Cardiac Arrhythmias Imprint Specific Signatures on Lorenz Plots

Abstract

Background: Despite the growing number of studies using Lorenz (Poincaré) plots (LPs) for the analysis of heart rate variability (HRV), a possible correlation between the underlying ECG waveforms and the RR scatter plots has never been systematically studied. We report a comprehensive investigation of distinct Lorenz plot patterns (LPPs) encountered in the context of major cardiac tachyarrhythmias as assessed by 24‐hour Holter monitoring and detail the mechanisms underlying the specific LPPs.

Methods: The 24‐hour ambulatory electrocardiograms (AECGs) of 2700 patients with atrial and/or ventricular tachyarrhythmias and the AECGs of 200 controls with pure sinus rhythm were analyzed using an Elatec arrhythmia analyzing system (Elamedical, Paris 1996). This system allows for the generation of two‐dimensional LPs and the exploration of the underlying ECG waveforms. Each LPP obtained was categorized according to its shape and basic geometric parameters. In accordance with the most characteristic LPP feature, the LPPs were grouped into the following distinct classes: 1) comet shape; 2) torpedo shape; 3) H‐Fan shape; 4) SZ‐Fan shape; 5) double side lobe pattern type A (DSLP‐A); 6) double side lobe pattern type B (DSL‐B); 7) triple side lobe pattern type A (TSLP‐A); 8) triple side lobe pattern type B (TSLP‐B);9 island pattern type A (IP‐A); 10) island pattern type B (IP‐B).

Results: While a comet or a torpedo shape was associated with sinus rhythms, the other LPPs were specifically linked to the presence of cardiac tachyarrhythmias. Thus, a Fan shape was associated with atrial fibrillation or multifocal atrial tachycardia, whereas a DSLP indicated the presence of atrial premature beats, and a TSLP was highly specifically linked to frequent ventricular premature beats. An island pattern was exclusively associated with the presence of an atrial tachycardia or atrial flutter (sensitivity: 100%, specificity: 100%).

Conclusion: Major tachyarrhythmias imprint specific patterns on two‐dimensional Lorenz plots generated from 24‐hour Holter recordings. Thus, the Lorenz plot method has the potential to significantly improve the accuracy of arrhythmia detection and differentiation, particularly with respect to supraventricular tachyarrhythmias.

In recent years, clinicians have become increasingly interested in measuring heart rate variability (HRV) for a variety of purposes. ¹ An elegant method to assess HRV is a two‐dimensional scatter plot of successive intervals versus immediately preceding RR intervals. Plots of such nature were first introduced by Henri Poincaré ² as a representation of nonlinear system dynamics. After publication of the famous article by Lorenz on chaotic dynamics, ³ Poincaré plots have become broadly popular; hence they are also often referred to as Lorenz plots (LPs). More recently, Lorenz plots have been introduced into medicine by Woo et al., ⁴ , ⁵ , ⁶ whose work has elicited considerable interest and spurred an ever‐increasing number of studies using LP graphic representation of the heart rate data. ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² In this context, comet and torpedo like LP shapes have been extensively investigated and used for both graphic display and quantitative assessment of HRV. ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² However, in spite of the growing number of studies using LPs for HRV evaluation, a possible correlation between the underlying ECG waveforms and scatter plots has never been systematically investigated and the effects of major cardiac arrhythmias on LP shapes are widely unknown.

The present article is aimed at filling this gap and comprehensively exploring the connections between the apparent morphologies of two‐dimensional Lorenz plots and the pathologies of underlying cardiac rhythms. We report below a systematic investigation of distinct Lorenz plot patterns (LPPs) encountered in the context of major cardiac arrhythmias as assessed by 24‐hour Holter monitoring. Based on theoretical considerations, we hypothesized that specific arrhythmias produce specific shapes on two‐dimensional Lorenz plots.

MATERIALS AND METHODS

Inclusion Criteria

The 24‐hour Holter recordings obtained from the patients admitted to the Holter laboratory at our institution for clinical or scientific indications were screened for the presence of tachyarrhythmias and considered eligible for this study, if they met the following criteria:

• 1frequent atrial premature depolarizations (APDs), i.e., sinus rhythm with ≥ 100 APDs per recording or,
• 2frequent ventricular premature depolarizations (VPDs), i.e., sinus rhythm with. ≥ 100 VPDs per recording or,
• 3sustained atrial fibrillation (AF), i.e., AF present throughout the recording period or,
• 4sustained atria flutter (AFL), i.e., AFL present throughout the recording period or,
• 5sustained atrial tachycardia (AT), i.e., AT present throughout the recording period,
• 6artifact‐free recording time of at least 22 hours.

Patients with cardiac pacemakers, dual chamber pacing devices, and implantable cardioverter/defibrillators were excluded from the study. In addition, 200 Holter recordings with sustained arrhythmias absent or with only very infrequent atrial and/or ventricular premature depolarizations (< 15 ectopic beats per recording) were used as a control group. Thus, overall for final Lorenz plot analysis, 2700 Holter recordings with well‐defined tachyarrhythmias (group A) and 200 control cases with sinus rhythm (group B) were available. The patients' characteristics are summarized in Table 1. The arrhythmia types observed in the group A subjects are detailed in Table 2.

Table 1.

Patients' Characteristics

	Group A (Arrhythmias) n = 2700	Group B (Sinus Rhythm) n = 200
Age	53 ± 7 years	47 ± 11 years*
Female gender	45.0%	20%**
Coronary artery disease	56.0%	15%**
Myocardial infarction	27.0%	0.0%**
CABG	13.0%	0.0%**
Mitral valve disease	8.0%	0.0%**
Aortic valve disease	7.2%	0.0%**
Dilated cardiomyopathy	7.0%	5.0%***
Left ventricular hypertrophy	3.2%	20%**
No organic heart disease	0.0%	60%**

CABG = Coronary artery bypass grafting; *P < 0.05, **P < 0.01, ***P > 0.05.

Table 2.

Arrhythmia Types Observed in Group A Subjects (n = 2700 Holter Tapes)

Rhythm	N (%)
(A) Sustained* arrhythmias	1412 (52.3%)
‐ Atrial fibrillation (AF)	1255
‐ Multifocal atrial tachycardia (MAT)	41
‐ Atrial flutter	102
‐ Atrial tachycardia	14
(B) Frequent† Ectopic Beats
‐ Atrial premature depolarizations (APDs)	256 (9.5%)
○ Isolated APDs	214
○ Frequent APD bigeminy	42
‐ Ventricular premature depolarizations (VPDs)	1032 (38.2%)
○ Isolated VPDs & constant CI	832
○ Isolated VPDs & variable CI	113
○ Interpolated VPDs	78
○ Frequent VPD bigeminy	9

*Persistent throughout recording;^† frequent ectopic beats ≥ 100 per recording.

Holter Analysis

The ambulatory electrocardiograms were obtained using a Tracker II or III™ tape recorder (Reynolds Medical, Hertford, UK) at a sampling rate of 128 Hz. Lead configurations used were CM5 and CM7, which in our experience had the highest yield of artifact free tracings with excellent display of arrhythmia relevant ECG waves, particularly the R and P wave. Also, T wave oversensing was not a problem with these leads, since they usually exhibited flat or inverted T waves and the R‐ to T wave amplitude ratio was 5.8 ± 4.7 (range: 1.3–23.0) in CM5, and 5.6 ± 4.6 (range: 1.4–22.0) in CM7. Hence, double counting (i.e., pseudoarrhythmia detection) was virtually precluded in our patients.

Arrhythmia diagnosis was based on standard electrocardiographic criteria, ¹³ , ¹⁴ and the 24‐hour ambulatory ECG tracings that were edited as full disclosure printouts in each patient. In addition, in a subset of patients with small complex tachycardia, the results of invasive electrophysiologic testing were taken into account. Each ECG diagnosis was independently confirmed by two board‐certified cardiologists and, in dubious cases, a consensus had to be reached, otherwise the case was discarded.

LPP Exploration

For electrocardiographic LP exploration, the Holter tapes were reanalyzed on an Elatec™ analyzing system (Elamedical, Paris 1996). The Elatec system incorporates dedicated software (Elatec V3.03 B) that permits the immediate generation and visualization of LPs on a computer screen by plotting points represented by pairs (T _k‐1,T _k) of successive intervals in a two‐dimensional Cartesian coordinate system. A unique feature of this software, which rendered it perfectly suitable for electrocardiographic LP exploration on a beat‐to‐beat basis, was that it allowed us to unambiguously reassign an underlying ECG waveform to each of the data points manifest on a given LP. Thus, exact LP exploration was possible with regard to accurate and precise determination of the electrocardiographic rhythm underlying a specific LP pattern. It should be emphasized that in accordance with our objective the arrhythmia filter was disabled, and the complete time series (including normal and aberrant QRS complexes) were used for the generation of Lorenz plots. A systematic procedure was used to identify a grid of points located both on the external contour of the plot, and of points located internal to the contour. At each grid point, the electrocardiographic waveforms were examined (Fig. 1).

Figure 1.

Schematic (contour) representations of two typical Lorenz plots. The lines on the plots illustrate the steps in determining a discrete grid for ECG exploration of the Lorenz plots.

Classification of LPPs

Each LPP was categorized according to its shape and basic geometrical parameters. Based on previous experience, ¹¹ the LP shapes were classified according to their visual appearance, including the shape of the contour of the central cluster (CC) and the following geometrical characteristics (Fig. 2):

Figure 2.

Geometrical and taxonomical definitions used for classification of Lorenz plot patterns (LPPs). Lmax‐maximal length of the projection of the data point cluster on bisector, Wmax = maximal length of projection of the data point cluster on perpendicular to bisector; CC = central data point cluster; ECC = eccentric data point cluster.

• 1Ratio of the maximum length to the maximum width (L _max/W _max), and
• 2Number of central (n _C) and eccentric (n _EC) clusters.

The LPPs were then grouped into distinct, broad morphologic classes in accordance with the most characteristic feature of the distinct patterns' shape (Table 3). For finer nomenclature of the LP morphologies we used the terms from published literature when available (e.g., comet and torpedo pattern), ⁴ , ⁵ , ⁶ and introduced new nomenclature when necessary.

Table 3.

Geometrical Characteristics of the Prototypical LP Morphologies

Lorenz Plot Prototype	Lmax/Wmax	N (C)	N (CE)	CC Morphology
Comet‐shape (Com)	> 1	1	0	Club like
Torpedo‐shape (Tor)	> 1	1	0	Elliptical
Fan‐shape (Fan)
‐ H‐Fan	≤ 1	1	0	Triangular
‐ SZ‐Fan	≤ 1	1	0	Triangular & SZ
Double side lobe pattern (DSLP)
‐ Type A	∼ 1 or > 1	1	2	Club or elliptical or discoid
‐ Type B	∼ 1 or > 1	1	2	Club or elliptical or discoid
Triple side lobe pattern (TSLP)
‐ Type A	∼ 1 or > 1	1	3	Club or elliptical or discoid
‐ Type B	∼ 1 or > 1	1	3	Club or elliptical or discoid
Island pattern (IP)
‐ Type A	‐	2	2	Discoid
‐ Type B	‐	3	6	Discoid

L_max/W_max= ratio of maximal length to maximal width of the central cluster; N(C) = number of central cluster; N (CE) = number of eccentric clusters; CC = central cluster; SZ = silent zone.

Statistical Methods

Quantitative results are indicated as mean values with pertinent standard deviations, or as percentages, if appropriate. Nonparametric testing was used to test for significant differences between groups. A P‐value ≤ 0.5 was considered the threshold of significance. Reproducibility of LPP classification was determined through intraobserver and interobserver agreement. For this purpose, effective proportions of observed agreement and proportions of expected agreement were calculated.

We also determined Cohen's Kappa as a measure of “true agreement,” that is, agreement beyond that than expected by chance. ¹⁵ Diagnostic efficiency of LPP in arrhythmia diagnosis was quantified in terms of sensitivity (Sn) and specificity (Sp) using the following formulas: (1) Sn = TP/(TP + FN), where TP and FN are the number of true‐positive and‐false‐negative results, respectively; (2) Sp = TN/(TN + FP), where TN and FP represent the number of true‐negative and‐false‐positive results, respectively.

RESULTS

Observed LPPs

Lorenz plot representation of the interval data revealed a wide variety of eye‐catching patterns. Morphological categorization of these was performed using a total of 10 distinct prototypical patterns: (1) comet pattern, (2) torpedo pattern, (3) homogeneous fan pattern (H‐Fan), (4) fan pattern with one or more silent zones (SZ‐Fan), (5) island pattern with four distinct islets (IP type A), (6) island pattern with nine distinct islets (IP type B), (7) double side‐lobe pattern resembling a symmetric blossom (DSLP type A), (8) Double side‐lobe pattern resembling a lyre (DSLP type B), (9) Triple side‐lobe pattern resembling an asymmetric blossom (TSLP type A), and (10) Triple side‐lobe pattern resembling a propeller (TSLP type B). Representative examples of the 10 prototypes are shown in Figures 3 and 4, and the frequencies of the observed prototypes are summarized in Tables 4 and 5.

Figure 3.

Examples of the comet (A) and torpedo (B) protoype patterns.

Figure 4.

Prototypical Lorenz plot morphologies other than comet or torpedo: (1) fan pattern type A (H‐Fan); (2) fan pattern type B (SZ‐Fan); (3) island pattern type A (IP‐A); (4) island pattern type B (IP‐B); (5) double side lobe pattern type A (DSL‐A); (6) double side lobe pattern type B (DSL‐ B); (7) triple side lobe pattern type A (TSL‐ A); (8) triple side lobe pattern type B (TSL‐B).

Table 4.

Frequency of Prototypical LP Patterns in Group A (Arrhythmias)

LP Prototype	N (%)
Fan pattern	1296 (48)
H‐Fan (Homogeneous fan)	712 (26.4)
SZ‐Fan (fan with silent zone(s))	584 (21.6)
Island pattern	116 (4.3)
Type A (4 islets)	109 (4.0)
Type B (9 islets)	7 (0.3)
Double side lobe pattern (DSL)	343 (12.7)
Type A (“Symmetric blossom)	292 (10.8)
Type B (“Lyre”)	51 (1.9)
Triple side lobe pattern (TSLP)	945 (35)
Type A (“Asymmetric blossom”)	832 (30.8)
Type B (“Propeller”)	113 (4.2)
Total	2700 (100)

Table 5.

Frequency of Prototypical LP Patterns in Group B (Sinus Rhythm)

LP Prototype	N (%)
Comet pattern	144 (72)
Torpedo pattern	56 (28)
Total	200 (100)

Reproducibility of LPPs

Intraobserver agreement of Lorenz plot classification was excellent (Table 6). Interobserver agreement was excellent for 8 of the 10 prototypical classes. Interobserver agreement concerning the classification of comets and torpedo patterns, though still being substantial, ¹⁵ was not as perfect as was categorization of the other prototypical classes (Table 7).

Table 6.

Intraobserver Agreement Regarding LPP Classification

LPP Class	PA	PA–CI	PA (C)	κ± S.E.
Comet	0.9800	0.9462–0.9936	0.5625	Comet vs. Torpedo:
Torpedo	0.9310	0.8245–0.9777	0.1628	0.9504 ± 0.0245
H‐Fan	1.0	0.9933–1.0000	0.3787	H‐Fan vs. SZ‐Fan:
SZ‐Fan	1.0	0.9920–1.0000	0.2908	1.0 ± 0.0
Island –A	1.0	0.9576–1.000	0.8862	Island‐A vs. Island‐B:
Island –B	1.0	0.5609–1.000	0.0311	1.0 ± 0.0
DSL‐A	1.0	0.9838–1.000	0.7411	DSL‐A vs. DSL‐B:
DSL‐B	1.0	0.9127–1.000	0.0803	1.0 ± 0.0
TSL‐A	1.0	0.9943–1.000	0.7686	TSL‐A vs. TSL‐B:
TSL‐B	1.0	0.959–1.000	0.036	1.0 ± 0.0

LPP = Lorenz plot pattern; PA = observed proportion of agreement; C.I.: = 95% confidence interval of PA; PA(C) = PA expected by chance; K = Cohen's Kappa; S.E = standard error.

Table 7.

Interobserver Agreement Regarding LPP Classification

LPP Class	PA	95% CI	PA (C)	κ± S.E.
Comet	0.8750	0.8112– 0.9201	0.5566	Comet vs. Torpedo:
Torpedo	0.7143	0.5920 – 0.8182	0.1594	0.7667 ± 0.0493
H‐Fan	0.9888	0.9772 – 0.9948	0.3787	H‐Fan vs. SZ‐Fan:
SZ‐Fan	0.9864	0.9723 – 0.9937	0.2908	0.9875 ± 0.0044
Island –A	1.000	0.9576 – 1.000	0.8862	Island‐A vs. Island‐B:
Island –B	1.000	0.5609 – 1.000	0.0311	1.0 ± 0.0
DSL‐A	1.000	0.9838 – 1.000	0.7411	DSL‐A vs. DSL‐B:
DSL‐B	1.000	0.9127 – 1.000	0.0803	1.0 ± 0.0
TSL‐A	1.000	0.9943 – 1.000	0.7686	TSL‐A vs. TSL‐B:
TSL‐B	1.000	0.959 – 1.000	0.036	1.0 ± 0.0

LPP = Lorenz plot pattern; PA = observed proportion of agreement; 95% C.I. = 95% confidence interval of the observed proportion of agreement; PA(C) = proportion of agreement expected by chance; κ= Cohen's Kappa; S.E. = standard error of Kappa.

Sinus Rhythm and LPPs

In the individuals with pure sinus rhythm on the 24‐hour ambulatory ECG (group B) only Lorenz plots with a comet (n = 144) or a torpedo shape (n = 56) were observed (Fig. 3).

Arrhythmia Substrates of Distinct LPPs

Fan Pattern

Electrocardiographic exploration of the 1296 Holter tapes with a fan morphology revealed sustained atrial fibrillation (AF) to be present in 1255 cases (96.8%), and sustained multifocal atrial tachycardia (MAT) in 41 cases (3.2%). Among the 1296 fan patterns 712 (55%) showed a homogeneous appearance (H‐Fan, Fig. 5A), while 584 (45%) exhibited a silent zone phenomenon (i.e., a well‐demarcated region only sparsely filled with data points or completely devoid of any data points) ¹⁶ located in the middle and/or at the distal edges of the fan (SZ‐Fan,Fig. 5B). Interestingly, none of the SZ‐Fan patterns was associated with MAT, but consistently showed AF as the underlying arrhythmia.

Figure 5.

Example of H‐Fan (A) and SZ‐Fan (B) with pertinent ECG tracings. Note, in the “silent zone” phenomenon (B, arrow) the silent zone (SZ).

Neither of the two fan types exhibited significant differences regarding mean interval lengths: 817 ± 301 ms (H‐Fan) versus 721 ± 169 ms (SZ‐Fan) (P > 0.05). However, comparison of the interval density distribution and the temporal structure of the time series revealed striking differences between the two fan morphologies: while the histograms of the H‐Fans showed a monomodal distribution in all cases, the SZ‐Fans exhibited interval distributions that were bimodal in 502 (86%), trimodal in 70 (12%), and quadrimodal in 12 (2%) of the cases. Performing high‐resolution tachogram analysis (Fig. 6) we observed sequences with alternating cycle lengths in the recordings associated with a SZ‐Fan. These alternans (RRA) sequences varied in length between 4 and 20 cycles and were randomly interspersed with longer interval sequences that showed the characteristic irregular beat‐to‐beat irregularity usually seen in atrial fibrillation. ¹⁷ The occurrence of RRA did not follow a specific temporal (e.g., circadian) distribution, but was rather erratic. RRA was characterized by either beat‐to‐beat alternation with every other cycle length repeating (S‐L‐S‐L), or occurred as 2:1‐ or 3:1‐ alternans with a short‐short‐long (S‐S‐L) or short‐short‐short‐long (S‐S‐S‐L) cycle length behavior, respectively. Often, the alternans ratio changed from 1:1‐ into 2:1‐ or 3:1‐ alternation, and vice versa (Fig. 6). The RRA phenomenon, which has not been described before, was consistently observed in each of the SZ‐Fans, but never seen in any of the H‐Fans. It is worth noting that, during RRA, the pertinent ECG tracings revealed no recognizable P waves or atrial flutter waves.

Figure 6.

Intermittent interval alternans (RRA) from a patient with a SZ‐Fan pattern. The upper panel shows the ECG sequence from which the tachogram was obtained (lower panel). Note that cycle lengths alternans ratios change from 1:3 (arrow head) to 1:2 (long arrow) and back to 1:3.

Island Pattern (IP)

Electrocardiographic scrutiny revealed atrial flutter (AFL) to be present in 102 (88%), and atrial tachycardia (AT) in 14 (12%) among the 116 recordings associated with an island pattern (Figs. 4 and 7). In the type A island patterns (IP‐A), both AFL and AT were characterized by a constantly alternating A‐V block resulting in 2:1‐and 4:1‐atrioventricular conduction. In contrast, AFL associated with a type B island pattern (IP‐B) exhibited markedly higher variability of A‐V conduction behavior resulting in episodes with 2:1‐, 4:1‐, and 6:1 A‐V conduction. There was no significant difference in mean atrial cycle length (i.e., electrocardiographically determined intervals) between AFL associated with an IP‐A pattern and AFL associated with an IP‐B pattern: 200 ± 55 ms (IP‐A) versus. 220 ± 47 ms (IP‐B). In contrast, mean atrial cycle length was significantly longer in AT (466 ± 57 ms) as compared to AFL (P < 0.01). In the island pattern type A (IP‐A), the interval distribution exhibited a bimodal histogram, whereas, in the IP‐B, the density distribution was trimodal.

Figure 7.

Example of an island type A pattern (left panel) and corresponding interval density distribution (right panel). Lower panel shows pertinent ECG tracings. The Lorenz plot displays four distinct islets, two of which are aligned along the bisector, while two are symmetrically located below and above it. The four ECG tracings are examples of the arrhythmia substrate associated with the four islets marked 1 through 4. The number to the left of each ECG tracing indicates to which islet in the Lorenz plot the ECG pertains. ECG tracing 1 shows AFL with constant 2:1 A‐V block resulting in approximately identical intervals; ECG tracings 2 and 3 display AFL with constantly alternating 2:1 and 4:1 A‐V conduction resulting in cycle length alternans. ECG 4 displays an AFL episode with constant 4:1 A‐V conduction producing approximately identical RR intervals.

Systematic exploration of the four clusters of the IP‐As revealed that depending on the ratio of atrioventricular conduction, the data points mapped either to the central clusters (i.e., clusters located on the bisector) or to the eccentrically located (i.e., apart from the bisector) clusters (Fig. 7). Thus, shorter sequences due to 2:1 A‐V block mapped exclusively to cluster 1, whereas longer sequences resulting from 4:1 A‐V conduction mapped exclusively to cluster 4 (Fig. 7). In contrast, clusters 2 and 3 were produced by alternating cycle lengths due to changing A‐V block ratios resulting in alternating 2:1 and 4:1 conduction.

In the island pattern type B (Fig. 4, panel #4), the nine distinct clusters observed were produced by intervals alternating between three distinct cycle length values, which were due to A‐V conduction ratios varying between 2:1, 4:1, and 6:1.

DSLP

Type A

In 214 (73.3%) of the 292 type A DSLPs (Fig. 8A), sinus rhythm with frequent APDs was found to be the underlying arrhythmia. In the remaining 78 (26.7%) patients with a DSLP‐A on the Lorenz plot, sinus rhythm with frequent interpolated ventricular depolarizations (VPD_i) was found. The number of APDs during the recording time varied greatly from subject to subject. Mean APD incidence was 2546 ± 2190 APD/24 hour with a median value of 2000 APD/24 hour (range: 175–3500 APD/24 hour). Mean incidence of interpolated VPDs was 407 ± 45 VPD_i/24 hour with a median value of 340 VPD_i/24 hour (range: 115‐560 VPD_i/24hour).

Figure 8.

(A) Mechanism of the genesis of a DSL pattern Type A. The ECG tracing (lower panel) shows normal sinus rhythm and an atrial premature beat. The bent arrows indicate correlation of successive intervals, which are marked as N‐1 (pre‐ectopic interval), CI (coupling interval), PEI (postectopic pause), and N+1(first normal postectopic interval). Explanation is given in text. The mapping behavior of the resulting data points A,B, and C is shown in upper panel. (B) Example of a prototypical Type B‐DSL pattern and ECG – Correlates. The central part (1) of the DSL shape reflects normal sinus rhythm, while the left (2) and right (3) side lobe reflects very frequent atrial premature depolarizations manifesting as atrial bigeminy.

Type B

While, in 42 (71%) of the 51 type B double side‐lobe patterns (Fig. 8B), sinus rhythm with very frequent bigeminiform APDs was found, in the remaining nine cases (18%), sinus rhythm with very frequent bigeminiform VPDs were observed. Mean relative duration of ECG occurrence time of APD bigeminy was 83%± 16% (range 23%–100%) of the total 24‐hour recording time. Mean relative occurrence time of VPD bigeminy was 46%± 29% (range 19%–91%) of the total recording time.

In both DSLP‐A and DSLP‐B, the number of ectopic beats was positively correlated with the number of datapoints mapping to the two eccentric clusters (side‐lobes), that is, the more frequent the ectopic beats were, the more data points mapped on to the side lobes resulting in a denser and thicker appearance of the latter. Thus, for example, in the patient whose DSLP is shown in Figure 8A the APD incidence was significantly lower than the APD incidence in the patient whose DSLP is shown in Figure 8B. As a result of the former patient's lower APD incidence the side lobes in his Lorenz plot (Fig. 8A) were significantly thinner than the side lobes (Fig. 8B) in the Lorenz plot of the latter patient exhibiting a higher APD incidence.

TSLP

Type A

TSLP‐A (Fig. 9, left panel) was exclusively associated with sinus rhythm and frequent VPDs characterized by both a full compensatory postectopic interval (PEI) and a constant coupling interval (CI). Mean VPD incidence per 24‐hour recording was 407 ± 45 VPD/24 hour (median: 340 VPD/24 h, range: 115–560 VPDs/24 hour). The interval density distribution was trimodal reflecting the fact, that due to the full compensatory PEIs three distinct interval types arose in the time series: (1) normal sinus cycles (NOM), (2) coupling intervals (CIs), and (3) postectopic intervals (PEIs).

Figure 9.

Mechanism of TSL pattern generation: Upper panel depicts the time structure imposed by the occurrence of a VPD. The arrows pointing to LSL, RSL, and ISL, resp. indicate that the side lobes are generated by correlating the neighboring intervals marked with NOM_PCI, CI, PEI, and NOM_PEI; Lower left panel: TSL pattern obtained in sinus rhythm with frequent VPDs with constant CIs; Lower right panel: TSL pattern seen in sinus rhythms with frequent VPD with varying CIs and constant interectopic intervals (parasystolic mechanism).

Type B

The TSLPs type B (propeller type) (Fig. 9, right panel, and Fig. 10) were exclusively associated with sinus rhythm and frequent VPDs with fully compensatory PEIs but varying coupling intervals. As in the TSLP‐As, the interval histogram was trimodal due to three distinct interval populations: (1) normal sinus cycles (NOMs), (2) coupling intervals (CIs), and postectopic intervals (PEIs). However, in contrast to the TSLP‐As, in the TSLP‐Bs, VPDs exhibited both marked variability of the coupling intervals and constant interectopic intervals. Therefore, the TSLP‐Bs disclosed a spatial arrangement of the three side lobes, which was significantly different from that seen in the TSLP ‐As. Figure 11 shows a representative B‐TSLP example with two magnified regions of the left lower side lobe (LLSL). The arrows indicate the relationship between the CIs and the data point position in the LLSL. The further to the left the ECG exploring courser is set, the shorter are the CIs on the ECG tracings. This suggests a positive correlation between LLSL length and the range of the coupling interval lengths observed.

Figure 10.

ECG substrate of a type B‐TSL pattern: The two different regions marked with 1 and 2 in the left lower side lobe (LLSL) refer to the ECG tracings shown in the respective upper panels. As can be clearly seen the pixel position in the LLSL represents the length of the coupling interval.

Figure 11.

Mixed LPPs. Left panel: comet+ fan associated with intermittent AF; right panel: DSLP+TSLP+fan associated with intermittent AF, frequent APDs and VPDs.

In both TSLP types, the number of VPDs was positively correlated with the number of data points mapping to the three‐side lobes. Hence, the thickness of the side lobes correlated positively with the number of VPDs present in a given Holter recording.

Diagnostic Efficacy of LPPs

The rhythm substrates associated with the various Lorenz plot prototypes are listed in Table 8, and the diagnostic accuracy parameters summarized in Table 9. It can be seen that the distinct LPP classes exhibited excellent diagnostic efficacy regarding arrhythmia detection and diagnosis. While comet and torpedo patterns were specific for normal sinus rhythm, the other LPP prototypes suggested the presence of one or more tachyarrhythmias.

Table 8.

Rhythm Substrates of the Prototypical LPPs

LP Morphology	Rhythm Substrate
Comet	Sinus rhythm with normal HRV (SDNN ≥ 100 ms)
Torpedo	Sinus rhythm with reduced HRV (SDNN < 100 ms)
Fan
H‐Type	AF or MAT
SZ‐Type	Atrial fibrillation (AF)
Island
Type A	AFL & alternating AVB (2:1, 4:1) or
	AT with alternating AVB (2:1, 4:1)
Type B	AFL & alternating AVB (2:1, 4:1, 6:1) or
	AT & alternating AVB (2:1, 4:1, 6:1)
Double side lobe pattern
APDs or
Type A	APDs or interpolated VPDs
Type B	APD bigeminy or
	VPD bigeminy
Triple side lobe pattern
Type A	VPD with constant coupling interval
Type B	VPDs with varying coupling intervals & constant interectopic intervals

SDNN = standard deviation of normal intervals; AF = atrial fibrillation; AFL = atrial flutter; AT = atrial tachycardia; APDs = atrial premature depolarizations; AVB = atrioventricular block; MAT = multifocal atrial tachycardia; VPDs = ventricular premature depolarizations; SZ = silent zone.

Table 9.

Diagnostic Efficacy of Lorenz Plot Patterns in Arrhythmia Diagnosis

LP Pattern	Arrhythmia	Sensitivity (%)	Specificity (%)
Fan (H&SZ)	Atrial fibrillation	100.0	97.0
SZ‐Fan	Atrial fibrillation	100.0	100.0
Island pattern	AFL/AT with variable A‐V block	100.0	100.0
DSLP (A&B)	Atrial premature beats	100.0	96.7
TSLP (A&B)	Ventricular premature beats	99.1	100.0
TSLP‐B	Parasystolic VPDs	100.0	100.0

The fan pattern indicated atrial fibrillation with a sensitivity of 100% and a specificity of 97%. Thus, although present in every case of AF, a fan pattern was not absolutely specific of AF, but was also observed in multifocal atrial tachycardia. If only SZ‐Fans were considered, the association with AF had a sensitivity of 100% and a specificity of 100%.

The island pattern proved highly sensitive and specific of either AFL with varying A‐V block or AT with varying A‐V block and no other arrhythmia form was found to be associated with an island pattern. Although the DSLP was highly sensitive for the presence of APDs, in some cases, it was due to interpolated VPDs, which decreased its specificity for the presence of APDs.

The TSLP (types A and B) had an excellent sensitivity and specificity for the presence of ventricular premature depolarizations with a fully compensated postectopic pause. Finally, the TSLP type B was highly sensitive and specific for the presence of ventricular premature depolarizations exhibiting both a varying coupling interval and constant interectopic intervals.

DISCUSSION

The main findings of our study can be summarized as follows:

• 1Lorenz plots derived from 24‐hour Holter recordings of individuals with pure sinus rhythm on the one hand and frequent or sustained tachyarrhythmias on the other produced a variety of conspicuous patterns that can be morphologically categorized into a set of 10 geometrically different prototype classes.
• 2Reproducibility of visual Lorenz plot classification was excellent in terms of intrarater agreement, and good to excellent regarding interrater agreement.
• 3Thorough electrocardiographic exploration of the prototypical LP morphologies revealed that distinct arrhythmia forms were highly specifically associated with distinct LPPs.
• 4A subgroup of patients with chronic atrial fibrillation exhibited a SZ‐Fan pattern, which was found to be due to periods of irregularly varying intervals interspersed with short sequences of regularly alternating cycles (alternans). The presence of such an alternans phenomenon has not been reported before.
• 5We also describe for the first time an island‐like pattern that has not been reported previously and show that it is associated with either atrial flutter or atrial tachycardia with alternating A‐V block

It has often been assumed that the different LP shapes are due to variations in efferent sympathetic and parasympathetic activity, ⁸ , ⁹ , ¹⁰ and conclusions have been drawn as to the prognostic value of the LP method in cardiac risk stratification. ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ⁹ , ¹⁰ However, the contribution of arrhythmias to the LP shapes has not been adequately considered. Here we show that in fact many LP shapes, which often are referred to as “complex” in the literature, ⁴ , ⁵ , ⁶ , ⁷ are closely related to arrhythmias, which may be intermittent, yet dominate the off‐diagonal points in the Lorenz plot. A prerequisite of making inferences about possible alterations of the efferent sympathovagal activity by means of certain HRV indices is that these indices truly reflect sinus node activity. Therefore, by definition, such analyses are valid only if they are based on time series obtained during sinus rhythm. HRV measurements based on series that are polluted with ectopic beats or entirely consist of arrhythmic activity are not meaningful with respect to reflecting the autonomic modulation of the electrical activity of the sinus node, thus precluding inferences with regard to alterations of the cardiac autonomic system's activity. In previous studies using Lorenz plot‐based HRV indices the above prerequisites may not always have been met, because the electrocardiographic basis of the various LPPs observed was not well understood. ⁴ , ⁵ , ⁶ , ⁷ Obviously, conclusions based on misinterpretation of Lorenz plots may reduce the value of this method as a means of cardiac risk stratification. In the light of our work, conflicting prior results may be reconciled and the predictive value of HRV significantly increased.

Numerous clinical studies ¹ , ² , ³ , ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² have demonstrated that an interval series obtained during sinus rhythm with well‐preserved heart rate variability will produce a cluster of points grouped around the bisector with a club like appearance. According to accepted nomenclature ⁴ , ⁵ , ⁶ , ⁷ such a pattern is usually referred to as a “comet” shape (Fig. 3A). In contrast, reduced heart rate variability has been shown ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ to be associated with a cigar like LPP (Fig. 3B), which is commonly referred to as “torpedo shape.” ⁴ , ⁵ , ⁶ , ⁷ Experimental correlation studies ⁸ , ⁹ have concluded that the width of the comet or torpedo pattern is a marker of instantaneous heart rate variability, while the length of the comet or torpedo pattern is related to overall heart rate variability. Recently, these conclusions have been corroborated in computer simulations using a physiologically extended firing HRV model. ¹⁰

Except for inappropriate sinus tachycardia, ¹⁸ atrial fibrillation, ¹⁶ , ¹⁹ , ²⁰ , ²¹ ectopic atrial tachycardia ¹⁸ and ventricular premature depolarizations, ²¹ , ²² so far no systematic results have been available regarding manifestations of cardiac tachyarrhythmias in the Lorenz plots. The results of this study bridge this gap and set up a foundation for theoretical predictions regarding the imprinting effects on two‐dimensional Lorenz plots that arise from clinically relevant dysrhythmias, such as frequent atrial and ventricular ectopy, atrial fibrillation, atrial flutter, and atrial tachycardia with alternating A‐V conduction block. In a large study sample, we could demonstrate that these arrhythmias produce distinct LP patterns, which are significantly different from each other both in their visual appearance and the values of geometric parameters. We will briefly discuss these results in more detail.

Fan Pattern

Confirming prior findings, ¹⁶ , ¹⁹ , ²⁰ , ²¹ we consistently observed widely scattered data points in the Lorenz plots of patients with sustained atrial fibrillation. All such LPs had a triangular, fan‐like shape (Fig. 2, left panel). This suggests that despite apparent irregular irregularity of the intervals ¹⁷ during atrial fibrillation there are some nonlinear interactions (nonlinear filtering) that underlie the transformation of the atrial waves into ventricular excitations due to specific electrophysiologic properties of the A‐V node and ventricular conduction system. This observation is consistent with the now commonly held view suggesting that ventricular excitation in atrial fibrillation is not a random process, but rather the result of a nonlinear interaction of the atrial wave fronts with the A‐V node. Such behavior has been shown to arise, if the A‐V node is modeled as an intrinsic oscillator that interacts with the irregularly arriving electrical input from the atria. ¹⁷ , ²³ As we observed, not only AF, but also multifocal atrial arrhythmias resulted in a fan pattern. This lends further support to the clinical validity of the model experiments of Cohen et al. ²³

That frequent sequences of interval alternans (Fig. 6) were associated with an SZ‐Fan pattern (Fig. 5B) may offer an explanation for the occurrence of multimodal interval distributions observed by us and others ¹⁶ in a subset of patients with chronic AF. It is tempting to speculate that the alternans phenomenon we observed is an expression of the presence of multiple A‐V nodal pathways in a specific subgroup of AF patients. The existence of such multiple A‐V nodal pathways had first been postulated by Olsson et al. ²⁴ Recently, it has been shown ²⁵ , ²⁶ that radiofrequency ablation of A‐V nodal pathways abolishes bi‐ and trimodal interval distributions in patients with chronic AF. This adds strong support to the validity of the concept of multiple A‐V nodal pathways in these patients. That we observed alternans consistently and exclusively associated with an SZ‐Fan pattern might suggest that it is due to the presence of one or more AV‐nodal pathways. Thus, the alternans phenomenon would provide a specific marker of AF patients who may benefit from electrophysiologic modification of the A‐V node. However, there are also other explanations for the alternans phenomenon including nonlinear dynamical behavior of the S‐A node, the A‐V node, and the ventricular conduction system. Further study is needed to clarify this issue.

Island Pattern

To our knowledge, the island pattern has not been reported before. We found it to be due to atrial flutter or atrial tachycardia with both arrhythmia types exhibiting varying A‐V block ratios. The different islet‐like clusters (Fig. 7) were produced by two distinct cycle length populations (i.e., short–short cycles (S‐S) and long–long cycles (L‐L)) resulting from the two A‐V conduction ratios. We observed that all theoretically possible cycle length correlations were realized: S‐S, L‐L, S‐L, and L‐S. Thus, according to the relationship i = n ² (where i denotes the number of islets, and n the number of distinct interval populations), successive correlation of neighboring intervals produced data points mapping to four discrete areas in the Lorenz plot, which were symmetrically grouped with respect to each other and the bisector.

The fact that we always observed four rather smeared discoid clusters instead of four single points on the Lorenz plot is probably due to fluctuations in the activity of the efferent autonomic cardiac nervous system constantly modulating the A‐V nodal conduction properties. ¹⁷ , ²³ Of course, we cannot exclude that the discoid shape may also have resulted from aliasing due to the relatively low sampling rate (128 HZ) of the Holter recorders used. It could also have been caused by minute irregularities of cycle lengths and irregularities associated with the revolution of the Holter tapes. However, in a test series with well‐defined cycles, we observed only a very small variability in the intervals and almost no smearing of the data points on the Lorenz plots. Applying the above derived relationship “i = n ² ” it could be predicted that atrial flutter with three distinct A‐V block ratios would produce an island pattern consisting of nine discrete clusters, and this was exactly what we observed (Fig. 4, panel #4).

DSL Pattern

The DSL pattern was associated with either APDs or interpolated VPDs. Its genesis is due to a second population of cycles, which is brought about by the CIs of the ectopic beats (Fig. 8A, lower panel). While sinus cycles map directly onto, or in close proximity to the bisector of the Lorenz plot (Fig. 8A, upper panel) producing a central comet or torpedo shaped cluster, the CIs embedded in the sinus cycles produce data points (CI→N₋₁) that map eccentrically onto the Lorenz plane. This mapping behavior results in a “left‐side lobe” located at some distance from the central cluster (Fig. 8A, upper panel). A “right‐side lobe” arises through correlation of the PEIs with the pertinent CIs (PEI→CI) (Fig. 8A, lower panel). Since APDs and interpolated VPDs do not exhibit a full compensatory PEI, the lengths of the PEIs will be in the range of the embedding sinus cycles. Therefore, correlation of each PEI with its very preceding sinus cycle will produce data points mapping onto, or at least very close to the central cluster and will not produce any further distinct side lobe.

TSL pattern

The different clusters defining a TSL shape represent correlations between different cycle length populations, which are introduced through frequent VPDs with a full compensatory postectopic pause. The specific electrophysiology of the VPDs imposes a well‐defined time structure on the interval series, which explains that only the following correlations were observed (Fig. 9, upper panel):

(1) correlation of NOM→NOM resulting in data points that map onto the central cluster; (2) correlation of NOM_PPEI→PEI producing data points that map to an eccentrically located side lobe; (3) correlation of PEI→CI producing data points that map to another distinct side lobe; and (4) correlation of CI→NOM_PCI resulting in data points that map to a third side lobe. Consecutive sinus cycles not interrupted by VPDs (i.e., NOM→NOM) produced data points that mapped exclusively to the central cluster. Depending on the degree of heart rate variability, the central cluster showed either a comet (high or normal HRV) or a torpedo shape (reduced HRV). The principles of TSLP generation are exemplified in Figure 9.

It is noteworthy that an intermediate side lobe (ISL) was observed only, if the lengths of the PEI were significantly longer than the prevailing sinus cycle (NOM) lengths. Otherwise, only two side lobes were observed, as was the case in the patients with frequent APDs or frequent interpolated VPDs without a full compensatory postectopic pause.

Although the above described principles explain the TSLP, they are not sufficient to explain the significantly different geometric arrangements seen in the two TSLP types (Fig. 9). The different side‐lobe arrangements are the manifestation of differences in the dynamics of the coupling intervals. Whereas, in TSLP‐A, the VPDs were dynamically related to the mean heart rate, this was not the case in TSLP‐B. In the latter, the VPDs exhibit highly variable coupling intervals, which together with the constant interectopic intervals, also observed, are highly suggestive of a parasystolic arrhythmia mechanism. ¹³ The fact that due to their parasystolic nature, the VPDs were not dynamically related to the sinus cycles (NOMs) readily explains the finding that the long axis of the left side lobe of the TSL‐B pattern always comprised an obtuse angle (∠α≅135°) with the bisector of the coordinate system (Fig. 10, right panel). Also, the fact that the variable CIs showed considerable overlap with the lengths of the NOMs, explains the observation that the side lobes of type B‐TSLP were originating in closer proximity to the origin of the central cluster as compared to the TSLP‐A. Thus, the angle∠α, may be useful as a diagnostic feature for differentiation of an extrasystolic from a parasystolic VPD mechanism.

Limitations

We focused on examining the effects of frequent tachyarrhythmias on the shape of 24‐hour Lorenz plots, which implies that arrhythmic episodes with a low incidence were ignored. Since the LP patterns investigated represent the visual display of 100,000 to 140,000 intervals, the effects of short tachycardia runs on the LP shape may have been obscured by the sinus beats outnumbering infrequent arrhythmia episodes.

A second limitation is that the Holter tapes were recorded with conventional cassette rather than digital recorders. Cassette recording is inherently associated with noise due to small anomalies of the cassette movement. This and the relatively low sampling rate of 128 Hz could have introduced some blurring of the signal particularly at shorter intervals, thus affecting the scatter of data points on the Lorenz plot. However, if this effect played a role, it should have introduced a systematic error unlikely to disrupt the principles of the arrhythmias' mapping behavior on the LP shapes.

Another limitation is that we were not able to examine all possible tachyarrhythmia constellations, such as ventricular tachycardias (VT) or fibrillation (VF). Nevertheless, our results exemplify the basic principles of how tachyarrhythmias assessed through their intervals map to a two‐dimensional Lorenz plot. Applying these principles, it is possible to extrapolate our results to other arrhythmia types, such as VT and VF, and predict their mapping behavior as well as the resulting LPPs. It should be mentioned that we observed a great variety of mixed LPPs, if more than one rhythm was present, such as in paroxysmal atrial fibrillation (Fig. 11, left panel) or in intermittent AF with APDs and VPDs during the sinus rhythm periods (Fig. 11, right panel). The principles elucidated in this article hold also true for such mixed LPPs.

Finally, we did not specifically address the potential influence of the patients' cardiovascular medication on characteristics of the time series. However, although the drugs may have affected cycle lengths and A‐V block ratios, these effects were completely irrelevant with regard to the principles governing the Lorenz plot mapping behavior.

CONCLUSIONS

This study confirms the hypothesis that major tachyarrhythmias imprint specific patterns on two‐dimensional Lorenz plots obtained from 24‐hour Holter recordings. We could show that a fan pattern was highly specific for atrial fibrillation, while an island pattern was highly specific for atrial flutter or atrial tachycardia. We also demonstrated that a DSLP was specifically associated with frequent atrial depolarizations or interpolated VPDs, and a TSLP was highly specifically related to the presence of ventricular premature depolarizations. It is concluded that both in the context of Holter and telecardiographic monitoring, the Lorenz plot method has the potential to significantly improve the accuracy of arrhythmia detection and differentiation. This holds true particularly for supraventricular tachyarrhythmias, whose detection and differentiation still pose a problem for available algorithms. Also, in patients at risk of paroxysmal atrial arrhythmias, the Lorenz plot method may prove very useful for online surveillance and risk stratification. Finally, our results provide a sound framework for a meaningful interpretation of Lorenz plots obtained by recorders devoid of whole ECG signal recording. ²⁷