The data from 27 consecutive patients with either paAF or peAF admitted to the electrophysiology unit of Niguarda Hospital, Milan, Italy, in January 2022, who underwent CA of AF, were prospectively collected and analyzed. The study was conducted in collaboration with the department of Computer Science of the University of Milan, Italy. Inclusion criteria were as follows: patients aged >18 years with paAF or peAF who had a first indication for AF ablation. Exclusion criteria were as follows: the presence of LA appendage thrombus at pre-operatory imaging, previous ablations of any type, and the need for additional ablations (i.e., cavotricuspid isthmus isolation). Baseline clinical characteristics were recorded through digital medical reports. Electroanatomic maps of LA were obtained using the CARTO 3 electroanatomic mapping system (Biosense Webster, Diamond Bar, CA, United States). For each patient undergoing AF ablation, a bipolar, high-density map of the LA was obtained. The resulting data, comprising the spatial position of the catheters, electrical signals, and vertices and triangles of the LA mesh, were extracted, exported, and analyzed offline. After discharge, patients were followed up with 24-hour Holter monitoring and clinical examinations performed at 3, 6, and 12 months. The primary endpoint was to compare the LASE with the AF-type and LA electroanatomical map (EAM).

The study was approved by the Ethics Committee of Niguarda Hospital in compliance with the Declaration of Helsinki. All patients provided informed consent before the procedure.

All procedures were performed under general anesthesia by an electrophysiologist experienced in AF ablation, assisted by at least one additional electrophysiologist or fellow. The whole CA methodology has been previously described in the work by Pratola et al. (2008). A deflectable decapolar catheter (Bard Dynamic) (Boston Scientific, Marlborough, MA, United States) was positioned in the coronary sinus. A single trans-septal puncture was performed with the standard electrophysiological approach. After a trans-septal puncture, intravenous heparin was administered to maintain an activated clotting time of >300 s. Real-time 3D LA maps were reconstructed using the PentaRay mapping catheter (Biosense Webster, Diamond Bar, CA, United States) with a minimum of 2,000 anatomical points acquired. The maps were acquired independently in the presence of SR or AF, and the normal LA substrate was distinguished from the abnormal LA substrate according to universally accepted voltage thresholds, setting low and high band pass thresholds at <0.05 mV and >0.5 mV, respectively (Vlachos et al., 2017). In particular, the LVA was defined by ≥ 5 adjacent points of <0.5 mV acquired during SR and using a multipolar HD catheter. The accuracy of point acquisition was evaluated through the Tissue Proximity Index (TPI) algorithm using the CARTO 3 system to limit low-contact artifacts. Furthermore, multiple local remaps with a minimum density of ≥10 points were performed to reduce wavefront direction distortion. The entire mapped LA was generally as defined abnormal by >1 LVAs adjacent or localized in different LA regions. In addition, to reduce the acquisition of false positive LVAs due to inadequate contact with the wall, all EAMs were acquired using the activated Tissue Proximity Indicator (TPI) tool of PentaRay. Anatomic reconstruction of the LA, including the LA–pulmonary vein (PV) junction, was performed. In all patients, radiofrequency (RF) ablation was performed to create a single circumferential line around contiguous veins. RF pulses were delivered with a temperature setting of up to 43°C and 35 W using the THERMOCOOL SMARTTOUCH SF Catheter (Biosense Webster, Diamond Bar, CA, United States) targeting an ablation index (AI) of 500 for both the anterior wall and roof and 400 for the posterior wall and floor of LA. The ablation lines consisted of contiguous local lesions <5 mm from each other and at a distance of >5 mm from the ostia of the PVs using the wide antral circumferential ablation technique (Proietti et al., 2014). In cases of LVAs on the LA posterior wall, posterior box isolation was performed (Romero et al., 2023). Procedural success was defined according to universally accepted criteria for pulmonary vein isolation (PVI) and LA posterior war isolation by checking entrance and exit blocks (Tzeis et al., 2024).

During LA mapping, bipolar signals were routinely acquired for 2.5 s and stored along with the 3D location of the mapping catheter at the time of recording. The set of locations visited by the mapping electrodes (mean = 13,000 ± 4,242) was presented as a cloud of points in space. An atrial mesh was also derived using signals <3.5 mV of amplitude, which was considered the noise threshold (more details on its creation are given in Section 2.3.1). The main steps of data acquisition and processing are summarized in green and blue boxes in Figure 1, respectively.

All quantitative variables displayed a normal distribution, which was verified empirically by the visual inspection of the histogram. They were reported as the mean ± standard deviation and compared using a one-tailed Student’s t-test. p < 0.05 was considered significant. To evaluate the degree of agreement or comparability between continuous variables of measurements obtained from the calculation of entropy on the first mesh and the downsampled mesh, a Bland–Altman analysis was performed. Discrimination, i.e., the model’s ability to differentiate between patients with abnormal and normal LA, was examined using the area under the receiver operating characteristic (AUROC) curve. AUROC analysis was also performed to calculate cutoff values, sensitivity, and specificity. Finally, the cutoff points were calculated by obtaining the best Youden index (sensitivity + specificity −1). All statistical analyses were performed by two blinded researchers, and then, the results were compared for reproducibility using k-statistics. Data were analyzed using R software version 3.6.2 (R Foundation for Statistical Computing, Vienna, Austria).

The main characteristics of the study population (mean age, 63 ± 14 years; 41% male) are summarized in Table 1. Overall, 16 patients (59%) suffered from paAF, while the remaining patients were affected by the persistent type. A normal LA substrate was reported in 15 patients with paAF (94%) and 2 patients with peAF (18%). The EAM was obtained during SR in 13 patients (48%), and the average number of collected EGMs per map was 3,029 ± 702 points. The mean skin-to-skin time was 56.3 ± 7.2 min, with a mean mapping time of 15.6 ± 3.4 min. Procedural success was achieved in all cases without procedural complications. After discharge, patients underwent follow-up for a mean time of 15 ± 2 months. At 1 year, two cases of AF recurrence were reported among peAF patients.

The mean entropy calculated from the original mesh was 5.87 ± 0.47. After mesh downsampling, the mean entropy was 6.27 ± 0.53. Figure 2 shows an example of the distribution of two patients with high and low entropy values, while the values computed for the entire dataset are given in Table 2. The Bland–Altman analysis was performed to evaluate the degree of agreement between measurements obtained from the calculation of entropy on the first mesh and on the downsampled mesh (Figure 3). The average of the differences was −0.35, a bias value related to the calculation of the entropy in the original mesh. The measurements were, however, largely in agreement, with all but one case falling within the 95% confidence interval of the mean (between −0.81 and 0.12) and most within a range ±0.2 with respect to the mean (23 cases out of 27). First, all samples and related histograms of entropy distribution were qualitatively examined. Statistical tests were carried out on the entropy values relating to the type of substrate, the type of AF, and the heart rhythm during the procedure. Entropy values significantly differed between patients with paAF and peAF (6.45 ± 0.41 versus 5.87 ± 0.53; p = 0.028), as well as in patients with normal and abnormal LA substrates (6.42 ± 0.42 versus 5.87 ± 0.56; p = 0.043). Finally, it is worth noting that the entropy values were independent of the presence of SR or AF during the procedure (6.33 ± 0.41 versus 6.11 ± 0.63; p = 0.619). LASE and EGM distributions according to patients’ characteristics are given in Figures 4, 5, respectively. Compared to LASE, the EGM boxplot analysis did not distinguish between paAF and peAF (p = 0.053) or between normal and abnormal LA substrates (p = 0.22). Moreover, the basal rhythm significantly influenced the EGM values (p = <0.001). The accordance between the LASE and abnormal substrate identified in the voltage map was confirmed using the ROC curve (AUC: 0.81; CI: 0.62–0.99) (Figure 6). The cutoff with the best accuracy, according to the Youden index, was estimated at 6.06, demonstrating a sensitivity of 80% and a specificity of 80%. All results were compared for reproducibility, with a k-statistic of 0.82.

At follow-up, patients with AF recurrence were characterized by the lowest LASE.

According to information theory (Shannon, 1948; Rivolta, 2024), entropy provides an estimate of the number of bits required to encode a random event. If the probability of a certain event is high, its informative content tends to 0. Therefore, if one event in the distribution is nearly certain to happen, only one bit is necessary. Conversely, if the probability of the event is low, the number of bits required for encoding it will be high (Ribeiro et al., 2021). Subsequently, the higher the probability of a group of events occurring with the same frequency, the higher the value of entropy. On the contrary, if the probability of the events occurring with the same frequency is low, entropy will be low.

Numerous studies used entropy to address multiple tasks related to physiological signals, including cardiac data recording (Rivolta, 2024; Ganesan et al., 2014; Manikandan and Soman, 2012). Applying this concept to the electrical activity of LA, if the range of atrial voltage amplitudes is uniform in every region, its entropy will be high. This occurs because the probability of encountering a specific voltage is similar across all locations explored during mapping. Conversely, if the electrical activity is not uniformly distributed due to the presence of fibrosis or LVAs, resulting in a skewed probability distribution, entropy will be lower.

In the context of the present study, the histogram pattern in panel A of Figure 2 (wider but more homogeneous distribution of probability) is representative (with statistical significance) of a typical profile for a normal substrate and paroxysmal AF, and it corresponds to the presence of similar amplitudes in different locations. Contrarily, panel B of Figure 2 is typical of an abnormal substrate, with different values of voltage across the atrial tissue. Intriguingly, the probability of voltage amplitude distribution seems independent of the rhythm present at the time of mapping. Therefore, it remains significantly higher in patients with normal substrate even if the data acquisition was performed during AF, which usually represents an important limitation for bipolar mapping. This is probably because the data acquisition of the explored area was based on a sample of voltage amplitude distribution and not only on the single voltage value recorded at a certain time. For this reason, LASE may overcome some well-known limitations of conventional bipolar mapping, such as arbitrary LVA thresholds, basal rhythm, and the direction of the wavefront relative to the orientation of the mapping catheter electrode (de Bakker, 2019; Yamaguchi et al., 2019).

As the variability observed in the original meshes across different patients may influence the comparability of the findings, we downsampled the mesh by reducing the vertex count, providing more uniformity. This reduction aimed to standardize the datasets for inter-patient comparison and provide faster computation and processing. This process did not lead to the loss of information, as confirmed by the results of the comparative analysis.

The criteria for selecting candidate EGMs considered their proximity to the normal to the inner surface of the LA. The aim was to address potential issues related to atrial movements and wall deformations during the electrophysiological procedure. This method added a valuable refinement layer based on the average distance between vertices.

The definition of LVA was historically arbitrarily defined, with large differences among studies (Junarta et al., 2022). Previously, LVAs were defined by at least three points of low voltage acquired using the ablation catheter, which is typically equipped with only two dipoles. This method has provided conflicting results regarding the long-term effectiveness of adding ablation of these regions to conventional PV ablation (Yang et al., 2022; Kircher et al., 2018). However, these studies confirmed the beneficial role of voltage maps in identifying patients with peAF and normal LA substrates, who may achieve excellent rhythm control with PV isolation alone. The proposed workflow enables the assessment of the SE across the entire atrium based on voltage maps. Alternative approaches based on localized evaluations within specific areas (e.g., left/right pulmonary veins) or leveraging surrogate data through bootstrapping techniques may offer a wider view of the entropy distribution and its variability.

The relevance of entropy within the electrophysiological framework supports its wider application, particularly in the field of AF, which is, by definition, the most chaotic rhythm (Nicolet et al., 2019). In addition, it may be interesting to explore other concepts of entropy applied to voltage maps, such as dispersion entropy (Rostaghi and Azami, 2016) and fuzzy entropy (Chen et al., 2007). In this regard, additional characteristics of the EGM signals different from voltage amplitude or SE of the time series may be analyzed.

To date, several mapping tools have been developed to improve our understanding of AF, such as CFAE (Hunter et al., 2011) and CARTOFINDER (Honarbakhsh et al., 2018), which aim to detect high-rate focal or rotational activity. However, these tools have failed to improve long-term outcomes and are dependent on the presence of FA during mapping (Narayan and John, 2024). Recently, omnipolar and multipolar mapping techniques have been introduced to overcome the well-known limitations of bipolar mapping, providing optimistic results in substrate mapping and identifying gaps in the ablation lines around the pulmonary veins (Butcher et al., 2023). Finally, the most recent functional mapping method was proposed to analyze, during SR, the response to short-coupled atrial extrastimuli to identify areas of hidden slow conduction within the LA (Silva Garcia et al., 2023). In our study, we investigate the relationship between LASE and the clinical patterns of AF, as well as LASE and LA substrate. The clinical behavior of AF and the presence of LVAs in the voltage map are widely accepted surrogate markers of the degree of atrial structural and electrical remodeling and are associated with a worse outcome after ablation (Starek et al., 2023). However, these factors lack accuracy in predicting AF recurrence patient by patient. This is partially explained by the fact that AF is a complex arrhythmia without a full understanding of its underlying mechanisms. Therefore, performing CA with the EAM system is not only a therapeutic procedure but also a diagnostic opportunity, providing useful insights into the degree of the disease.

Since high-density substrate mapping of the LA encounters several limitations, LASE was used to increase its diagnostic accuracy. Previous studies used entropy to improve the diagnostic power of already existing tools designed to identify such functional electrical anomalies underlying arrhythmia sustainability (Ng et al., 2010). However, all these methods reported contrasting results in terms of effectiveness and capability, and their use is not yet suggested by the guidelines. Our research aimed to identify a novel indicator capable of working synergistically with the EAM system to provide useful information about the underlying AF mechanism and risk recurrence at follow-up. The LASE diagnostic potential was significant, reporting an AUC of 0.81 with 80% sensibility and specificity in predicting abnormal LA substrates. Of note, patients with early recurrence of AF at follow-up were characterized by very low LASE. This finding may be proof for further studies exploring the utility of this tool in predicting post-CA arrhythmia recurrences, compared to conventional parameters that are routinely considered.

Ultimately, LASE demonstrated to be both a feasible and reliable measure, capable of being calculated from a standard bipolar map at any given moment after retrospective exporting and processing. This might facilitate eventual comparative analysis of ablations within the same patient or across different patients. Consequently, this novel tool can be easily translated into the clinical setting of CA, assisting a tailored substrate-based strategy.

The small sample is a major limitation to the study, warranting the need for larger validation studies to confirm our findings. Since all EAMs were produced using the CARTO 3 system, LASE remains, at present, a tool developed for a single-mapping system and, therefore, influenced by all its inherent limitations, limiting its applicability to other mapping technologies. The accuracy and reliability of the results should be independent of the number and density of acquired points. In this study, we adhered to a general practice of utilizing maps comprising a minimum of 1,000 points to ensure accuracy and reliability. However, the selection of the threshold was arbitrary, and the impact of such map density on LASE remains uncertain. This hypothesis necessitates further confirmation. Finally, the specific supplementary insights provided by LASE with respect to standard voltage mapping and its power in predicting AF recurrences after CA are still unresolved questions. Regional LASE assessed at different parts of LA may potentially guide the ablation strategy, particularly in non-exhaustive bipolar maps.