A review of beat-to-beat vectorcardiographic (VCG) parameters for analyzing repolarization variability in ECG signals

VCG from Frank (X, Y, and Z) lead

For clinical studies, the VCG signal is recorded directly from the surface of the body. However, in older studies, VCG was recorded from the body using a special approach that directly provided the three orthogonal components of the dipole vector, based on the Frank VCG lead system [25]. This system consists of seven electrodes. There are five electrodes in the transverse plane; one electrode is on the back of the neck and one on the left foot, as shown in Figure 2. By utilizing the Frank VCG lead system, a three-dimensional representation of electrical heart activity can be found directly by measuring ECG in three different directions (Figure 2), i.e., right-to-left (X-axis), head-to-feet (Y-axis), and front-to-back (Z-axis).

Figure 2:

Frank VCG lead system (adapted after [1]).

The Frank VCG lead system consists of seven unipolar electrodes, and signals are viewed in three (X, Y, and Z) directions.

There are a number of reasons why the Frank VCG lead system is no longer used for clinical practice, mainly due to its non-standard lead configuration. Hence, an important current issue is to derive VCG from standard 12-lead ECG for improving diagnosis of heart signals. Although, a study demonstrated quantitatively for deriving VCG signal using the non-linear optimization technique from three-lead ECG (I, II, V₂), which is believed to have higher correlation with the corresponding measured scalar leads [77]. However, this study needs further research for deriving beat-to-beat VCG signal from multiple databases, as the technique is based on a median beat of three-lead ECG.

VCG from 12-lead ECG

To derive VCG from standard 12-lead ECG, several techniques have been proposed [33, 63, 78, 79]. However, existing methods are limited and not yet standardized. One of the techniques suggested by Edenbrandt and Pahlm [23] is called the IDT, which is the pseudo-inverse of the matrix proposed by Dower [22]. Another technique was introduced by Kors et al. [54] for synthesizing the VCG from standard 12-lead ECG. These simple estimated transformation matrices are most commonly used to synthesize the VCG from 12-lead ECG. However, a number of studies have investigated the reliability of these estimated matrices, where the findings showed that this type of transformation has a number of limitations in achieving orthogonal VCG reconstruction [32, 33, 63]. The main problem of the proposed transform matrices is due to estimation during reconstruction that gives rise to potential information loss or even unwanted information. Furthermore, the derived orthogonal leads from 12-lead ECG by applying these matrices may differ from those obtained from the actual VCG leads.

However, an alternative technique using SVD is suggested by Acar and Koymen [2] for deriving the VCG from 12-lead standard ECG for a single ECG beat. Here, the SVD is applied to the eight independent leads (I, II, V₁, V₂, V₃, V₄, V₅, and V₆) of the standard 12-lead ECG configuration to obtain eight decomposed signals. The first three decomposed signals comprise an ECG dipole (see Figure 3), and 99% of the ECG energy can be represented in a three-dimensional minimum subspace [2], which are similar to the orthogonal components obtained from the Frank VCG. However, the method of Acar et al. [3], for single ECG beat analysis, does not provide detailed analysis on a beat-by-beat basis and does not completely provide the characteristics of beat-to-beat VCG based analysis. This is an issue as cardiac electrical activity is not regular or stationary but has non-linear characteristics. Therefore, to address this problem, our recent article [39] considered and extended beat-to-beat VCG analysis by employing an SVD approach, which was introduced by Acar and Koymen [2]. For extracting the beat-to-beat QT intervals, we have used the T-wave template matching algorithm proposed by Berger et al. [10]. We computed the beat-to-beat QT interval for each individual lead in 12-lead ECGs by adopting an approach that has been previously described [40]. Thus, we are able to obtain beat-to-beat QRS- and T-wave signals from standard 12-lead ECGs for beat-to-beat VCG analysis.

Figure 3:

Eight independent leads.

Eight independent leads as input (top left) and eight decomposed ECG signal (top right) for a single-beat ECG after applying SVD transformation. The QRS and T wave loop for a single-beat ECG (bottom), where arrow refers the main vector of QRS and T wave.

Moreover, in the reconstructed VCG, the signals are resolved into three components (X, Y, and Z directions). These three orthogonal signals facilitate the construction of ventricular depolarization (QRS wave) and the repolarization (T wave) loop (see Figure 3) for various VCG-based parameter extractions. These parameters and indices may be essential factors for characterizing the temporal and spatial changes in the QRS and T loops in ventricular depolarization and repolarization.

Total cosine R to T

Total cosine R to T (TCRT) measures the vector deviation between the depolarization and the repolarization waves by calculating cosine values between the dominant QRS loop vectors and the main T-wave loop vectors within the optimized decomposition space [3]. Note that TCRT values are limited to the range of -1 to +1 range. Minus one corresponds to an angle of 180°, indicating that the QRS- and T-wave loops are pointing in opposite directions. By contrast, +1 corresponds to an angle of 0°, indicating that the QRS- and T-wave loops are pointing at the same direction. In [3], the mean value of TCRT was found to be negative in hypertrophic cardiomyopathy (HCM) patients but positive in healthy subjects. The negative TCRT value in HCM patients indicates increased deviation between repolarization (QRS) and depolarization (T) waves in terms of their principal direction in a three-dimensional time-orthogonal space.

T-wave morphology dispersion

T-wave morphology dispersion (TMD) represents the variation of morphology of T-waves between different ECG leads during complete ventricular repolarization [3]. It is computed as the average of angles between all possible pairs of the reconstruction vector, as shown in Figure 4. A small TMD value implies the reconstruction vectors of different ECG leads are close to each other or T-wave morphologies in different ECG leads are similar. The TMD is defined as the mean of all θ_ij excluding V₁ as follows:

Figure 4:

T-wave morphology dispersion.

Projection of different constructed ECG leads on u₁ and u₂ planes for T-wave loop.

In the study by Acar et al. [3], a significantly increased TMD value was observed in HCM patients compared to healthy subjects, which basically reflects the spatial and temporal variations of repolarization (T-wave) pattern in HCM patients.

Percentage of loop area

Generally, percentage of loop area (PL) is computed as the ratio of the T-wave loop area to the area of the surrounding rectangle, where the rectangular area is divided into 100 equal rectangular cells, as shown in Figure 5. This parameter defines the regularity of the T-wave loop [3]. For large PL, the T-wave loop is considered to be smooth and connected, but a lower value of PL is due to a more irregular T-wave loop. A higher PL value was found in healthy subjects compared to HCM patients that indicates a smooth and connected T-wave loop (not crossing itself) in normal ECGs compared to HCM ECGs [3].

Figure 5:

Percentage of loop area (PL).

Projection of T-wave loop on u₁ and u₂ planes.

Lead dispersion

Lead dispersion (LD) measures temporal variation in inter-lead relationships during ventricular repolarization [3]. This is the measurement of the temporal homogeneity of the propagation of the repolarization wave. If the value of LD is significantly different between two groups of subjects, then T-wave loops are discriminative. In the study by Acar et al. [3], the mean values of LD were similar in healthy subjects and HCM patients, which shows that the loop itself is not discriminative for healthy subjects and HCM patients. However, Lin et al. [59] demonstrated a significantly higher LD in patients with ventricular tachycardia (VT)/ventricular fibrillation (VF) compared to patients without VT.

Azimuth and elevation

Generally, the spatial orientation of the maximum T-wave vector is defined by its azimuth and elevation. Usually, the azimuth is considered as the angle in the transverse plane. The value of azimuth can be interpreted as follows: 0^o, left; +90^o, front; -90^o, back; and 180^o, right. In addition, the elevation is defined as the angle from 0^o (caudal direction) to 180^o (cranial direction), basing the elevation of the T-wave on the angle in the cranio-caudal direction. Significant leftward azimuthal orientation was found compared with left circumflex artery patients and downward elevation compared with both right coronary artery and left coronary artery patients [75].

Complexity ratio

The index complexity ratio (CR) reflects the complexity of repolarization. The principal component analysis provides the identification of a set of eight values, which represent the relative magnitude of spatial components of repolarization [70]. This parameter describes the global shape abnormalities of the repolarization wave, which is defined as the second component divided by the first component of eigenvalue decomposition given as a percentage. The relative contribution of these components can be used to estimate the complexity. This index may provide identification of patients with abnormal repolarization. In the study by Zabel et al. [96], the CR value was found to be significantly different in all patient groups, but it was not significant in patients with and without arrhythmic events.

However, in this article, a brief description of VCG-based parameters is discussed in the following sections based on a single-beat and a beat-to-beat basis.

Single-beat VCG-based parameters

Patients with various cardiac condition (arrhythmogenesis, myocardial infarction, heart failure, hypertrophic myocardiopathy) were investigated using several VCG parameters in several studies [3, 27, 59, 96]. A summary of the VCG-based parameters employed in single-beat analysis is given in Table 1.

Beat-to-beat VCG-based parameters

The analysis of VCG parameters based on single-beat ECG for different cardiac conditions and the investigation of prognostic capabilities have received significant interest. However, little is known of VCG parameter analysis based on beat-to-beat cases. In addition to that, how these VCG parameters are influenced by beat-to-beat ECG is not completely understood. Nevertheless, recently, a few studies have investigated beat-to-beat VCG parameters in different cardiac populations and tested their independent predictive power for classifying patients [38, 39, 86]. A brief description of relevant beat-to-beat VCG-based parameters and their relationship to the findings in a number of studies is summarized in Table 2.

Another interesting study was carried out by Karsikas et al. [47], where beat-to-beat variability of QRS-T angle was observed during an incremental exercise test. This study reported that the TCRT trend during exercise was negative and became more negative in healthy subjects compared to the patients with coronary artery disease (CAD). However, theoretically, TCRT ought to be toward a positive value in healthy subjects, compared to the CAD patient, due to the homogeneity of repolarization lability in healthy subjects, which was investigated by several studies for a single-beat ECG analysis [3]. The greater trend of TCRT toward a negative value might be found in healthy subjects due to a consequence of the experimental setup. Nevertheless, the study of Karsikas et al. [47] highlights that further research is required for beat-to-beat analysis for QRS-T angle measurements to assess the reliability of this parameter.

Two further different studies have found that the beat-to-beat three-dimensional ECG variability predicts ventricular arrhythmia (VA) in patients with structural disease and implanted implantable cardioverter defibrillator (ICD) using the same (R-peak cloud volume, T-peak cloud volume, T-/R-peak cloud volume) VCG-based parameters [35, 86]. They suggested that large T-peak cloud volume (this cloud volume was computed as the volume within the convex hull) is associated with the increased risk of VA. However, this study was limited to an analysis of 30 consecutive beats. The VCG analysis of a higher number of beats may increase the validity of the outcome significantly.

In the same year, in 2010, Kenttä et al. [50] studied the beat-to-beat rate dependency and gender affect on spatial angle (TCRT or QRS-T angle) between QRS-T loops during exercise ECG. They suggested that the beat-to-beat individual patterns of TCRT and QRS/T angle are influenced by heart rate (HR) and gender. However, further study is required for ultimate validation before considering clinical implementation. Another study by Kenttä et al. [49] suggests that spatial angles (TCRT and QRS-T angles) might be strong predictors of sudden cardiac death for risk stratification where a larger database was used for analysis.

Correa et al. [16] introduced six (maximum magnitude of the depolarization vector of QRS loop, volume of QRS loop, planar area of QRS loop, ratio between the area and the perimeter of QRS loop, ratio between the major and the minor axes of QRS loop, and QRS loop energy) different VCG-based parameters to investigate the morphological changes in the QRS loop for ischemic patients that underwent percutaneous transluminal coronary angioplasty (PTCA). They showed that VCG-based parameters were significantly different before, during, and after PTCA. However, they considered only the QRS-loop VCG parameters for ischemic patients and the morphological changes in repolarization loop descriptors. Therefore, it might be interesting if future analysis can be extended by considering the T-wave loop as well.

Hasan et al. [39] proposed two new descriptors along with some existing depolarization and repolarization indices for beat-to-beat VCG analysis. Point-to-point distance variability (DV) is one of them, which was determined based on the coefficient of variance of point-to-point distance from each loop to the mean loop of QRS- and T-wave loop. In addition, another new descriptor was mean loop length (MLL), which was calculated for the mean loop of the QRS and the T loop by adding the distance from each point to the next point in the loop. Significantly higher DV of the QRS- and T-wave loop was found in MI patients compared to healthy subjects [39]. However, the beat-to-beat TCRT value was not significant for identifying the MI patients in this study, which brings to attention the need for requiring further research before using these parameters for analyzing repolarization heterogeneity and cardiac risk stratification study.

Recent research in 2013, Sur et al. [85] suggested several VCG-based parameters for the analysis of ventricular depolarization and repolarization in healthy subjects based on gender. In this work, they suggested that the repolarization lability is gender dependent, with mostly men having higher repolarization lability than the women. In addition, Correa et al. [15] also studied seven VCG-based parameters (maximum vector magnitude, volume, planar area, maximum distance between centroid and loop, angle between XY and optimum plane, perimeter, and area-perimeter ratio). In this study, they demonstrated that several VCG-based parameters are found to be a significant marker for differentiating healthy subjects from ischemic patients. The details of the VCG-based parameters list are given in the Table 2 and their findings.

Heart rate dependency

The relationship between HR and VCG-based parameters has been investigated by a few studies [50, 76, 88]. Some of the studies demonstrated that the VCG parameters are dependent on the HR. Scherptong et al. [76] investigated VCG parameters (QRS-T angle and spatial ventricular gradient) on a young healthy population. They showed a significant influence of HR on the spatial ventricular gradient magnitude, with an apparent inverse relation between HR and the spatial ventricular gradient. They concluded that the increased HR is associated with decreased spatial ventricular gradient magnitude.

Kenttä et al. [50] investigated the affect of HR on spatial VCG parameters during exercise ECG for healthy subjects and concluded that the HR has significant influence on VCG parameters (TCRT and QRS-T angle). Particularly, HR affects TCRT during exercise and recovery periods. In a supine position, the TCRT values were found to be higher compared to sitting and standing positions [7]; however, HR is increased during the exercise. As a result, the QRS-T angle increased, decreasing the value of TCRT. Thus, TCRT is influenced by HR. Vahedi et al. [88] also found that some computed VCG parameters (QRS_area, T_area, and T_amplitude) were also influenced by HR, where a decrease in heterogeneity of ventricular activity was observed due to increased HR.

Respiration

Respiration is one of the most important factors that may affect VCG loops or parameters. Respiratory activity influences ECG measurements with respect to both beat morphology and HR. The morphological beat-to-beat variations can be found in the ECG, during the respiratory cycle, and are mainly due to chest movements and changes in the position of the heart. The respiratory frequency is generally estimated from the respiration signal. As a result, the derived VCG loops are not synchronized due to the respiratory-induced changes or respiratory frequency in the electrical axis of the heart [74]. In addition, cardiac motion abnormalities may have some affect on VCG parameters during the process of magnetic resonance imaging (MRI). Due to the respiratory motion or irregular cardiac rhythms, the imaging of the heart is inherently prone to imaging artifact [64]. Thus, one needs to take into account the respiratory signal or respiratory frequency for the analysis of VCG loops. Thereby, the VCG analysis results may be affected. However, in 1998 and 2000, the articles published by Sörnmo [81] and Astrom et al. [5] developed the method for reducing the affect of respiration and muscular activity on VCG loops in a beat-to-beat manner. Mainly, they reduced the respiration influence by performing spatial and temporal maximum-likelihood (ML) alignment of the VCG loops, and this alignment was based on scaling, rotation, and time synchronization of the loops. Moreover, the affect of respiration on VCG loops has been validated further, and the respiration frequency was estimated in the article proposed by Leanderson et al. [57]. In 2006, Bailón et al. [6] also estimated the respiratory frequency from VCG during the stress testing, which has demonstrated the influence of respiration and existence in the VCG loops. Recently, in 2009, Karsikas et al. [47] suggested that respiration significantly affects the beat-to-beat variability of all the QRS-T angle measures. Therefore, this study suggested that care should be taken when considering the reliability of VCG angle measures for one-beat analysis as compared to beat-to-beat analysis.

Nevertheless, this proposed ML VCG loop alignment technique was limited [5, 81]. For example, the proposed technique reduces the ability to include apriori information in any of the transformations. In addition, for low-quality signals, such as fetal ECG signal, the reliability of this method is reduced. To address this situation, in 2013, Vullings et al. [91] introduced the generic Bayesian framework to derive the beat-to-beat VCG loop alignment, where the existing ML method can also be derived. This Bayesian probability theory was applied to derive maximum a posteriori estimation for robust VCG loop alignment.

Gender

The problem of gender influence on VCG parameters is not fully understood yet. However, several studies have attempted to explore the relation between gender and VCG-based parameters. In 1968, a study was carried on 101 healthy male and 102 healthy female subjects to analyze VCG dependency on gender [82]. They found significant gender differences in several VCG-based parameters (maximal QRS and T vectors). In another study in 2002, Smetana et al. [80] observed substantial differences in repolarization homogeneity between male and female subjects. In 2008, Scherptong et al. [76] also tested spatial parameter dependency on gender and proposed that they are strongly sex dependent. Later, in 2012, Vahedi et al. [89] found that there were significant differences in spatial VCG-based parameters with gender and that the parameters are significantly higher in men compared to women. In agreement with the previous investigation, a recent study was conducted on healthy subjects for analyzing the VCG parameters by Sur et al. [85] in 2013. They concluded that healthy men showed higher repolarization lability for several VCG parameters compared to healthy women, which questions the factors that may contribute to influence the VCG parameters.

Age

Several researchers have investigated the influence of VCG parameters by considering the age effect [11, 24, 34]. All of the studies have found that the VCG-based parameters are age dependent. Guller et al. [34] observed that the size of the maximal spatial QRS vector was significantly decreased in first three days of a newborn baby. In their study, they found that the QRS duration is age dependent, and the most probable reason for the change in QRS configuration in newborn infants differences in the ventricular activation process. In addition, Brohet et al. [11] also demonstrated that infants younger than 6 months have higher levels of dispersion and disparate variation in VCG parameters (maximal spatial QRS vector, QRS-T angle) than older children.