System for measuring the electrophysiological substrate in atrial fibrillation

Abstract

The present invention is directed to a system for monitoring and evaluating electrogram signals representing electric activities of a heart chamber by computing the entropy of the electrogram signals, said system comprising a signal input that is connected to a mapping catheter comprising at least one electrode pole for picking up electric potentials and generating electrogram signals from the picked up electric potentials, along with the 3D location of the catheter at the time of recording and a signal processing and evaluation unit for processing and evaluating electrogram signals received at the signal input. The invention is further to a non-transitory computer readable medium for use in a system for monitoring and evaluating electrogram signals representing electric activities of a heart.

Description

[0001] SYSTEM FOR MEASURING THE ELECTROPHYSIOLOGICAL SUBSTRATE IN ATRIAL

[0002] FIBRILLATION

[0003] Introduction

[0004] The present invention is directed to a system for measuring the electrophysiological substrate in atrial fibrillation of a patient and in particular, for the measuring of the Left Atrial Spatial Entropy of a patient heart.

[0005] Atrial fibrillation (AF) is the most common arrhythmia worldwide and it is related to an increased morbidity and mortality1. Sinus rhythm (SR) maintenance is the main target of AF treatment, and catheter ablation (CA) is currently the gold standard to prevent arrhythmia recurrences2. Continuous technological advances in substrate characterization and ablation methods allowed to better understand AF mechanisms and improve treatment3. However, despite a number of electrophysiological risk factors were identified, many patients still experiment AF recurrence, and prediction of further events after CA is a matter of debate4-6. During bipolar mapping, the identification of low-voltage areas (LVAs) by using universally accepted thresholds is considered proof of cardiomyocytes disease and atrial fibrosis. Indeed, it was associated to more advanced stage of AF and consequently related to higher risk of recurrence7. However, bipolar mapping after electrogram (EGM) acquisition have some well-known limitations, mainly for the variability of signal morphology according to the wavefront direction respect to electrode position8. In addition, voltage mapping depends on other several variables including electrode length, interelectrode spacing, and tissue contact9. In some cases, especially during irregular rhythms, the tissue may show complex electrical patterns which can be difficult to interpret through simple techniques such as bipolar mapping and voltage amplitudes. Indeed, the rhythm highly impacts the data and thus its interpretation. For example, Jadidi and colleagues found difficulties in the identification of low voltage areas in AF after SR was restored10. In addition, the information provided may not be sufficient to pinpoint the location of the arrhythmogenic focus.

[0006] Entropy was introduced in thermodynamics as a measure of randomness and of “disorder” in a molecular system about 160 years ago. Subsequently, its application has expanded across numerous scientific domains, encompassing disciplines such as information theory, data mining, and mathematical linguistics11. In the medical field, entropy was largely used in neurology, for example to evaluate the state of consciousness12and, recently, in cardiac imaging as well. The latter application involves evaluating the heterogeneous nature and inhomogeneity of the heart tissue and its relationship with cardiac events13. Of particular interest for arrhythmology are entropy characterization and its links to probability theory as described in information theory. In particular, Shannon entropy quantified from the distribution of signal values (estimated with a histogram) was applied to cardiac electrophysiology. It was used to differentiate complex fractionated atrial electrograms in patients with AF from noise14and to distinguish bipolar EGMs recorded at pivot points of rotors from EGMs detected at peripheral regions15. Furthermore, Hwang and colleagues highlighted the potential use of Shannon entropy to evaluate the nature of rotors in 2D and 3D in-silico models of persistent AF16. Thus far, although the potential relevance in this field, no studies applied and evaluated entropy of EGM-based voltage maps across diverse cohorts of AF patients, characterized by different substrates, types of AF, rhythm, and AF recurrence. Furthermore, no studies evaluated the impact of an entropy value of the entire left atrial chamber (global atrial entropy) for the electrophysiological substrate characterization.

[0007] According to embodiments can also include generating, from the time series data, an entropy dataset including a plurality of Shannon entropy values corresponding to the plurality of spatial locations in the heart.

[0008] LIS2015080752 discloses a device that monitors and evaluates electrogram signals representing electric activities of a heart chamber, and includes a signal input connected to a mapping catheter, and a signal processing and evaluation unit. The mapping catheter includes one or more electrode poles that pick up electric potentials and generate electrogram signals therefrom.

[0009] US2017156616 discloses herein are techniques for graphically indicating aspects of rotors associated with atrial or ventricular fibrillation. Embodiments can include receiving, using a processor, an electrogram for each of a plurality of spatial locations in a heart, each electrogram comprising time series data including a plurality of electrical potential readings over time.

[0010] WO2023031415 is directed to the field of computer implemented methods for the quantification of arrhythmia complexity and is particularly related to a method for obtaining the reproducibility score (RS) of any type of cardiac arrhythmia.

[0011] Document from NEIC ALIREL ET AL: "Automating image-based mesh generation and manipulation tasks in cardiac modelling workflows using Meshtool", SOFTWAREX, vol. 11, 1 June 2020 (2020-06-01), page 100454, discloses the utilization of a mesh, typically a series of 2.5-second EGMs with their corresponding xyz coordinates, and modify it through a mesh tool, which is a common approach in many endocavitary navigation and mapping systems. The aim of this invention is a system to quantify left atrial spatial entropy (LASE) of the amplitude of bipolar EGMs routinely collected during LA mapping for a further characterization of the atrial tissue in a population of paroxysmal and persistent AF patients.

[0012] There is a need to measure the electrophysiological substrate in atrial fibrillation of a patient and in particular for the measuring of the Left Atrial Spatial Entropy of a patient heart.

[0013] Further, there is a need to quantify left atrial spatial entropy (LASE) of the amplitude of bipolar EGMs routinely collected during LA mapping for a further characterization of the atrial tissue in a population of paroxysmal and persistent AF patients.

[0014] BRIEF SUMMARY OF THE INVENTION

[0015] One or more embodiments of the invention include a system for monitoring and evaluating electrogram signals representing electric activities of a heart chamber by computing the entropy of the electrogram signals according to claim 1. The system comprises a signal input that is connected to a mapping catheter, which comprises at least one electrode pole for picking up electric potentials and generating electrogram signals from the picked up electric potentials, along with the 3D location of the catheter at the time of recording and a signal processing and evaluation unit for processing and evaluating electrogram signals received at the signal input. According to the invention the signal processing and evaluation unit is configured to perform the following steps when an electrogram signal is received by the signal input, reconstructing a three-dimensional mesh representation of said hearth chamber obtained from the navigation catheter in a atrium of said hearth chamber by composing vertices and triangles, wherein the resolution varies according to the number of triangles, the accuracy of the exploration and the exporting procedure, and preparing voltage maps obtained from original and down-sampled meshes and bipolar EGMs from which entropy is computed. The mesh representation step occurs by setting a number of vertices per patienttest, down-sampling or up-sampling of the mesh in those cases in which the number of vertices in the original map was smaller of that settled number, preferably the number of vertices was settled between 4000 and 6000.

[0016] According to further preferred embodiments the down-sampling was carried out through a source software which reduces mesh resolution by initially collapsing all edges smaller than a specified minimum value, subsequently, said open software divides edges larger than the maximum edge length.

[0017] The procedure for preparing the voltage maps comprises: determining a vector that is the normal to the mesh at each vertex; generating a sphere of empirically chosen radius with its center located at the vertex; associating to the vertex only those EGMs collected at positions inside the sphere, defining the candidate EGMs; selecting among the candidate EGMs, only those within a predefined distance from the normal; acquiring the range of voltage amplitudes on the EGMs at each selected neighboring points and the average of the amplitude range of all neighbors’ vertices as the voltage range of the voltage map. determining the voltage map by computing for each vertex v of the mesh, the range of voltage amplitudes on the EGMs acquired at each selected neighboring points and the average of the amplitude range of all neighbors’ vertices as the voltage range of the voltage map.

[0018] According to a preferred embodiment of the invention, the empirically chosen radius of the sphere with its centre located at the vertex is selected between 6 and 8 mm and the predefined distance from the normal associated to the vertex is selected between 1.5 and 2.5 mm, whereas the computation of the entropy is carried out from the probability distribution of the voltage map, that is the amplitude range values associated to each vertex of the mesh. According to a further preferred embodiment of the invention, the distribution of the voltage map is calculated as a number of vertex of voltage within a bin of a multiple w of a given voltage exemplified as a set of histogram of width w and to define its entropy as the discrete entropy H of a quantization of said voltage map; and more preferably the entropy results as formulation expressed as a sum over all bins of the histogram is: where w is the width of each bin (100 a.u. correspondent to 0.3 mv, with conversion a factor of 0.003 mV / a.u.), whereas l= {1 ,... ,i} is the set comprising all bins of the histogram with cardinality l=#l.

[0019] The invention is further directed to a non-transitory computer readable medium for use in a system for monitoring and evaluating electrogram signals representing electric activities of a heart chamber according to the invention as claimed in claim 8.

[0020] Further preferred embodiments of the claimed non-transitory computer readable medium are disclosed in claims 9-14. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1.1 Cloud of points in space, set of the locations visited by the mapping electrodes’ catheter.

[0022] Figure 1.2 Mesh reconstruction by the CARTO system in a three-dimensional representation of the cardiac chamber obtained from the navigation catheter in the atrium.

[0023] Figure 1.3 Down-sampling or up-sampling of the mesh, setting a value of 5000 vertices per patient with a tolerance of ± 100 vertices.

[0024] Figure 2.1 (a to 2.5 (h, workflow of data processing, summarizing the processing steps to associate points and signals to the vertices of the mesh.

[0025] Figure 3. Examples of voltage maps superimposed to their corresponding atrial mesh (right panels) as well as their distributions (left panels) for a patient suffering paroxysmal AF (a) and persistent AF (b).

[0026] Figure 4. Bland Altman Plot between entropy values obtained from the original and down sampled meshes.

[0027] Figure 5. Distributions of the entropy values according to patients’ characteristics.

[0028] DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0029] Embodiments of the present disclosure are described more fully hereinafter with reference to the accompanying drawings. Elements that are identified using the same or similar reference characters refer to the same or similar elements. The various embodiments of the present disclosure may, however, be embodied in many different forms and the invention should not be construed as limited to only the embodiments set forth herein.

[0030] Specific details are given in the following description to provide a thorough understanding of the embodiments. However, it is understood by those of ordinary skill in the art that the embodiments may be practiced without these specific details. For example, circuits, systems, networks, processes, frames, supports, connectors, motors, processors, and other components may not be shown, or shown in block diagram form in order to not obscure the embodiments in unnecessary detail.

[0031] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and / or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0032] It will be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, if an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present.

[0033] It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. Thus, a first element could be termed a second element without departing from the teachings of the present disclosure.

[0034] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this present disclosure belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0035] Materials and methods

[0036] Study Design

[0037] Data from 27 consecutive patients with either paroxysmal or persistent AF admitted to the electrophysiology unit of Niguarda Hospital, Milan, Italy, who underwent CA of AF, were prospectively collected and analysed. Baseline clinical characteristics were recorded through digital medical reports. Electroanatomic maps (EM) of LA were performed using the CARTO 3 electroanatomic mapping system (Biosense Webster, Diamond Bar, CA, USA). For each patient undergoing AF ablation, a bipolar, high-density EM of the LA was obtained. The resulting data composed of the spatial positions of the catheters, the electrical signals recorded by the catheter’s electrodes and vertices and triangles of the atrial mesh were prepared, anonymized to protect the privacy of the patients, securely exported via encryption, and analysed offline. After discharge, patients were followed-up with 24-hour Holter monitoring and clinical examinations performed at 1 and 3 months. The Ethic Committee of Niguarda Hospital approved the routine test performed to the patients and found it in compliance with the Declaration of Helsinki.

[0038] Mapping and Ablation Procedure

[0039] The procedures were performed under general anaesthesia by an electrophysiologist experienced in AF ablation, who was assisted by at least one additional electrophysiologist or fellow. The whole CA methodology has already been described in a previous work by Pratola and colleagues17. A decapolar deflectable catheter Bard Dynamic (Boston Scientific, Marlborough, MA, USA) was positioned in the coronary sinus. A single transseptal puncture was performed with the standard electrophysiological approach. After transseptal puncture, intravenous heparin was administered to maintain an activated clotting time >250 seconds. Real-time 3D LA maps were reconstructed using the CARTO 3 navigation system and PentaRay mapping catheter (Biosense Webster, Diamond Bar, CA, USA) with a minimum of 2000 anatomical points acquired. Maps were acquired independently from the presence of SR or AF, and normal LA substrate was distinguished from abnormal LA substrate according to universally accepted thresholds for LVAs, either during SR or AF [7],

[0040] Anatomic reconstruction of the LA, including 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 up to 43°C and 35W by using Thermocool Smarttouch SF Catheter (Biosense Webster, Diamond Bar, CA, USA) targeting an Ablation Index (Al) of 500 for both the anterior wall and roof and 400 for posterior wall and floor of LA. The ablation lines consisted of a contiguous local lesion deployed at a distance >5 mm from the ostia of the PVs. After anatomic pulmonary vein (PV) encircling with voltage abatement confirmation, electrophysiological PV mapping was performed by using the PentaRay catheter. Procedural success was defined as complete voltage abatement inside the veins, PV disconnection and exit block.

[0041] Data Acquisition and Processing

[0042] During the mapping procedure, which is part of the intervention, bipolar endo-cavitary signals were routinely acquired for 2.5 seconds and stored along with the 3D location of the mapping catheter at the time of recording. The set of the locations visited by the mapping electrodes’ catheter (n = 13000 ± 4242) represented a cloud of points in space, see Fig. 1.1. An atrial mesh was also derived as later explained.

[0043] After the ablation procedure, data stored and exported from the navigation system were processed. The atrial mesh reconstructed by the CARTO system and the spatial coordinates of the catheter were employed. Among all electrodes on the catheter, the selection was directed towards the bipolar signals due to their superior signal-to-noise ratio. Voltages higher than 3.5mv were considered as noise and not further considered. The main steps of data acquisition and processing are summarized in Figures 1.1 to 1.3 and figures 2.1 (a to 2.5 (h, respectively.

[0044] Mesh Creation and Down-sampling

[0045] The mesh reconstructed by the CARTO system is a three-dimensional representation of the cardiac chamber obtained from the navigation catheter in the atrium. It is composed of vertices and triangles, see Fig. 1.2. The resolution varies according to the number of triangles, the accuracy of the exploration and the exporting procedure. The resulting meshes are not homogeneous among the different patients and there is no univocal correspondence between their vertices and the acquired signals.

[0046] In order to compare results among different patients, a down-sampling of the mesh was performed, setting a value of 5000 vertices per patient with a tolerance of ± 100 vertices (or up-sampling in those very few cases in which the number of vertices in the original map was smaller than 5000), see Fig. 1.3. In particular, the resampling process was carried out through the open-source software meshtool™. This tool reduces mesh resolution by initially collapsing all edges smaller than a specified minimum value. Subsequently, it divides edges larger than the maximum edge length. The triangles are defined according to the Delaunay triangulation.

[0047] Voltage map determination

[0048] Subsequently, a procedure was developed to prepare the voltage maps obtained from original and down-sampled meshes and bipolar EGMs. The pieces of data employed are represented in Figures 1.1 to 1.3. More specifically, this methodology was designed to associate EGMs with the given vertex of the mesh to obtain voltage maps, from which entropy was derived.

[0049] 27 patients divided according to normal / abnormal substrate, paroxysmal / persistent AF, SR / AF underwent catheter ablation. For each of them, a cloud of points, representing the 3D locations of the catheter where EMG signals were acquired during the intervention, was collected, Fig. 1.1. An atrial mesh was obtained, Fig. 1.2. The atrial mesh was then downsampled using the Meshtool software, Fig.1.3.

[0050] In figures 2.1 (a to 2.5 (h the processing steps to associate points and signals to the vertices of the mesh were summarized. In fig.2.1 (a, the normal of the vertex V1, dotted line, was outlined and represented; in fig. 2.1 (b, the sphere with center in the vertex, white circle, was used to exclude the points inside the sphere, black circles, from the farthest points in dashed circle. In fig. 2.2 (c, and fig. 2.2 (d, the additional criterion based on the distance between the vertex, white circle, and the points is represented to obtain the neighboring area (a cylinder) outlined in fig. 2.3 (d. The two characteristic criteria were summarized in fig. 2.4 (f: the black round points ideally represent the vertices of the mesh, the triangles, black and dashed , represent the locations of the acquired EGM signals, while the resulting associated points are depicted by dashed triangles. From these, the average peak-to-peak (PP) of the EMGs, fig. 2.4_(g, was computed as shown in fig. 2.4 (g, obtaining a voltage map of the mesh on which the Shannon Entropy was computed fig 2.5 (h.

[0051] To accomplish this objective, several steps were encompassed. First, the vector that is the normal to the mesh at each vertex V1 (outward direction aligned with the mesh’s conformation and passing through the vertex) was determined, as shown in Figure 2.1 (a. Second, a sphere was generated, with its center located at the vertex V1. Only those EGMs collected at positions inside the sphere were “candidates” associated to the vertex, as indicated by black dots in Figure 2.1 (b. The radius of the sphere was chosen empirically (8 mm), to encompass positions that, due to atrial movements, fell either below or above the vertex along the normal. Finally, among the candidate EGMs, only those within a predefined distance from the normal were selected. This distance is represented with the dotted line in Figure 2.2 (c. This further criterion was conceived to consider possible movements of the atria and to account for deformations of the atrial wall during the electrophysiological procedure. It enforced the concept of neighbourhood determination for each vertex which assumes the shape of a cylinder with its axis normal to the internal surface of the mesh and a radius of 2 mm (empirically determined considering the average distance between vertices), as represented in Figure 2.2 (d.

[0052] Upon the completion of the neighbouring points’ identification phase described and shown in figure 2.3 (e, it is possible to define a set of vertices V = {1, ... , v}, which are those of the mesh, associated to a set of neighbours = {n : n neighbour ofv} v e V. Hence, the neighboring points related to a vertex v are defined as those within the sphere, and having a distance from the normal vector that is less than the average distance between vertices (2 mm). This set of points has cardinality Nv= #NVand they are indicated with same colors in Figure 2.2 (e and by green triangles in Figure 2.3 (f.

[0053] For each vertex v of the mesh, the range of voltage amplitudes (through the peak-to-peak amplitude formulation max(xn) - mjn(xn)) was computed on the EGMs acquired at each selected neighbouring points, where x„ represents the nth2.5 s EGM associated to the n point. The average of the amplitude range of all neighbours, that is — NvXn=i(maxCxn) ~ mjn(xn)), was then taken as the voltage range in v and used to determine the voltage map. This step is reported in Figure 2.4 (g.

[0054] Entropy Computation

[0055] The computation of the entropy was carried out from the probability distribution of the voltage map, that is the amplitude range values associated to each vertex of the mesh. It is possible to represent this distribution with an histogram, as exemplified in Figure 2.5 (h, and to define its entropy as the discrete entropy H of a quantization of voltage map. The resulting formulation expressed as a sum over all bins of the histogram is: where w is the width of each bin (100 a.u. correspondent to 0.3 mv, with conversion a factor of 0.003 mV / a.u.), whereas J = {1, ..., 1} is the set comprising all bins of the histogram with cardinality I = #J. Summarizing the methodology, it is possible to define the probability of the jthbin as follows (where w0is a constant value):

[0056] Statistical Analysis

[0057] All quantitative variables displayed a normal distribution, which was verified empirically by visual inspection of the histogram. They were reported as mean ± standard deviation and compared used one tailed Student's t-test. P < 0.05 was considered as significant.

[0058] Discrimination, that is, the model’s ability to differentiate between patients with abnormal and normal LA, was examined using the area under the receiver operating characteristic curve (ALIROC). ALIROC analysis was also performed to calculate cutoff values, sensitivity, and specificity. Finally, cutoff points were calculated by obtaining the best Youden index (sensitivity + specificity - 1). Data were analyzed with R version 3.6.2 software (R Foundation for Statistical Computing, Vienna, Austria).

[0059] Results

[0060] Study Population and Procedure Characteristics

[0061] Main characteristics of the study population (mean age 63 ± 14 years, 41% males) are summarized in Table 1. Twenty-seven consecutive patients were enrolled and underwent CA. No patients had anamnestic history of previous CA. Sixteen patients (59%) had paroxysmal AF and fifteen of them showed electrically normal LA substrate at substrate map. Similarly, ten of eleven patients with persistent AF had an electrically normal LA substrate. Electroanatom ic mapping was performed during SR in 13 patients (48%) and the average number of collected EGMs per map was 3029 ± 702 points. The CA was successful in all patients according to guidelines criteria17. No procedural complications were reported.

[0062] Table 1.

[0063] LASE values

[0064] First, all samples and related histograms of entropy distribution were qualitatively examined. Figure 3. reports examples of voltage maps superimposed to their corresponding atrial mesh (right panels) as well as their distributions (left panels) for a patient suffering paroxysmal AF (a) and persistent AF (b). Figure 3 reports an example of the distribution of two patients with high and low entropy values, while the values computed for the entire dataset are reported in Table 2. The mean entropy calculated from the original mesh was 5.87 ± 0.47. After mesh down-sampling, the mean entropy was 6.27 ± 0.53. To evaluate the degree of agreement or comparability between measurements obtained from the calculation of entropy on the first mesh and on the downsampled one, a Bland-Altman analysis was performed and reported in Figure 4. The horizontal axis in figure 4 shows the average of the two entropy values and the vertical axis the difference between the two values. 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, and all but one case was 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).

[0065] Table 2. Substrates, AF types and calculated entropy values for each patient in the study.

[0066]

[0067] Statistical tests were carried out on the entropy values relating the type of substrate, the type of AF and the heart rhythm during the procedure. Entropy values significantly differed between patients with paroxysmal and persistent AF (6.45 ± 0.41 versus 5.87 ± 0.53, p= 0.028), as well as in patients with normal and abnormal LA substrate (6.42 ± 0.42 versus 5.87 ± 0.56, p= 0.043). Finally, it is worth noting that the entropy values were independent from the presence of SR or AF during the procedure (6.33 ± 0.41 versus 6.11 ± 0.63, p=0.619). Entropy distributions according to patients’ characteristics are reported in Figure 5.

[0068] According to the invention, LASE measurements showed correlation with the presence of normal or abnormal substrate and AF clinical features: patients with a healthy electrical substrate showed higher entropy values when compared to patients with an unhealthy atrial substrate and it was significantly higher in patients with paroxysmal AF compared to patients with persistent AF

[0069] LASE remains significantly higher in patient with normal substrate than abnormal, regardless of the heart rhythm (SR vs AF) during map acquisition; and, (3) LASE predicted LA abnormal substrate with a high sensibility and specificity (80%).

[0070] Accordingly with information theory1920, 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 zero. 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 high21. In other words, the higher is the probability of a group of events to occur with the same frequency, the higher is the value of entropy. On the other hand, if the probability of the events to occur with the same frequency is low, entropy will be low.

[0071] Numerous works employed entropy to address multiple tasks related to physiological signals, such as those related to cardiac data recordings20’22 23. Applying this concept to the electrical activity of LA, whether the range of atrial voltage amplitudes is uniform in every region its entropy will be higher. 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 fibrotic or LVAs, resulting in a skewed probability distribution, entropy will be lower.

[0072] The histogram pattern in the panel A of Figure 3 (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 location. Contrarily, panel B of Figure 3 is typical of an abnormal substrate, with different values of voltage range across the atrial tissue. I ntriguingly, the probability of voltage amplitude distribution seems to be independent on 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 that usually represent an important limitation for bipolar mapping. This is due to the data acquisition of explored area was based on a sample of voltage amplitude distribution and not only on the single voltage value recorded in a certain time. For this reason, LASE measurements overcome some well-known limitations of conventional bipolar mapping such as arbitrary LVAs thresholds, basal rhythm and the direction of wavefront relative to the orientation of the mapping catheter electrode89.

[0073] LASE computation.

[0074] The variability observed in the original meshes across different patients was a possible limit with respect to the uniformity of the findings. A down sampling process of the mesh advantageously allows, reducing the vertex count, and providing uniformity. This reduction standardizes the datasets for inter-patients’ comparison and a faster computation and processing. The comparative analysis confirmed the fact that the process did not produce an information loss.

[0075] Furthermore, the criteria for selecting candidate EGMs considered their proximity to the normal to the inner surface of LA. The aim was to address potential issues related to atrial movements and wall deformations during the electrophysiological procedure. This inclusion adds a valuable refinement layer based on the average distance between vertices.

[0076] Advantageously entropy appears to have within the electrophysiological framework supports its wider application, for other related tasks as well. It is indeed well-known that the concept of entropy can be valuable for dimensionality reduction within similar contexts24. In future perspective, it will be interesting to explore other formulations of entropy applied on voltage maps, for example using metrics like Dispersion25and Fuzzy Entropy26. Also in here we estimated the entropy of voltage maps, but other characteristics of the EGM signals and not only their voltage range, should be considered in the future.

[0077] Clinical implications

[0078] The relation of entropy with clinical patterns of AF and with different substrates is of particular interest. The presence of LVAs on LA bipolar map as well as the persistent behavior are widely accepted surrogate markers of the degree of atrial structural and electrical remodeling. Furthermore, they are usually correlated with a worse outcome after AF ablation Baseline left atrial low-voltage area predicts recurrence after pulmonary vein isolation: WAVE-MAP AF results. Starek Z, Di Cori A, Betts TR, Clerici G, Gras D, Lyan E, Della Bella P, Li J, Hack B, Zitella Verbick L, Sommer P. Europace. 2023 Aug 2;25(9):euad194. doi: 10.1093 / europace / euad194.. 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 supporting mechanisms. AF ablation performed with a mapping system is not only a therapeutic procedure but also a diagnostic opportunity, providing useful insights about the degree of the disease.

[0079] Since high density substrate mapping of the LA encounters several limitations, LASE was employed to increase diagnostic accuracy. Previous studies employed entropy to improve diagnostic power of already existing tools designed to identify such functional electrical anomalies underlying arrhythmia sustainability. Measuring the complexity of atrial fibrillation electrograms. Ng J, Borodyanskiy Al, Chang ET, Villuendas R, Dibs S, Kadish AH, Goldberger JJ. J Cardiovasc Electrophysiol. 2010 Jun 1;21(6):649-55. doi: 10.1111 / j.1540- 8167.2009.01695.x. Epub 2010 Feb 1. However, all these methods reported contrasting results in terms of effectiveness and reliability and their use is not suggested yet by guidelines. Our research study centered on identifying a novel clinical indicator of the electrical atrial substrate. Through dedicated analysis, this indicator aims to enhance the diagnostic accuracy of the mapping system. LASE diagnostic potential was significant, reporting an AUC of 0.81, with 80% of sensibility and specificity in predicting a pathological LA substrate. Of note, patients with early recurrence of AF at follow-up were characterized by very low LASE that indicated the presence of advanced atrial remodeling.

[0080] Ultimately, LASE demonstrated to be both feasible and reliable. The data necessary for calculating LASE can be directly extracted from a standard bipolar map at any given moment, retrospectively exported and processed. This facilitates comparative analysis of procedures within the same patient or across different patients consistently. Consequently, this novel tool can be easily translated into the clinical setting of CA, assisting tailored substrate-based strategy.

[0081] Bibliography

[0082] 1. Chugh SS, Havmoeller R, Narayanan K, Singh D, Rienstra M, Benjamin EJ, et al. Worldwide Epidemiology of Atrial Fibrillation: A Global Burden of Disease 2010 Study. Circulation 2014;129:837-47.

[0083] 2. Arbelo E, Brugada J, Hindricks G, Maggioni AP, Tavazzi L, Vardas P, et al. The Atrial Fibrillation Ablation Pilot Study: an European Survey on Methodology and results of catheter ablation for atrial fibrillation conducted by the European Heart Rhythm Association. Eur Heart J 2014;35:1466-78.

[0084] 3. Parameswaran R, Al-Kaisey AM, Kalman JM. Catheter ablation for atrial fibrillation: current indications and evolving technologies. Nat Rev Cardiol 2021;18:210-25.

[0085] 4. Berruezo A, Tamborero D, Mont L, Benito B, Tolosana JM, Sitges M, et al. Preprocedural predictors of atrial fibrillation recurrence after circumferential pulmonary vein ablation. Eur Heart J 2007;28:836^1.

[0086] 5. Li K, Xu C, Zhu X, Wang X, Ye P, Jiang W, et al. Multi-centre, prospective randomized comparison of three different substrate ablation strategies for persistent atrial fibrillation. EP Eur 2023;25:euad090.

[0087] 6. Marcon L, Bergonti M, Spera F, Saenen J, Huybrechts W, Miljoen H, et al. Dynamic changes of left atrial substrate over time following pulmonary vein isolation: the Progress-AF study. EP Eur 2023; 25:euad299.

[0088] 7. Vlachos K, Efremidis M, Letsas KP, Bazoukis G, Martin R, Kalafateli M, et al. Low- voltage areas detected by high-density electroanatom ical mapping predict recurrence after ablation for paroxysmal atrial fibrillation. J Cardiovasc Electrophysiol 2017;28:1393-402.

[0089] 8. Bakker JM de. Electrogram recording and analyzing techniques to optimize selection of target sites for ablation of cardiac arrhythmias. Pacing Clin Electrophysiol 2019;42: 1503- 16.

[0090] 9. Yamaguchi T, Fukui A, Node K. Bipolar Voltage Mapping for the Evaluation of Atrial Substrate: Can We Overcome the Challenge of Directionality? J Atr Fibrillation 2019; 11:2116.

[0091] 10. Jadidi AS, Lehrmann H, Keyl C, Sorrel J, Markstein V, Minners J, et al. Ablation of Persistent Atrial Fibrillation Targeting Low- Voltage Areas With Selective Activation Characteristics. Circ Arrhythm Electrophysiol 2016; 9:e002962.

[0092] 11. Shaw D, Davis CH. Entropy and information: A multidisciplinary overview. J Am Soc Inf Sci 1983;34:67-74. 12. Mateos DM, Guevara Erra R, Wennberg R, Perez Velazquez JL. Measures of entropy and complexity in altered states of consciousness. Cogn Neurodyn 2018;12:73-84.

[0093] 13. Wu KC, Chrispin J. More Than Meets the Eye. JACC Cardiovasc Imaging 2022;15:793-5.

[0094] 14. Ng J, Borodyanskiy Al, Chang ET, Villuendas R, Dibs S, Kadish AH, et al. Measuring the Complexity of Atrial Fibrillation Electrograms. J Cardiovasc Electrophysiol 2010;21 :649- 55.

[0095] 15. Ganesan AN, Kuklik P, Lau DH, Brooks AG, Baumert M, Lim WW, et al. Bipolar Electrogram Shannon Entropy at Sites of Rotational Activation. Circ Arrhythm Electrophysiol American Heart Association; 2013;6:48-57.

[0096] 16. Hwang M, Song J-S, Lee Y-S, Li C, Shim EB, Pak H-N. Electrophysiological Rotor Ablation in In-Silico Modeling of Atrial Fibrillation: Comparisons with Dominant Frequency, Shannon Entropy, and Phase Singularity. PLOS ONE Public Library of Science; 2016;11:e0149695.

[0097] 17. Pratola C, Baldo E, Notarstefano P, Toselli T, Ferrari R. Radiofrequency Ablation of Atrial Fibrillation: Is the Persistence of All Intraprocedural Targets Necessary for Long-Term Maintenance of Sinus Rhythm? Circulation 2008;117:136-43.

[0098] 18. NeicA, Gsell MAF, Karabelas E, Prassl AJ, Plank G. Automating image-based mesh generation and manipulation tasks in cardiac modeling workflows using Meshtool. SoftwareX 2020;11: 100454.

[0099] 19. Shannon CE. A mathematical theory of communication. Bell Syst Tech J 1948;27:379-423.

[0100] 20. Rivolta MW. Information Theory and Fetal Heart Rate Variability Analysis. In: Pani D, ed. Innovative Technologies and Signal Processing in Perinatal Medicine: Volume 2 Cham: Springer Nature Switzerland; 2024. p. 171-88.

[0101] 21. Ribeiro M, Henriques T, Castro L, Souto A, Antunes L, Costa-Santos C, et al. The Entropy Universe. Entropy Multidisciplinary Digital Publishing Institute; 2021;23:222.

[0102] 22. Ganesan AN, Kuklik P, Gharaviri A, Brooks A, Chapman D, Lau DH, et al. Origin and Characteristics of High Shannon Entropy at the Pivot of Locally Stable Rotors: Insights from Computational Simulation. PLOS ONE Public Library of Science; 2014;9:e110662.

[0103] 23. Manikandan MS, Soman KP. A novel method for detecting R-peaks in electrocardiogram (ECG) signal. Biomed Signal Process Contra / 2012;7:118-28. 24. Nicolet JJC, Restrepo J F, Schlotthauer G. Classification of intracavitary electrograms in atrial fibrillation using information and complexity measures. Biomed Signal Process Control 2020; 57 : 101753.

[0104] 25. Rostaghi M, Azami H. Dispersion Entropy: A Measure for Time-Series Analysis. IEEE Signal Process Lett 2016;23:610-4.

[0105] 26. Chen W, Wang Z, Xie H, Yu W Characterization of Surface EMG Signal Based on Fuzzy Entropy. IEEE Trans Neural Syst Rehabil Eng 2007;15:266-72.

Claims

Claims1. A system for monitoring and evaluating electrogram signals representing electric activities of a heart chamber by computing the entropy of the electrogram signals, said system comprising:• a signal input that is connected to a mapping catheter comprising at least one electrode pole for picking up electric potentials and generating electrogram signals from the picked up electric potentials, along with the 3D location of the catheter at the time of recording and• a signal processing and evaluation unit for processing and evaluating electrogram signals received at the signal input, wherein the signal processing and evaluation unit is configured to perform the following steps when an electrogram signal is received by the signal input:• reconstructing a three-dimensional mesh representation of said hearth chamber obtained from the navigation catheter in a atrium of said hearth chamber by composing vertices and triangles, wherein the resolution varies according to the number of triangles, the accuracy of the exploration and the exporting procedure,• setting a number of vertices per patient-test between 4000 and 6000,• down-sampling or up-sampling of the mesh in those cases in which the number of vertices in the original map was smaller of that settled number• down-sampling of the mesh by setting a value of 5000 vertices per patient with a tolerance of ± 100 vertices,• up-sampling in those cases in which the number of vertices in the original map was smaller than 5000,• preparing voltage maps obtained from original and down-sampled meshes and bipolar EGMs from which entropy is computed.

2. The system of claim 1 , wherein the down-sampling was carried out through a source software which• reduces mesh resolution by initially collapsing all edges smaller than a specified minimum value,• subsequently, said source software divides edges larger than the maximum edge length.

3. The system according to any claims 1-2, wherein the procedure for preparing the voltage maps comprises: determining a vector that is the normal to the mesh at each vertex; generating a sphere of empirically chosen radius with its center located at the vertex, associating to the vertex only those EGMs collected at positions inside the sphere, defining the candidate EGMs; selecting among the candidate EGMs, only those within a predefined distance from the normal; acquiring the range of voltage amplitudes on the EGMs at each selected neighboring points and the average of the amplitude range of all neighbors’ vertices as the voltage range of the voltage map determining the voltage map by computing for each vertex v of the mesh from the range of voltage amplitudes on the EGMs at each selected neighboring points and the average of the amplitude range of all neighbors’ vertices.

4. The system according to any claim 3, wherein the empirically chosen radius of the sphere with its center located at the vertex is selected between 6 and 8 mm and the predefined distance from the normal associated to the vertex is selected between 1.5 and 2.5 mm.

5. The system according to claim 4, wherein the computation of the entropy was carried out from the probability distribution of the voltage map, that is the amplitude range values associated to each vertex of the mesh.

6. The system according to claim 5, wherein the distribution of the voltage map is calculated as a number of vertex of voltage within a bin of a multiple w of a given voltage exemplified as a set of histogram of width w and to define its entropy as the discrete entropy H of a quantization of said voltage map;7. The system according to claim 6, wherein the entropy results as formulation expressed as a sum over all bins of the histogram is:where w is the width of each bin (100 a.u. correspondent to 0.3 mv, with conversion a factor of 0.003 mV / a.u.), whereas I = {1, ..., i} is the set comprising all bins of the histogram with cardinality I = #1.

8. A non-transitory computer readable medium for use in a system for monitoring and evaluating electrogram signals representing electric activities of a heart chamber according to claim 1, comprising a signal input (22) that is connected to a mapping catheter comprising at least one electrode pole (18) for picking up electric potentials and a signal processing and evaluation unit for processing and evaluating electrogram signals received at the signal input (22), wherein said non-transitory computer readable medium comprises steps for computing the entropy of the electrogram signals, by generating electrogram signals from the picked up electric potentials, along with the 3D location of the catheter at the time of recording by performing the processing steps when an electrogram signal is received by the signal input (22), characterized in that• said non-transitory computer readable medium reconstructs a three-dimensional mesh representation of said hearth chamber obtained from the navigation catheter in a atrium of said hrarth chamber by composing vertices and triangles, wherein the resolution varies according to the number of triangles, the accuracy of the exploration and the exporting procedure,• setting a number of vertices per patient-test between 4000 and 6000,• down-sampling or up-sampling of the mesh in those cases in which the number of vertices in the original map was smaller of that settled number,• down-sampling of the mesh by setting a value of 5000 vertices per patient with a tolerance of ± 100 vertices,• up-sampling in those cases in which the number of vertices in the original map was smaller than 5000,• said non-transitory computer readable medium prepares voltage maps obtained from original and down-sampled meshes and bipolar EGMs from which entropy was is computed.

9. The non-transitory computer readable medium of claim 7, wherein the down-sampling is carried out through a source software which reduces mesh resolution by initially collapsing all edges smaller than a specified minimum value, and subsequently, said source software divides edges larger than the maximum edge length.

10. The non-transitory computer readable medium to any claims 7-8, wherein the procedure for preparing the voltage maps comprises:• determining a vector that is the normal to the mesh at each vertex;• generating a sphere of empirically chosen radius with its center located at the vertex,• associating to the vertex only those EGMs collected at positions inside the sphere, defining the candidate EGMs;• selecting among the candidate EGMs, only those within a predefined distance from the normal;• acquiring the range of voltage amplitudes on the EGMs at each selected neighboring points and the average of the amplitude range of all neighbors’ vertices as the voltage range of the voltage map;• determining the voltage map by computing for each vertex v of the mesh the range of voltage amplitudes on the EGMs and the average of the amplitude range of all neighbors’ vertices,11. The non-transitory computer readable medium of claim 10, wherein the empirically chosen radius of the sphere with its center located at the vertex is selected between 6 and 8 mm and the predefined distance from the normal associated to the vertex is selected between 1.5 and 2.5 mm.

12. The non-transitory computer readable medium according to claim 10, wherein the computation of the entropy was carried out from the probability distribution of the voltage map, that is the amplitude range values associated to each vertex of the mesh.

13. The non-transitory computer readable medium according to claim 12, wherein the distribution of the voltage map is calculated as a number of vertex of voltage within a bin of a multiple w of a given voltage exemplified as a set of histogram of width w and to define its entropy as the discrete entropy H of a quantization of said voltage map.

14. The non-transitory computer readable medium according to claim 13, wherein the entropy results as formulation expressed as a sum over all bins of the histogram is:where w is the width of each bin (100 a.u. correspondent to 0.3 mv, with conversion a factor of 0.003 mV / a.u.), whereas l= {1 ,... ,i} is the set comprising all bins of the histogram with cardinality l=#l.

Images