Convex Optimization and Statistical Learning for Non-Invasive Electrical Cardiac Activity Estimation in Atrial Fibrillation

Abstract

Atrial fibrillation (AF) is the most common type of cardiac arrhythmia in clinical practice, affecting more than 33 million patients in the world [1]. AF is also a condition that increases the risk of the patients to suffer embolism, cardiac failure, stroke and, in the worst of cases, death [2]. Therefore, one of the clinical goals in AF patients is to restore sinus rhythm. This objective is usually accomplished by ablation of the cardiac tissue. Main targets of ablation are AF onset locations and drivers responsible for AF perpetuation [4]. Previous human in vivo research showed different strategies to locate AF drivers and guide pulmonary veins isolation (PVI). In the case of invasive mapping procedures [5]–[7], several catheters are introduced inside the atrial chambers to record from 8 to 128 simultaneous electrograms (EGMs) [5]. Despite the number of intracardiac signals, the large distance between catheter sensors and the complex atrial anatomy limits the capability of intracardiac mapping systems to characterize the global electrical activity in AF [8]. Non-invasive procedures based on ECG imaging (ECGI) have been also tested to guide PVI [9]–[11]. ECGI has been previously proposed to effectively reconstruct the electrophysiological activity on the heart surface, solving the spatio-temporal limitations of classical ECG, by using a non-invasive recording of body surface potentials (BSPs) [15], [16]. ECGI combines both numerical modeling of the bioelectric properties of the thorax and signal processing. However, ECGI is an ill-posed problem because the propagation between the epicardium and the torso implies information loss [17], and the BSPs are also blurred compared to the signals on the heart due to the laws of electromagnetic field theory. Regularization methods are then needed to obtain reliable and stable epicardial potential reconstructions [18]–[22]. On the other hand, ECGI requires an accurate mathematical modeling of both atria and torso, mainly from computerized tomography (CT) or magnetic resonance (MR) images. Previous research have shown that including any available a priori information during electrophysiological studies (EPSs) may improve the estimation of electrical activity on the heart [18], [29], [30]. Thus, combining non-invasive and invasive recordings during the ablation procedures may overcome some of the limitations of each individual technique and lead to more accurate identification of AF drivers. Moreover, in the last decade, Machine Learning and Deep Learning techniques have undergone considerable development in bioengineering, and this include novel research in AF. However, most of Deep Learning-based research which focus on AF is based on event detection and classification [31]–[33], and they do not include the estimation of ablation targets. Nonetheless, recent research showed that Machine Learning and Deep Learning methods can be also used in more complex tasks, like heart surface potentials estimation from BSPs [34] and rotor identification from 12- lead ECG [35]. Therefore, the main aim of the present Thesis is to overcome or avoid the limitations of ECGI in terms of epicardial potential estimation and rotor identification. To do that, two specific objectives are going to be defined: Inclusion of intracardiac information in ECGI during AF.We are going to assess new method to incorporate intracardiac information to solve ECGI, that is able to combine near-field (EGMs) and far-field (BSPs) information to provide a more complete picture of the electrical activity of the atria during AF. This objective will be carried out with a Tikhonov-based formulation for inverse problem that includes EGM-based intracavitary measurements obtained from the endocardium, simultaneously to BSPs. Implementation of a non-invasive Deep Learning-based method to estimate AF driver location. We are going to model the location of AF drivers from BSPs as a supervised classification problem with Deep Learning techniques, to address the location of AF drivers from previously-labeled realistic computerized AF models. The main aim of this point is to predict those regions without using ECGI, which requires accurate mathematical modeling of torso and atria. In both cases, we have used realistic tridimensional models for atria and torso, which simulated different AF propagation patterns. These synthetic cardiac models included simulated EGMs, from which BSPs were computed using the forward problem of electrocardiography. To simulate a realistic scenario, gaussian noise was added to these BSPs. We first proposed a new method to include intracavitary information from endocardial EGMs into the ECGI methodology. That is, we have included this information as an additional constraint on the Tikh regularization method. The proposed model improved the estimation of epicardial potentials by using first-order Constrained Tikhonov (Cons-Tikh) method, which was able to reproduce high frequency components in the solution, avoiding the low-pass filtering behavior of the classical Tikh approach. However, epicardial potential estimation degraded severely for all the methods as the complexity of AF increases. Moreover, although this methodology has two free regularization parameters to be estimated (very computationally expensive), we have diminished the computational cost by using an iterative regularization parameter estimation method. Finally, combined BSPs-EGMs measurements could be easily achieved in a real environment, since several studies simultaneously recorded BSPs and endocardial EGMs. Therefore, it is possible to integrate both types of signals in the proposed formulation in a clinical setting. Then, we designed MultiLayer Perceptron (MLP) and Convolutional Neural Network (CNN)-based models to identify target regions for ablation using a non-invasive procedure, as BSP mapping, by dividing the atrial geometry into 7 regions where the AF driver can be found. The main advantage of this methodology is to predict those regions without using ECGI, which requires accurate mathematical modeling of torso and atria. In the case of CNNs, where BSPs were converted into images, this methodology has been demonstrated to be accurate and robust to noise. Moreover, the proposed methodology makes transfer learning very easy to apply, since it can be used to adapt much more complex pre-trained models to our specific task with promising results. Finally, the proposed classification models can be easily extrapolated to other atrial geometry divisions based on a higher number of smaller regions, being able to get a higher resolution in the driver classification.