Adaptive step ODE algorithms for the 3D simulation of electric heart activity with graphics processing units

Non-invasive estimation of atrial fibrillation driver position using long-short term memory neural networks and body surface potentials

BACKGROUND AND OBJECTIVE

Atrial Fibrillation (AF) is a supraventricular tachyarrhythmia that can lead to thromboembolism, hearlt failure, ischemic stroke, and a decreased quality of life. Characterizing the locations where the mechanisms of AF are initialized and maintained is key to accomplishing an effective ablation of the targets, hence restoring sinus rhythm. Many methods have been investigated to locate such targets in a non-invasive way, such as Electrocardiographic Imaging, which enables an on-invasive and panoramic characterization of cardiac electrical activity using recording Body Surface Potentials (BSP) and a torso model of the patient. Nonetheless, this technique entails some major issues stemming from solving the inverse problem, which is known to be severely ill-posed. In this context, many machine learning and deep learning approaches aim to tackle the characterization and classification of AF targets to improve AF diagnosis and treatment.

METHODS

In this work, we propose a method to locate AF drivers as a supervised classification problem. We employed a hybrid form of the convolutional-recurrent network which enables feature extraction and sequential data modeling utilizing labeled realistic computerized AF models. Thus, we used 16 AF electrograms, 1 atrium, and 10 torso geometries to compute the forward problem. Previously, the AF models were labeled by assigning each sample of the signals a region from the atria from 0 (no driver) to 7, according to the spatial location of the AF driver. The resulting 160 BSP signals, which resemble a 64-lead vest recording, are preprocessed and then introduced into the network following a 4-fold cross-validation in batches of 50 samples.

RESULTS

The results show a mean accuracy of 74.75% among the 4 folds, with a better performance in detecting sinus rhythm, and drivers near the left superior pulmonary vein (R1), and right superior pulmonary vein (R3) whose mean sensitivity bounds around 84%-87%. Significantly good results are obtained in mean sensitivity (87%) and specificity (83%) in R1.

CONCLUSIONS

Good results in R1 are highly convenient since AF drivers are commonly found in this area: the left atrial appendage, as suggested in some previous studies. These promising results indicate that using CNN-LSTM networks could lead to new strategies exploiting temporal correlations to address this challenge effectively.

Characterization of the Electrophysiological Characteristics of Chronic Atrial Fibrillation for Efficient Simulations

Atrial biophysical simulations have the potential to enhance outcomes by enabling the simulation of pharmacological and ablative strategies. However, the high computational times associated with such simulations render them unsuitable for diagnostic purposes. To address this challenge, discrete models such as cellular automata (CA) have been developed, which consider a finite number of states, thus significantly reducing computational times. Yet, there is a pressing need to determine whether CA can replicate pathological simulations with accuracy. The analysis of simulations under different degrees of electrical remodeling shows an expected increase of Action Potential Duration (APD) with the previous Diastolic Interval (DI) interval, indicating short-term memory of atrial cardiomyocytes: shorter APD0 provoked shorter APD+1, and previous DI has a similar effect on APD+1. Independent prediction using both APD0 and DI was found to provide a far better estimation of APD+1 values, compared to relying on DI alone (p<<0.01). Finally, the CA models were able to replicate reentrant patterns and cycle lengths of different states of atrial remodeling with a high degree of accuracy when compared to biophysical simulations. Overall, the use of atrial CA with short-term memory allows accurate reproduction of arrhythmic behavior in pathological tissue within a clinically relevant timeframe.Clinical Relevance- Discrete electrophysiological models simulate pathological self-sustained arrhythmias in diagnostic times.

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

Non-invasive Estimation of Atrial Fibrillation Driver Position With Convolutional Neural Networks and Body Surface Potentials

Atrial fibrillation (AF) is characterized by complex and irregular propagation patterns, and AF onset locations and drivers responsible for its perpetuation are the main targets for ablation procedures. ECG imaging (ECGI) has been demonstrated as a promising tool to identify AF drivers and guide ablation procedures, being able to reconstruct the electrophysiological activity on the heart surface by using a non-invasive recording of body surface potentials (BSP). However, the inverse problem of ECGI is ill-posed, and it requires accurate mathematical modeling of both atria and torso, mainly from CT or MR images. Several deep learning-based methods have been proposed to detect AF, but most of the AF-based studies do not include the estimation of ablation targets. In this study, we propose to model the location of AF drivers from BSP as a supervised classification problem using convolutional neural networks (CNN). Accuracy in the test set ranged between 0.75 (SNR = 5 dB) and 0.93 (SNR = 20 dB upward) when assuming time independence, but it worsened to 0.52 or lower when dividing AF models into blocks. Therefore, CNN could be a robust method that could help to non-invasively identify target regions for ablation in AF by using body surface potential mapping, avoiding the use of ECGI.

Atrial location optimization by electrical measures for Electrocardiographic Imaging

BACKGROUND

The Electrocardiographic Imaging (ECGI) technique, used to non-invasively reconstruct the epicardial electrical activity, requires an accurate model of the atria and torso anatomy. Here we evaluate a new automatic methodology able to locate the atrial anatomy within the torso based on an intrinsic electrical parameter of the ECGI solution.

METHODS

In 28 realistic simulations of the atrial electrical activity, we randomly displaced the atrial anatomy for ±2.5 cm and ±30° on each axis. An automatic optimization method based on the L-curve curvature was used to estimate the original position using exclusively non-invasive data.

RESULTS

The automatic optimization algorithm located the atrial anatomy with a deviation of 0.5 ± 0.5 cm in position and 16.0 ± 10.7° in orientation. With these approximate locations, the obtained electrophysiological maps reduced the average error in atrial rate measures from 1.1 ± 1.1 Hz to 0.5 ± 1.0 Hz and in the phase singularity position from 7.2 ± 4.0 cm to 1.6 ± 1.7 cm (p < 0.01).

CONCLUSIONS

This proposed automatic optimization may help to solve spatial inaccuracies provoked by cardiac motion or respiration, as well as to use ECGI on torso and atrial anatomies from different medical image systems.

A memory optimization method combined with adaptive time-step method for cardiac cell simulation based on multi-GPU

Cardiac electrophysiological simulation is a very complex computational process, which can be run on graphics processing unit (GPU) to save computational cost greatly. The use of adaptive time-step can further effectively speed up the simulation of heart cells. However, if the adaptive time-step method applies to GPU, it suffers synchronization problem on GPU, weakening the acceleration of adaptive time-step method. The previous work ran on a single GPU with the adaptive time-step to get only 1.5 times (× 1.5) faster than the fixed time-step. This study proposes a memory allocation method, which can effectively implement the adaptive time-step method on GPU. The proposed method mainly focuses on the stimulus point and potential memory arrangement in order to achieve optimal memory storage efficiency. All calculation is implemented on GPU. Large matrices such as potential are arranged in column order, and the cells on the left are stimulated. The Luo-Rudy passive (LR1) and dynamic (LRd) ventricular action potential models are used with adaptive time-step methods, such as the traditional hybrid method (THM) and Chen-Chen-Luo's (CCL) "quadratic adaptive algorithm" method. As LR1 is solved by the THM or CCL on a single GPU, the acceleration is × 34 and × 75 respectively compared with the fixed time-step. With 2 or 4 GPUs, the acceleration of the THM and CCL is × 34 or × 35 and × 73 or × 75, but it would decrease to × 5 or × 3 and × 20 or × 15 without optimization. In an LRd model, the acceleration reaches × 27 or × 85 as solved by the THM or CCL compared with the fixed time-step on multi-GPU with linear speed up increase versus the number of GPU. However, with the increase of GPUs number, the acceleration of the THM and CCL is continuously weakened before optimization. The mixed root mean square error (MRMSE) lower than 5% is applied to ensure the accuracy of simulation. The result shows that the proposed memory arrangement method can save computational cost a lot to speed up the heart simulation greatly. Graphical abstract Acceleration ratio compared with CPU with fixed time-step (dt = 0.001 ms).

A robust wavelet-based approach for dominant frequency analysis of atrial fibrillation in body surface signals

OBJECTIVE

Atrial dominant frequency (DF) maps undergoing atrial fibrillation (AF) presented good spatial correlation with those obtained with the non-invasive body surface potential mapping (BSPM). In this study, a robust BSPM-DF calculation method based on wavelet analysis is proposed.

APPROACH

Continuous wavelet transform along 40 scales in the pseudo-frequency range of 3-30 Hz is performed in each BSPM signal using a Gaussian mother wavelet. DFs are estimated from the intervals between the peaks, representing the activation times, in the maximum energy scale. The results are compared with the traditionally widely applied Welch periodogram and the robustness was tested on different protocols: increasing levels of white Gaussian noise, artificial DF harmonics presence and reduction in the number of leads. A total of 11 AF simulations and 12 AF patients are considered in the analysis. For each patient, intracardiac electrograms were acquired in 15 locations from both atria. The accuracy of both methods was assessed by calculating the absolute errors of the highest DF _BSPM (HDF _BSPM ) with respect to the atrial HDF, either simulated or intracardially measured, and assumed correct if ≤1 Hz. The spatial distribution of the errors between torso DFs and atrial HDFs were compared with atria driving mechanism locations. Torso HDF regions, defined as portions of the maps with [Formula: see text] Hz were identified and the percentage of the torso occuping these regions was compared between methods. The robustness of both methods to white Gaussian noise, ventricular influence and harmonics, and to lower spatial resolution BSPM lead layouts was analyzed: computer AF models (567 leads vs 256 leads down to 16 leads) and patient data (67 leads vs 32 and 16 leads).

MAIN RESULTS

The proposed method allowed an improvement in non-invasive estimation of the atria HDF. For the models the median relative errors were 7.14% for the wavelet-based algorithm vs 60.00% for the Welch method; in patients, the errors were 10.03% vs 12.66%, respectively. The wavelet method outperformed the Welch approach in correct estimations of atrial HDFs in models (81.82% vs 45.45%, respectively) and patients (66.67% vs 41.67%). A low positive BSPM-DF map correlation was seen between the techniques (0.47 for models and 0.63 for patients), highlighting the overall differences in DF distributions. The wavelet-based algorithm was more robust to white Gaussian noise, residual ventricular activity and harmonics, and presented more consistent results in lead layouts with low spatial resolution.

SIGNIFICANCE

Estimation of atrial HDFs using BSPM is improved by the proposed wavelet-based algorithm, helping to increase the non-invasive diagnostic ability in AF.

Combination of "generalized Trotter operator splitting" and "quadratic adaptive algorithm" method for tradeoff among speedup, stability, and accuracy in the Markov chain model of sodium ion channels in the ventricular cell model

The fast hybrid operator splitting (HOS) and stable uniformization (UNI) methods have been proposed to save computation cost and enhance stability for Markov chain model in cardiac cell simulations. Moreover, Chen-Chen-Luo's quadratic adaptive algorithm (CCL) combined with HOS or UNI was used to improve the tradeoff between speedup and stability, but without considering accuracy. To compromise among stability, acceleration, and accuracy, we propose a generalized Trotter operator splitting (GTOS) method combined with CCL independent of the asymptotic property of a particular ion-channel model. Due to the accuracy underestimation of the mixed root mean square error (MRMSE) method, threshold root mean square error (TRMSE) is proposed to evaluate computation accuracy. With the fixed time-step RK4 as a reference, the second-order GTOS combined with CCL (30.8-fold speedup) for the wild-type Markov chain model with nine states (WT-9 model) or (7.4-fold) for the wild-type Markov chain model with eight states (WT-8 model) is faster than UNI combined with CCL (15.6-fold) for WT-9 model or (1.2-fold) for WT-8 model, separately. Besides, the second-order GTOS combined with CCL has 3.81% TRMSE for WT-9 model or 4.32% TRMSE for WT-8 model more accurate than 72.43% TRMSE for WT-9 model or 136.17% TRMSE for WT-8 model of HOS combined with CCL. To compromise speedup and accuracy, low-order GTOS combined with CCL is suggested to have the advantages of high precision and low computation cost. For high-accuracy requirements, high-order GTOS combined with CCL is recommended. Graphical abstract.

Clinical Characteristics and Electrophysiological Mechanisms Underlying Brugada ECG in Patients With Severe Hyperkalemia

Background

Several metabolic conditions can cause the Brugada ECG pattern, also called Brugada phenotype (BrPh). We aimed to define the clinical characteristics and outcome of BrPh patients and elucidate the mechanisms underlying BrPh attributed to hyperkalemia.

Methods and Results

We prospectively identified patients hospitalized with severe hyperkalemia and ECG diagnosis of BrPh and compared their clinical characteristics and outcome with patients with hyperkalemia but no BrPh ECG. Computer simulations investigated the roles of extracellular potassium increase, fibrosis at the right ventricular outflow tract, and epicardial/endocardial gradients in transient outward current. Over a 6‐year period, 15 patients presented severe hyperkalemia with BrPh ECG that was transient and disappeared after normalization of their serum potassium. Most patients were admitted because of various severe medical conditions causing hyperkalemia. Six (40%) patients presented malignant arrhythmias and 6 died during admission. Multiple logistic regression analysis revealed that higher serum potassium levels (odds ratio, 15.8; 95% CI, 3.1–79; P=0.001) and male sex (odds ratio, 17; 95% CI, 1.05–286; P=0.045) were risk factors for developing BrPh ECG in patients with severe hyperkalemia. In simulations, hyperkalemia yielded BrPh by promoting delayed and heterogeneous right ventricular outflow tract activation attributed to elevation of resting potential, reduced availability of inward sodium channel conductance, and increased right ventricular outflow tract fibrosis. An elevated transient outward current gradient contributed to, but was not essential for, the BrPh phenotype.

Conclusions

In patients with severe hyperkalemia, a BrPh ECG is associated with malignant arrhythmias and all‐cause mortality secondary to resting potential depolarization, reduced sodium current availability, and fibrosis at the right ventricular outflow tract.

Phase singularity point tracking for the identification of typical and atypical flutter patients: A clinical-computational study

Atrial Flutter (AFL) termination by ablating the path responsible for the arrhythmia maintenance is an extended practice. However, the difficulty associated with the identification of the circuit in the case of atypical AFL motivates the development of diagnostic techniques. We propose body surface phase map analysis as a noninvasive tool to identify AFL circuits. Sixty seven lead body surface recordings were acquired in 9 patients during AFL (i.e. 3 typical, 6 atypical). Computed body surface phase maps from simulations of 5 reentrant behaviors in a realistic atrial structure were also used. Surface representation of the macro-reentrant activity was analyzed by tracking the singularity points (SPs) in surface phase maps obtained from band-pass filtered body surface potential maps. Spatial distribution of SPs showed significant differences between typical and atypical AFL. Whereas for typical AFL patients 70.78 ± 16.17% of the maps presented two SPs simultaneously in the areas defined around the midaxialliary lines, this condition was only satisfied in 5.15 ± 10.99% (p < 0.05) maps corresponding to atypical AFL patients. Simulations confirmed these results. Surface phase maps highlights the reentrant mechanism maintaining the arrhythmia and appear as a promising tool for the noninvasive characterization of the circuit maintaining AFL. The potential of the technique as a diagnosis tool needs to be evaluated in larger populations and, if it is confirmed, may help in planning ablation procedures.

Solving Inaccuracies in Anatomical Models for Electrocardiographic Inverse Problem Resolution by Maximizing Reconstruction Quality

Electrocardiographic Imaging has become an increasingly used technique for non-invasive diagnosis of cardiac arrhythmias, although the need for medical imaging technology to determine the anatomy hinders its introduction in the clinical practice. This paper explores the ability of a new metric based on the inverse reconstruction quality for the location and orientation of the atrial surface inside the torso. Body surface electrical signals from 31 realistic mathematical models and four AF patients were used to estimate the optimal position of the atria inside the torso. The curvature of the L-curve from the Tikhonov method, which was found to be related to the inverse reconstruction quality, was measured after application of deviations in atrial position and orientation. Independent deviations in the atrial position were solved by finding the maximal L-curve curvature with an error of 1.7 ± 2.4 mm in mathematical models and 9.1 ± 11.5 mm in patients. For the case of independent angular deviations, the error in location by using the L-curve was 5.8±7.1° in mathematical models and 12.4° ± 13.2° in patients. The ability of the L-curve curvature was tested also under superimposed uncertainties in the three axis of translation and in the three axis of rotation, and the error in location was of 2.3 ± 3.2 mm and 6.4° ± 7.1° in mathematical models, and 7.9±10.7 mm and 12.1°±15.5° in patients. The curvature of L-curve is a useful marker for the atrial position and would allow emending the inaccuracies in its location.

Performance evaluation of GPU parallelization, space-time adaptive algorithms, and their combination for simulating cardiac electrophysiology

The use of computer models as a tool for the study and understanding of the complex phenomena of cardiac electrophysiology has attained increased importance nowadays. At the same time, the increased complexity of the biophysical processes translates into complex computational and mathematical models. To speed up cardiac simulations and to allow more precise and realistic uses, 2 different techniques have been traditionally exploited: parallel computing and sophisticated numerical methods. In this work, we combine a modern parallel computing technique based on multicore and graphics processing units (GPUs) and a sophisticated numerical method based on a new space-time adaptive algorithm. We evaluate each technique alone and in different combinations: multicore and GPU, multicore and GPU and space adaptivity, multicore and GPU and space adaptivity and time adaptivity. All the techniques and combinations were evaluated under different scenarios: 3D simulations on slabs, 3D simulations on a ventricular mouse mesh, ie, complex geometry, sinus-rhythm, and arrhythmic conditions. Our results suggest that multicore and GPU accelerate the simulations by an approximate factor of 33×, whereas the speedups attained by the space-time adaptive algorithms were approximately 48. Nevertheless, by combining all the techniques, we obtained speedups that ranged between 165 and 498. The tested methods were able to reduce the execution time of a simulation by more than 498× for a complex cellular model in a slab geometry and by 165× in a realistic heart geometry simulating spiral waves. The proposed methods will allow faster and more realistic simulations in a feasible time with no significant loss of accuracy.

Technical Considerations on Phase Mapping for Identification of Atrial Reentrant Activity in Direct- and Inverse-Computed Electrograms

BACKGROUND

Phase mapping has become a broadly used technique to identify atrial reentrant circuits for ablative therapy guidance. This work studies the phase mapping process and how the signal nature and its filtering affect the reentrant pattern characterization in electrogram (EGM), body surface potential mapping, and electrocardiographic imaging signals.

METHODS AND RESULTS

EGM, body surface potential mapping, and electrocardiographic imaging phase maps were obtained from 17 simulations of atrial fibrillation, atrial flutter, and focal atrial tachycardia. Reentrant activity was identified by singularity point recognition in raw signals and in signals after narrow band-pass filtering at the highest dominant frequency (HDF). Reentrant activity was dominantly present in the EGM recordings only for atrial fibrillation and some atrial flutter propagations patterns, and HDF filtering allowed increasing the reentrant activity detection from 60% to 70% of time in atrial fibrillation in unipolar recordings and from 0% to 62% in bipolar. In body surface potential mapping maps, HDF filtering increased from 10% to 90% the sensitivity, although provoked a residual false reentrant activity ≈30% of time. In electrocardiographic imaging, HDF filtering allowed to increase ≤100% the time with detected rotors, although provoked the apparition of false rotors during 100% of time. Nevertheless, raw electrocardiographic imaging phase maps presented reentrant activity just in atrial fibrillation recordings accounting for ≈80% of time.

CONCLUSIONS

Rotor identification is accurate and sensitive and does not require additional signal processing in measured or noninvasively computed unipolar EGMs. Bipolar EGMs and body surface potential mapping do require HDF filtering to detect rotors at the expense of a decreased specificity.

Regularization Techniques for ECG Imaging during Atrial Fibrillation: A Computational Study

The inverse problem of electrocardiography is usually analyzed during stationary rhythms. However, the performance of the regularization methods under fibrillatory conditions has not been fully studied. In this work, we assessed different regularization techniques during atrial fibrillation (AF) for estimating four target parameters, namely, epicardial potentials, dominant frequency (DF), phase maps, and singularity point (SP) location. We use a realistic mathematical model of atria and torso anatomy with three different electrical activity patterns (i.e., sinus rhythm, simple AF, and complex AF). Body surface potentials (BSP) were simulated using Boundary Element Method and corrupted with white Gaussian noise of different powers. Noisy BSPs were used to obtain the epicardial potentials on the atrial surface, using 14 different regularization techniques. DF, phase maps, and SP location were computed from estimated epicardial potentials. Inverse solutions were evaluated using a set of performance metrics adapted to each clinical target. For the case of SP location, an assessment methodology based on the spatial mass function of the SP location, and four spatial error metrics was proposed. The role of the regularization parameter for Tikhonov-based methods, and the effect of noise level and imperfections in the knowledge of the transfer matrix were also addressed. Results showed that the Bayes maximum-a-posteriori method clearly outperforms the rest of the techniques but requires a priori information about the epicardial potentials. Among the purely non-invasive techniques, Tikhonov-based methods performed as well as more complex techniques in realistic fibrillatory conditions, with a slight gain between 0.02 and 0.2 in terms of the correlation coefficient. Also, the use of a constant regularization parameter may be advisable since the performance was similar to that obtained with a variable parameter (indeed there was no difference for the zero-order Tikhonov method in complex fibrillatory conditions). Regarding the different targets, DF and SP location estimation were more robust with respect to pattern complexity and noise, and most algorithms provided a reasonable estimation of these parameters, even when the epicardial potentials estimation was inaccurate. Finally, the proposed evaluation procedure and metrics represent a suitable framework for techniques benchmarking and provide useful insights for the clinical practice.

Balance between sodium and calcium currents underlying chronic atrial fibrillation termination: An in silico intersubject variability study

BACKGROUND

Atrial remodeling as a result of long-standing persistent atrial fibrillation (AF) induces substrate modifications that lead to different perpetuation mechanisms than in paroxysmal AF and a reduction in the efficacy of antiarrhythmic treatments.

OBJECTIVE

The purpose of this study was to identify the ionic current modifications that could destabilize reentries during chronic AF and serve to personalize antiarrhythmic strategies.

METHODS

A population of 173 mathematical models of remodeled human atrial tissue with realistic intersubject variability was developed based on action potential recordings of 149 patients diagnosed with AF. The relationship of each ionic current with AF maintenance and the dynamics of functional reentries (rotor meandering, dominant frequency) were evaluated by means of 3-dimensional simulations.

RESULTS

Self-sustained reentries were maintained in 126 (73%) of the simulations. AF perpetuation was associated with higher expressions of I_Na and I_CaL (P <.01), with no significant differences in the remaining currents. I_CaL blockade promoted AF extinction in 30% of these 126 models. The mechanism of AF termination was related with collisions between rotors because of an increase in rotor meandering (1.71 ± 2.01cm²) and presented an increased efficacy in models with a depressed I_Na (P <.01).

CONCLUSION

Mathematical simulations based on a population of models representing intersubject variability allow the identification of ionic mechanisms underlying rotor dynamics and the definition of new personalized pharmacologic strategies. Our results suggest that the underlying mechanism of the diverging success of I_CaL block as an antiarrhythmic strategy is dependent on the basal availability of sodium and calcium ion channel conductivities.

Noninvasive Estimation of Epicardial Dominant High-Frequency Regions During Atrial Fibrillation

INTRODUCTION

Ablation of high dominant frequency (DF) sources in patients with atrial fibrillation (AF) is an effective treatment option for paroxysmal AF. The aim of this study was to evaluate the accuracy of noninvasive estimation of DF and electrical patterns determination by solving the inverse problem of the electrocardiography.

METHODS

Four representative AF patients with left-to-right and right-to-left atrial DF patterns were included in the study. For each patient, intracardiac electrograms from both atria were recorded simultaneously together with 67-lead body surface recordings. In addition to clinical recordings, realistic mathematical models of atria and torso anatomy with different DF patterns of AF were used. For both mathematical models and clinical recordings, inverse-computed electrograms were compared to intracardiac electrograms in terms of voltage, phase, and frequency spectrum relative errors.

RESULTS

Comparison between intracardiac and inverse computed electrograms for AF patients showed 8.8 ± 4.4% errors for DF, 32 ± 4% for voltage, and 65 ± 4% for phase determination. These results were corroborated by mathematical simulations showing that the inverse problem solution was able to reconstruct the frequency spectrum and the DF maps with relative errors of 5.5 ± 4.1%, whereas the reconstruction of the electrograms or the instantaneous phase presented larger relative errors (i.e., 38 ± 15% and 48 ± 14 % respectively, P < 0.01).

CONCLUSIONS

Noninvasive reconstruction of atrial frequency maps can be achieved by solving the inverse problem of electrocardiography with a higher accuracy than temporal distribution patterns.

Atrial sources identification by causality analysis during atrial fibrillation

Ablation of electrical drivers during atrial fibrillation (AF) has been proved as an effective therapy to prevent recurrence of fibrillatory episodes. This study presents a new methodology based on causality analysis that is able to identify the hierarchical dominance of atrial areas driving AF. Realistic mathematical models of the atrial electrical activity during AF were used to assess the validity of our method. Identification of the dominant atrial propagation patterns was achieved by computing causal relations between multiple electrogram signals. The causal relationships between atrial areas during the fibrillatory processes were summarized into a recurrence map, highlighting the hierarchy and dominant areas. Recurrence maps computed from causality analysis allowed the identification of sites responsible for maintenance of the arrhythmia. These maps were able to locate the position of the atrial driver in fibrillatory processes with a single rotor, with 2 rotors or with several drivers. Additionally, the correspondence between the nodal values of the recurrence map and the distance to the rotor core has been established. Causal analysis consistently estimated propagation patterns and location of atrial drivers during AF. This methodology could guide ablation procedures in AF patients.

Data analysis in cardiac arrhythmias

Cardiac arrhythmias are an increasingly present in developed countries and represent a major health and economic burden. The occurrence of cardiac arrhythmias is closely linked to the electrical function of the heart. Consequently, the analysis of the electrical signal generated by the heart tissue, either recorded invasively or noninvasively, provides valuable information for the study of cardiac arrhythmias. In this chapter, novel cardiac signal analysis techniques that allow the study and diagnosis of cardiac arrhythmias are described, with emphasis on cardiac mapping which allows for spatiotemporal analysis of cardiac signals.Cardiac mapping can serve as a diagnostic tool by recording cardiac signals either in close contact to the heart tissue or noninvasively from the body surface, and allows the identification of cardiac sites responsible of the development or maintenance of arrhythmias. Cardiac mapping can also be used for research in cardiac arrhythmias in order to understand their mechanisms. For this purpose, both synthetic signals generated by computer simulations and animal experimental models allow for more controlled physiological conditions and complete access to the organ.