A finite element formulation for atrial tissue monolayer.

OBJECTIVES: Using computer models for the study of complex atrial arrhythmias such as atrial fibrillation is computationally demanding as long observation periods in the order of tens of seconds are required. A well established approach for reducing computational workload is to approximate the thin atrial walls by curved monolayers. On the other hand, the finite element method (FEM) is a well established approach to solve the underlying partial differential equations. METHODS: A generalized 2D finite element method (FEM) is presented which computes the corresponding stiffness and coupling matrix for arbitrarily shaped monolayers (ML). Compared to standard 2D FEM, only one additional coordinate transformation is required. This allows the use of existing FEM software with minor modifications. The algorithm was tested to simulate wave propagation in benchmark geometries and in a model of atrial anatomy. RESULTS: The ML model was able to simulate electric activation in curved tissue with anisotropic conductivity. Simulations in branching tissue yielded slightly different patterns when compared to a volumetric model with finite thickness. In the model of atrial anatomy the computed activation times for five different pacing protocols displayed a correlation of 0.88 compared to clinical data. CONCLUSIONS: The presented method provides a useful and easily implemented approach to model wave propagation in MLs with a few restrictions to volumetric models.

Detection of phase singularities in triangular meshes.

OBJECTIVES: Phase singularities have become a key marker in animal and computer models of atrial and ventricular fibrillation. However, existing algorithms for the automatic detection of phase singularities are limited to regular, quadratic mesh grids. We present an algorithm to automatically and exactly detect phase singularities in triangular meshes. METHODS: For each node an oriented path inscribing the node with one unit of spatial discretization is identified. At each time step the phase information is calculated for all nodes. The so-called topological charge is also computed for each node. A non-zero (+/- 2pi) charge is obtained for all nodes with a path enclosing a phase singularity. Thus all charged nodes belonging to the same phase singularity have to be clustered. RESULTS: With the use of the developed algorithm, phase singularities can be detected in triangular meshes with an accuracy of below 0.2 mm - independent of the type of membrane kinetics used. CONCLUSIONS: With the possibility to detect phase singularities automatically and exactly, important quantitative data on cardiac fibrillation can be gained.

Fibrillatory conduction in branching atrial tissue--Insight from volumetric and monolayer computer models.

Increased local load in branching atrial tissue (muscle fibers and bundle insertions) influences wave propagation during atrial fibrillation (AF). This computer model study reveals two principal phenomena: if the branching is distant from the driving rotor (>19 mm), the load causes local slowing of conduction or wavebreaks. If the driving rotor is close to the branching, the increased load causes first a slow drift of the rotor towards the branching. Finally, the rotor anchors, and a stable, repeatable pattern of activation can be observed. Variation of the bundle geometry from a cylindrical, volumetric structure to a flat strip of a comparable load in a monolayer model changed the local activation sequence in the proximity of the bundle. However, the global behavior and the basic effects are similar in all models. Wavebreaks in branching tissue contribute to the chaotic nature of AF (fibrillatory conduction). The stabilization (anchoring) of driving rotors by branching tissue might contribute to maintain sustained AF.

Prediction of countershock success in patients using the autoregressive spectral estimation.

OBJECTIVES: Ventricular fibrillation (VF) is a life-threatening cardiac arrhythmia and within of minutes of its occurrence, optimal timing of countershock therapy is highly warranted to improve the chance of survival. This study was designed to investigate whether the autoregressive (AR) estimation technique was capable to reliably predict countershock success in VF cardiac arrest patients. METHODS: ECG data of 1077 countershocks applied to 197 cardiac arrest patients with out-of-hospital and in-hospital cardiac arrest between March 2002 and July 2004 were retrospectively analyzed. The ECG from the 2.5 s interval of the precountershock VF ECG was used for computing the AR based features Spectral Pole Power (SPP) and Spectral Pole Power with Dominant Frequency weighing (SPPDF) and Centroid Frequency (CF) and Amplitude Spectrum Area (AMSA) based on Fast Fourier Transformation (FFT). RESULTS: With ROC AUC values up to 84.1% and diagnostic odds ratio up to 19.12 AR based features SPP and SPPDF have better prediction power than the FFT based features CF (80.5%; 6.56) and AMSA (82.1%; 8.79). CONCLUSIONS: AR estimation based features are promising alternatives to FFT based features for countershock outcome when analyzing human data.

Prediction of countershock success: a comparison of autoregressive and fast fourier transformed spectral estimators.

OBJECTIVES: Spectral analysis of the ventricular fibrillation (VF) ECG has been used for predicting countershock success, where the Fast Fourier Transformation (FFT) is the standard spectral estimator. Autoregressive (AR) spectral estimation should compute the spectrum with less computation time. This study compares the predictive power and computational performance of features obtained by the FFT and AR methods. METHODS: In an animal model of VF cardiac arrest, 41 shocks were delivered in 25 swine. For feature parameter analysis, 2.5 s signal intervals directly before the shock and directly before the hands-off interval were used, respectively. Invasive recordings of the arterial pressure were used for assessing the outcome of each shock. For a proof of concept, a micro-controller program was implemented. RESULTS: Calculating the area under the receiver operating characteristic (ROC) curve (AUC), the results of the AR-based features called spectral pole power (SPP) and spectral pole power with dominant frequency (DF) weighing (SPPDF) yield better outcome prediction results (85%; 89%) than common parameters based on FFT calculation method (centroid frequency (CF), amplitude spectrum area (AMSA)) (72%; 78%) during hands-off interval. Moreover, the predictive power of the feature parameters during ongoing CPR was not invalidated by closed-chest compressions. The calculation time of the AR-based parameters was nearly 2.5 times faster than the FFT-based features. CONCLUSION: Summing up, AR spectral estimators are an attractive option compared to FFT due to the reduced computational speed and the better outcome prediction. This might be of benefit when implementing AR prediction features on the microprocessor of a semi-automatic defibrillator.