Identification of Cardiac Rhythm Features by Mathematical Analysis of Vector Fields

Abstract

Automated techniques for locating cardiac arrhythmia features are limited, and cardiologists generally rely on isochronal maps to infer patterns in the cardiac activation sequence during an ablation procedure. Velocity vector mapping has been proposed as an alternative method to study cardiac activation in both clinical and research environments. In addition to the visual cues that vector maps can provide, vector fields can be analyzed using mathematical operators such as the divergence and curl. In the current study, conduction features were extracted from velocity vector fields computed from cardiac mapping data. The divergence was used to locate ectopic foci and wavefront collisions, and the curl to identify central obstacles in reentrant circuits. Both operators were applied to simulated rhythms created from a two-dimensional cellular automaton model, to measured data from an in situ experimental canine model, and to complex three-dimensional human cardiac mapping data sets. Analysis of simulated vector fields indicated that the divergence is useful in identifying ectopic foci, with a relatively small number of vectors and with errors of up to 30 degrees in the angle measurements. The curl was useful for identifying central obstacles in reentrant circuits, and the number of velocity vectors needed increased as the rhythm became more complex. The divergence was able to accurately identify canine in situ pacing sites, areas of breakthrough activation, and wavefront collisions. In data from human arrhythmias, the divergence reliably estimated origins of electrical activity and wavefront collisions, but the curl was less reliable at locating central obstacles in reentrant circuits, possibly due to the retrospective nature of data collection. The results indicate that the curl and divergence operators applied to velocity vector maps have the potential to add valuable information in cardiac mapping and can be used to supplement human pattern recognition.

Automated Classification and Identification of Slow Wave Propagation Patterns in Gastric Dysrhythmia

“…Other techniques have been used to analyze HR cardiac mapping studies 10, 14, 35, 36 . However these methods could not be directly translated to the GI field due to the significantly different characteristics in the spatio-temporal patterns, time course and signals between cardiac and GI electrophysiology 9, 8 .…”

An Improved Method for the Estimation and Visualization of Velocity Fields from Gastric High-Resolution Electrical Mapping

“…Velocity estimation from the isochronal maps generated from HR mapping can provide a complimentary qualitative and quantitative view of the data on the slow wave propagation patterns, particularly in dysrhythmic states. Mathematical operations on the velocity vectors such as dot product, cross product, curl and divergence have been found to yield valuable information about the underlying electrical activity in cardiac electro-physiology [24]. In cardiology, it has been shown that the atrial electrogram fractionation [25], a feature in atrial fibrillation, occurs in regions of slow conduction.…”

Time-Delay Mapping of High-Resolution Gastric Slow-Wave Activity

“…The velocity was calculated using the following linear model (2) at each of the subset reference electrode grids [25] (Fig. 1A).…”

“…This approach is computationally less intensive compared to the ptraditional approach and is able to quantitatively assess key parameters such as velocity and amplitude profiles of slow wave activity in a reliable manner, without manual intervention. Similar methods have been used in cardiac electrophysiology [22–25], but this is the first time this method has been adapted and applied for GI HR slow wave recording analysis, requiring important modifications to account for multiple wavefronts in the mapped field.…”

“…This technique was inspired by, and originated from, the cardiac field [22–25]. It was anticipated that these techniques would be reliable and be substantially more efficient when applied to large data sets, enabling rapid and effective analytics of slow wave propagation characteristics.…”