L. Azzolin, L. Dedè, A. Gerbi, and A. Quarteroni. Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles. In Mathematics in Engineering, vol. 2(4) , pp. 614-638, 2020
This work concerns the mathematical and numerical modeling of the heart. The aim is to enhance the understanding of the cardiac function in both physiological and pathological conditions. Along this road, a challenge arises from the multi-scale and multi-physics nature of the mathematical problem at hand. In this paper, we propose an electromechanical model that, in bi-ventricle geometries, combines the monodomain equation, the Bueno-Orovio minimal ionic model, and the Holzapfel-Ogden strain energy function for the passive myocardial tissue modelling together with the active strain approach combined with a model for the transmurally heterogeneous thickening of the myocardium. Since the distribution of the electric signal is dependent on the fibres orientation of the ventricles, we use a Laplace-Dirichlet Rule-Based algorithm to determine the myocardial fibres and sheets configuration in the whole bi-ventricle. In this paper, we study the influence of different fibre directions and incompressibility constraint and penalization on the compressibility of the material (bulk modulus) on the pressure-volume relation simulating a full heart beat. The coupled electromechanical problem is addressed by means of a fully segregated scheme. The numerical discretization is based on the Finite Element Method for the spatial discretization and on Backward Differentiation Formulas for the time discretization. The arising non-linear algebraic system coming from application of the implicit scheme is solved through the Newton method. Numerical simulations are carried out in a patient-specific biventricle geometry to highlight the most relevant results of both electrophysiology and mechanics and to compare them with physiological data and measurements. We show how various fibre configurations and bulk modulus modify relevant clinical quantities such as stroke volume, ejection fraction and ventricle contractility.
This work uses a highly detailed computational model of human atria to investigate the effect of spatial gradient and smoothing of atrial wall thickness on inducibility and maintenance of atrial fibrillation (AF) episodes. An atrial model with homogeneous thickness (HO) was used as baseline for the generation of different atrial models including either a low (LG) or high thickness gradient between left/right atrial free wall and the other regions. Since the model with high spatial gradient presented non-natural sharp edges between regions, either 1 (HG1) or 2 (HG2) Laplacian smoothing iterations were applied. Arrhythmic episodes were initiated using a rapid pacing protocol and long-living rotors were detected and tracked over time. Thresholds optimised with receiver operating characteristic analysis were used to define high gradient/curvature regions. Greater spatial gradients increased the atrial model inducibility and unveiled additional regions vulnerable to maintain AF drivers. In the models with heterogeneous wall thickness (LG, HG2 and HG1), 73.5 ± 8.7% of the long living rotors were found in areas within 1.5 mm from nodes with high thickness gradient, and 85.0 ± 3.4% in areas around high endocardial curvature. These findings promote wall thickness gradient and endocardial curvature as measures of AF vulnerability.
L. Azzolin, O. Dössel, and A. Loewe. Influence of the protocol used to induce arrhythmia on atrial fibrillation vulnerability. In 41 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2019
Several works have studied arrhythmogenicity of a given atrial model using different methods to initiate and simulate the perpetuation of re-entrant activity. We evaluated and compared two state-of-the-art methods showing their influence on the estimated vulnerability to arrhythmia of an atrial model.
Nowadays, a large share of the global population is affected by heart rhythm disorders. Computational modelling is a useful tool for understanding the dynamics of cardiac arrhythmias. Several recent clinical and experimental studies suggest that atrial fibrillation is maintained by re-entrant drivers (e.g. rotors). As a consequence, numerous works have addressed atrial arrhythmogenicity of a given electrophysiological model using different methods to simulate the perpetuation of re-entrant activity. However, no common procedure to test atrial fibrillation vulnerability has yet been defined. Here, we systematically evaluate and compare two state-of-the-art methods. The first one is rapid extrastimulus pacing from rim of the four pulmonary veins. The second consists of placing phase singularities in the atria, estimating an activation time map by solving the Eikonal equation and finally using this as initial condition for the electrical cardiac propagation simulation. In this way, we are forcing the wavefronts to follow re-entrant circuits with low computational cost thus less simulation time. We aim to identify a methodology to quantify arrhythmia vulnerability on patient-specific atrial geometries and substrates. We will proceed with in-silico experiments, comparing the results of these two methods to initiate re-entrant activity, checking the influence of the different parameters on the dynamics on the re-entrant drivers and finally extracting a valid set of parameters allowing to reliably assess re-entry vulnerability. The final objective is to come up with an easily reproducible minimal set of simulations to assess vulnerability of a particular atrial substrate (cellular and tissue model) or of distinct anatomical atrial geometries to arrhythmic episodes. Given the great need of exploring susceptibility to atrial arrhythmias, i.e. after a first ablation procedure, this study can provide a useful tool to test new treatment strategies and to learn how to prevent the onset and progression of atrial fibrillation.
Atrial fibrillation (AF) is an irregular heart rhythm due to disorganized atrial electrical activity, often sustained by rotational drivers called rotors. In the present work, we sought to characterize and discriminate whether simulated single stable rotors are located in the pulmonary veins (PVs) or not, only by using non-invasive signals (i.e., the 12-lead ECG). Several features have been extracted from the signals, such as Hjort descriptors, recurrence quantification analysis (RQA), and principal component analysis. All the extracted features have shown significant discriminatory power, with particular emphasis to the RQA parameters. A decision tree classifier achieved 98.48% accuracy, 83.33% sensitivity, and 100% specificity on simulated data. Clinical relevance— This study might guide ablation proce- dures, suggesting doctors to proceed directly in some patients with a pulmonary veins isolation, and avoiding the prior use of an invasive atrial mapping system.
Atrial fibrillation (AF) is the most frequent irregular heart rhythm due to disorganized atrial electrical activity, often sustained by rotational drivers called rotors. The non-invasive localization of AF drivers can lead to improved personalized ablation strategy, suggesting pulmonary vein (PV) isolation or more complex extra- PV ablation procedures in case the driver is on other atrial regions. We used a Machine Learning approach to characterize and discriminate simulated single stable rotors (1R) location: PVs, left atrium (LA) excluding the PVs, and right atrium (RA), utilizing solely non-invasive signals (i.e., the 12-lead ECG). 1R episodes sustaining AF were simulated. 128 features were extracted from the signals. Greedy forward algorithm was implemented to select the best feature set which was fed to a decision tree classifier with hold-out cross-validation technique. All tested features showed significant discriminatory power, especially those based on recurrence quantification analysis (up to 80.9% accuracy with single feature classification). The decision tree classifier achieved 89.4% test accuracy with 18 features on simulated data, with sensitivities of 93.0%, 82.4%, and 83.3% for RA, LA, and PV classes, respectively. Our results show that a machine learning approach can potentially identify the location of 1R sustaining AF using the 12-lead ECG.