2.4. Lorenz Plot Analysis

Once the aforementioned steps were completed, the arrhythmia filter was disabled, and the complete population of recorded complexes was used to create LPs from the entire time of recording. On LPs, each R-R interval (R-Rn, dots depicted on the X-axis) was plotted against the following one (R-Rn + 1, dots depicted on the Y-axis), so that the coordinates of each dot were: R-R, R-R + 1 (Figure 1).

Example figure showing the basic principles of Lorenz plot generation. On the figure bottom, a selected portion of a Holter recording from this study shows a sinus rhythm with regular R-R intervals transiently interrupted by a ventricular premature complex with a post-ectopic pause (PP). Above the tracing, a two-dimensional Cartesian coordinates map of R-R intervals is illustrated. The X-axis is the R-Rn interval and the Y-axis is the R-Rn + 1 interval. In this example, the first two R-R intervals are regular (a), creating a dot on the diagonal line (identity line) (A). The third R-R interval is premature (b); therefore, the correspondent dot moves below the line to point B. The fourth R-R interval is longer due to the PP; thus, the correspondent dot moves above the line to point C. The fifth R-R interval returns to the initial value (a); consequently, the correspondent dot moves to point D. Since the last R-R interval is identical to the preceding one (a), the last dot returns to point A. Repetition of this process using the entire population of R-R intervals recorded during a Holter monitoring creates the final Lorenz plot.

The resulting cloud of dots was characterized by: (1) a shape, fitted to the plot with the mean R-R interval as its center; (2) a length, the major axis passing through the mean R-R interval along the bisector (line of identity); and (3) a width, the minor axis passing through the mean R-R interval perpendicular to the major axis [1,2,5]. Then, as previously described in humans [2], each LP was studied qualitatively by assessing the specific shape of the contour of the main central cluster (CC) of dots, and also quantitatively by assessing three geometrical indexes: (1) the ratio of the maximal length to the maximal width; (2) the number of CCs and eccentric clusters (ECs) of dots; and (3) the number of branches arising from the main CC (Figure 2). Clusters of dots located along and outside the line of identity were defined as ‘central’ and ‘eccentric’, respectively [2]. When more than one CC was present, the term ‘main’ was used to define the cluster of dots located at the left lower corner of the graph. Table 1 reports the criteria of classification of LP patterns. The nomenclature already proposed in humans [2] and dogs [5,6,7] was used when the characteristics of patterns obtained from dogs included in the study were similar to those previously described; otherwise, a new nomenclature was proposed.

Graphic criteria used for classification of Lorenz plot patterns. (A): Example Lorenz plot generated from a Holter recording obtained from a dog with atrial fibrillation. Maximal length (Lmax) and maximal width (Wmax) of the cluster of dots are illustrated by blue and red lines, respectively. (B): Example Lorenz plot generated from a Holter recording obtained from a dog with sinus rhythm associated with a normal heart rate variability and frequent ventricular premature complexes. The central cluster (CC) and eccentric cluster (EC) are illustrated by red and blue dotted lines, respectively. Note that both CCs are located along the line of identity and that the main CC is placed at the lower left corner of the graph. Note also that both ECs arise from the lower left corner of the graph close to the body of the main CC and then extend outside the line of identity, one approximately parallel to the X-axis and the other approximately parallel to the Y-axis of the plot. (C): Example Lorenz plot from a Holter recording obtained from a dog with a diagnosis of sinus rhythm associated with a normal heart rate variability. Red dotted lines outline the margin of the CC and its diverging arms. Note that both arms are clearly attached to the CC, acting as its direct continuation and not as distinct ECs.

Quantitative and qualitative features of Lorenz plot patterns.

CC: central cluster; CSZ: central silent zone; DSL: double side lobe; EC: eccentric cluster; Lmax/Wmax: ratio of the maximal length to the maximal width; LP: Loren plot; NA: not applicable; QSL: quadruple side lobe; TSL: triple side lobe.