Catalina Tobón

Modeling atrial fiber orientation in patient-specific geometries: a semi-automatic rule-based approach

Atrial myofiber orientation is complex and has multiple discrete layers and bundles. A novel robust semi-automatic method to incorporate atrial anisotropy and heterogeneities into patient-specific models is introduced. The user needs to provide 22 distinct seed-points from which a network of auxiliary lines is constructed. These are used to define fiber orientation and myocardial bundles. The method was applied to 14 patient-specific volumetric models derived from CT, MRI and photographic data. Initial electrophysiological simulations show a significant influence of anisotropy and heterogeneity on the excitation pattern and P-wave duration (20.7% shortening). Fiber modeling results show good overall correspondence with anatomical data. Minor modeling errors are observed if more than four pulmonary veins exist in the model. The method is an important step towards creating realistic patient-specific atrial models for clinical applications.

A Three-Dimensional Human Atrial Model with Fiber Orientation. Electrograms and Arrhythmic Activation Patterns Relationship

The most common sustained cardiac arrhythmias in humans are atrial tachyarrhythmias, mainly atrial fibrillation. Areas of complex fractionated atrial electrograms and high dominant frequency have been proposed as critical regions for maintaining atrial fibrillation; however, there is a paucity of data on the relationship between the characteristics of electrograms and the propagation pattern underlying them. In this study, a realistic 3D computer model of the human atria has been developed to investigate this relationship. The model includes a realistic geometry with fiber orientation, anisotropic conductivity and electrophysiological heterogeneity. We simulated different tachyarrhythmic episodes applying both transient and continuous ectopic activity. Electrograms and their dominant frequency and organization index values were calculated over the entire atrial surface. Our simulations show electrograms with simple potentials, with little or no cycle length variations, narrow frequency peaks and high organization index values during stable and regular activity as the observed in atrial flutter, atrial tachycardia (except in areas of conduction block) and in areas closer to ectopic activity during focal atrial fibrillation. By contrast, cycle length variations and polymorphic electrograms with single, double and fragmented potentials were observed in areas of irregular and unstable activity during atrial fibrillation episodes. Our results also show: 1) electrograms with potentials without negative deflection related to spiral or curved wavefronts that pass over the recording point and move away, 2) potentials with a much greater proportion of positive deflection than negative in areas of wave collisions, 3) double potentials related with wave fragmentations or blocking lines and 4) fragmented electrograms associated with pivot points. Our model is the first human atrial model with realistic fiber orientation used to investigate the relationship between different atrial arrhythmic propagation patterns and the electrograms observed at more than 43000 points on the atrial surface.

The Relative Role of Refractoriness and Source–Sink Relationship in Reentry Generation during Simulated Acute Ischemia

During acute myocardial ischemia, reentrant episodes may lead to ventricular fibrillation (VF), giving rise to potentially mortal arrhythmias. VF has been traditionally related to dispersion of refractoriness and more recently to the source–sink relationship. Our goal is to theoretically investigate the relative role of dispersion of refractoriness and source–sink mismatch in vulnerability to reentry in the specific situation of regional myocardial acute ischemia. The electrical activity of a regionally ischemic tissue was simulated using a modified version of the Luo-Rudy dynamic model. Ischemic conditions were varied to simulate the time-course of acute ischemia. Our results showed that dispersion of refractoriness increased with the severity of ischemia. However, no correlation between dispersion of refractoriness and the width of the vulnerable window was found. Additionally, in approximately 50% of the reentries, unidirectional block (UDB) took place in cells completely recovered from refractoriness. We examined patterns of activation after premature stimulation and they were intimately related to the source–sink relationship, quantified by the safety factor (SF). Moreover, the isoline where the SF dropped below unity matched the area where propagation failed. It was concluded that the mismatch of the source–sink relationship, rather than solely refractoriness, was the ultimate cause of the UDB leading to reentry. The SF represents a very powerful tool to study the mechanisms responsible for reentry.

Dynamic Approximate Entropy Electroanatomic Maps Detect Rotors in a Simulated Atrial Fibrillation Model

There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.

Dominant frequency and organization index maps in a realistic three-dimensional computational model of atrial fibrillation

AIMS To study, using simulation, the spectral characteristics of different patterns of atrial fibrillation (AF) at high spatial resolution. Dominant frequency (DF) and organization index (OI) maps have been used to approximate the location of the focal source of high frequency during AF events. METHODS AND RESULTS A realistic three-dimensional model of the human atria that includes fibre orientation, electrophysiological heterogeneity, and anisotropy was implemented. The cellular model was modified to simulate electrical remodelling. More than 43 000 electrograms were calculated on the surface, and were processed to reconstitute the DF and OI maps. Atrial fibrillation episodes were triggered by a source of transitory and of continuous activity (both with a cycle length of 130 ms) in five different locations. The maps obtained during the AF events triggered by transitory foci did not show areas with high DF or OI values. When continuous foci were applied, the DF maps show ample zones with high values in the atrium where the focus was applied; while OI maps display smaller areas with high values, always within the areas of high DF and, in three of five locations, this high-value area was located at the site of focus application and at the nearby area. In the other two locations, the area presenting the highest OI values is small and located at the site of focus application, which allowed its precise localization. CONCLUSION Organization index maps provide a better approximation than DF maps for the localization of ectopic sources of high frequency and continuous activity during episodes of simulated AF in remodelled tissue.

Vulnerability for reentry in a three dimensional model of human atria: a simulation study

Atrial tachycardias are the most common cardiac arrhythmias in clinical practice, which induce changes in atrial properties that help to perpetuate them. These changes are called “atrial remodeling”. Recent studies have shown that rapid ectopic activity principally on the pulmonary veins can trigger reentrant mechanisms and lead to atrial tachycardias. However, the influences of ectopic foci location, the number of ectopic beats and its frequency on the likelihood of triggering reentries are not well known. In this work the effects of electrical remodeling were incorporated in an atrial cell model and integrated in a three-dimensional model of human atria, to develop a study of vulnerability for reentries. To carry out the study, an ectopic beat and a burst of six ectopic beats at two different frequencies were applied in six different locations in the atria. The results show greater vulnerability in the left pulmonary veins when we applied a single ectopic beat. When we increase the number of ectopic beats to six, a greater width of the vulnerable window was observed when ectopic focus frequency was high. The location, the number of ectopic beats and their frequency affect the vulnerability for reentry.

Reentrant mechanisms triggered by ectopic activity in a three-dimensional realistic model of human atrium. a computer simulation study

Atrial fibrillation (AF) is the most common tachiarrhythmia. The pulmonary veins (PVs) have the predominant source of ectopic activity involved in the initiation of AF. Atrial remodelling, due to rapid and irregular activation during AF, leaves the tissue vulnerable to reentries. In this work the effects of electrical remodelling were incorporated in a 3D anisotropic model of human atrium. An ectopic focus was applied near to PVs. Electrograms were computed in simulated-electrodes in back wall of left atrial. The ectopic focus induced a figure-of-eight reentry that degenerated to mother rotor, after collisions and wave breaks were observed. Electrograms were more irregular during figure-of-eight reentry and collisions than during rotor activity. Spectral analysis shows multiple frequency peaks, as a consequence of changes of reentrant patterns. Dominant frequency was similar in all measuring points.

Effect of the electrograms density in detecting and ablating the tip of the rotor during chronic atrial fibrillation: an in silico study

AIMS Identification in situ of arrhythmogenic mechanisms could improve the rate of ablation success in atrial fibrillation (AF). Our research group reported that rotors could be located through dynamic approximate entropy (DApEn) maps. However, it is unknown how much the spatial resolution of catheter electrodes could affect substrates localization. The present work looked for assessing the electrograms (EGMs) spatial resolution needed to locate the rotor tip using DApEn maps. METHODS AND RESULTS A stable rotor in a two-dimensional computational model of human atrial tissue was simulated using the Courtemanche electrophysiological model and implementing chronic AF features. The spatial resolution is 0.4 mm (150 × 150 EGM). Six different lower resolution arrays were obtained from the initial mesh. For each array, DApEn maps were constructed using the inverse distance weighting (IDW) algorithm. Three simple ablation patterns were applied. The full DApEn map detected the rotor tip and was able to follow the small meander of the tip through the shape of the area containing the tip. Inverse distance weighting was able to reconstruct DApEn maps after applying different spatial resolutions. These results show that spatial resolutions from 0.4 to 4 mm accurately detect the rotor tip position. An ablation line terminates the rotor only if it crosses the tip and ends at a tissue boundary. CONCLUSION A previous work has shown that DApEn maps successfully detected simulated rotor tips using a high spatial resolution. In this work, it was evinced that DApEn maps could be applied using a spatial resolution similar to that available in commercial catheters, by adding an interpolation stage. This is the first step to translate this tool into medical practice with a view to the detection of ablation targets.

Atrial Rotor Dynamics Under Complex Fractional Order Diffusion

The mechanisms of atrial fibrillation (AF) are a challenging research topic. The rotor hypothesis states that the AF is sustained by a reentrant wave that propagates around an unexcited core. Cardiac tissue heterogeneities, both structural and cellular, play an important role during fibrillatory dynamics, so that the ionic characteristics of the currents, their spatial distribution and their structural heterogeneity determine the meandering of the rotor. Several studies about rotor dynamics implement the standard diffusion equation. However, this mathematical scheme carries some limitations. It assumes the myocardium as a continuous medium, ignoring, therefore, its discrete and heterogeneous aspects. A computational model integrating both, electrical and structural properties could complement experimental and clinical results. A new mathematical model of the action potential propagation, based on complex fractional order derivatives is presented. The complex derivative order appears of considering the myocardium as discrete-scale invariant fractal. The main aim is to study the role of a myocardial, with fractal characteristics, on atrial fibrillatory dynamics. For this purpose, the degree of structural heterogeneity is described through derivatives of complex order γ = α + jβ. A set of variations for γ is tested. The real part α takes values ranging from 1.1 to 2 and the imaginary part β from 0 to 0.28. Under this scheme, the standard diffusion is recovered when α = 2 and β = 0. The effect of γ on the action potential propagation over an atrial strand is investigated. Rotors are generated in a 2D model of atrial tissue under electrical remodeling due to chronic AF. The results show that the degree of structural heterogeneity, given by γ, modulates the electrophysiological properties and the dynamics of rotor-type reentrant mechanisms. The spatial stability of the rotor and the area of its unexcited core are modulated. As the real part decreases and the imaginary part increases, simulating a higher structural heterogeneity, the vulnerable window to reentrant is increased, as the total meandering of the rotor tip. This in silico study suggests that structural heterogeneity, described by means of complex order derivatives, modulates the stability of rotors and that a wide range of rotor dynamics can be generated.

Reconstruction of Multi Spatial Resolution Feature Maps on a 2D Model of Atrial Fibrillation: Simulation Study

Catheter ablation is a technique used as treatment for atrial fibrillation, this procedure is guided using 3D electro anatomic mapping systems. Ablation is one of the treatments for AF whose effectiveness depend on the location of the rotor tip and this depend of the quality of mapping obtained from a re-duced set of real signals. This paper presents a comparison study between three approaches for reconstruction of features maps of a 2D model of simulated atrial fibrillation. The model was char-acterized using the mean, Shannon entropy and approximate entropy of the electrograms (EGM). The model is made up of 22500 EGM and reductions of 75%, 93.5% and 97.3% in the spatial resolution of the model was conducted. Thereupon a reconstruction of the feature maps was realized using inverse distance weighted (IDW), inverse distance weighted-median filter (IDW-MF) and backpropagation artificial neural networks (BPANN), the performance of the techniques was analyzed using the root mean square error (RMSE) and the peak signal to noise ratio (PSNR). IDW shows a general RSME of 4.2% and a PSNR of 27.5dB, IDW-MF exhibited a RSME of 17.5% and a PSNR of 21.8 dB, finally BPANN shows a RSME of 9% and PSNR of 22.8 dB. IDW shows the best performance at any degree of reduction while IDW-MF represent the best approach for Shannon entropy and mean maps reconstruction and IDW has the best perfor-mance for approximate entropy maps reconstruction.