Pressure Event Detection Based on the Dyadic Wavelet Transform

The physiological condition of the human cardiovascular system is primarily determined from the electrocardiogram (ECG) and blood pressure signals. Diagnostic and therapeutic medical procedures and the operation of various medical devices often rely on the temporal location of various events observed in these signals. The QRS complex (R wave) is one distinguishing characteristic of the ECG waveform; whereas the systolic peak, upstroke and the dicrotic notch are the most prominent events in the arterial blood pressure signal. Detection of these waveform characteristics may be used for calculating I heart rate and the systolic time intervals including the pre-ejection period (PEP), left ventricular ejection time (L VET) and electromechanical systole (QS2). This report describes an algorithm which accurately and consistently locates the dicrotic notch in the arterial blood pressure waveform for a range of heart rates, arrhythmias and irregular pressure waveforms (including baseline drift, catheter artifact, signal damping and noise) using the dyadic wavelet transform (DyWT). Simultaneous occurrences of minima in the DyWT across several successive dyadic scales indicates a transient in the pressure waveform, from which the corresponding temporal location of the dicrotic notch is determined for each cardiac cycle. The dyadic wavelet transform scheme for dicrotic notch detection has been tested on arterial blood pressure waveforms (radial, femoral, and axillary) with various heart rates, ranging from 40 to 140 beats per minute (bpm). Algorithm performance was evaluated using 71 patient data files from the Massachusetts General Hospital (MGH) database which includes simultaneous ECG and arterial pressure recordings. Four criteria were used to indicate detection performance: sensitivity, positive productivity, false positive rate and false negative rate. The accuracy of the proposed DyWT based dicrotic notch detection algorithm outperformed five previously published detection algorithms in terms of each of the four performance criteria. The Dy WT based detection algorithm achieved a sensitivity of 84%, a positive productivity of 85%, a false positive rate of 15 % and a false negative rate of 16% when tested 72 patient arterial blood pressure files of various waveform types, illustrative of a clinical environment. The next highest performers achieved a sensitivity as high as 66%, positive productivity of 72%, a false positive rate as low as 25 %, and a false negative rate of34%.

peak, upstroke and the dicrotic notch are the most prominent events in the arterial blood pressure signal. Detection of these waveform characteristics may be used for calculating I heart rate and the systolic time intervals including the pre-ejection period (PEP), left ventricular ejection time (L VET) and electromechanical systole (QS2).
This report describes an algorithm which accurately and consistently locates the dicrotic notch in the arterial blood pressure waveform for a range of heart rates, arrhythmias and irregular pressure waveforms (including baseline drift, catheter artifact, signal damping and noise) using the dyadic wavelet transform (DyWT). Simultaneous occurrences of minima in the DyWT across several successive dyadic scales indicates a transient in the pressure waveform, from which the corresponding temporal location of the dicrotic notch is determined for each cardiac cycle.
The dyadic wavelet transform scheme for dicrotic notch detection has been tested on arterial blood pressure waveforms (radial, femoral, and axillary) with various heart rates, ranging from 40 to 140 beats per minute (bpm). Algorithm performance was evaluated using 71 patient data files from the Massachusetts General Hospital (MGH) database which includes simultaneous ECG and arterial pressure recordings. Four criteria were used to indicate detection performance: sensitivity, positive productivity, false positive rate and false negative rate. The accuracy of the proposed DyWT based dicrotic notch detection algorithm outperformed five previously published detection algorithms in terms of each of the four performance criteria. The Dy WT based detection algorithm achieved a sensitivity of 84%, a positive productivity of 85%, a false positive rate of 15 % and a false negative rate of 16% when tested 72 patient arterial blood pressure files of various waveform types, illustrative of a clinical environment. The next highest performers achieved a sensitivity as high as 66%, positive productivity of 72%, a false positive rate as low as 25 %, and a false negative rate of34%.  brachial, (d) femoral, (e) pedal and (f) axillary pressures, [22] showing the locations of the systolic peak and the dicrotic notch.

Justification of Study
The blood pressure waveform reflects the mechanical function of the myocardium as well as of the arteries and veins and represents the hemodynamic pressures generated by the heart muscle throughout the systolic and diastolic cycles. The most commonly used features in the arterial waveform are systolic upstroke, systolic peak and the dicrotic notch. The dicrotic notch is observed in arterial pressure waveforms as a consequence of the closing of the aortic valve, after left ventricular ejection, indicating the start of the diastolic cycle. Locating the dicrotic notch is critical for analyzing systolic time interval (STI) [1][2][3][4][5][6][7][8][9][10], for determining the heart rate relative to the beginning of the diastolic cycle and for determining the proper inflation time of an intraaortic balloon [11][12][13][14][15][16][17][18][19][20][21].
The detection of the dicrotic notch is non-trivial in that the blood pressure signal may be corrupted by noise, contain motion artifacts, respiratory modulation, or change abruptly with arrhythmias; and in sick patients, the pressure curve may deviate greatly from the norm. The blood pressure waveform also varies depending on which part of the circulatory system is being monitored, (aortic, radial, brachial, femoral, pedal or axillary pressures) and is dependent upon the fidelity of the pressure sensor. Previously developed dicrotic notch detection algorithms have accommodated some but not all of these waveform irregularities.

1
One signal processing technique, the dyadic wavelet transform, has been applied to detect the dicrotic notch in a variety of pressure signals available in the Massachusetts General Hospital (MGR) clinical waveform database [22]. Physiological signals such as the blood pressure, are classified as time varying or non-stationary. The wavelet transform provides local frequency information of a signal and is used for analyzing a waveform according to its changing spectral position by altering the filter function according to the local spectral information in the signal [23][24][25][26][27][28][29][30]. The wavelet transform is well suited to process non-stationary signals that exhibit transient behavior and for time-frequency analysis where linear time invariant systems fail. Application of the wavelet transform allows high frequency components of a signal to be studied with sharper time resolution than low frequency components [31] .
The dyadic wavelet transform uses scaled and translated versions of the mother wavelet. This scaling produces variable length windows, providing variable resolution in the time or frequency domain. Thus, varying the scale of the wavelet allows for a multiresolution view of a signal. Application of the wavelet transform therefore provides a means of analyzing a range of time varying signals, such as slow, fast and arrhythmic heart rhythms, to observe both high frequency transient information from lower frequency signal behavior [25][26][27][28]. Signal transients or discontinuities, such as the dicrotic notch, can be isolated from background noise by comparing the DyWT across successive dyadic scales, thus making the DyWT an appropriate method for dicrotic notch detection. Band limited noise whose spectra lies outside of the frequency resolution of any of the dyadic wavelet scales will not correlate between scales of the dyadic wavelet transform. For such cases, actual events such as the dicrotic notch can be detected in relatively noisy signals. The ability of the dyadic wavelet based algorithm to detect the dicrotic notch in non-stationary and noisy signals enhances its performance over the preexisting detection algorithms.

Physiological Background
The human heart is a hollow muscle whose contractile motion controls blood flow through the circulatory system. The heart contains four muscular chambers: the left and right atria and the left and right ventricles, which are each separated from the remaining cardiac system by one way valves as shown in figure l. I [36]. The rnitral valve separates the left atrium from the left ventricle; the tricuspid valve separates the right atrium from the right ventricle; the aortic valve enables blood flow out from the left ventricle into the aorta; and the pulmonary valve controls the blood flow out of the right ventricle into the vena cava.
The function of the heart muscle is governed by electrical impulses that contract the muscle fibers . Each of the four chambers of the heart contains a certain blood volume.
When a cardiac chamber receives an electrical signal, the muscle contracts and blood is forced out of the chamber. The left ventricle (L V) is responsible for forcing blood into the aorta (through the aortic valve) with enough pressure to allow circulation of blood throughout the body. The arterial pressure waveform is the pressure of the blood flow out of the L V into the aorta and through the arterial system over time.
The complete series of cardiac events which occur in a single heartbeat is referred to as a cardiac cycle. An outline of the events in the cardiac cycle are listed in table I . I [3 7] including the 8 phases of each cycle, the events at the onset, during and at the end of each phase. Also provided are the durations (in seconds) of each of the 8 phases for both man and dog. Figure 1.2 [37] shows the coordination of the electrocardiogram, left ventricular, left atrial and aortic pressure curves, the heart sounds and the left ventricular    The cardiac cycle begins with an electrical signal generated by the Sino-Atrial (SA) node, located in the right atrium. This signal, which is recorded on the electrocardiogram, propagates to the atrioventricular (AV) node where it is delayed so the left atrium can adequately empty its blood volume into the left ventricle. The signal then travels along the AV bundle (or Bundle of His) which stimulates contraction of the ventricle, defining the onset of the systolic cycle [38]. Contraction of the left ventricle corresponds with the QRS complex observed in the ECG waveform. The time between the generated electrical impulse and actual contraction of the left ventricle is called the pre-ejection period (PEP).
Once the left ventricle generates enough pressure relative to the aortic root pressure, the aortic valve opens. Left ventricular ejection into the arterial system increases to a maximum, observed on the left ventricular and aortic pressures as the systolic peak, then decreases as the remaining blood volume empties into the aorta. Once the aortic and left ventricular pressures equalize, the aortic valve closes, defining the end of systole and the beginning of the diastolic cycle. As the aortic valve closes, there is a slight retraction of blood flow and a dip in the pressure waveform. After valve closure, blood flow continues forward into the arterial system and the pressure increases slightly. The result of the aortic valve closure appears as a · notch (dicrotic notch (DN)) in the arterial blood pressure (BP) waveform. Blood then flows through the systemic circulation while the left atrium refills the left ventricle for the next cardiac cycle, shown as a gradual decay in the aortic pressure.
The pressure waveform represents the pressure state during both the systolic and diastolic phases of the cardiac cycle. A peak systolic pressure (PSP) of 120 mmHg and a diastolic pressure of 60 mmHg is typical for a healthy adult human. The contour of the pressure waveform varies depending on which part of the circulatory system is being monitored. Figure 1.3 a-f [22] show the typical waveform shape at various points along 7 the circulatory track, with the locations of the systolic peak and the dicrotic notch labeled.
Arterial Pressure versus Time ( e) pedal and (f) axillary pressures, [22] depicting the locations of the systolic peak and theDN. 8

Clinical Implications
Locating the dicrotic notch in arterial blood pressure signals has several clinically important applications. The location of the dicrotic notch indicates the closure of the aortic valve which occurs at the end of left ventricular ejection. Thus, the dicrotic notch represents the end of the systolic phase and the start of diastole and left ventricular relaxation. The duration of the systolic phases, including pre-ejection and left ventricular ejection, provides valuable diagnostic information of the condition of the myocardium and of cardiac performance. Locating the dicrotic notch is also important for evaluating the accuracy of a set of linear regression equations used to predict systolic time interval according to heart rate. The information of the regression equation is also used in the intraaortic balloon pump cardiac assistance device for determining the proper inflation time of an intraaortic balloon at the end of the systolic cycle [ 14].

Systolic Time Intervals
Information of the systolic time intervals are useful in assessing cardiac condition and various cardiac disease states (including L V failure, myocardial infarction, coronary artery disease, and valve disorders) in man. The time intervals of the various stages of the cardiac cycle have been observed to change under cardiac disease conditions and pharmacological influence [1][2][3][4][5][6][7][8][9][10].
The three basic systolic time intervals are the pre-ejection period (PEP), left ventricular ejection time (L VET) and total electromechanical systole (QS2). The first stage of the systolic cycle, referred to as the pre-ejection period, involves an electromechanical delay (30 to 40 msec) followed by initial isovolumetric contraction of the left ventricle (60 to 80 msec). The PEP is immediately followed by left ventricular ejection which lasts throughout the remaining systolic cycle. The entire systolic cycle time is defined from the Q wave of the ECG to the occurrence of the second heart sound 9 in the phonocardiogram signal or the dicrotic notch in the arterial blood pressure signal.
Thus, the duration of QS2 includes both the PEP and the L VET as shown in figure 1.4 [ 1].
The PEP is effected by a change in the rise of left ventricular pressure (L VP). The PEP is shortened by lower L V isovolumetric pressure and more forceful ventricular contraction; and becomes longer in duration during L V failure, L V conduction delay, diminished preload and reduced L V contractile intensity. Left ventricular ejection time is shortened by nearly all deviations from a normal cardiac state, including L V failure, a decrease in stroke volume relative to end diastolic volume, or by a more rapid rate of ejection. The QS2 provides information on the increased contractile motion (inotropic stimulation) since both the PEP and the L VET are shortened.
Linear relationships between heart rate and the duration of the systolic phases of the left ventricle have been derived from patient observations [1,2,4,6].

Intraaortic Balloon Pump Timing
Hemodynamic benefit from the intraaortic balloon pump (IABP) is achieved by allowing inflation and deflation of the balloon to occur relative to the function of the left ventricle. Since the IABP is used for life saving circulatory assistance, it is vital that the device correctly time balloon inflation and deflation. The intraaortic balloon should be inflated at the closing of the aortic valve, thus, knowledge of the temporal location of the dicrotic notch in the pressure signal is crucial.
IABP is most extensively applied in cases of cardiac pump failure which includes cardiogenic shock, myocardial infarction, weaning from bypass and low output syndrome. With an estimated 800,000 myocardial infarctions occurring annually in the United States, [39] the potential use of IABP therapy for this and related symptoms is quite large and increasing. Since the first clinical use of the IABP in 1967 for the treatment of cardiogenic shock, the complication rate has been reduced and its clinical usage has broadened. Clinical experience with IABP has grown from more than 50,000 insertions between 1968 and 1980, [40] to more than 300,000 by 1989, [41] with an estimated 70,000 IABP procedures performed annually [11] . Once the left ventricle has emptied its blood volume into the aorta and the aortic valve closes, the balloon is inflated. This action, occurring at the beginning of diastole, displaces blood both back towards the ascending aorta, into the coronary arteries, to enhance coronary artery perfusion, and outward along the descending aorta to enhance the systemic circulation. If inflation occurs much before this, the balloon would present a resistance to the blood flow out of the L V and make the L V work harder to empty, with the added risk of pushing blood up into the brachiocephalic, subclavian or carotid arteries. Early inflation would also cause a reduction is stroke volume, and an increase in end systolic volume, effecting ventricular preload.
The IAB is deflated for left ventricular ejection. The effect of reduced afterload is a decrease in cardiac work and myocardial oxygen consumption and an increase in cardiac output. Balloon deflation occurring much beyond this point imposes a resistance to the ensuing ventricular ejection, create intraventricular wall stress and effects the amount of stroke volume; (slightly late deflation has been shown to be acceptable). 13

Signal Processing Requirements
The dyadic wavelet transform dicrotic notch detection scheme has been designed to accommodate various types of arterial blood pressure waveforms, with various heart rates, arrhythmias and signal irregularities, encountered in a clinical setting. No assumptions of catheter type or signal acquisition method were made since prerecorded MGH patient clinical data was used to verify the performance of the detection algorithm.
Originally, it was hypothesized that since the aortic valve resonates upon closure at a characteristic frequency, that this frequency, once detected, would provide the temporal location of the dicrotic notch. Also, the algorithm used in this regard would therefore have to be robust for nonstationary signals. The Fourier transform (FT), short time Fourier transform (STFT) and eventually the wavelet transform methods were considere.d. Research into the FT and STFT led to the discovery of the wavelet transform as a possible method of detecting the dicrotic notch frequency. However, it was also observed at this time that there was no distinctive frequency content of the dicrotic notch in the arterial pressure waveform, except for the possibility of defining dicrotic notch frequency related to the velocity of valve closure. Otherwise, the desired notch frequency, referred to as the second heart sound, may be found with the FT and STFT if applied to a patient's phonocardiogram rather than the blood pressure signal [42][43][44][45][46][47][48][49][50]. Rather than locating the time in which the resonant frequency occurs, the task of detecting the event of notch closure focused on observing the change in the contour of the pressure waveform that corresponded to the dicrotic notch. Smaller scale wavelets are compressed in time and the resulting DyWT would therefore accentuate higher frequency transients of shorter duration, such as edges in images or sudden signal discontinuities. The dyadic wavelet transform detection method can therefore provide a multiresolution (or multi spectral) view of a signal and be used to isolate a portion of the actual signal from background noise [23][24][25][26][27][28][29][30][31][32][33][34][35]. It is these two aspects of the wavelet transform method, (time varying signal analysis and noise reduction capabilities), that prompted a feasibility study for the dyadic wavelet transform dicrotic notch detection scheme.

Feasibility Study
Several signal processing methods for time varying signals were found from a search of the current literature, including the wavelet transform, Fourier transform and short time Fourier transform analysis techniques [29,31 , 51-70]. Although other signal processing techniques were explored [71], it appeared that the dyadic wavelet transform method would provide the best detection scheme for normal, arrhythmic and noisy time varying signals. Thus, the dyadic wavelet transform approach was taken to detect the dicrotic notch in the pressure signal. Initial feasibility tests indicated successful dicrotic notch detection with the dyadic wavelet technique for a radial pressure signal containing preventricular contractions (PVC), and with added broad band white noise, as shown in The feasibility study [72] demonstrated that it was possible to distinguish signal transients, such as the dicrotic notch, systolic peak and the upstroke following end diastole, from background noise by comparing the DyWT across several successive dyadic scales. The cubic spline, Mexican Hat, Morlet, Harr and Shannon wavelet functions were tried in early feasibility tests of the wavelet analysis method, of which the cubic spline and the Mexican Hat wavelets showed the best results. Since the specific frequency bandwidth of the dicrotic notch does not overlap with any of the other characteristics of the arterial blood pressure signal, such as the systolic peak or end diastole, the DyWT was found to be applicable for dicrotic notch detection.
The dicrotic notch detection algorithm based on the dyadic wavelet transform is able to detect the dicrotic notch in cases of non-stationary circumstances of changing patient condition which is reflected in changing pressure waveform characteristics. This is accomplished by calculating the DyWT with several time dilated scales of the wavelet function. Also, since the clinical environment is sensitive to its surroundings and the fidelity of its sensor equipment, noise is always a factor in the recorded signals. Since band limited noise does not correlate between scales, this method of dicrotic notch detection is appropriate for the clinical environment.

16
Various methods of signal analysis were initially applied to evaluate the pressure signal [71], including the fast Fourier transform (FFT), power spectral density (PSD), auto and cross covariance and the first and second derivatives of the pressure signal [52][53]. These signal analysis tools were applied to pig blood pressure data. The results provided information on the waveform's FFT, power spectral density and derivatives and on the catheter effects on signal measurement. No algorithms for dicrotic notch detection were devised from these results. This information led to the testing of several methods (including Butterworth filtering, inverse FFT, signal damping, Jackson's Poles method [73], and Prony's method) to clean the pressure signal of unwanted oscillations from IABP for future for dicrotic notch detection.

18
Introduction to the Dyadic Wavelet Transform

Motivation
Typical methods of dicrotic notch detection rely on slope characteristics of the arterial pressure waveform. An alternative observation of the signal can be made on the signal analyzed in terms of its frequency content. It was originally hypothesized that aortic valve closure would correspond to a unique frequency; and once the frequency was detected, the location of the dicrotic notch would be found . Dicrotic notch frequency is defined as either valve closure vibrations or the velocity of valvular closure, (not heart rate), whichever would be characteristic of the dicrotic notch and be observable in the physiological signal of interest, (arterial pressure or phonocardiogram) [42][43][44][45][46][47][48][49][50]. Thus, signal processing techniques, such as .the Fourier transform [51][52]74], the short time Fourier transform {30-31 , 54-57, 67, 76-78] and eventually the dyadic wavelet transform were explored for the purpose of dicrotic notch detection [29-35, 59-71 , 79-81]. This section describes the mathematics of the time domain to frequency domain transformations according to their relative applicability to dicrotic notch detection.

Time Varying Signal Analysis
The Fourier transform, FTx(t), of a signal x(t), shown in equation (2.1) [51] is typically used for frequency analysis of stationary signals, whose characteristics do not change with time [51][52]. The magnitude of the FT provides information on the frequency content of the original signal. Since the FT represents a signal as the decomposition of a basis of complex sinusoidal functions of infinite extent, ( e-j2nft), any temporal variation in the waveform is spread out over the entire frequency plane. Thus, although the frequency corresponding to the dicrotic notch may be discerned, the actual temporal location of the dicrotic notch is not available. Therefore, the FT method does not provide any information regarding the time of notch closure, but rather the existence of it in terms of acknowledgment that its frequency was present in the analyzed signal.  [82] pictorially describes the lack of temporal resolution in the resulting FT magnitude spectrum for a signal containing three different frequencies.
By applying the Fourier transform to a portion of the signal x(t), isolated using a sliding temporal window function, h(t), frequency · information can be located as a function of the time in which these frequencies occurred [29][30][54][55][56][57][58]. For example, a change in the pattern of the waveform's slope, such as with the dicrotic notch, the systolic peak or the upstroke following end diastole, would indicate a change in the waveform's frequency pattern. The time of this frequency change would be recorded at the time in which it occurred. This method, known as the windowed Fourier transform [29,31] or the short time Fourier transform, STFTx('t,t), shown in equation (2.2) [30], is a two dimensional, (time versus frequency) representation of a signal.

+ <Xl
STFI' The frequency information is obtained for the portion of the waveform which overlaps the time duration of the window function, where 't is the center time of the window function . In this time window, time varying signals are approximated as stationary (the signal is assumed to be quasi-stationary where the spectral properties of the signal do not vary within the analysis window length) [57]. The STFT is computed each time the window is shifted. Translation of the window in time provides a frequency analysis of the entire data string localized within each time frame . Thus, temporal resolution of each frequency contained in the analyzed signal depends upon the duration of the window function. Good time resolution is obtained with small windows at the cost of reduced frequency resolution, due to the Heisenberg uncertainty principle [30,75,[83][84] which establishes a lower bound on the time-bandwidth product, shown in equation (2.3) [30]. Higher frequencies are resolved using windows of shorter duration; and as the window duration is increased, lower signal frequencies are resolved with the STFT method. The STFT calculated using a Gaussian window function provides a good compromise for both frequency and temporal resolution, and is referred to as the Gabor transform [29, 3 i, 67, 75, 85]. Along with expressing a local FT, the STFT can be interpreted as the time-frequency filtered output (low or band pass) of the signal with the window function or as an inner product of the signal with the window function. 3) The STFT however, is limited by the constant duration of the window h(t), resulting in the same signal time-frequency resolution (filter pass band) for all signal frequencies at 21 all times. Thus, the STFT would not be an adequate analysis tool for accommodating changing patient conditions. It is desirable to have a window function which can be altered to accommodate a variety of possible frequencies, (varying filter band). In this regard, the wavelet transform is an extension of the STFT incorporating various window durations for a multiresolution view of the signal and its frequency content. Figure 2.2 [30] window durations corresponding to the various frequencies for both the STFT and the wavelet transform (WT). Notice that the STFT windows have the same duration regardless of the signal frequency being analyzed. Whereas, the wavelet transform uses modified window durations for difference frequencies. By having smaller window widths for higher frequencies and longer window durations for lower frequencies, the WT has improved frequency resolution over a larger spectral range than the STFT.

The W av el et Transform
The

l Historical Background
The concept of looking at a signal at various scales and analyzing it with various resolutions has emerged independently in different scientific fields . Mathematical constructs of what is now referred to as wavelet theory had been presented mathematically in the early twentieth century [86][87], with application to harmonic analysis [87]. Wavelet transform mathematics were introduced by Calderon [88] in 1964 and have been developed under various names, including scale-space transforms [89].
The mathematical formulation and terminology of a wavelet as a decomposition of a signal into dilated and translated basis functions was introduced as a signal processing tool by Grossmann and Morlet [79] in 1984. Mathematical development of the continuous wavelet transform by Grossmann and Morlet [79,90] and maJor contributions from Daubechies [31,63,[91][92][93][94][95][96] and Mallat [26][27][28][29] have increased the utility and application of the wavelet transform in numerous disciplines.

Applications of the Wavelet Transform
Various scientific disciplines have applied the wavelet transform to analyze an assortment of signals, including image processing and coding, analysis of acoustic signals, physiological signals, and astronomical data. Mallat demonstrated the utility of the multiresolution wavelet transform for edge detection, represented as high frequency signal transients, and outlined fast algorithms for analyzing 1 and 2 dimensional signals [33]. Mallat showed that high frequency signal components produce local maxima in the dyadic wavelet transform which occur simultaneously across several consecutive scales using a smoothing wavelet function [33]. Applications of similar algorithms using the wavelet transform are presented in table 2.1. Applications of the Wavelet Transform • Edge detection [33][34][35] • Pitch detection in speech [81,[97][98][99][100] • Analysis of acoustical signals [101][102][103][104][105] • Medical applications include detection of the onset of the QRS complex in the electrocardiogram signal [82,[106][107][108], ventricular late potentials [ 109-11 O] and analysis of other biomedical signals [111][112][113][114][115][116][117].

Definition and Significance
Physiological signals, such as the blood pressure and the electrocardiogram are classified as time-varying or nonstationary. Since physiological signals, in general can exhibit erratic behavior due to changing patient condition, the wavelet transform is more appropriate than the FT and the STFT for analyzing these time-varying signals. The wavelet transform technique for waveform analysis accommodates nonstationary signals and is able to resolve low and high frequency information by incorporating windows of of the magnitude of the Fourier transform of the mother wavelet [30,98,111]. The mother wavelet, however, must have a unimodal spectrum, such as the Mexican Hat wavelet function .

Discrete Wavelet Transform
The continuous time wavelet transform is a function of both a continuous translation parameter and a continuous scale parameter, making the CWT computationally intensive.
An alternative approach to describing and implementing the discrete time wavelet transform is through the use of filter banks [28,30,67,[168][169][170][171][172]. The wavelet can be interpreted as "the impulse response of a band-pass filter and the wavelet transform as a convolution with a band-pass filter which is dilated", [35]. The wavelet transform decomposition uses a cascade of constant Q, low pass and high pass quadrature mirror filters as shown in figure 2.3 [67]. The dyadic wavelet transform corresponds to an 28 octave band filter scheme (as in music where increasing a tone by an octave involves doubling the frequency) . The data decimation process corresponds to the dyadic scaling and the output of the high pass filters corresponds to the wavelet transform output.
Although the DWT is more computationally

2.4
The Dyadic Wavelet Transform

Definition and Significance
A reduction in computation is achieved by discretizing the scale parameter [173].
The dyadic wavelet transform (DyWT) [33,35,81,98] of a signal x(t), shown in equation (2.8) is mathematically equivalent to the wavelet transform with a dyadic time scale, a=2m, where mis an integer.
Since the spectral resolution of the WT depends on the time duration and bandwidth of the wavelet, scaling the mother wavelet has the effect of changing the center frequency and bandwidth of the wavelet, as observed in its Fourier transform. As the scale is increased, the center frequency of the equivalent band pass filter is reduced and the bandwidth becomes narrower. The effect of dyadically scaling the cubic spline wavelet function is shown in figure 2.4a for the dyadic scales, m = 1, 2, 3. The width of the wavelet function is doubled in time as the scale is dyadically increased. The magnitude of the FT of these three scaled versions of the mother wavelet is shown in figure 2.4b. As the scale is dyadically increased, the FT magnitude becomes narrower and has a lower center frequency which is half of the center frequency of the previous scaled version. Thus, as the scale is increased dyadically, the wavelet is expanded in time (doubled) and compressed in frequency, (halved).  · ·~··· ·· · ···; · · ······:····· ···T········-:-·· · · · · · t· · · ·· ···{· · ··· ·· ··~·· · · · ··· . . Each of the scaled versions of the mother wavelet are convolved with the signal x(t) to achieve the dyadic wavelet decompositions of the signal at various levels of frequency resolution. Therefore, successful implementation of the dyadic wavelet transform for a particular application is dependent upon the choice of the wavelet function and the magnitude of the time scaling.

Cubic Spline Wavelet Function g( ~)
The term 'wavelet' refers to a portion of an oscillating wave. The wavelet function, in general, follows several constraints. The mother wavelet must be a zero mean function, therefore, it must oscillate in time. The wavelet function must also be absolutely integrable and have finite energy as in equations (2.9a) and (2 .9b) [81]. For signal reconstruction purposes, (not necessary for dicrotic notch detection) the magnitude of the Fourier transform of the wavelet function must not contain any de (co = 2nf = 0), according to the admissibility condition in equation (2 .9c) [30,35,79,81], by virtue of energy conservation, where G(2m co) is the FT of the wavelet function. This constraint also ensures that the WT represents the signal as a complete set of basis functions that encompass the entire frequency axis [35]. As with the FT, where si.l}usoidal basis functions to expand nonperiodic signals, time shifted and time scaled versions of the mother wavelet incorporate the set of basis functions for the wavelet transform.

Properties
The wavelet transform and therefore the dyadic wavelet transform possess several desirable properties consistent with the properties of the continuous wavelet transform (CWT) as listed in table 2.2. The proofs for the properties are found in references [26,34,79,[81][82]103].
ii) The DyWT is scale invariant. A scale change in the input corresponds to a change in both the scale and shift parameters of the DyWT, to within a magnitude factor (M) as shown in equation (2.11). Scaling the wavelet function changes the center frequency and bandwidth of its Fourier transform. The wavelet is compressed in time for small scales and expanded in time for larger scales. Thus, varying the scale parameter allows for low or high frequency analysis for a multi resolution characterization of a signal. Analysis of the DyWT at several dyadic scales is the mechanism by which the DyWT adjusts to the specific time and frequency characteristics of a particular signal. Transient detection based on the DyWT is based on calculating the DyWT across several dyadic scales and comparing the DyWT outputs for simultaneous peaks across consecutive dyadic scales.
The property is also useful for wideband Doppler analysis where moving targets produce scale changes in reflected signals. This property is also useful for fractal analysis (where certain properties exist regardless of scale) and for analyzing the cochlea and other such octave band systems [ 174].

DyWT x(at)
DyWT x(t)(ab,a2m) (2.11) iii to analyze seismic data [ 68,163]. (2.12) iv) The DyWT operation preserves the energy, (E) of a signal. Thus, the transform operator is isometric in that the energy in the time domain is equal to the energy in the wavelet domain as shown in equation (2.13). Since the DyWT is an alternate representation of a signal, it should maintain the energy characteristics of the signal. For signal reconstruction, it is important that the signal and its Dy WT are of finite energy and that the Dy WT operation does not alter the energy of the signal. that are contained in the signal. "Lines of constant phase of the Dy WT converge toward the points of discontinuity" at, t-t 0 [81,90].
;- (2.15) vii) Under certain constraints on the signal x(t) and the mother wavelet g(t/2m), the original signal can be reconstructed from its Dy WT as shown in equation (2.16) where g-(t) = g(-t). The Fourier transform of the wavelet function G(2mf) must be zero at de and the signal x(t) must be of finite energy. Thus, the DyWT is a one to one transform which is critical for most mathematical analysis and synthesis.
00 00 ix) If a signal x( t) and the wavelet function are real valued, then the Dy WT is real.

Motivation
A reliable dicrotic notch detection algorithm provides physiological information useful in the diagnosis of cardiac condition as patient condition changes, through such tools as the systolic time interval. The development of intelligent cardiovascular monitoring devices with robust signal processing algorithms is increasingly important.
Monitors that can detect pathological condition and differentiate true signal events and fluctuations from artifacts are necessary for this task.
The dicrotic notch is observed in arterial pressure waveforms as a change in slope, as a consequence of the closing of the aortic valve, following left ventricular ejection, indicating the end of systole and the start of the diastolic cycle. Detection of the dicrotic notch is non-trivial in that the blood pressure signal may be damped, corrupted by noise, contain motion artifacts, respiratory modulation, or change abruptly due to preventricular contractions (PVCs) or arrhythmias.   Once all of the available minima have been found for all cardiac cycles in all of the DyWT scales, the sample locations of the minima are compared between dyadic scales.
For a given cardiac cycle, the algorithm will locate all minima which occur within a neighborhood of ± 50 milliseconds (msec) across consecutive dyadic scales. This neighborhood is evaluated in terms of sample numbers and for a sample rate of 180 Hz, ± 50 msec becomes ± 9 data samples and for a sample rate of 360 Hz, ± 50 msec becomes ± 18 data samples. If there are minima that exist across dyadic scales within the given neighborhood, the sample number of the minima of the higher scale is retained.
All minima which do not exist within ± 50 msec between consecutive dyadic scales are eliminated. The surviving minima are the sample locations of all possible dicrotic notches for all of the cardiac cycles in the data file stored in computer memory.
The dicrotic notch is defined as the first minima in each cardiac cycle which exceeds a threshold. The threshold is equal to 65% of the local minimum amplitude of the Dy WT (of the highest scale) defined within the search window for that particular cardiac cycle. Once the dicrotic notch is found for a given cardiac cycle, then the next cycle is evaluated. The temporal locations of the dicrotic notches are obtained directly from the sample numbers in terms of the sample rate in which the data was recorded.

Selection of the Wavelet Function
Multiresolution analysis can be obtained using the dyadic wavelet transform from scaled and translated versions of a variety of mother wavelet functions g ( r~b) . The issue of wavelet function selection depends upon the particular application of the wavelet transform [61 , 176-180]. This section discusses the rationale for selecting the Mexican .6a-f [31,[180][181]. Each of the wavelet functions oscillates in time and has no de content. Both the temporal and spectral characteristics were considered when selecting the wavelet function. A wavelet function acts as both a time window and a filtering device when implemented into the wavelet transform. The wavelet function (referred to as 'wavelet') is of finite duration, thus, it is part of a continuous oscillating wave. In this regard, the wavelet acts as a finite duration window.
The continuous wavelet transform, equation (2.3), rewritten in equation (3 .1 ), is the correlation between the signal x(t) and the scaled version of the mother wavelet [30].
The correlation provides a measure of the similarity between two signals. Thus, wavelets having similar shape to the analysis signal correlate better and effectively slope changes in the signal are accentuated. The DyWT dicrotic notch detection algorithm, presented in this research correlates the scaled versions of the mother wavelet with the filtered pressure signal. Since the dicrotic notch can be a rather subtle slope change in the pressure signal, a higher correlation between the signal and the wavelet helps to emphasize the notch area. Therefore, the Mexican Hat [31] was selected as the mother wavelet since it best approximated the shape of the pressure signal.
The scale (a) parameter is used to control the temporal and spectral resolution of the mother wavelet as well as the dyadically scaled (a = 2m) versions of the Mexican Hat wavelet chosen such that the main lobe of the scaled wavelets are narrower (in time) than the dicrotic notch. If the width of oscillation is larger, the wavelet will effectively pass right over the notch area; the correlation will be small and the notch frequency will not be resolved .
The corresponding spectral resolution of each of the scaled versions of the wavelet is observed in its Fourier transform. The magnitude of a wavelet's FT indicates its center frequency and bandwidth. Thus, the DyWT operation, from each dyadically scaled version of the wavelet, acts as a band pass filter on the data. The scaling operation is the mechanism by which the DyWT is adjusted to the duration of the transient being analyzed, which in this case is the dicrotic notch. As scale is increased the magnitude of the FT has a narrower bandwidth and a lower center frequency, as demonstrated in implemented on the computer has been defined as less than 10-10. The relatively small scales produces somewhat sharp (impulsive) wavelet shape, symmetric about the origin, which quickly tends to zero. As the scale is increased dyadically, the wavelet is expanded in time (by 2), with twice as many non-zero points and the frequency, observed in the FT magnitude, is compressed by Yz.  " ~ a.

Selection of Algorithm Procedures
The dicrotic notch detection algorithm, outlined in the block diagram in figure 3 .2, prefilters the input pressure signal. The filtered signal is then convolved with the scaled versions of the mother wavelet and the algorithm proceeds to locate the dicrotic notches from the DyWT results. The rationale for each of the steps in this procedure is presented.

Prefilter
The original work of the wavelet feasibility test were performed without any prefiltering. It was shown that the dyadic wavelet could be used to resolve the dicrotic notch for relatively normal and noiseless waveforms. Further testing of the algorithm involved adding white Gaussian noise to the pressure signal. The algorithm was not accurate below a signal to noise ratio (SNR) of 30 dB. The DyWT detection scheme with the prefiltered signal was more accurate than the notch detection algorithm without the prefilter for noisy signals containing oscillations within the same frequency band of the dicrotic notch. Also, the detection of the temporal location of the dicrotic notch was nearly identical on highly damped signals with and without the prefilter.
A 4th order Butterworth low pass filter with a cµtoff frequency (fc) of 20 Hz was added from which the algorithm attained better noise performance. A Butterworth filter was selected because it has a magnitude response that is maximally flat in the pass band and has a smooth but not exceedingly steep roll off [ 67]. The pole zero plot of this Butterworth filter is shown in figure 3.8. The filter's frequency response, magnitude and phase are shown in figure 3.9a and b, respectively, generated with a sample rate of 180 Hz. The zero phase Butterworth filter was implemented in the detection algorithm using a digital filtering process.
c.  The results show spikes at the ends of the DyWT, especially for scales 1 and 2.
Detection of the dicrotic notch is not affected by these spikes since the algorithm does not take a global minimum of the data for threshold purposes but rather a local minimum between consecutive R waves. These spikes have been discarded in the plots of the Dy WT algorithm performance.

ECG R wave Detection Algorithm
The R wave is used by the dicrotic notch detection algorithm to locate the start and end of each cardiac cycle. The cardiac cycle is used as reference in determining the search window for minima in the DyWT as possible dicrotic notch locations which will be used for comparison across dyadic scales. The R wave detection algorithm has been modified from that proposed by Elghazzawi et al [175] finding peaks above 60% of a global maximum threshold. Where this algorithm fails, the ECG has been manually observed and the locations of the R waves predetermined for a patient file . Although there exists a robust method of detecting the R wave using the wavelet transform [82], it was not necessary to involve a more developed detection algorithm.

Search Windows
Two types of search windows are discussed. The first partitions a time segment of each cardiac cycle to focus the search for minima in the DyWT. The second search "window" defines the time range of data for comparison of the minima across dyadic scales of the Dy WT. The eventual location of the dicrotic notch for a given cardiac cycle will be a minimum which lies within the search window of the cardiac cycle (first search window), and exists within a neighborhood of ± 50 msec samples (second search window) across dyadic scales.
A limited portion of each cardiac cycle is searched for the dicrotic notch. The dicrotic notch will occur between the time of maximum left ventricle pressure (systolic peak) and the start of the next ventricular contraction (the next R wave). This window length was chosen also to accommodate blood pressure waveforms recorded from various points along the arterial system (as shown in figure 1.3). The further the pressure reading is from the aortic root, the longer the delay between the systolic peak and the dicrotic notch. Thus, the algorithm can examine waveforms from various locations including the aorta, radial artery, femoral artery or pedal locations. The systolic peak is relatively easy to detect and R wave informati~n is readily available. A relatively simple algorithm is used to estimate the location of the peak systolic pressure for each cardiac cycle. The systolic peak algorithm locates a maximum in the blood pressure waveform between the times of consecutive R waves in the ECG signal.
Minima which occur in the DyWT within the search window for each cardiac cycle are compared across dyadic scales. Minima which exist within ± 50 msec between dyadic scales (± 9 data samples for sample frequency= 180 Hz and ± 18 data samples for sample frequency= 360 Hz) is retained while all other minima are discarded from the total set of minima found in the cardiac cycle search window. A first estimate of ± 5 data samples was used for the detection algorithm based on the algorithm for pitch 57 detection [98]. This range, tested on files recorded at a rate of 180 Hz, was found to be too small. Inspection of the resulting Dy WT coefficients for several files indicated that ± 9 samples, (± 50 msec), would suffice. If increased much beyond this point, minima in the DyWT representing different transients would be compared across dyadic scales, and this is to be avoided.

Threshold Level
The dicrotic notch location for each cardiac cycle is defined as the first minima, that survived the DyWT comparison across dyadic scales, which has a magnitude greater than 65 % of the local minimum amplitude of the DyWT. The local amplitude of the DyWT is defined within the confines of the search window for that cardiac cycle. The threshold method was used such that the detection algorithm did not falsely select the minimum due to minor inflections in the curve located between the systolic peak and the actual dicrotic notch, (as was the case in figure 3 .1 d). The actual dicrotic notch is more transient and is represented in the DyWT as a minimum with a higher absolute amplitude.
The threshold is set relatively low such that minima due to oscillatory noise in roughly the same frequency band as the dicrotic notch are not detected. A range of threshold levels were tested between 40 and 90 % and the threshold of 65 % seemed to provide the best results. If there are no minima which exist above the threshold, then the first minimum in the search window is selected. This occurs if the blood pressure waveform is very damped or the dicrotic notch is a very subtle inflection in the signal.

Introduction
Various methods of dicrotic notch detection have been found in the literature [175 , 182-185] and a summary of these detection techniques is presented. Predominantly, dicrotic notch detection techniques rely on slope characteristics of the pressure waveform [175,[183][184]186]. Analysis using the derivative of the pressure signal is prone to error with noisy signals in which minor changes in slope are accentuated.
Various computational methods were devised to obtain the signal's relative minimum and reduce the effects of oscillatory disturbances around the dicrotic notch detection area using amplitude threshold and slope bar curve fitting techniques [183 , 185]. Also, the use of the ECG in defining a search window for locating the dicrotic notch in the arterial blood pressure signal has been published [ 175]. After the detection of the R-wave, a search for a zero crossing in the derivative waveform is initiated to find the location of the dicrotic notch. Although these methods may accommodate somewhat noisy signals, they are primarily not designed to characterize a wider range of irregular waveforms.
The five leading dicrotic notch detection algorithms [175,[182][183][184][185] which operate on the arterial pressure waveform were reprogrammed (in the Matlab environment). These algorithms, identified in table 3 .1 by reference number, author and a brief description of the detection · method, were tested on the MGH patient database files and their performance has been compared to the proposed dyadic wavelet based dicrotic notch detection algorithm. Threshold peak then analysis of global (11 data samples) and local data samples) operators locate notch as "slope changes" Iterative use of slope bars to detect systolic peak and dicrotic notch Identify negative slope after intersection of pressure wave with delayed filtered wave Identify curvature zones of bent points using slope bar iteration Several algorithms localize the systolic peak [182][183], ECG R wave [175] or other characteristics in the pressure signal derivative [185] to define the beginning of a search range for the dicrotic notch. Once a reference point in a cardiac cycle is defined, the algorithm selectively searches a given region of time in the signal for the slope changes corresponding to the dicrotic notch. A windowed search for the dicrotic notch is important because the dicrotic notch is a rather subtle point in the blood pressure waveform compared to the upstroke between end diastole and peak systole or the minimum (end diastole) or maximum (systolic peak) of the waveform which are more easily detected.
Dicrotic notch detection has also been applied to the derivative of the left ventricular pressure waveform [42], and to arterial flow [186], and valve closure resonance has been rendered from the second heart sound detected form non invasive phonocardiograms (PCGs) [43][44][45][46][47].
Attempting to define the mean cardiac cycle of aortic flow and pressure during steady state conditions, Burattini et al [186] designed an algorithm to single out the dicrotic notch from aortic flow. This was used to separate consecutive cardiac cycles during steady state conditions. The algorithm is based on a double threshold method applied to previously digitized recordings of aortic flow and pressure. The locatjpn of the dicrotic notch is determined using a technique to find the minimum of the curve between two maxima defined above a certain threshold value, as outlined in the flow diagram in Among other dicrotic notch detection schemes found in the literature, Smith and Craige [ 42] compared canine aortic pressure, left ventricular dP/dt and aortic surface vibrations. The comparison showed that the maximal negative spike ofLV dP/dt seems to consistently occur just after the notch. Also, a US patented circuit design for detecting the dicrotic notch has been devised by Gebber and Welch in 1974 [187].

Lee Algorithm
Lee et al [182] first locate a negative to positive change in the pressure derivative which is declared as the "foot" (end diastolic pressure (EDP). After each foot, a maxima above a threshold equal to 85% of maximum pressure amplitude is declared as the systolic peak. The particular threshold of 85% was used in order to avoid recognizing an anacronic notch as the systolic peak. This particular algorithm works well in noisy environments but does not locate the dicrotic notch on arrhythmic beats or low pressure beats following higher amplitude beats due to the amplitude threshold governing the systolic peak detection. The algorithm has relatively good noise performance since it evaluates the first difference with a global operator (reducing higher frequency noise content).

Jundanian Algorithm
Jundanian et al [183] devised a slope analysis method to detect systolic peak and the "diastolic value" from arterial blood pressure waveforms. The diastolic value is

Martino Algorithm
A real time (80 msec) algorithm for detecting dicrotic notch and systolic upstroke developed by Martino and Risso [ 184] uses a first order digital (or analog) filter scheme with a cut-off frequency at 1.2 Hz (reprogrammed with a lowpass Butterworth filter design). The algorithm then identifies the intersections between the original and filtered (delayed) signals. The original pressure signal rises above the filtered signal during upstroke and falls below the filtered signal just prior to the dicrotic notch. Figure 3.13a shows the raw and filtered arterial pressure waveforms along with a step indicating systolic upstroke when the raw signal is greater in magnitude than the filtered signal.
The upstroke determination is used to set a search window for the location of the dicrotic notch since the blood pressure signal falls below the filtered signal just prior to the notch. The detection of dicrotic notch is performed using the step waveform using four consecutive positive slopes in the first derivative, dP/dt.

Kinias Algorithm
Kinias et al [185] developed a bent point selection method to analyze a digitized blood pressure waveform filtered such that high frequency components (such as the dicrotic notch) are retained. The algorithm proceeds to detect the dicrotic notch based on an iterative bent point selection which identifies critical points where the curve changes in direction or concavity. The algorithm finds curvature zones, changes in the direction of the pressure derivative identified by an iterative "chord" approach, which uses successive chords with different lengths which slide along the pressure waveform, as shown in

Elghazzawi Algorithm
Elghazzawi et al [175] have developed a program to locate end diastole and the systolic peak. Within a period of time after the recognition of the ECG R wave, end diastole is declared as the last minimum in this time window by identifying the maximum amplitude of a negative to positive slope change for a given cardiac cycle. The peak systolic pressure is then identified as the last maximum in a defined time interval after the ECG R wave. The minima and maxima are determined from the slope of the arterial pressure waveform. This slope characterization of the critical points in the pressure waveform has been expanded to also locate the dicrotic notch.
The dicrotic notch algorithm was not published by Elghazzawi, but has been inferred from their method of signal analysis using the derivative of the pressure signal with the use of an appropriate search window within each cardiac cycle. In general, the algorithm

MGH Database of Clinical Recordings
The Massachesetts General Hospital (MGH) Database [22] contains 250 patient files each with roughly 1 hour worth of data, contained on a total of 10 CDROMs ( 100,103,108,115,116,117,121,128,136,137

Performance Criteria
The original portions of the blood pressure waveforms, (which have been applied to the Dy WT and each of the previously published dicrotic notch detection algorithms), were examined by Dr. W. Ohley, who annotated the dicrotic notch locations.
Annotations were made on the original MGH file BP waveforms, prior to algorithm simulations.
The algorithm test results have been normalized in that each algorithm was evaluated for the same group of cardiac cycles for each patient file. The detection algorithms were

Statistical and Comparative Results of Simulation
A summary of the results of the dyadic wavelet dicrotic notch detection algorithm performance is presented. The 5 leading published algorithms, written by Lee et al [182], Jundanian et al [183], Martino et al [184], Kinias et al [185] and Elghazzawi et al [175] have been programmed and evaluated on the MGR database for comparison with the dyadic wavelet method. All algorithms including the dyadic wavelet method were tested on three test sets containing:  table 4.9 indicate that a stable or convergent representation of algorithm performance was achieved with test set B. Three algorithms [175,183,185] were stable to within ± 5 % of the statistics generated from the A to B test sets; whereas all algorithms maintained stable between test sets B and C to within ± 2 %.

Observations
There are several observed cases where the DyWT based dicrotic notch detection algorithm was not effective.
• The R wave or systolic peak was not predetermined for a given cardiac cycle. Thus, there was no search window in that cardiac cycle for dicrotic notch detection. The search window spans from the time of the systolic peak in the BP signal to the time of the next R wave of the ECG signal.
• The R wave of the next cardiac cycle occurs before aortic valve closure of the current cardiac cycle (some preventricular contractions), as shown in figure 4. l 4a, for MGH filel20. , This occurrs due to the definition of the dicrotic notch search window which terminates at the R wave of the next cardiac cycle. If the search window definition is altered to include BP signal beyond the R wave of the next cardiac cycle, then the dicrotic notch is acknowledged as indicated in figure 4. l 4b, which was generated by eliminating the detected occurance of the R wave for the next cardiac cycle.
• The pressure waveform contour has irregularities ~hat resemble the dicrotic notch, in terms of its amplitude and spectral content, which are located in the search window between the systolic peak and the actual dicrotic notch. An example of this is shown in figure 4 .15, for MGH file02 l .
• The dicrotic notch detection algorithm based on the DyWT has moderate success when the duration of the dicrotic notch is relatively long, as shown in figure 4. l 4a, for MGH file033 . The DyWT algorithm tends to locate the start of valve closure, as does the algorithms presented by Lee [182], Martino [184] and Kinias [185] as shown in figure 4.14 b, d and e.  The dicrotic notch is observed in arterial pressure waveforms as a consequence of the closing of the aortic valve, after left ventricular ejection, indicating the start of the diastolic cycle. The detection of the dicrotic notch is non-trivial in that the blood pressure signal may be corrupted by noise, contain motion artifacts, respirtaory modulation, change abruptly with arrhythmias or deviate from the classical arterial pressure wave shape, especially in sick patients. The dyadic wavelet transform method of dicrotic notch detection was devised to estimate the dicrotic notch location in arterial blood pressure signals for the various clinical situations.
The dyadic wavelet transform method of signal analysis inherently filters out band limited noise and low frequency variations by the comparison of the Dy WT results across consecutive dyadic scales. Three consecutive dyadic scales of a Mexican Hat wavelet were generated and convolved with the arterial blood pressure signal to obtain the DyWT decompostion at these scales. The proposed dicrotic notch detection algorithm locates minima which occur within a neighborhood of± 33 msec across consecutive dyadic scales of the Dy WT within a seach window, defined from the systolic peak in the blood pressure signal to the R wave of the next cardiac cycle in the ECG signal. This algorithm is robust for signals which are noisy, contain irregular heart rhythms and those which exhibit erratic behavior. The dyadic wavelet transform based detection algorithm had only moderate success when the pressure waveform contained irregularities that resembled the dicrotic notch in terms of amplitude and frequency, located between the systolic peak and the actual dicrotic notch.
The dyadic wavelet transform method of detecting the dicrotic notch favorably compared and outperformed the five other leading detection algorithms found in the literature with respect to each of the four performance criteria: sensitivity (by 18% ), positive productivity (by 13%), false positive rate (by 11%) and false negative rate (by 18%). The DyWT dicrotic notch detection algorithm has the highest sensitivity and positive productivity, and the lowest false positive and false negative rates, which are listed in table 5.1 for test set C (72 patient files), compared to the other leading detection algorithms. The original premise of the project was that the dicrotic notch detection algorithm was to be implemented as a background verification system for the accuracy of the regression equation used to predict the temporal location of the dicrotic notch from previous R-wave information from the electrocardiogram. Thus, a real time algorithm was not a concern, but optimization of algorithm speed and accuracy was taken into consideration. Also, the R wave detection and search window criteria were designed such that simple modifications would allow implementation into the medical device environment for evaluating systolic time interval or analyzing prerecorded physiological data.
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