_detector(segment)

ax=1; % x-position of vertex A ay=segment(ax); % y-position of vertex A cx=length(segment); % x-position of vertex C cy=segment(cx); % y-position of vertex C

% triangle area S=f(B) S=zeros(length(segment),1); for k=1:length(segment) % from A to C bx=k; % x-position of vertex B by=segment(k); % y-position of vertex B S(k)=0.5*abs((cx-ax)*(by-ay)-(cy-ay)*(bx-ax)); % area end [~,bx_max]=max(S); % x-position of vertex B correspond to the maximal area

2) In for-cycle test R-R intervals and parametrise all waves

for i=1:length(Rm)-1 seg=fII(Rm(i):Rm(i+1)-1); % R-R segment II 0,5-40 Hz % 1. derivation (local extreme=0 for continuous signal)

df=diff([seg(1); seg]); % decrease to increase change (local minimum for digital signals) sgn=sign(df); % wave S, Q

S=find(diff(sgn)>0,1); % first local minimum Q=find(diff(sgn)>0,1,'last'); % last local minimum

S Q

% wave T, P [~,T]=max(seg(S:floor(end/2))); % maximum between S and (R-R)/2 T=T+S-1; [~,P]=max(seg(floor(end/2):Q)); % maximum between (R-R)/2 and Q P=P+floor(length(seg)/2)-1;

% end of T-wave: find foot of wave using triangle-detector between

% T-maximum and half of R-R interval

Tend=triangle_detector(seg(T:floor(end/2))); Tend=Tend+T-1;

% onset of T-wave: find foot of wave using triangle-detector between % double of R-S interval (2*S) and T-maximum Tstart=triangle_detector(seg(2*S:T)); Tstart=Tstart+2*S-1;

% onset of P-wave: find a foot of wave using triangle-detector between

% half of R-R interval and P-maximum Pstart=...

% enf of P-wave: find foot of wave using triangle-detector between

% P-maximum and double Q-R interval before end of segment (end-2QR)

QR=length(seg)-Q;

Pend=triangle_detector(seg(P:end-2*QR)); Pend=...

% onset of Q-wave: find a foot of wave using

% triangle-detector between the end of P-wave and

% Q-maximum

Qstart=... % end of Q-wave: find the index of first crossing the

% amplitude of Q-onset

Qend=... % end of S-wave: find a foot of wave using triangle-

% detector between S-maximum and T-onset

Send=...

% Save the detection in indexes from start of ECG signal

Sm(i)=S+Rm(i)-1; Se(i)=Send+Rm(i)-1; Qs(i)=Qstart+Rm(i)-1; Qm(i)=Q+Rm(i)-1;

Qe(i)=Qend+Rm(i)-1; Ts(i)=Tstart+Rm(i)-1; Tm(i)=T+Rm(i)-1; Te(i)=Tend+Rm(i)-1; Ps(i)=Pstart+Rm(i)-1; Pm(i)=P+Rm(i)-1; Pe(i)=Pend+Rm(i)-1; end

P T

Qstrat

Q

Qend

R

II (

mV

)

time (s)

Send

Sm Ts

Tm

Te

Pm

Ps Pe

Qm

Qs

Se (J)

× Qe

3) Show all detection in ECG signal (II. lead) plot(t,fII); axis tight; hold on plot(t(Rm),fII(Rm),'or') plot(t(Sm),fII(Sm),'^r') plot(t(Se),fII(Se),'xr') ...

4) Encapsulate algorithm to function for future using! function [Ps,Pm,Pe,Qs,Qm,Qe,Rm,Sm,Se,Ts,Tm,Te]=my_ecg_fun(II,fs) ...

3) Use indexes for measuring ECG parameters. Remember, the order of detection in R-R interval

is R, S, T, P, Q, but interval measurement requires the heart cycle as P, Q, R, S, T. 1) Measure intervals and amplitudes

HR – heart rate per minute (BPM)

P – P-wave duration

PQ –P-Q interval, from P-onset to Q-onset

Q – Q-wave duration

QRSD – QRS complex duration, from Q-onset to S-end

QT –Q-T interval, from Q-onset to T-end

QTc – corrected QT by the HR, Bazett’s formula 𝑄𝑇𝑐𝐵 =𝑄𝑇

√𝑅𝑅⁄ ; where RR is R-R interval in

seconds

Amplitudes: P, R, T, and ST segment (S-end to T-onset) P_amp=median(fII(Pm)-fII(Ps));

...

ST_amp(i)=mean(fII(Se(i):Ts(i)));

2) Compute electrical heart exes for P, R, T waves.

Remember filter the I. and II. leads. fIII=fII-fI; faVf=(fII+fIII)/2; faVr=-(fI+fII)/2; faVl=(fI-fIII)/2;

% P-maximum can be under zero line in I. lead. Compute

the amplitude from isoline in P-onset

Paxis=median(-atand(-faVf(Pm)./(fI(Pm)-fI(Ps))));% 0-75° Raxis=median(-atand(-faVf(Rm)./fI(Rm))); % 0-120°

Taxis=median(-atand(-faVf(Tm)./fI(Tm))); % 15-75°

3) Show appropriate 10 seconds of all ECG leads in normalised time/amplitude

scale: 25mm/s and 10mm/1mV. For simple plotting use only one window, the

leads separate DC offset (2mV). Insert an amplitude/time referential

marker (1mV, 40ms, i.e. y=1cm, x=1mm). xr=25; % 25mm/s yr=10; % 10mm/mV xmm=[0 10]; % show 0-10s

ymm=[-12 2]; % show -12 mV až 2 mV

cmark=[zeros(round(0.04*fs),1);

ones(round(0.04*fs),1); % the marker 0.04s~25mm/s

zeros(round(0.04*fs),1)]; tmark=linspace(0,length(cmark)/fs,length(cmark)); % time axis of the marker

figure(); hold on plot(t,fI,'k'); xlim(xmm); plot(t,fII-2,'k'); xlim(xmm); % -2mV offset ...

plot(t,faVf-10,'k'); xlim(xmm); % -10mV offset

stairs(xmm(1)+tmark,cmark,'k','linewidth',2) stairs(xmm(1)+tmark,cmark-2,'k','linewidth',2); % -2mV offset ... stairs(xmm(1)+tmark,cmark-10,'k','linewidth',2); % -10mV offset

title('ECG 0.5-40 Hz')

xlabel(['time(s) [' num2str(xr) 'mm/s]']);

ylabel(['(mV) [' num2str(yr) 'mm/mV]']);

% grid of graph paper -------------------------------------------------------------

--

grid on; grid minor; % show main and minor grid axes=gca; % load graph properties

axes.YAxis.TickValues=ymm(1):0.5:ymm(2); % big square 0.5 mV (5mm) axes.XAxis.TickValues=xmm(1):0.2:xmm(2); % small square 200 ms (5mm)

axes.YAxis.MinorTickValues=ymm(1):0.1:ymm(2); % big square 0.1 mV (1mm) axes.XAxis.MinorTickValues=xmm(1):0.04:xmm(2); % small square 40 ms (1mm)

axes.YAxis.TickLabel=repmat({''},1,length(axes.YAxis.TickValues)); %y no-labels axes.YAxis.TickLabel(5:4:25)={'aVF','aVL','aVR','III','II','I'}; % leads’ names xtickangle(90); % 90° rotation of labels in x-axis

pbaspect(gca,[max(xmm)*xr (ymm(2)-ymm(1))*yr 1]) % normalized ratio of y-x axes

% text panel of measured properties

text(xmm(2),ymm(2),{... ['==LEAD II==']; ['HR=' num2str(HR,'%.1f') ' (55-90) BPM']; ...

},'VerticalAlignment','Top','EdgeColor','k','BackgroundColor','w');

4) Compute and show an average of ECG cycle in II. lead synchronized by R-peak. Compare manual measuring (e.g. ginput) to automatic analysis.

Parameter AUTO MANUAL NORM

HR 55-90

Duration (ms)

P <110

PQ 120-200

Q <30

QRSD <110

QT 250-500

Voltage (mV)

P 0-0.25

R 0.5-3

ST <±0.1

T >0