Advanced Methods and Tools for ECG Data Analysis - Part 8 docx

P1: Shashi August 24, 2006 11:50 Chan-Horizon Azuaje˙Book Appendix 9A Description of the Karhunen-Lo ` eve Transform 265 Consider a set of M-dimensional random vectors, {x}, the range of which is part or all of P-dimensional Euclidean space. An efficient eigenbasis to represent {x} requires that the fewest eigenvectors be used to approximate {x} to a desired level of expected MSE. Suppose that any sample pattern vector x = (x 1 , x 2 , , x M ) T from this set belongs to L possible pattern classes {ω l , l = 1, 2, , L}, where the a priori probability of the occurrence of the lth class is p(ω l ). Further assume that each class is centralized by subtracting the mean µ l of the random pattern vectors x l in that class. Denoting the centralized observation from ω l by z l , we write z l = x l − µ l (9A.1) The centralized pattern vector z l can be represented by a special finite expansion of the following form: z l = M  m=1 c lm Φ m (9A.2) where Φ m are orthonormal deterministic vectors satisfying the condition Φ m Φ k = δ mk (9A.3) and δ mk is the Kronecker delta function, δ mk =  1 m = k 0 m = k (9A.4) while the coefficients c lm satisfy E(c lm ) = 0, (E(c l ) = 0) (9A.5) and are mutually uncorrelated random coefficients for which L  l=1 p(ω l )E{c lm c lk }=ρ 2 m δ mk (9A.6) The deterministic vectors Φ m in (9A.2) are termed the KLT basis functions. These vectors are the eigenvectors (also known as principal components) of the covariance matrix R of z, R = L  l=1 p(ω l )E{z l z T l } (9A.7) and λ m = ρ 2 m (9A.8) P1: Shashi August 24, 2006 11:50 Chan-Horizon Azuaje˙Book 266 Introduction to Feature Extraction are their associated eigenvalues, where ρ m are the standard deviations of the coeffi- cients. Since the basis vectors are the eigenvectors of a real symmetric matrix, they are mutually orthonormal. The eigenvectors Φ m of the covariance matrix R and their corresponding eigenvalues λ m are found by solving RΦ m = λ m Φ m (9A.9) Denoting the KLT basis vectors ( 1 ,  2 , ,  M ) in matrix notation , the KLT transformation pair for pattern vector z l , and the coefficients of the expansion c l , may be expressed as z l = c l (9A.10) c l =  T z l (9A.11) It is important to arrange the KLT coordinate vectors Φ m in descending order of the magnitude of their corresponding eigenvalues λ m , λ 1 ≥ λ 2 ≥ ≥ λ N ≥ ≥ λ M (9A.12) By this ordering, the optimal reduced KLT coordinate system is obtained in which the first N coordinate coefficients contain most of the “information” about random patterns {x}. The KLT expansion possesses three optimal properties. If an approximation  z l of z l is constructed as  z l = N  m=1 c lm Φ m (9A.13) where N < M, the expected MSE, e 2 (N) = L  l=1 p(ω l )E{|z l −  z l | 2 } (9A.14) is minimized for all N. Another optimal property of the KLT expansion is that the ratio between the MSE when using N eigenvectors for approximation, e 2 (N), and the expected total power of x, E{z T z}, can be calculated as η(N) = 1 − N  m=1 ξ m (9A.15) where ξ m defined as: ξ m = λ m  M k=1 λ k (9A.16) P1: Shashi August 24, 2006 11:50 Chan-Horizon Azuaje˙Book Appendix 9A Description of the Karhunen-Lo ` eve Transform 267 represents the expected fraction of the total power of z associated with the eigen- vector Φ k . Next, if an approximation  z l of z l is constructed according to (9A.13) where N < M, the entropy function, given by H(N) =− M  m=N λ m log λ m (9A.17) is minimized for all N. This property guarantees that the expansion is of minimum entropy and therefore a measure of minimum entropy or dispersion is associated with the coefficients of the expansion. P1: Shashi August 24, 2006 11:50 Chan-Horizon Azuaje˙Book P1: Shashi September 4, 2006 11:6 Chan-Horizon Azuaje˙Book CHAPTER 10 ST Analysis Franc Jager In this chapter, we first review ECG ST segment analysis perspectives/goals and current ST segment analysis approaches. Then, we describe automated detection of transient ST change episodes with special attention to reference databases, the problem of correcting the reference ST segment level, and a procedure to detect tran- sient ST change episodes which strictly models human-expert established criteria. We end the chapter with a description of specific performance measures and an eval- uation protocol to assess the performance and robustness of ST change detection algorithms and analyzers. Performance comparisons of a few recently developed ST change analyzers are presented. It is assumed that the reader is familiar with the background presented in Chapter 9. 10.1 ST Segment Analysis: Perspectives and Goals Typically ambulatory ECG data shows wide and significant (> 50 µV) transient changes in amplitude of the ST segment level which are caused by ischemia, heart rate changes, and a variety of other reasons. The major difficulties in automated ST segment analysis lie in the confounding effects of slow drifts (due to slow diurnal changes), and nonischemic step-shape ST segment shifts which are axis-related (due to shifts of the cardiac electrical axis) or conduction-change related (due to changes in ventricular conduction). These nonischemic changes may be significant, with behavior similar to real transient ischemic or heart rate related ST segment episodes, and complicate manual and automated detection of true ischemic ST episodes. The time-varying ST segment level due to clinically irrelevant nonischemic causes defines the time-varying ST segment reference level. This level must be tracked in order to successfully detect transient ST segment episodes and then to distinguish nonischemic heart rate related ST episodes from clinically significant ischemic ST episodes. In choosing the ST segment change analysis recognition technique, the following aspects and requirements should be taken into consideration: 1. Accurate QRS complex detection and beat classification is required. The positioning of the fiducial point for each heartbeat should be accurate. 2. Simultaneous analysis of two or more ECG leads offer the improvement of analysis accuracy in comparison to the single channel analysis with regard to noise immunity and ST episode identification. 269 P1: Shashi August 24, 2006 11:52 Chan-Horizon Azuaje˙Book 270 ST Analysis 3. The analysis technique should include robust preprocessing techniques, ac- curate differentiating between nonnoisy and noisy events, and accurate ST segment level measurements. 4. The representation technique should be able to encode as much informa- tion as possible about the subtle structure of ST segment pattern vectors, if possible in terms of uncorrelated features. 5. The distribution of a large collection of ST segment features for normal heartbeats usually form a single cluster. During ST change episodes, sig- nificant excursion of ST segment features over the feature space may be observed. The problem of detecting ST change episodes may be formulated as a problem of detecting changes in nonstationary time series. 6. The recognition technique should be able to efficiently and accurately cor- rect the reference ST level by tracking the cluster of normal heartbeats due to the nonischemic slow drift of the ST segment level and due to sudden nonischemic step changes of the ST segment level. 7. Classification between normal and deviating ST segments should take into account interrecord and intrarecord variability of ST segment deviations. 8. The recognition technique should be robust and able to detect transient ST change episodes and to differentiate between ischemic and heart rate related ST episodes. 9. The analysis technique may be required to function online in a single-scan mode with as short a decision delay as possible or in a multiscan mode (or perhaps using retrospective off-line analysis). 10.2 Overview of ST Segment Analysis Approaches The development and evaluation of automated systems to detect transient ischemic ST episodes has been most prominent since the release of the ESC DB [1], a standard- ized reference database for development and assessment of transient ST segment and T wave change analyzers. In the recent years, several excellent automated systems were developed based on different approaches and techniques. Traditional time-domain analysis uses an ST segment function calculated as the magnitude of the ST segment vector determined from two ECG leads [2, 3], or the filtered root mean square series of differences between the heartbeat ST seg- ment (or ST-T complex) and an average pattern segment [4], or ST segment level function determined as ST segment amplitude measured at the heart rate adaptive delays after the heartbeat fiducial point [5]. The Karhunen-Lo ` eve transform (KLT) approaches use sequential classification of ST segment KLT coefficients as normal or deviating ones in the KLT feature space [6, 7]. A technique for representing the overall ST-T interval using KLT coefficients was proposed [8, 9] and used to detect ischemia by incorporating a filtered and differentiated KLT-coefficient time series [10]. To improve the SNR of the estimation of the KLT coefficients, an adap- tive estimation was proposed [11]. Another study showed that a global representa- tion of the entire ST-T complex appears to be more suitable than local measurements when studying the initial stages of myocardial ischemia [12]. Neural network–based P1: Shashi September 4, 2006 11:7 Chan-Horizon Azuaje˙Book 10.2 Overview of ST Segment Analysis Approaches 271 approaches to classify ST segments as normal or ischemic include the use of a coun- terpropagation algorithm [13], a backpropagation algorithm [14], a three-layer feedforward paradigm [15], a bidirectional associative memory neural network [16], or an adaptive backpropagation algorithm [17]. In these systems, a sequence of ST segments classified as ischemic forms an ischemic ST episode. A variety of neural network architectures to classify ST segments have been implemented, tested, and compared with competing alternatives [18]. Architectures combining principal component analysis techniques and neural networks were investigated as well [18–20]. Further efforts in seeking accurate and reliable neural network ar- chitecture to maximize the performance detecting ischemic cardiac heartbeats has resulted in sophisticated architectures like nonlinear principal component analy- sis neural networks [21] and the network self-organizing map model [22, 23]. The self-organizing map model was successfully used to detect ischemic abnormalities in the ECG without prior knowledge of normal and abnormal ECG morphology [24]. Yet another system successfully detects ischemic ST episodes in long-duration ECG records using a feed-forward neural network and principal component analysis of the input to the network to achieve dimensionality reduction [25]. Other automated systems to detect transient ischemic ST segment and T wave episodes employ fuzzy logic [26–28], wavelet transformation [29], a hidden Markov model approach [30], or a knowledge-based technique [31] implemented in an expert system [32]. Intel- ligent ischemia monitoring systems employ fuzzy logic [33] or describe ST-T trends as changes in symbolic representations [34]. The detection of transient ST segment episodes is a problem of detecting events that contain a time dimension. There are insufficient distinct classes of ST segments and/or T waves with differing morphologies to allow the use of efficient classifica- tion techniques. Some studies on the characterization of ST segment and T wave changes [7, 35] have shown that morphology features of normal heartbeats form a single cluster in the feature space. This cluster of normal heartbeats is moving slowly or in step shape fashion in the feature space due to slow nonischemic changes (drifts) or due to sudden nonischemic changes (axis shifts). Ischemic and heart rate related ST segment episodes are then defined as faster episodic trajectories (or excursions) of morphology features out from and then back to the cluster of normal heartbeats. Therefore, it makes, sense to develop a technique which would efficiently track the cluster of normal heartbeats and would detect faster transient trajectories of morphology features. The majority of automated systems do not deal adequately (or even at all) with nonischemic events. It was previously thought that the KLT-based systems and in particular neural-network systems (since they extract information of morphology from the entire ST segment), would separate subtle ischemia-related features of the ST segment adequately from nonischemia related features. Unfortunately, the suc- cess of these techniques has been limited. The problem of separating ischemic ST episodes from nonischemic ST segment events remains, in part due to the nonsta- tionarity of an ST segment morphology-feature time series, and the lack of a priori knowledge of their distributions. Furthermore, an insufficient number of nonis- chemic ST segment events present in the ESC DB prevents studying these events at length and only short (biased or unrepresentative) segments of the database records (2 hours) have been used (since they were selected to be sufficiently “clean”). The P1: Shashi August 24, 2006 11:52 Chan-Horizon Azuaje˙Book 272 ST Analysis other reference database for development and assessment of transient ST segment change analyzers, the LTST DB [35], contains long-duration (24-hour) records with a large number of human-annotated ischemic and nonischemic ST segment events. Only a few automated systems deal explicitly with nonischemic events such as slow drifts and axis shifts. One of the early systems [36] dealt with nonischemic events by discriminating between “stable” and “unstable” ST segment baseline time periods and correcting the ST segment reference level for nonischemic shifts between stable periods. Other systems employ ST segment level trajectory-recognition based on heuristics in time domain [3], in the KLT feature space [7], or a combination of traditional time-domain and KLT-based approaches [37]. These systems are capable (to a certain extent) of detecting transient ST segment episodes and of tracking the time-varying ST segment reference level. A few other systematic approaches to the problem of detecting body position changes which result in axis shifts have been made. A technique based on a spatial approach by estimating rotation angles of the electrical axis [38] and a technique using a scalar-lead signal representation based on the KLT [39] were investigated. Another study used a measurement of R wave duration to identify changes in body position [40]. In all these investigations, the authors developed their own databases which contain induced axis shifts. Currently developed ST episode detection systems are capable of detecting tran- sient ST segment episodes which are ischemic or heart rate related ST episodes, but are not able to distinguish between them. Automatic classification of these two types of episodes is an interesting challenge. This task would require additional analysis of heart rate, original raw ST segment patterns, and clinical information concerning the patients. A recognition algorithm would need to distinguish between typical ischemic and nonischemic ST segment morphology changes [35]. These in- clude typical ischemic ST segment morphology changes (horizontal flattening, down sloping, scooping, elevation), which may or may not be accompanied by a change in heart rate, and typical heart rate related ST segment morphology changes (J point depression with positive slope, moving of the T wave into the ST segment, T wave peaking, and parallel shifts of the ST segment compared with the reference or basal ST segment), which are accompanied by an obligatory change in heart rate. The inclusion of clinical information also makes room for the development of sophisti- cated techniques leading to intelligent ischemia detection systems. 10.3 Detection of Transient ST Change Episodes Automated detection of transient ST segment changes requires: (1) accurate mea- surement and tracking of ST segment levels and (2) detection of ST segment change episodes with correct identification of the beginning and end of each episode, and the time and magnitude of the maximum ST deviation. The main features of an ST change detection system may be: (1) the automatic tracking of the time-varying ST segment reference level in the ST segment level time series of each ECG lead, s l (i, k) (where i denotes the lead number and k denotes the sample number of the ST segment level time series) to construct the ST reference function, s r (i, k); (2) the ST deviation function, s d (i, k), in each lead which is constructed by taking the algebraic P1: Shashi August 24, 2006 11:52 Chan-Horizon Azuaje˙Book 10.3 Detection of Transient ST Change Episodes 273 difference between the ST level and ST reference function; (3) a combination of the ST deviation functions from the leads into the ST detection function, D(k); and (4) the automatic detection of transient ST episode. 10.3.1 Reference Databases Two freely available international reference databases to develop and evaluate ST segment analyzers are currently in use: the ESC DB [1] and the LTST DB [35], and as such they complement each other in the field of automated analysis of transient ST segment changes. The ESC DB contains 90 two-channel 2-hour annotated AECG records of varying lead combinations, collected during routine clinical practice. ST segment annotations were made on a beat-by-beat basis by experts. The ischemic ST seg- ment episodes were annotated in each lead separately according to an annotation protocol which incorporates the ST segment deviation defined as a change in the ST segment level from that of the ST segment level of a single reference heartbeat measured at the beginning of a record. The goal of the LTST DB is to be a representative research resource for de- velopment and evaluation of automated systems to detect transient ST segment changes, and for supporting basic research into the mechanisms and dynamics of transient myocardial ischemia. The LTST DB contains 86 two- and three-channel 24-hour annotated AECG records of 80 patients (of varying lead combinations), collected during routine clinical practice. ST segment annotations were made on av- erage heartbeats after considerable preprocessing. A large number of nonischemic ST segment events mixed with transient ischemic ST episodes allows development of reliable and robust ST episode detection systems. The ischemic and heart rate related ST segment episodes were annotated in each lead separately according to an annotation protocol. This protocol incorporates the ST segment deviation defined as the algebraic difference between the ST segment level and the time-varying ST segment reference level (which was annotated throughout the records using local- reference annotations). The annotated events include: transient ischemic ST segment episodes, transient heart rate related nonischemic ST segment episodes, and nonis- chemic time-varying ST segment reference level trends due to slow drifts and step changes caused by axis shifts and conduction changes. The expert annotators of the ESC DB and LTST DB annotated transient ST segment episodes which satisfied the following clinically defined criteria: 1. An episode begins when the magnitude of the ST deviation first exceeds a lower annotation detection threshold, V lower = 50 µV. 2. The deviation then must reach or exceed an upper annotation detection threshold V upper throughout a continuous interval of at least T min s (the minimum duration of an ST episode). 3. The episode ends when the deviation becomes smaller than V lower = 50 µV, provided that it does not exceed V lower in the following T sep = 30 seconds (the interval separating consecutive ST episodes). According to annotation protocol of the ESC DB, the values of the upper annotation detection thresholds and minimum width of ST episodes are V upper = 100 µV and P1: Shashi August 24, 2006 11:52 Chan-Horizon Azuaje˙Book 274 ST Analysis T min = 30 seconds. The database contains 250 transient lead-independent ischemic ST episodes combined using the logical OR function. Episode annotations of the LTST DB are available in three variant annotation protocols: (A) V upper = 75 µV, T min = 30 seconds; (B) V upper = 100 µV, T min = 30 seconds, equivalent to the protocol of the ESC DB; (C) V upper = 100 µV, T min = 60 seconds. According to the protocol A, the database contains 1,490 transient lead-independent ischemic and heart rate related ST episodes combined using the logical OR function. Combining only ischemic ST segment changes yields 1,155 ischemic ST episodes. 10.3.2 Correction of Reference ST Segment Level Next we describe an efficient technique developed in [37] to correct the reference ST segment level. Using a combination of traditional time-domain and KLT-based approaches, the analyzer derives QRS complex and ST segment morphology fea- tures, and by mimicking human examination of the morphology-feature time series and their trends, tracks the time-varying ST segment reference level due to clinically irrelevant nonischemic causes. These include slow drifts, axis shifts, and conduction changes. The analyzer estimates the slowly varying ST segment level trend, identifies step changes in the time series, and subtracts the ST segment reference level thus obtained from the ST segment level to obtain the measured ST segment deviation time series that is suitable for detection of ST segment episodes. 10.3.2.1 Estimation of ST Segment Reference Level Trend Human experts track the slowly varying trend of ST segment level and skip the more rapid excursions during transient ST segment events. Similarly, the analyzer [37] es- timates the time-varying global and local ST segment reference level trend [s rg (i, k) and s rl (i, k), respectively], of the ST level functions, s l (i, k), by applying two moving- average lowpass filters. The ST level functions were obtained using preprocessing, exclusion of noisy outliers, resampling, and smoothing of the time series (as de- scribed in the Chapter 9). The two moving-average lowpass filters are: h g , over 6 hours and 40 minutes in duration estimating the global nonstationary mean of the ST level function, and h l , over 5 minutes in duration estimating local excursions of the ST level function. Moving-average lowpass filters posses useful frequency characteristic which are simple to realize and computationally inexpensive. The ST reference function is estimated as follows: s r  (i, k) =  s rg (i, k):if|s rg (i, k) − s rl (i, k)| > K s s rl (i, k) : otherwise (10.1) where K s = 50 µV is the “significance threshold” (i.e., the threshold to locate significant excursions of the ST level function from its global trend, and is equivalent to a lower annotation detection threshold, V lower =50µV). 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