Cardiac arrhythmia in the upper chamber of the heart (atrial fibrillation) can be cured by burning. Physicians burn very small pieces of abnormal tissue. It is important to know where to burn. The investigators propose a new way to find out where to burn. The investigators will use a new way to analyze electrical signals inside the heart and build a new electric map. The study may lead to the development of new technology. In the future, novel technology may increase the success rate and the number of cured atrial fibrillation patients. This study is a retrospective study of data collected during routine clinical care: atrial fibrillation ablations. The investigators will compare intracardiac electrograms and atrial activation maps in patients who had successful ablation outcomes (no recurrence within 1 year) and those who experienced a recurrence of arrhythmia within 1 year after the procedure.

Atrial fibrillation (AF) ablation is an important treatment strategy, potentially capable of curing AF. However, there is a variable degree of success of the persistent AF ablation procedure. Therefore, it is necessary to improve the success rate of persistent AF ablation. To improve the success rate of persistent AF ablation, the investigators proposed a novel analytical approach to AF mapping. Analysis of intracardiac electrograms (EGMs) is the key component of AF mapping. In the past, several approaches to atrial EGM analysis have been developed, aiming to help guide AF ablation beyond pulmonary vein isolation (PVI). However, none (except PVI) have been established to guide the AF catheter ablation procedure. The most widely used approach for AF ablation is an empiric, anatomic AF ablation approach (PVI). Previously tested (and ultimately failed) methods included complex fractionated atrial electrogram (CFAÉ), dominant frequency (DF) mapping, activation (FIRM) mapping, and fibrosis-detected-by-CMR-mapping AF ablation. A novel solution to the known AF mapping problem is necessary to improve AF ablation outcomes. Successful completion of the proposed project will suggest a path to improve the success rate of persistent AF ablation, which is crucially necessary for further progress in the cardiac electrophysiology field. The investigators proposed a novel analytical approach. The investigators will apply phase-aligned spectral filtering to AF atrial EGM mapping data to identify spatially structured dynamic components and thus identify AF ablation targets. Spectral filtering is an efficient dimension reduction for high-dimensional time series, which has not been applied to AF mapping data analysis. Such an approach assumes that the observed spatiotemporal data (AF EGM mapping data) represent superimposed lower-rank smooth oscillations and movements from a dynamic generative system (AF ablation target) mixed with higher-rank random noises. Separating the signals from noises is essential for us to locate and understand these lower-rank dynamic systems. It could be that such a lower-rank dynamic system has multiple independent components corresponding to different trends or functionalities of the system. The investigators propose a novel framework for identifying lower-rank dynamics and their components embedded in a high-dimensional spatiotemporal system (AF EGM map). It is based on a known statistical approach of structural decomposition and phase-aligned construction in the frequency domain, which has not been applied to AF EGM analysis.

Inclusion Criteria:

1. Records of patients with persistent AF who underwent pulmonary vein isolation (PVI) with any additional AF ablation strategy with available stored digital AF mapping data. Persistent AF is defined as AF lasting more than 7 days.
2. One/First AF ablation procedure (no prior atrial ablation procedures)
3. Documented complete pulmonary vein isolation at the end of the ablation
4. Available uniform, high-quality (as described below) clinical data required to detect AF recurrence during ≥ 1 year after ablation, and/or ECG monitoring (implantable loop recording or repeated long-term ECG monitoring via ECG patch or similar)

Exclusion Criteria:

1. Familial AF, AF as a syndrome in rare diseases (cardiomyopathies / WPW/ channelopathies).
2. Missing data of exposure (AF ablation map), outcome (definition of cases and controls), or covariates

Study design: a retrospective case-control study of patients who underwent persistent AF ablation at Cleveland Clinic. The goal of the case-control study is to identify differences in AF mapping (using the proposed novel analytical approach) and persistent AF ablation strategy between the successful and failed persistent AF ablation cases. The selection of cases and controls will pay special attention to well-documented and verified successful and complete pulmonary vein isolation, as failed PVI is a well-known cause of failed AF ablation procedures, but it is not the goal of this study.