A meshless fragile points method for rule-based definition of myocardial fiber orientation

Background and objective: Rule-based methods are commonly used to estimate the arrangement of myocardial fibers by solving the Laplace problem with appropriate Dirichlet boundary conditions. Existing algorithms are using the Finite Element Method (FEM) to solve the Laplace–Dirichlet problem. However, meshless methods are under development for cardiac electrophysiology simulation. The objective of this work is to propose a meshless rule based method for the determination of myocardial fiber arrangement without requiring a mesh discretization as it is required by FEM. Methods: The proposed method employs the Fragile Points Method (FPM) for the solution of the Laplace–Dirichlet problem. FPM uses simple discontinuous trial functions and single-point exact integration for linear trial functions that set it as a promising alternative to the Finite Element Method. We derive the FPM formulation of the Laplace–Dirichlet and we estimate ventricular and atrial fiber arrangements according to rules based on histology findings for four different geometries. The obtained fiber arrangements from FPM are compared with the ones obtained from FEM by calculating the angle between the fiber vector fields of the two methods for three different directions (i.e., longitudinal, sheet, transverse). Results:The fiber arrangements that were generated with FPM were in close agreement with the generated arrangements from FEM for all three directions. The mean angle difference between the FPM and FEM vector fields were lower than for the ventricular fiber arrangements and lower than for the atrial fiber arrangements. Discussion:The proposed meshless rule-based method was proven to generate myocardial fiber arrangements with very close agreement with FEM while alleviates the requirement for a mesh of the latter. This is of great value for cardiac electrophysiology solvers that are based on meshless methods since they require a well defined myocardial fiber arrangement to simulate accurately the propagation of electrical signals in the heart. Combining a meshless solution for both the determination of the fibers and the electrical signal propagation can allow for solution that do not require the definition of a mesh. To our knowledge, this work is the first one to propose a meshless rule-based method for myocardial fiber arrangement determination

On the standardization of approximate entropy: multidimensional approximate entropy index evaluated on short-term HRV time series

Background. Nonlinear heart rate variability (HRV) indices have extended the description of autonomic nervous system (ANS) regulation of the heart. One of those indices is approximate entropy, ApEn, which has become a commonly used measure of the irregularity of a time series. To calculate ApEn, a priori definition of parameters like the threshold on similarity and the embedding dimension is required, which has been shown to be critical for interpretation of the results. Thus, searching for a parameter-free ApEn-based index could be advantageous for standardizing the use and interpretation of this widely applied entropy measurement. Methods. A novel entropy index called multidimensional approximate entropy, , is proposed based on summing the contribution of maximum approximate entropies over a wide range of embedding dimensions while selecting the similarity threshold leading to maximum ApEn value in each dimension. Synthetic RR interval time series with varying levels of stochasticity, generated by both MIX(P) processes and white/pink noise, were used to validate the properties of the proposed index. Aging and congestive heart failure (CHF) were characterized from RR interval time series of available databases. Results. In synthetic time series, values were proportional to the level of randomness; i.e., increased for higher values of P in generated MIX(P) processes and was larger for white than for pink noise. This result was a consequence of all maximum approximate entropy values being increased for higher levels of randomness in all considered embedding dimensions. This is in contrast to the results obtained for approximate entropies computed with a fixed similarity threshold, which presented inconsistent results for different embedding dimensions. Evaluation of the proposed index on available databases revealed that aging was associated with a notable reduction in values. On the other hand, evaluated during the night period was considerably larger in CHF patients than in healthy subjects. Conclusion. A novel parameter-free multidimensional approximate entropy index, , is proposed and tested over synthetic data to confirm its capacity to represent a range of randomness levels in HRV time series. values are reduced in elderly patients, which may correspond to the reported loss of ANS adaptability in this population segment. Increased values measured in CHF patients versus healthy subjects during the night period point to greater irregularity of heart rate dynamics caused by the disease

Modelización matemática y simulación computacional de la variabilidad espacio-temporal en la actividad eléctrica cardíaca

The electrical activity of the heart is the result of complex biophysical and biochemical processes occurring at different scales ranging from submicroscopic to macroscopic. The variability arising from these processes has important effects on cardiac function under both physiological and pathological conditions. In this review, mathematical modeling and simulation of cardiac electrical variability at the level of the cell, tissue and whole organ will be reviewed. A set of studies will be presented, which investigate the role that the stochastic gating of ion channels of cardiac cell membranes plays in the generation of electrical voltage variations along time. Also, methodologies for the development, calibration and evaluation of populations of mathematical models able to represent variations in cardiac electrophysiology across space, i.e. among cells, tissues or individuals, will be described. In particular, methods based on state-space representations, dimension reduction techniques and nonlinear adaptive filtering will be presented and their capacity to replicate experimentally measured spatio-temporal variability will be illustrated. The importance of these methodologies will be shown as a means to ascertain the mechanisms underlying variability, to establish the link between variability and cardiac arrhythmias (irregularities in heart beating) and to propose clinical markers for diagnosis, monitoring and treatment of cardiac diseases

Comparison of ECG T-wave Duration and Morphology Restitution Markers for Sudden Cardiac Death Prediction in Chronic Heart Failure

An index of T-wave morphology restitution, TMR, has previously shown to be a sudden cardiac death (SCD) predictor in a population of chronic heart failure (CHF) patients. The aim of this study is to compare the predictive value of TMR, T-wave width restitution (TWR), Tpeak-to-end (Tpe) morphology restitution (TpeMR) and Tpe duration restitution (T peR) indices in the same CHF population. Holter ECG recordings from 651 CHF patients of the MUSIC study, including SCD victims and survivors, were analyzed. TMR was significantly correlated with T W R (¿=0.66), T peM R (¿=0.70) and T peR (¿=0.42). SCD victims showed significantly higher values of TMR, TWR and TpeMR than the rest of patients, with T M R being the index most strongly associated with SCD (p=0.002, p=0.006 and p=0.011, respectively). T peR values were only borderline significantly higher in SCD victims (p=0.061). Univariate Cox analysis showed that T M R was the restitution index with the strongest predictive value (hazard ratio (HR) of 1.466, p<0.001), followed by TWR (HR of 1.295, p=0.005), TpeR (HR of 1.297, p=0.004) and T peM R (HR of 1.164, p=0.020). In conclusion, considering the predictive value of the four Twave restitution indices, TMR is the preferred index for SCD risk stratification, followed by TpeMR. However, the marker TWR could also be used for SCD prediction when computational efficiency is an issue

Strain Echocardiography to Predict Postoperative Atrial Fibrillation

Postoperative atrial fibrillation (POAF) complicates 15% to 40% of cardiovascular surgeries. Its incidence progressively increases with aging, reaching 50% in octogenarians. This arrhythmia is usually transient but it increases the risk of embolic stroke, prolonged hospital stay, and cardiovascular mortality. Though many pathophysiological mechanisms are known, POAF prediction is still a hot topic of discussion. Doppler echocardiogram and, lately, strain echocardiography have shown significant capacity to predict POAF. Alterations in oxidative stress, calcium handling, mitochondrial dysfunction, inflammation, fibrosis, and tissue aging are among the mechanisms that predispose patients to the perfect "atrial storm". Manifestations of these mechanisms have been related to enlarged atria and impaired function, which can be detected prior to surgery. Specific alterations in the atrial reservoir and pump function, as well as atrial dyssynchrony determined by echocardiographic atrial strain, can predict POAF and help to shed light on which patients could benefit from preventive therapy

Techniques for ventricular repolarization instability assessment from the ECG

Instabilities in ventricular repolarization have been documented to be tightly linked to arrhythmia vulnera- bility. Translation of the information contained in the repolar- ization phase of the electrocardiogram (ECG) into valuable clinical decision-making tools remains challenging. This work aims at providing an overview of the last advances in the pro- posal and quantification of ECG-derived indices that describe repolarization properties and whose alterations are related with threatening arrhythmogenic conditions. A review of the state of the art is provided, spanning from the electrophysio- logical basis of ventricular repolarization to its characteriza- tion on the surface ECG through a set of temporal and spatial risk markers

Differential Responses to Beta-Adrenergic Stimulation in the Long-QT Syndrome Type 1: Characterization and Mechanisms

Long QT syndrome type 1 (LQT1) is caused by muta- tions that impair the function of the slow delayed rectifier potassium (IK s ) channels. Most LQT1 patients experience arrhythmic events during beta-adrenergic stimulation (β- AS). A full description of the ionic mechanisms underlying arrhythmogenecity in LQT1 patients and their relation to β-AS is still lacking. In this study we constructed a set of stochastic human ventricular cell models reproducing ex- perimental AP properties at baseline and following ionic inhibitions. Using the constructed models, we showed that AP duration, morphology and beat-to-beat variability in LQT1 are highly specific of the underlying ionic character- istics. Likewise, the response of individual IK s -deficient cells to β-AS can range from negligible to as much as 200% increase in AP temporal variability, recognized as a marker of arrhythmogenesis in the setting of LQT1. By partial correlation analysis, major ionic factors driving AP changes associated with LQT1 and β-AS were ascer- tained

A human ventricular cell model for investigation of cardiac arrhythmias under hyperkalaemic conditions

In this study, several modifications were introduced to a recently proposed human ventricular action potential (AP) model so as to render it suitable for the study of ventricular arrhythmias. These modifications were driven by new sets of experimental data available from the literature and the analysis of several well-established cellular arrhythmic risk biomarkers, namely AP duration at 90 per cent repolarization (APD 90 ), AP triangulation, calcium dynamics, restitution properties, APD 90 adaptation to abrupt heart rate changes, and rate dependence of intracellular sodium and calcium concentrations. The proposed methodology represents a novel framework for the development of cardiac cell models. Five stimulation protocols were applied to the original model and the ventricular AP model developed here to compute the described arrhythmic risk biomarkers. In addition, those models were tested in a one-dimensional fibre in which hyperkalaemia was simulated by increasing the extracellular potassium concentration, [K + ] o . The effective refractory period (ERP), conduction velocity (CV) and the occurrence of APD alternans were investigated. Results show that modifications improved model behaviour as verified by: (i) AP triangulation well within experimental limits (the difference between APD at 50 and 90 per cent repolarization being 78.1 ms); (ii) APD 90 rate adaptation dynamics characterized by fast and slow time constants within physiological ranges (10.1 and 105.9 s); and (iii) maximum S1S2 restitution slope in accordance with experimental data ( S S1S2 =1.0). In simulated tissues under hyperkalaemic conditions, APD 90 progressively shortened with the degree of hyperkalaemia, whereas ERP increased once a threshold in [K + ] o was reached ([K + ] o ≈6 mM). CV decreased with [K + ] o , and conduction was blocked for [K + ] o &gt;10.4 mM. APD 90 alternans were observed for [K + ] o &gt;9.8 mM. Those results adequately reproduce experimental observations. This study demonstrated the value of basing the development of AP models on the computation of arrhythmic risk biomarkers, as opposed to joining together independently derived ion channel descriptions to produce a whole-cell AP model, with the new framework providing a better picture of the model performance under a variety of stimulation conditions. On top of replicating experimental data at single-cell level, the model developed here was able to predict the occurrence of APD 90 alternans and areas of conduction block associated with high [K + ] o in tissue, which is of relevance for the investigation of the arrhythmogenic substrate in ischaemic hearts. </jats:p

Arrhythmic risk prediction based on the analysis of ventricular repolarization markers from surface ECG

La dependencia de la duración del potencial de acción (APD, del inglés "Action Potential Duration") con el ritmo cardiaco (HR, del inglés "Heart Rate"), también conocida como cinética de restitución, es crítica a la hora de generar inestabilidades eléctricas en el corazón y proporciona información relevante en la estratificación del riesgo a sufrir arritmias ventriculares. La curva dinámica de restitución del APD (APDR, del inglés "APD restitution") cuantifica la relación entre el APD y el intervalo RR (inverso de HR) en condiciones estacionarias. Heterogeneidades en el ventrículo dan lugar a propiedades de la restitución no uniformes, haciendo que las curvas APDR presenten variaciones espaciales. La dispersión es una medida de dicha variación espacial. Recientemente se propuso en la literatura un índice derivado del electrocardiograma (ECG), Δα, que cuantifica la dispersión en las pendientes de las curvas dinámicas de APDR mediante la caracterización de la relación entre los intervalos del pico al final de la onda T (Tpe) y RR bajo condiciones estacionarias diferentes. En este Trabajo Fin de Máster (TFM) se ha desarrollado un método automático para obtener y evaluar, a partir de registros ambulatorios, Δα, como predictor independiente de muerte súbita cardiaca (SCD, del inglés "Sudden Cardiac Death") en pacientes con fallo cardiaco crónico (CHF, del inglés "Chronic Heart Failure"). Pacientes con CHF sintomático formaron parte del estudio "MUSIC" (MUerte Súbita en Insuficiencia Cardiaca). La base de datos contenía los registros Holter de 609 pacientes (48 víctimas de SCD, 64 de otras causas cardiacas, 25 de causas no cardiacas y 472 supervivientes) con ritmo sinusal. El preprocesado de las señales ECG realizado en este TFM consistió en un filtrado paso bajo a 40 Hz, interpolación de splines cúbicos y un detector de latidos ectópicos. Se aplicó una técnica de delineación "uniderivacional más reglas a posteriori" para seleccionar las muestras pertenecientes a la onda T y realizar un análisis de componentes principales. A continuación, se delineó la primera componente principal mediante una técnica uniderivacional y, a partir de las marcas de delineación, se obtuvieron las series de los intervalos RR y Tpe. Posteriormente, se interpolaron a una frecuencia de muestreo fs = 1 Hz. Como cada valor de la curva APDR está medido a un valor específico de RR, el índice de ECG Δα debería calcularse usando segmentos de ECG de ritmos cardiacos estables. Dichos segmentos son difíciles de conseguir en la práctica clínica y por lo tanto se modeló la dependencia del intervalo Tpe con una historia de intervalos previos de RR y se compensó por el retardo de memoria de Tpe. La relación entre Tpe y RR se caracterizó en los registros completos de ECG. Un umbral fijado en Δα>0.046 discriminó los pacientes en alto y bajo riesgo a sufrir SCD (p-valor = 0.003). El tiempo hasta el evento (SCD) fue aproximadamente el doble en los pacientes con Δα0.046 (p-valor = 0.001). Al combinar Δα con el índice de media de alternancias de onda T se mejoró la estratificación del riesgo a sufrir SCD (p-valor<0.001). Este estudio demuestra que la dispersión en APDR, cuantificada a partir de registros ECG Holter, es un predictor de SCD fuerte e independiente en pacientes con CHF. Estos resultados apoyan la hipótesis de que una dispersión de APDR elevada refleja un funcionamiento cardiaco anormal, con predisposición a sufrir SCD