On Learning and Generalization to Solve Inverse Problem of Electrophysiological Imaging

In this dissertation, we are interested in solving a linear inverse problem: inverse electrophysiological (EP) imaging, where our objective is to computationally reconstruct personalized cardiac electrical signals based on body surface electrocardiogram (ECG) signals. EP imaging has shown promise in the diagnosis and treatment planning of cardiac dysfunctions such as atrial flutter, atrial fibrillation, ischemia, infarction and ventricular arrhythmia. Towards this goal, we frame it as a problem of learning a function from the domain of measurements to signals. Depending upon the assumptions, we present two classes of solutions: 1) Bayesian inference in a probabilistic graphical model, 2) Learning from samples using deep networks. In both of these approaches, we emphasize on learning the inverse function with good generalization ability, which becomes a main theme of the dissertation. In a Bayesian framework, we argue that this translates to appropriately integrating different sources of knowledge into a common probabilistic graphical model framework and using it for patient specific signal estimation through Bayesian inference. In learning from samples setting, this translates to designing a deep network with good generalization ability, where good generalization refers to the ability to reconstruct inverse EP signals in a distribution of interest (which could very well be outside the sample distribution used during training). By drawing ideas from different areas like functional analysis (e.g. Fenchel duality), variational inference (e.g. Variational Bayes) and deep generative modeling (e.g. variational autoencoder), we show how we can incorporate different prior knowledge in a principled manner in a probabilistic graphical model framework to obtain a good inverse solution with generalization ability. Similarly, to improve generalization of deep networks learning from samples, we use ideas from information theory (e.g. information bottleneck), learning theory (e.g. analytical learning theory), adversarial training, complexity theory and functional analysis (e.g. RKHS). We test our algorithms on synthetic data and real data of the patients who had undergone through catheter ablation in clinics and show that our approach yields significant improvement over existing methods. Towards the end of the dissertation, we investigate general questions on generalization and stabilization of adversarial training of deep networks and try to understand the role of smoothness and function space complexity in answering those questions. We conclude by identifying limitations of the proposed methods, areas of further improvement and open questions that are specific to inverse electrophysiological imaging as well as broader, encompassing theory of learning and generalization

Bayesian Active Learning for Personalization and Uncertainty Quantification in Cardiac Electrophysiological Model

Cardiacvascular disease is the top death causing disease worldwide. In recent years, high-fidelity personalized models of the heart have shown an increasing capability to supplement clinical cardiology for improved patient-specific diagnosis, prediction, and treatment planning. In addition, they have shown promise to improve scientific understanding of a variety of disease mechanisms. However, model personalization by estimating the patient-specific tissue properties that are in the form of parameters of a physiological model is challenging. This is because tissue properties, in general, cannot be directly measured and they need to be estimated from measurements that are indirectly related to them through a physiological model. Moreover, these unknown tissue properties are heterogeneous and spatially varying throughout the heart volume presenting a difficulty of high-dimensional (HD) estimation from indirect and limited measurement data. The challenge in model personalization, therefore, summarizes to solving an ill-posed inverse problem where the unknown parameters are HD and the forward model is complex with a non-linear and computationally expensive physiological model. In this dissertation, we address the above challenge with following contributions. First, to address the concern of a complex forward model, we propose the surrogate modeling of the complex target function containing the forward model – an objective function in deterministic estimation or a posterior probability density function in probabilistic estimation – by actively selecting a set of training samples and a Bayesian update of the prior over the target function. The efficient and accurate surrogate of the expensive target function obtained in this manner is then utilized to accelerate either deterministic or probabilistic parameter estimation. Next, within the framework of Bayesian active learning we enable active surrogate learning over a HD parameter space with two novel approaches: 1) a multi-scale optimization that can adaptively allocate higher resolution to heterogeneous tissue regions and lower resolution to homogeneous tissue regions; and 2) a generative model from low-dimensional (LD) latent code to HD tissue properties. Both of these approaches are independently developed and tested within a parameter optimization framework. Furthermore, we devise a novel method that utilizes the surrogate pdf learned on an estimated LD parameter space to improve the proposal distribution of Metropolis Hastings for an accelerated sampling of the exact posterior pdf. We evaluate the presented methods on estimating local tissue excitability of a cardiac electrophysiological model in both synthetic data experiments and real data experiments. Results demonstrate that the presented methods are able to improve the accuracy and efficiency in patient-specific model parameter estimation in comparison to the existing approaches used for model personalization

Interpretable Modeling and Reduction of Unknown Errors in Mechanistic Operators

Prior knowledge about the imaging physics provides a mechanistic forward operator that plays an important role in image reconstruction, although myriad sources of possible errors in the operator could negatively impact the reconstruction solutions. In this work, we propose to embed the traditional mechanistic forward operator inside a neural function, and focus on modeling and correcting its unknown errors in an interpretable manner. This is achieved by a conditional generative model that transforms a given mechanistic operator with unknown errors, arising from a latent space of self-organizing clusters of potential sources of error generation. Once learned, the generative model can be used in place of a fixed forward operator in any traditional optimization-based reconstruction process where, together with the inverse solution, the error in prior mechanistic forward operator can be minimized and the potential source of error uncovered. We apply the presented method to the reconstruction of heart electrical potential from body surface potential. In controlled simulation experiments and in-vivo real data experiments, we demonstrate that the presented method allowed reduction of errors in the physics-based forward operator and thereby delivered inverse reconstruction of heart-surface potential with increased accuracy.Comment: 11 pages, Conference: Medical Image Computing and Computer Assisted Interventio

Learning Geometry-Dependent and Physics-Based Inverse Image Reconstruction

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper, we present a new approach to learn inverse imaging that exploit the underlying geometry and physics. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then learn the geometry-dependent physics in between the two domains by explicitly modeling it via a bipartite graph over the graphical embedding of the two geometry. We applied the presented network to reconstructing electrical activity on the heart surface from body-surface potential. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the presented network to generalize across geometrical changes underlying the data in comparison to its Euclidean alternatives

Deep Learning Formulation of ECGI Integrating Image & Signal Information with Data-driven Regularisation

International audienceAims: Electrocardiographic Imaging (ECGI) is a promising tool to map the electrical activity of the heart non-invasively using body surface potentials (BSP). However, it is still challenging due to the mathematically ill-posed nature of the inverse problem to solve. Novel approaches leveraging progress in artificial intelligence could alleviate these difficulties. Methods: We propose a Deep Learning (DL) formulation of ECGI in order to learn the statistical relation between BSP and cardiac activation. The presented method is based on Conditional Variational Autoencoders (CVAE) using deep generative neural networks. To quantify the accuracy of this method, we simulated activation maps and BSP data on six cardiac anatomies. Results: We evaluated our model by training it on five different cardiac anatomies (5 000 activation maps) and by testing it on a new patient anatomy over 200 activation maps. Due to the probabilistic property of our method, we predicted 10 distinct activation maps for each BSP data. The proposed method is able to generate volumetric activation maps with a good accuracy on the simulated data: the mean absolute error is 9.40 ms with 2.16 ms standard deviation on this testing set. Conclusion: The proposed formulation of ECGI enables to naturally include imaging information in the estimation of cardiac electrical activity from body surface potential. It naturally takes into account all the spatio-temporal correlations present in the data. We believe these features can help improve ECGI results

Deep Learning Formulation of ECGI for Data-driven Integration of Spatiotemporal Correlations and Imaging Information

International audienceThe challenge of non-invasive Electrocardiographic Imaging (ECGI) is to recreate the electrical activity of the heart using body surface potentials. Specifically, there are numerical difficulties due to the ill-posed nature of the problem. We propose a novel method based on Conditional Variational Autoencoders using Deep generative Neural Networks to overcome this challenge. By conditioning the electrical activity on heart shape and electrical potentials, our model is able to generate activation maps with good accuracy on simulated data (mean square error, MSE = 0.095). This method differs from other formulations because it naturally takes into account spatio-temporal correlations as well as the imaging substrate through convolutions and conditioning. We believe these features can help improving ECGI results

Learning with Limited Labeled Data in Biomedical Domain by Disentanglement and Semi-Supervised Learning

In this dissertation, we are interested in improving the generalization of deep neural networks for biomedical data (e.g., electrocardiogram signal, x-ray images, etc). Although deep neural networks have attained state-of-the-art performance and, thus, deployment across a variety of domains, similar performance in the clinical setting remains challenging due to its ineptness to generalize across unseen data (e.g., new patient cohort). We address this challenge of generalization in the deep neural network from two perspectives: 1) learning disentangled representations from the deep network, and 2) developing efficient semi-supervised learning (SSL) algorithms using the deep network. In the former, we are interested in designing specific architectures and objective functions to learn representations, where variations in the data are well separated, i.e., disentangled. In the latter, we are interested in designing regularizers that encourage the underlying neural function\u27s behavior toward a common inductive bias to avoid over-fitting the function to small labeled data. Our end goal is to improve the generalization of the deep network for the diagnostic model in both of these approaches. In disentangled representations, this translates to appropriately learning latent representations from the data, capturing the observed input\u27s underlying explanatory factors in an independent and interpretable way. With data\u27s expository factors well separated, such disentangled latent space can then be useful for a large variety of tasks and domains within data distribution even with a small amount of labeled data, thus improving generalization. In developing efficient semi-supervised algorithms, this translates to utilizing a large volume of the unlabelled dataset to assist the learning from the limited labeled dataset, commonly encountered situation in the biomedical domain. By drawing ideas from different areas within deep learning like representation learning (e.g., autoencoder), variational inference (e.g., variational autoencoder), Bayesian nonparametric (e.g., beta-Bernoulli process), learning theory (e.g., analytical learning theory), function smoothing (Lipschitz Smoothness), etc., we propose several leaning algorithms to improve generalization in the associated task. We test our algorithms on real-world clinical data and show that our approach yields significant improvement over existing methods. Moreover, we demonstrate the efficacy of the proposed models in the benchmark data and simulated data to understand different aspects of the proposed learning methods. We conclude by identifying some of the limitations of the proposed methods, areas of further improvement, and broader future directions for the successful adoption of AI models in the clinical environment

Transferring Generalized Knowledge from Physics-based Simulation to Clinical Domain

A primary factor for the success of machine learning is the quality of labeled training data. However, in many fields, labeled data can be costly, difficult, or even impossible to acquire. In comparison, computer simulation data can now be generated at a much higher abundance with a much lower cost. These simulation data could potentially solve the problem of data deficiency in many machine learning tasks. Nevertheless, due to model assumptions, simplifications and possible errors, there is always a discrepancy between simulated and real data. This discrepancy needs to be addressed when transferring the knowledge from simulation to real data. Furthermore, simulation data is always tied to specific settings of models parameters, many of which have a considerable range of variations yet not necessarily relevant to the machine learning task of interest. The knowledge extracted from simulation data must thus be generalizable across these parameter variations before being transferred. In this dissertation, we address the two outlined challenges in leveraging simulation data to overcome the shortage of labeled real data, . We do so in a clinical task of localizing the origin of ventricular activation from 12 lead electrocardiograms (ECGs), where the clinical ECG data with labeled sites of origin in the heart can only be invasively available. By adopting the concept of domain adaptation, we address the discrepancy between simulated and clinical ECG data by learning the shift between the two domains using a large amount of simulation data and a small amount of clinical data. By adopting the concept of domain generalization, we then address the reliance of simulated ECG data on patient-specific geometrical models by learning to generalize simulated ECG data across subjects, before transferring them to clinical data. Evaluated on in-vivo premature ventricular contraction (PVC) patients, we demonstrate the feasibility of utilizing a large number of offline simulated ECG datasets to enable the prediction of the origin of arrhythmia with only a small number of clinical ECG data on a new patient