Biomedical. Measurement and Design ELEC4623. Lectures 15 and 16 Statistical Algorithms for Automated Signal Detection and Analysis

Transcription

1 Biomedical Instrumentation, Measurement and Design ELEC4623 Lectures 15 and 16 Statistical Algorithms for Automated Signal Detection and Analysis

2 Fiducial points Fiducial point A point (or line) on a scale used for reference or comparison purposes Sometimes we need to find reference points in biological waveforms before any feature extraction can be done Most relevant to heart beat synchronous signals (ECG, pulse oximetry, arterial pressure, thoracic bioimpedance) For ECG, the best way to detect each heart beat is to try and detect the QRS waves since they are very sharp and distinct The principles will be similar for detection in other signals, so QRS detection is a good starting point

3 Traditional QRS detection The purpose of the filtering stage is emphasise desirable features (QRS) and de-emphasise undesirable elements (noise) or other waveform characteristics ti (P wave or T wave) Traditionally, the filtering is linear (e.g. analogue, FIR, IIR) but there is no strict requirement for linearity The non-linear transformation ti might commonly be (say) ay 2 term followed by an integration The decision rule examines the output of the preprocessor and determines the existence of QRS complexes Can be simply threshold detection May be more complicated

4 ECG spectral content Figure shows typical spectral components of a ECG signal P and T waves have comparatively lower frequency content than QRS The QRS has high frequency information A high pass filter (such as a differentiator) helps separate P-T from QRS waves. Not included on the figure is 50/60Hz interference

5 Differentiation ECG ECG First derivative The first derivative (bottom trace) has a peak during the QRS rise and a trough during QRS fall Differentiation enhances threshold pulse detection by: Attenuation of P and T waves with respect to the QRS (improves SNR) Removes baseline wander caused by say respiration Disadvantage: Differentiation amplifies high frequency noise! (Requires lowpass filtering. That is maybe bandpass is better)

6 Bandpass filter SNR From the power spectral analysis of the various signal components in the ECG signal, a filter can be designed which effectively selects the QRS complex from the ECG The study of the power spectra of 3875 ECG beats vs. noises revealed that a maximum SNR value is obtained for a bandpass filter with a center frequency of 17 Hz and a Q of 3 Variations on this filter are found in most QRS detectors

7 Filter responses for different values of Q Q needs to be chosen optimally as well as f 0 Q too high will result in a very oscillatory response (a) The ripples must die down within 200 ms so that the ripples from one QRS complex do not interfere with the ripples from the next one With a center frequency of 17 Hz, the maximal permissible Q was found to be 5 The figure shows the effect of different values of Q (8, 3 and 1)

8 Q factor The bandwidth, Δf, of a damped d oscillator is shown on a graph of energy versus frequency The Q factor of the damped oscillator, or filter, is f 0 / Δf The higher the Q, the narrower and 'sharper' the peak is

9 QRS detection based on differentiation Various signal stages in the QRS detection algorithm based on differentiation (a) Original ECG (b) Smoothed and rectified first derivative (c) Smoothed and rectified second derivative (d) Smoothed sum of (b) and (c) (e) Square pulse output for each QRS complex Ahlstrom and Tompkins (1983)

10 Ahlstrom and Tompkins - derivative method The absolute values of the first and second derivative are calculated l from the ECG signal y0(nt) = x(nt) x(nt 2T) y1(nt) ( ) = x(nt) ( ) 2x(nT 2T) + x(nt ( 4T) ) These two data buffers, y0(nt) and y1(nt), are scaled and then summed y2(nt) = 1.3y0(nT) + 1.1y1(nT) The data buffer y2(nt) is now scanned until a certain threshold is met or exceeded y2(it) >=1.0 Once this condition is met for a data point in y2(it), ( the next eight points are compared to the threshold. If six or more of these eight points meet or exceed the threshold, then the segment might be part of the QRS complex. In addition to detecting the QRS complex, this algorithm has the advantage that it produces a pulse which is proportional in width to the complex Assists feature extraction (Q on and S off) A disadvantage is that it is particularly sensitive to higher-frequency noise (as are most derivative-based detectors)

11 Pan, Hamilton and Tompkins QRS detector LPF and HPF are cascaded (rather than combined) for more robust design It is very common to split complex filters into a series of first and second order sections, especially when using integer arithmetic After differentiation is a nonlinear transformation that consists of point-by-point squaring of the signal samples This makes all the data positive prior to subsequent integration The squared waveform passes through a moving window integrator This integrator sums the area under the squared waveform over a moving 150-ms interval The window s width is chosen to be long enough to include the time duration of extended abnormal QRS complexes, but short enough so that it does not overlap significantly with an ectopic which may suddenly occur This is dictated by refractory period of myocardium

12 Low pass filter y(nt) = 2y(nT T) y(nt 2T) + x(nt) 2x(nT 6T) + x(nt 12T) H( z) = ( 6 ) 2 1 z ( 1 1 z ) 2 30 f s = 200 Hz Q: Group delay? (db) Magnitude Gain = Fc (-3 db) ~ 11 Hz Normalized Frequency ( π rad/sample)

13 ECG before and after low pass filtering The main difference is in the height of the QRS complex. (Remember the QRS has the highest typical frequency content) Note time delay introduced by the LPF

14 High pass filter H LPF ( z) 1 z = 1 z 32 1 H ( z) z HPF 16 = 1 z ( 1 z ) 1 32z + 32z z = z (1 z) Formed by subtracting the output of a low pass filter from a delayed version of the input signal Q: What is the delay of the low pass prototype? Why need the 16-sample delay term in the HPF? This type of filter is called a matched delay subtractive (MDS) filter. It has a linear phase characteristic as shown in the Bode plot.

15 Matched delay subtractive HPF

16 Bandpass filter characteristics The main reason we are so interested in using linear phase filters for the QRS detection is to precisely define the timing of R-wave, which can be useful for synchronisation purposes - e.g. measuring pulse transit time (PTT) time delay from R wave to a peripheral pressure/volume pulse) If the phase is not linear: time delay of filter not known + phase distortion, so precise location of R-wave cannot be found

17 Derivative Aft filt i th i l i th diff ti t d t After filtering the signal is then differentiated to accentuate the QRS complex and suppress P and T wave

18 Squaring The squaring function is a nonlinear operation, y(nt) = [x(nt)] 2 This operation makes all data points in the processed signal positive, and amplifies the output of the derivative process nonlinearly (mainly QRS part) The output of this stage should be hard-limited to a certain maximum level corresponding to the number of bits used to represent the data type of the signal.

19 Moving window integration N point moving average filter [ ] yn ( ) = 1/ N xn ( ) + xn ( 1) + xn ( 2) xn ( N 1) The slope of the R wave alone is not a guaranteed way to detect a QRS event. Many abnormal QRS complexes that have large amplitudes and long durations (not very steep slopes) might not be detected using information about slope of the R wave only Difference equation assumes sampling interval T is constant so that nt term is replaced by n Choose N such that it is about the same length as the widest possible QRS complex, but not so long that QRS and T waves are merged (150 ms about right)

20 QRS detection by Pans and Tompkins method Raw ECG Bandpass filtered Differentiated Squared Integrated (smoothed)

21 Threshold detection Various methods are used, from fixed threshold (generally poor) to variable thresholds (depends on previously detected peaks). The system output can vary in amplitude if measuring over a long period, or even over short period if abnormal beat occurs Often some sort of decay method is used The figure shows detection of an ectopic beat, which h typically has completely different appearance to normal beats But a sudden large amplitude (e.g. abnormal beat or artefact) can sometimes lead to missing out of subsequent pulses! Alternatively, may use moving average (or median) of previous peaks

22 Searchback methods Upper trace ECG signal, Lower trace filtered and integrated signal (a) Running threshold is 50% the peak value of filter output (b) Normal beats trigger an output when they occur (c) No beat was detected for a time interval of 168% of the average RR interval (d) Reduce the threshold to 25% of the peak filter output and search back (e) Find the ectopic beat (f) Resume normal threshold

23 Performance measurement There are many different types of QRS detectors. How can they be compared? They are often tested on some standard ECG databases, many of which can be downloaded from internet These databases often contain a wide variety of different types of ECG, with difficult to detect QRS complexes Beats have been pre-annotated by experts The best detectors have a total error of about 0.5% This still represents about 20 beats per hour or 500 per day! Automated QRS detection is quite a difficult task, especially for ambulatory ECG with high motion noise and abnormal QRS of patients

24 Performance evaluation Two parameters should be used to evaluate the algorithms Se = sensitivity +P = positive predictivity TP = number of true positive detections FN = number of false negatives FP = number of false positives TP Se = TP + FN P TP + = TP + FP

25 Performance evaluation Matching window False positive detection True positive detection False negative detection

26 Morphological QRS detectors The strength of digital signal processing is that we are not constrained by the limitations of analogue electronics There has been a lot of focus on mimicking analogue hardware via IIR filter, but this is changing For example, the filter does not need to be linear Morphological QRS detection is one example of this

27 Morphological QRS detector Based on mathematical morphological opening and closing A peak valley extractor (PVE) is used to extract peaks and valleys from the ECG The structuring element could have variable length L or fixed length An optimal fixed length was found to be about 12 sample points (24 ms at fs=500 Hz)

28 Morphological QRS detectors Upper trace ECG signal Second trace Peaks extracted (erosion, dilation,subtraction) Third trace valleys extracted (dilation, erosion, subtraction) Final trace - combination of peaks and valleys Note this could be used for baseline and muscle noise filtration as well as for QRS emphasis

29 Morphological QRS detection This method has comparable accuracy to others (such as Tompkins) It only involves comparisons, no other mathematical operators (+, -, *, /) so can be used on very simple microcontrollers.

30 Other methods Hilbert transforms Length and energy transformations Wavelet transforms Filter banks Matched filters Zero crossing based Adaptive filters Neural networks Hidden Markov models Rule-based expert systems

31 Template matching techniques The system has a number of bins, which each stores an average QRS complex (the template) of a particular type of beat (e.g. ectopic) At each detection the ECG is compared against the QRS templates If the ECG is sufficiently similar to one of the bins, the detected QRS complex is classified into that t bin and the average QRS complex updated Similarit inde es sed are Similarity indexes used are Cross-correlation (maximum) Distance (Minimum)

32 Template creation by waveform averaging Original signal n = 10 n = 100 n = 1000 SNRn = n. SNR

33 Waveform averaging Waveform averaging is useful when spectra of noise and signal waveform overlap and we are measuring a comparatively stationary process The signal waveform must be repetitive (although h it does not have to be periodic), and the noise should be random and uncorrelated with the signal So by averaging, repetitive morphological features of signal waveform are emphasized, whereas random noise is suppressed The timing of each signal waveform must be accurately known, and that requires a consistently occuring fudicial point (e.g. R-wave) Any misalignment will lead to a low pass filtering effect on the signal Useful for: Feature extraction from ECG, since we emphasize morphological features (P, QRS, T) against noise Identification of artefacts and abnormal beats (e.g. ectopics), which tend to have lower correlations with the average waveform

34 ECG feature extraction

35 Pulse rate detection by autocorrelation Top figure shows ECG corrupted by noise A QRS detector might fair poorly at correctly detecting all QRS complexes If we are just interested in heart rate, we can find the autocorrelation function of the signal Should probably lowpass filter first The position of the peak indicates the base heart rate 100 samples in this case and since f s = 100Hz, heart rate = 1Hz = 60 BPM

36 References Biomedical Digital Signal Processing - C-Language Examples and Laboratory Experiments for the IBM PC. WILLIS J. TOMPKINS Editor. University of Wisconsin-Madison (chapter 12) The Principles of software QRS detection P.E. Trahanias. B.U. Kohler, C. Hennig, R. Orglmeister. IEEE Engineering in Medicine and Biology Magazine, 21(1):42-57, JAN-FEB 2002 An approach to QRS complex detection using mathematical morphology P.E. Trahanias. IEEE Transactions on Biomedical Engineering, VOL. 40, N0.2, FEBRUARY 1993