Is T-wave alternans T-wave amplitude dependent?

Biomedical Signal Processing and Control 7 (2012) 358–364

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Is T-wave alternans T-wave amplitude dependent? Laura Burattini a,∗ , Wojciech Zareba b , Roberto Burattini a a b

Department of Biomedical, Electronics and Telecommunication Engineering, Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona, Italy Heart-Research Follow-Up Program, Cardiology Unit, Department of Medicine and Department of Biomedical Engineering, University of Rochester, Rochester, NY, United States

a r t i c l e

i n f o

Article history: Received 17 January 2011 Received in revised form 17 June 2011 Accepted 21 June 2011 Available online 21 July 2011 Keywords: ECG repolarization T-wave variability ECG signal processing

a b s t r a c t The possible dependence of T-wave alternans (TWA) on T-wave amplitude was investigated in 3 orthogonal leads (X, Y, Z) 20-min resting ECG recordings and in the derived vector magnitude (VM) from 176 healthy (H) subjects and 200 coronary-artery-disease (CAD) patients. After application of our adaptive-match-filter based method for parameterization of TWA in terms of its amplitude (TWA A) and product-magnitude (TWA PM, defined as the product of TWA A times TWA duration), and once a TW A parameter was defined for T-wave amplitude quantification, the existence of intra- and intersubjects relationships of TWA A and TWA PM vs. TW A was tested. Compared to the H-population, the CAD-population showed a significant (P < 0.05) increase of TWA A (62 ± 38 ␮V vs. 54 ± 25 ␮V) and TWA PM (4029 ± 2974 beat ␮V vs. 3107 ± 1976 beat ␮V) and a significant decrease of TW A (298 ± 194 ␮V vs. 467 ± 246 ␮V). These repolarization changes, however, occurred with no significant intra- or intersubjects relationships of TWA A and TWA PM vs. TW A. Thus, in our CAD and H populations there was no evidence of TWA dependence on T-wave amplitude. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction T-wave alternans (TWA), consisting in an alternation on everyother-beat basis of the electrocardiographic (ECG) T-wave, has known growing interest in the last decades, due to a generally recognized association with malignant ventricular arrhythmias and sudden cardiac death [1–10]. After the recent experimental study by Pruvot et al. [11], who demonstrated the possibility of inducing various levels of TWA, some of which not necessarily associated to cardiac instability, the hypothesis that TWA is a phenomenon characterized by a continuously changing amplitude from physiological to pathological condition has gained increasing consideration. Such TWA continuity hypothesis is supported by our recent findings of the presence of various TWA levels in entire populations of healthy subjects [12–14]. These previous studies made use of our heart-rate adaptive match filter (AMF) based method for TWA identification, which allowed TWA parameterization in terms of its duration (TWA D, beats), amplitude (TWA A, ␮V), and productmagnitude (TWA PM, ␮V beats; defined as the product of TWA amplitude times TWA duration). Based on this parameterization, normal ranges of TWA were defined in [12] for each parameter by identifying three thresholds, computed as the 99.5th percentiles

of the TWA D, TWA A, and TWA PM distributions over a control population of 176 healthy (H) subjects, respectively. Abnormal levels of TWA (TWA+) were identified when at least one of the three parameters was characterized by a value falling outside the corresponding normality range. With this criterion, 21 TWA+ cases were identified over a population of 200 coronary artery disease (CAD) patients [12]. These TWA+ cases could be divided into four classes according to their pertinence to either one of the four subzones, characterized by low duration and low amplitude (LDLA), low duration and high amplitude (LDHA), high duration and low amplitude (HDLA), and high duration and high amplitude (HDHA), respectively. This discrimination enhances the possibility of a prospective application of our method to follow-up studies finalized to analyze pathophysiological implications and risk factors associated to the identification of the abnormal TWA cases. However, according to Madias [15,16], an investigation of the possible dependency of TWA amplitude on T-wave amplitude, and consequently, of a possible relationship between TWA+ subzones and T-wave amplitude levels, is compelled prior to any further development. Such an investigation is the aim of the present study. 2. Methods 2.1. Study populations

∗ Corresponding author. Tel.: +39 071 220 4461; fax: +39 071 220 4224. E-mail addresses: [email protected] (L. Burattini), Wojciech [email protected] (W. Zareba), [email protected] (R. Burattini). 1746-8094/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.bspc.2011.06.009

Study populations consisted of 176 healthy subjects (H population: mean age: 44 ± 12 yr, 89 men) and 200 coronaryartery-disease patients (CAD-population: mean age: 59 ± 11 yr, 165

L. Burattini et al. / Biomedical Signal Processing and Control 7 (2012) 358–364

men) with no history of myocardial infarction. All these subjects, who are the same used in [12], pertain to the Intercity Digital Electrocardiology Alliance (IDEAL) Study, approved by the Research Subject Review Board of the University of Rochester and conducted following required rules for human subjects’ research principles, according to the Declaration of Helsinki, as well as to Title 45, U.S. Code of Federal Regulations, Part 46, Protection of Human Subjects, Revised November 13, 2001, effective December 13, 2001. A subject was classified as belonging to the H-group when fulfilling the following criteria: 1. no overt cardiovascular disease or history of cardiovascular disorders (including stroke, transient ischemic attack, and peripheral vascular disease); 2. no history of high blood pressure (>150/90 mmHg); 3. not taking medication; 4. no other chronic illness (e.g. diabetes, asthma, chronic obstructive pulmonary disease, etc.); 5. diagnosed as being healthy if evaluated by a physician for cardiovascular-related syndrome (chest pain, palpitation, syncope); 6. normal physical examination; 7. sinus rhythm in 12-lead ECG without any suspicious abnormalities (e.g. signs of ventricular hypertrophy, inverted T-wave, intraventricular conduction disturbances); 8. normal echo and normal ECG exercise testing in presence of suspicious ECG changes; 9. no pregnancy. Instead, a patient was classified as belonging to the CAD group when satisfying the following criteria: 1. having diagnosis of CAD confirmed by positive angiogram (at least one vessel with critical narrowing >75%) with exerciseinduced ischemia on ECG or evidence of previous myocardial infarction; 2. being in stable phase of the ischemic heart disease with digital ECG recordings performed on an outpatients basis; 3. if a stable post myocardial infarction patient, being enrolled at least 2 month after the index event; 4. no evidence of congenital heart disease; 5. being in sinus rhythm. From each individual, a digital Holter ECG recording was acquired using a three pseudo-orthogonal lead configuration, with bipolar leads X, Y, Z corresponding to limb lead I, augmented limb lead aVF, and roughly precordial leads V3 (with the positive electrode anterior and negative pole posterior at the tip of the right scapula), respectively, using Burdick recorders (Burdick Inc., Milton, WI; sampling frequency: 200 Hz, resolution: 10 ␮V). Each recording, available at the THEW database (http://thewproject.org/), was about 20 min long and was obtained in supine resting conditions. The XYZ leads were then used to compute the vector magnitude (VM) as follows: VM =



X2 + Y 2 + Z2.

(1)

Each 20-min ECG recording (constituted by leads X, Y and Z and by the VM) was analyzed by recursively (every 10 s) extracting a 128 consecutive beats ECG segment [12] to be simultaneously submitted to our TWA identification and T-wave amplitude quantification algorithms. The first 128-beats ECG segment was used for the short-term intra-subjects analysis and for the inter-subjects analysis, whereas the entire 20 min ECG recording was used for the long-term intra-subjects analysis, as described below.

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2.2. T-wave alternans parameterization TWA was independently identified from each one of the 3 (X, Y, Z) 128-beat ECG lead and from the derived VM using our heartrate adapting match filter (AMF) based method. Details of this technique can be found elsewhere [12–14,17]. Briefly, the AMF consists of a narrow passing-band filter, with the passing band centered at the TWA typical frequency (fTWA ), which is, by definition, equal to half heart rate. Thus, the AMF receives the ECG tracing as an input, and filters out every ECG frequency component (included those related to noise) other than fTWA . The AMF output is the TWA signal, a sinusoidal signal, eventually amplitude modulated, whose amplitude, in correspondence of the T-waves apexes, provides a local (i.e. relative to a specific beat) estimate of the TWA amplitude, denominated ATWA (␮V), intended as the amplitude of the alternation of the only T-wave amplitude (and not of the entire ST/T segment). Specifically, a value of ATWA greater than zero indicates an alternating T-wave. The 128 ATWA values obtained from each 128-beat ECG lead are used for TWA characterization of each lead in terms of TWA duration (TWA D, beat; defined as the total number of beats with alternating T-waves), TWA amplitude (TWA A, ␮V; defined as the mean ATWA over all alternating T-waves), and TWA productmagnitude (TWA PM, beat ␮V; defined as the product of TWA A times TWA D). To answer the question as to the possible dependency of TWA amplitude on T-wave amplitude, the TWA A parameter was considered here together with the other TWA A dependent TWA parameter denoted as TWA PM. Thus, both the TWA A and the TWA PM were contrasted to a T-wave amplitude parameter that is defined in the following section.

2.3. T-wave amplitude definition The following ATW A parameter: ATW



A



= Tmax − Tmin 

(2)

was defined here to quantify the T-wave amplitude of each beat in an ECG tracing (single lead or the VM). In Eq. (2), Tmax and Tmin represent the maximum and the minimum amplitude of the ECG throughout the T-wave (Fig. 1). Eventually, the 128 ATW A values computed over a tracing were averaged to get an overall estimate of T-wave amplitude (TW A, ␮V).

2.4. Definition of T-wave alternans and T-wave amplitude normal ranges Normal ranges for TWA and T-wave amplitude were computed using the TWA A, TWA PM, and TW A distributions from the VM analysis over the H population. By definition, TWA A and TWA PM parameters have a minimal value of zero in the absence of TWA, while abnormal (TWA+) cases are characterized by threshold-exceeding values. In accordance with our previous study [12], two thresholds, one for TWA A and one for TWA PM, were defined as the 99.5th percentiles of the corresponding parameter distributions from the VM over our control H population. Analogously, TW A+ cases were characterized by an abnormal TW A falling outside a range delimited by an upper and a lower threshold values identified here, for the first time, as the 0.5th percentile and the 99.5th percentile, respectively, of the TW A distribution from the VM over our H population.

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Fig. 1. Amplitude (AT ) of a monophasic (panel A) and of a biphasic (panel B) T-wave.

2.5. TWA amplitude and product magnitude vs. T-wave amplitude 2.5.1. Intra-subjects analysis Two kinds of intra-subjects analysis were considered: the short-term intra-subjects analysis and the long-term intra-subjects analysis, performed on a 128-beats ECG segment and on the entire 20 min ECG recordings, respectively. The hypothesis of the existence of a short-term intra-subjects dependence of TWA from T-wave amplitude requires, within each 128-beats ECG lead (X, Y, Z, and VM), the existence of a significant correlation between the ATWA (i) sequence and the corresponding ATW A (i) sequence, with i = 1,2,. . .,128, identifying the T-wave from which the two parameters were computed. Moreover, in the presence of a short-term intra-subjects relationship between TWA amplitude and T-wave amplitude, the lead showing the largest TWA (in terms of TWA A and TWA PM) is expected to show, in a given subject, the largest (direct association) or the lowest (reverse association) TW A. On this basis, the number (in percent) of these possible occurrences was counted, among the H subjects and CAD patients, to test whether this number is significantly greater than 33%, which means that the intra-subjects association occurred by chance. Instead, the hypothesis of the existence of a long-term intrasubjects dependence of TWA from T-wave amplitude requires, within each 20-min ECG lead (X, Y, Z, and VM), the existence of a significant correlation between the TWA sequences, either TWA A(n) or TWA PM(n), and the corresponding TW A(n) sequence, with n = 0 s, 10 s, 20 s,. . .,1200s. 2.5.2. Inter-subjects analysis Inter-subject analysis was evaluated on short-term ECG recordings (128 consecutive beats). In the presence of an inter-subjects relationship between TWA amplitude and T-wave amplitude, the subjects showing the largest TWA (in terms of TWA A and TWA PM) are expected to show, in a given population, the largest (direct association) or the lowest (reverse association) TW A. Thus, an inter-subjects analysis was performed here by computing the correlation coefficients between TWA amplitude parameters (TWA A and TWA PM) and TW A over both the H and CAD populations, and by testing if CAD patients with abnormally high TWA levels (TWA+) were also characterized by abnormally high or abnormally low TW amplitude (TW A+). In the specific, the correlation coefficient values were computed for each ECG lead as well as for the VM. Instead, normal ranges for TWA and TW A parameters were computed only for the VM. 2.6. Statistics To be independent of normal distributions, non-parametric tests were used to perform comparisons among quantities. In the specific, the Kruskal–Wallis test was used to perform the one-way

ANOVA test to evaluate if, in a population, TW A, TWA A, and TWA PM parameters distributions over the three ECG leads were characterized by the same median value. Information about which pairs of leads had different median values was obtained using the multiple comparison procedure. Comparison between the distributions of a parameter over the two populations (H vs. CAD) was performed using the Wilcoxon rank sum test for equal medians. The 2 test was used to determine if concomitant occurrence of maximum TWA and maximum or minimum TW A in a specific ECG lead indicated the existence of an intra-subjects relationship or were due to noise. Eventually, a possible relationship between the distributions of a TWA parameter (either ATWA , TWA A or TWA PM) with a T-wave amplitude parameter (either ATW A or TW A) was evaluated computing the correlation coefficient . Statistical significance level was set at 5%. 3. Results 3.1. General features of T-wave alternans and T-wave amplitude Parameters values of the TWA and the TW amplitude for the H subjects and CAD patients are reported in Table 1. ANOVA analysis over the three ECG leads showed that no significant differences were found between TW A values characterizing each ECG lead in the H population, whereas comparable values of TW A from the Xlead and the Y-lead were significantly (P < 0.05) lower than those from the Z-lead in the CAD population. On the other hand, different values of TWA A and TWA PM were found among leads (P < 0.05) in both populations. In the specific, TWA A and TWA PM were significantly higher in lead Y than in lead X (P < 0.05), the former one showing significantly higher values than lead Z (P < 0.05). Thus, in the CAD population, lead Y was characterized by the highest TWA levels and the lowest T-wave amplitude (P < 0.05). Comparative analysis of parameters distributions over the two populations showed the presence of significantly higher TWA A and TWA PM concomitant with significantly lower TW A from the VM in the CAD population (Table 1). Analysis of individual leads showed that, in the CAD population, compared to the H population, TW A was significantly lower (P < 0.05) in leads X and Y but not in lead Z (Table 1). Conversely, TWA PM was significantly higher in the CAD patients than in the H subjects in all three leads (P < 0.05; Table 1), whereas TWA A was significantly higher in the CAD population only in lead Z (P < 0.05; Table 1). 3.2. TWA amplitude and product magnitude vs. T-wave amplitude 3.2.1. Intra-subjects analysis When analyzing short-term (128 beats) ECG tracings, negligible values of correlation between the ATWA (i) sequence and the corresponding ATW A (i) sequence (i = 1,2,. . .,128) computed within each 128-beats ECG lead (X, Y, Z, and VM) were found in both populations

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Table 1 Mean ± standard deviation values of the TWA and T-wave amplitude parameters relative to ECG leads X, Y, and Z, and to the vector magnitude (VM) from H subjects and CAD patients. Lead X

TW A (␮V) TWA A (␮V) TWA PM (beat ␮V) *

Lead Y

H (176)

CAD (200)

466 ± 197 40 ± 19 2422 ± 1410

335 ± 189 48 ± 39 3274 ± 3678* *

Lead Z

H (176)

CAD (200)

467 ± 198 48 ± 25 3016 ± 1890

317 ± 177 58 ± 44 3920 ± 3482* *

VM

H (176)

CAD (200)

H (176)

CAD (200)

460 ± 262 32 ± 24 1729 ± 1550

490 ± 277 37 ± 27* 2334 ± 1862*

467 ± 246 54 ± 25 3107 ± 1976

298 ± 194* 62 ± 38* 4029 ± 2974*

P < 0.05 when comparing corresponding parameter between CAD and H populations.

Table 2 Mean ± standard deviation values of the correlation coefficient () between the ATWA (i) sequence and the corresponding ATW A (i) sequence (i = 1,2,. . .,128) computed within each 128-beats ECG lead (X, Y, Z, and VM) for the H and CAD populations for the short-term intra-subjects evaluation of the TWA vs. T-wave amplitude relationship. H Lead X Lead Y Lead Z VM

CAD

0.02 0.02 0.04 0.01

± ± ± ±

0.11 0.10 0.13 0.09

−0.01 0.01 0.02 −0.01

± ± ± ±

0.10 0.10 0.11 0.09

(H: |mean | ≤ 0.04; CAD: |mean | ≤ 0.02; Table 2). Independently of the TW A absolute value and the lead of its maximum occurrence, the lead showing the highest TWA A or TWA PM was the one showing the highest TW A in 33% and 34% of cases, respectively, for the H population, and in 32% and 31% of cases, respectively, for the CAD population. Instead, the lead showing the highest TWA A or TWA PM was also the one showing the lowest TW A in 44% and 39% of cases, respectively, for the H population, and in 29% and 30% of cases, respectively, for the CAD population. None of these values were found to be significantly different from 33%, which indicate that the intra-subjects association occurred by chance. Analysis of long-term (20 min) ECG tracings also provided negligible mean values of correlation between the TWA parameters sequences (either TWA A(n) and TWA PM(n)) and the corresponding TW A(n) sequence (n = 0 s, 10 s, 20 s,. . .,1200s) within each 20 min ECG lead (X, Y, Z, and VM) for both populations (H: |mean | ≤ 0.09; CAD: |mean | ≤ 0.11; Table 3). The standard deviation values, however, were significantly higher (H: 0.38 ≤ |std | ≤ 0.41; CAD: 0.34 ≤ |mean | ≤ 0.42; Table 3), indicating that module and the sign of the correlation between TWA and T-wave amplitude, in long-term ECG, is subject dependent.

correlation coefficient was low (|| ≤ 0.33) and significant in only one case ( value of TWA A vs. TW A in lead X of the H population). Normal levels of TWA were found to be characterized by values of TWA A and TWA PM included in the ranges 0–135 ␮V and 0–9115 ␮V beat, respectively. As depicted in Fig. 2A and B, such definition of TWA normality intervals allowed identification of two TWA+ cases at the verge of abnormal conditions among the H subjects (TWA A = 126 ␮V; TWA PM = 10,584 beat ␮V and TWA A = 149 ␮V; TWA PM = 8791 beat ␮V), and 10 TWA+ cases among the CAD patients (TWA A = 160 ± 63 ␮V; TWA PM = 12,626 ± 4534 beat ␮V). In the specific, TWA PM values were abnormally high in 1 TWA+ H subject and in 9 TWA+ CAD patients, whereas TWA A was abnormally high in 1 H subject and 7 CAD patients. As depicted in Fig. 2C, our definition of a low and high thresholds for the TW A yielded a normality interval delimited by the values of 105 ␮V and 1212 ␮V. Accordingly, 2 H subjects were classified as TW A+, characterized by an abnormally high (TW A = 1254 ␮V) and an abnormally low (TW A = 101 ␮V), respectively. Instead, 10 CAD patients were classified as TW A+, among which only 1 had abnormally high TW A (TW A = 1453 ␮V), while the remaining 9 had abnormally low TW A (TW A = 82 ± 17 ␮V). TW A values of the TWA+ cases are evidenced in Fig. 2D, which shows that only 1 TWA+ case out of 12 (2 from the H group, and 10 from the CAD group) was also TW A+. On average, TW A over the 10 TWA+ CAD patients (251 ± 156 ␮V) was not significantly different from that of the remaining 190 CAD patients (300 ± 196 ␮V) falling within the normality intervals of TWA parameters. 4. Discussion 4.1. General features of T-wave alternans and T-wave amplitude

3.2.2. Inter-subjects analysis The values of the correlation coefficients between either TWA A and TWA PM distributions vs. TW A distribution over each population subjects are reported in Table 4. The absolute value of all

This study investigated the existence of a possible dependency of TWA amplitude on T-wave amplitude in short-term (128 beats) and long-term (20 min) resting ECG recordings. In the specific, TWA and T-wave amplitude were measured from 3-pseudo orthogonal

Table 3 Mean ± standard deviation values of the correlation coefficient () between the TWA sequences, either TWA A(n) or TWA PM(n), and the corresponding TW A(n) sequence (n = 0 s, 10 s, 20 s,. . .,1200s) computed over each 20-min ECG lead (X, Y, Z, and VM) in the H and CAD populations for the long-term intra-subjects evaluation of the TWA vs. T-wave amplitude relationship.

Table 4 Correlation coefficients values () between TWA amplitude parameters (TWA A and TWA PM) and TW A over both the H and CAD populations in ECG leads X, Y, Z and in the VM, for the inter-subjects evaluation of TWA vs. T-wave amplitude relationship.

TWA A vs. TW A  H (176) Lead X Lead Y Lead Z VM CAD (200) Lead X Lead Y Lead Z VM

TWA PM vs. TW A 

0.08 0.09 0.00 0.06

± ± ± ±

0.38 0.39 0.39 0.39

0.04 0.07 −0.01 0.02

± ± ± ±

0.38 0.41 0.39 0.39

0.07 0.11 0.01 0.00

± ± ± ±

0.42 0.44 0.40 0.36

0.06 0.06 −0.04 −0.03

± ± ± ±

0.39 0.40 0.41 0.34

TWA A vs. TW A  H (176) Lead X Lead Y Lead Z VM CAD (200) Lead X Lead Y Lead Z VM *

P < 0.05.

0.33* 0.07 0.13 0.11 0.12 0.05 0.04 −0.01

TWA PM vs. TW A  0.10 −0.08 −0.04 −0.07 0.05 0.04 0.02 −0.04

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Fig. 2. Definition of a normal range for TWA A (panel A) allowed identification of 1 H subject and 7 CAD patients characterized by abnormal TWA (TWA+). Definition of a normal range for TWA PM (panel B) allowed identification of 1 H subject and 9 CAD patients characterized by TWA+. Globally, TWA+ cases were 2 among the H subjects, and 10 among the CAD patients. Definition of a normal range for TW A (panel C) allowed identification of 2 H subjects and 10 CAD patients characterized by abnormal TW A (TW A+). Both TWA+ cases from the H population and 9 out of 10 TWA+ cases from both the CAD population showed normal TW A values (panel D).

(X, Y, Z) ECG leads and from the derived VM signal of 200 CAD patients and 176 H subjects. The 3-pseudo orthogonal lead system represents an approximation, generally accepted in clinical practice [18], of the Frank’s orthogonal leads, which are known to provide accurate information about the electrical activity of the heart in alternative to the information provided by the standard 12 ECG leads [19]. The VM is usually associated to the orthogonal leads, from which it is derived (see Eq. (1)), and it has been widely adopted in studies on cardiac repolarization [10,20,21]. For this reason it was preferred over other possibilities [2,7,9,12,22] and was used here for a synthetic and comprehensive representation of the cardiac activity by means of a single tracing. TWA was identified using our heart-rate adaptive match filter (AMF) based method, a technique widely tested in both simulated and clinical conditions [12–14,17,23,24]. Our AMF method characterizes TWA in terms of its duration (TWA D), amplitude (TWA A) and product magnitude (TWA PM), the latter parameter representing a measure of the “energy” associated to the TWA phenomenon. Thus, the last two parameters (TWA A and TWA PM), which involve TWA amplitude in their definition (intended as amplitude of the Twave apex alternation for monophasic T-waves, and as sum of the two T-wave peaks alternations for biphasic T-waves) were considered in the present study to investigate the possible existence of a relationship with T-wave amplitude, denominated TW A and defined as the absolute value of the ECG amplitude range along the repolarization segment (see Section 2). Thus, both TWA and T-wave amplitude parameters computation involved the same portion of the T-wave.

It is generally understood that diseased states, compared to healthy condition, are characterized by changes in the ECG repolarization morphology [12,13,25–34]. In our CAD population, compared with the H population, these changes consisted of a significant increment of TWA A and TWA PM, in concomitance with a significant TW A decrease (Table 1). In both populations, the lead Y was the one characterized by the highest TWA levels, but this did not imply better discrimination between the two populations in terms of TWA, which, instead, occurred in the lead Z, also characterized by the lowest TWA. Lead Z was, indeed, the only one showing a simultaneous, significant increase of TWA parameters in the CAD patients compared to the H subjects. The lead Y and the lead Z were also characterized by the lowest and the highest values of TW A, respectively. However, differently from what occurring for TWA, lead Y had a greater ability in discriminating the two populations (TW A significantly lower in the CAD patients than in the H subjects) than lead Z (no significant difference between TW A values were found in the two populations). Analysis of the VM yielded a significant increment of TWA (in both TWA amplitude parameters) and a simultaneous significant decrement of TW A.

4.2. TWA amplitude and product magnitude vs. T-wave amplitude 4.2.1. Intra-subjects analysis In the presence of a short-term intra-subjects relationship, a significant correlation should exist between the ATWA (i) sequence

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and the corresponding ATW A (i) sequence (i = 1,2,. . .,128), in each 128-beats ECG lead (X, Y, Z, and VM); or the lead showing the maximum level of TWA is expected to show the maximum (or the minimum, in case of a negative relationship) T-wave amplitude. Thus, according to our results, no short-term intra-subjects relationship links TWA and T-wave amplitude. Indeed, considering both H and CAD populations, the found correlation coefficient values were negligible (|mean | ≤ 0.04; Table 2). Moreover, at least one TWA parameter was maximum in the same lead where T-wave amplitude was maximum in 31–34% of cases, and where T-wave amplitude was minimum in 29–44% of cases. None of these values could be considered significantly different from 33%, which implies no intra-subjects relationship between TWA and T-wave amplitude (maximum TWA parameter uniformly distributed over the leads in which the corresponding T-wave was maximum, middle and minimum, respectively). No inference about the existence of an intra-subjects relationship between TWA and T-wave amplitude could also be derived from the long-term analysis. Indeed, on average values of the correlation coefficients were very close to zero (|mean | ≤ 0.04; Table 2), even though higher values of the standard deviation indicate that a certain relationship may occasionally occur in some subjects. Direction (correlation coefficient sign) and strength (correlation coefficient module) of such relationships, however, are strongly subject dependent. 4.2.2. Inter-subjects analysis In the presence of an inter-subjects relationship, in a given population, a correlation between TWA parameters and the corresponding T-wave amplitudes is expected. A correlative analysis showed that the values of the correlation coefficient, even when significant, was too weak (|| ≤ 0.33) to allow any general inference on this association. It is worth to notice, however, that higher correlation values were found for the H population (0.04 ≤ || ≤ 0.33) than for the CAD one (0.01 ≤ || ≤ 0.12), for which practically negligible correlations were found. Thus, in the CAD, the significant increase of TWA amplitude seems to be independent of the simultaneous significant decrease of T-wave amplitude. This finding is confirmed by the observation that 9 out of the 10 CAD patients showing abnormal levels of TWA (TWA+) did not show concomitant abnormal levels (TW A+) of TW A. The only one TWA+ CAD patients classified as TW A+ showed TW A values at the verge of normality. To identify TWA+ cases two thresholds, one for TWA A and one for TWA PM were considered. Being TWA A a differential quantity (absolute difference between consecutive T-wave amplitudes), the lower limit of TWA A and TWA PM parameters equals zero in the absence of TWA (no 2:1 alternation in the T-wave amplitudes), so that abnormal (TWA+) cases can only be identified as those exceeding arbitrary upper-threshold TWA A and TWA PM levels. More specifically, being TWA a non stationary phenomenon [12,35–37] characterized by a an amplitude and a duration, the threshold on TWA A is useful to identify abnormal cases with increased amplitude, whereas the threshold on TWA PM is useful to identify abnormal cases with increased duration, not necessarily associated to an amplitude increment. In this study such thresholds were identified as the 99.5th percentiles of the TWA A and TWA PM distributions from the VM over our control population (H) of 176 healthy subjects. These values strongly optimize specificity rather than sensitivity. The rationale for this choice is that TWA was initially supposed not be present in healthy conditions [38], so that the number of positive detections among the H subjects was forced to be negligible [12]. Our recent studies support the hypothesis that TWA is a phenomenon characterized by an amplitude continuously changing from physiological to pathological conditions [13,14]. Under this hypothesis,

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identification of thresholds levels at 99.5th percentile may result too restrictive, and probably does not represent the best choice for an optimal identification of abnormal TWA cases. Identification of an optimal threshold for abnormal (and thus potentially risky) levels of TWA, however, is beyond the scope of this work, and will be a matter of future investigations. In spite of the fact that the actual choice of the threshold values tends to minimize the number of TWA+ cases, 10 CAD TWA+ cases were identified (Fig. 2A and B), for a non negligible amount of 5% of the entire CAD population. Similarly, thresholds delimiting the TW A normality ranges were defined here for the first time as the 0.5th and 99.5th percentiles of the TW A distribution from the VM over the H population. Differently from TWA amplitude, a definition of both upper and lower limits was needed, since abnormal variations of TW A may occur in both directions. Such definition of TW A normality region yielded the identification of 10 CAD TW A+ patients, 9 of which characterized by an abnormally low TW A (Fig. 2C). Moreover, 9 out of 10 CAD TWA+ patients showed normal TW A levels (Fig. 2D), thus suggesting an inter-subjects TWA independence from T-wave amplitude in the CAD. It is worth to observe that, in a previous study from ourselves [12] performed on the same data, a TWA normality region was identified by averaging all three TWA parameters (TWA D, TWA A and TWA PM) over the three leads. Instead, in the present study, normal levels of TWA were identified using the TWA A and TWA PM values from the VM. Comparison of results shows that the former procedure has a greater CAD vs. H subjects discrimination power than the latter, since in [12], 21 CAD patients were classified as TWA+, in contrast with the 10 identified here. Such difference is due mainly to two factors: 1—the TWA D parameter has been used in [12] but not in the present study; and 2—due to its mathematical definition, the VM tends to underestimate TWA amplitude when it occurs with opposite polarity in two out of the three leads. The main of the present work, however, was not to discriminate normal from abnormal cases of TWA, but rather, to investigate the possible dependency of TWA from T-wave amplitude. In this context, the TWA D parameter, involving only the duration aspect of TWA, was neglected because hypothesized a priori independent of T-wave amplitude. Moreover, when measuring T-wave amplitudes, the use of the commonly used VM was considered more appropriate than the arbitrary averaging procedure. The results obtained in the present study are intended to hold under our working hypothesis and for 20 min ECG recordings. Extended experimental research on the biophysical aspects and further clinical studies involving different kinds of data and different pathologies are desirable for a definite understanding of the eventual link between TWA and T-wave amplitude. Especially, for the intra-subjects dependency evaluation, conventional 24-h ambulatory recordings are desirable, because they would secure the availability of large changes of T-wave amplitude due to circadian variation, exercise, position, sleep, large postprandial changes in order to evaluate whether T-wave alternans and T-wave amplitude are related or not. Moreover, repeated 24-h ambulatory recordings in the same subjects with stable clinical status will provide even more information for an intra-subject analysis and intra-, and inter-ECG exploration for a relationship between TWA and TW A.

5. Conclusions Our study suggests that, in short-term recordings (20 min), TWA and T-wave amplitude changes are linked together in absence of any significant intra- or inter-subjects relationships. It concerns both: healthy subjects and CAD patients.

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