Granger Causality-Based Analysis for Classification of Fibrillation Mechanisms and Localization of Rotational Drivers

Abstract

Background: The mechanisms sustaining myocardial fibrillation remain disputed, partly due to a lack of mapping tools that can accurately identify the mechanism with low spatial resolution clinical recordings. Granger causality (GC) analysis, an econometric tool for quantifying causal relationships between complex time-series, was developed as a novel fibrillation mapping tool and adapted to low spatial resolution sequentially acquired data.

Methods: Ventricular fibrillation (VF) optical mapping was performed in Langendorff-perfused Sprague-Dawley rat hearts (n=18), where novel algorithms were developed using GC-based analysis to (1) quantify causal dependence of neighboring signals and plot GC vectors, (2) quantify global organization with the causality pairing index, a measure of neighboring causal signal pairs, and (3) localize rotational drivers (RDs) by quantifying the circular interdependence of neighboring signals with the circular interdependence value. GC-based mapping tools were optimized for low spatial resolution from downsampled optical mapping data, validated against high-resolution phase analysis and further tested in previous VF optical mapping recordings of coronary perfused donor heart left ventricular wedge preparations (n=12), and adapted for sequentially acquired intracardiac electrograms during human persistent atrial fibrillation mapping (n=16).

Results: Global VF organization quantified by causality pairing index showed a negative correlation at progressively lower resolutions (50% resolution: P=0.006, R²=0.38, 12.5% resolution, P=0.004, R²=0.41) with a phase analysis derived measure of disorganization, locations occupied by phase singularities. In organized VF with high causality pairing index values, GC vector mapping characterized dominant propagating patterns and localized stable RDs, with the circular interdependence value showing a significant difference in driver versus nondriver regions (0.91±0.05 versus 0.35±0.06, P=0.0002). These findings were further confirmed in human VF. In persistent atrial fibrillation, a positive correlation was found between the causality pairing index and presence of stable RDs (P=0.0005,R²=0.56). Fifty percent of patients had RDs, with a low incidence of 0.9±0.3 RDs per patient.

Conclusions: GC-based fibrillation analysis can measure global fibrillation organization, characterize dominant propagating patterns, and map RDs using low spatial resolution sequentially acquired data.

Keywords: algorithm; atrial fibrillation; catheter ablation; incidence; ventricular fibrillation.

Figure 1.

Novel tools for measuring organization and localizing areas with rotational drivers (RDs). A, An example simplified 3×3 pixel grid with corresponding optical mapping signals below showing Granger causality (GC) vectors between signals with the strongest temporal dependence. B, Causality pairing index for data in (A) showing 4 pixel pairs with causal temporal dependence of propagation (corresponding to the GC vectors, shaded in color). Causality pairing index (CPI) was defined as the pixel pairs with causal dependence divided by all possible pixel pairings (excluding self-pairs, shaded in gray) in a data set. C, An example dominant frequency map showing all the dominant frequencies driving fibrillation in the left ventricular (LV) anterior wall. The histogram below plots these frequencies. The frequency dominance index (FDI) is defined as the proportion of area occupied by the largest organized dominant frequency area in the global fibrillatory spectrum divided by the total area of all regions with a defined dominant frequency (black arrow). D, Circulatory interdependence value (CIV) for 3 examples. For each GC vector (dark blue), a cross-product virtual 3-dimensional (3D) vector was generated (green arrow) relative to vector to the center (dashed black line). The resulting virtual 3D vector was binarized as pointing up or down as shown in example for vector a and vector b. CIV was calculated on a scale of 0 to 1 by subtracting the number of vectors pointing down from no of vectors pointing up divided by total number of vectors. The 3 examples above demonstrate expected values for example 1: stable RD, example 2: random propagation, example 3: linearly propagating wavefront. With this method areas of rotational activity will give a CIV value closer to 1.

Figure 2.

The causality pairing index (CPI) and frequency dominance index (FDI) can characterize the global organization of fibrillation at low spatial resolution. Graphs showing negative correlation between a measure of disorganization and instability, the number of locations occupied by nonsignificant short-lived phase singularities (PSs; locations occupied by PSs [l_ps]) and CPI (A) and l_ps and FDI (B), and no correlation between l_ps and Shannon entropy (Sh_en; C), at decreasing resolutions of 50% (left), 25% (middle), and 12.5% (right) of full spatial resolution from optical mapping of rat ventricular fibrillation. Nonsignificant PSs were defined as PSs with <2 rotations, and rotational drivers were defined as >2 rotations. Linear regression analysis, F test, coefficients of determination–R² and P values are indicated, n=18.

Figure 3.

Quantifying global organization in fibrillation infers the likely underlying mechanism. Representative data sets of rat ventricular fibrillation selected from organizational analysis categorization of fibrillation as low (left), intermediate (middle), and organized (right) from Figure 2. A, Rotational driver (RD) heat map showing incidence of significant RDs (≥2 rotations). B, The respective global dominant frequency histogram with frequency dominance index (FDI) value and (C) graphs showing characterization of RD for each data set, l_ps–number of locations/pixels occupied by nonsignificant phase singularity [PS] with <2rotation, l_r–number of locations occupied by significant RDs with ≥2 rotations, max [n_r]–maximum rotations for a single significant RDs. LV indicates left ventricular.

Figure 4.

Granger causality (GC) mapping can be used for analyzing fibrillation data. An example GC vector map of an organized rat ventricular fibrillation (VF) heart showing neighboring regions with causal interdependence (A) and zoomed localization of a driver region showing a signature continuous circular interdependence of neighboring GC vectors (B), with correlating optical mapping signals from the driver region showing repetitive sequential activation (C). Data analyzed at 25% of full spatial resolution, correlating rotational driver heat map in Figure 5—heart C. LV indicates left ventricular.

Figure 5.

Granger causality (GC) vector mapping can reliably localize and differentiate between areas harboring rotational drivers (RDs) and areas without RDs in ventricular fibrillation (VF). A, RD heat maps constructed from 3 organized rat VF data sets; heart A, B, and C (left) and the correlating limited coverage GC vector maps showing driver regions with continuous circular interdependence of GC vectors with 1-directional flow of GC vectors (blue) and nondriver regions showing no circular interdependence of GC vectors. Correlating circular interdependence value (CIV) values between 0 (minimum) and maximum (1) for each respective region listed below. Data analyzed at 25% of full spatial resolution. B, A graph showing CIV value of driver regions vs nondriver regions with sample GC maps (left, heart C). t test, n=3, P=0.0002. LV indicates left ventricular.

Figure 6.

Granger causality (GC)–based analysis of human ventricular fibrillation (VF) quantifies global fibrillatory organization and maps underlying mechanism. A, Graphs showing negative correlation between locations occupied by phase singularities and causality pairing index (CPI) at decreasing spatial resolution. B, Full spatial resolution rotational driver (RD) heat maps in VF of left ventricular (LV) wedge epicardial recordings with corresponding GC vector maps at 25% spatial resolution from 2 representative hearts above (heart A and Heart B). Linear regression analysis, F test, coefficients of determination–R² and P values are indicated, data from 33 VF recordings, n=12. CIV indicates circular interdependence value.

Figure 7.

Granger causality (GC) vector maps generated from intracardiac electrograms acquired with multipolar catheters. A, AFocusII mapping catheter 3-dimensional electrode (red dot) spatial configuration with corresponding bipoles (blue triangle) within the atrium (left). Electrograms processing for GC analysis (right)—(1) Sample raw bipolar electrograms, (2) 40–250 Hz bandpass filtering and low-pass filtering of signals <25 Hz, (3) signal rectification, (4) downsampling. B, Representative GC vector map for a paced rhythm mapped by the catheter (left) and correlating raw and rectified electrograms (right). CIV indicates circular interdependence value.

Figure 8.

Granger causality (GC) vector maps can localize rotational drivers (RDs) from intracardiac electrograms acquired with a multipolar catheter. Representative GC vector maps for an RD-positive site with high circular interdependence value (CIV) value (top) and RD negative site with low CIV value (bottom), corresponding (B) CIV values over time and (C) electrograms. *Dashed line=cutoff for a RD-positive site. D, Atrial fibrillation (AF) mapping data from 16 persistent AF patients showing the number of kernels and windows with RDs. E, Graph showing the positive correlation between causality pairing index (CPI) and number of RDs. Linear regression analysis, F test, coefficients of determination–R² and P value is indicated, n=16. Kernal denotes a single locational AFocus electrogram recording; Window denotes 8-s overlapping electrogram time windows with a window-shift of 1 s. PsAF indicates persistent AF.