Meet us at the Conference on Applications of Dynamical Systems organized by the Society for Industrial and Applied Mathematics (SIAM) from May 14-18th 2023 in Portland, Oregon, USA. The conference covers a wide range of topics: "The application of dynamical systems theory to areas outside of mathematics continues to be a vibrant, exciting, and fruitful endeavor. These application areas are diverse and multidisciplinary, covering areas that include biology, chemistry, physics, climate science, social science, industrial mathematics, data science, and more. This conference strives to amass a blend of application-oriented material and the mathematics that informs and supports the discipline. The goals of the conference are a cross-fertilization of ideas from different application areas and increased communication between those who develop dynamical-systems techniques and the mathematicians, scientists, and engineers who use them."
We will discuss in several mini-symposia the latest advances in applying concepts from dynamical systems theory and machine learning to heart research ('Nonlinear Dynamics of the Heart' 1, 2 & 3, 'Predicting Cardiac Dynamics using Machine Learning' 1 & 2, 'The Cardiac Fibrillation Challenge: From Principles to Patients' 1 & 2, 'Waves: Theory and Applications to Biomedical Sciences' 1 & 2, 'Phase Transitions in Electrophysiological Systems' 1). In our mini-symposium 'Predicting Cardiac Dynamics using Machine Learning' we will specifically discuss machine and deep learning methods applied to study cardiac disease: The heart is a highly dynamic organ, in which nonlinear waves of electrical excitation trigger mechanical contraction. During heart rhythm disorders, such as atrial or ventricular fibrillation, these coupled electromechanical waves degenerate into chaotic spatio-temporal dynamics. The measurement of these dynamics is pivotal for a better understanding of heart rhythm disorders and for guiding therapeutics, such as catheter ablation. However, the measurements are challenging because the dynamics are three-dimensional, rapidly evolving, chaotic, and can only be measured partially or indirectly. In this mini-symposium, we aim to discuss recent advances in applying machine learning methods to predict cardiac dynamics and therapeutic outcomes from various measurement data. We will discuss how complicated electrical wave patterns, such as spiral or scroll waves, can be reconstructed from sparse or noisy measurements, from partial measurements on the heart's surface, or be predicted from the heart's deformations. We will discuss various deep learning techniques, such as autoencoders, transformers, long short-term memory neural networks, and their combination with reservoir computing techniques. Moreover, we will discuss forecasting, classification and data-driven modeling of cardiac dynamics, and the prediction of ablation outcomes.
List of speakers:
Jan Lebert (UCSF) - Predicting Cardiac Dynamics using Deep Learning
In the heart, nonlinear waves of electrical excitation trigger mechanical contractions. The dynamics can become very complex, particularly during heart rhythm disorders, such as ventricular or atrial fibrillation. To date, it is a challenge to observe and visualize these dynamics, because they can only be measured partially or indirectly. In this talk, we introduce the current challenges in the field and discuss the potential to reconstruct cardiac wave dynamics using deep learning. We specifically discuss how convolutional neural networks can be used to denoise and interpolate measurement data, cross-predict electrical dynamics from tissue mechanics, infer fully three-dimensional dynamics from two-dimensional or otherwise partial observations, track discrete features such as phase singularities, and be trained on simulated and subsequently be applied to experimental data. This talk provides an overview and a basis for the following talks in this minisymposium.
Inga Kottlarz (Max Planck) - Reconstructing Spatiotemporal Chaos in Three-Dimensional Excitable Media
The cardiac muscle is an excitable medium that can exhibit complex dynamics, including spatiotemporal chaos associated with (fatal) cardiac arrhythmias. On a small scale, cardiac tissue consists of interacting cardiac muscle cells embedded in an extracellular matrix. These cells interact electrically and mechanically, and their (in-)coherent motion is triggered by the propagation of electrical excitation waves, including spiral or scroll waves during ventricular fibrillation. Electrical excitation can be measured optically using fluorescent dyes, but only at the surface of Langendorff-perfused isolated hearts. Therefore, a method to reconstruct the excitation inside the muscle based on surface data is needed. One possible approach to this reconstruction is the utilization of artificial neural networks (ANNs) that are trained on simulations of cardiac dynamics and later applied to real experimental data. To estimate the feasibility of this method, we trained and tested different ANNs on a simple model of isotropic, chaotic excitable media on a regular grid. Our investigations show that the reconstruction of these high-dimensional chaotic states is possible in principle, but as expected its quality depends on the network architecture used and in general decreases with increasing reconstruction depth. In our contribution we will present and discuss these results as well as extensions using different models and alternative machine learning methods.
Nathan Dermul (KU Leuven) - Estimation of Electrical Activation in the Heart from Local Deformations Using Neural Networks
Cardiac arrhythmias are a major health problem. As the local electrical activation triggers mechanical contraction of the muscle fibers, an aberrant electrical pattern causes suboptimal pumping of blood. A classical approach to diagnose and analyse cardiac arrhythmias occurs via the electrical signals. However, in recent years it was shown that excitation patterns such as traveling waves and rotors in the heart can also be observed via their effect on the mechanical deformation [Christoph, J. et al. Electromechanical vortex filaments during cardiac fibrillation. Nature 555, 667–672 (2018)], [Grondin J. et al. 4D cardiac electromechanical activation imaging. Comput Biol Med. 2019 Oct]. Here, we present a novel approach to infer the electrical pattern from local deformation using an underlying physics-based model. The combination of deep learning with physical constraints enables to recover detailed activation maps from local displacements in the presence of noise. Results are shown for simulated data and an outlook on analysing clinical data is given.
Elizabeth M. Cherry (Georgia Tech) - Predicting Complex Spatiotemporal Electrical Dynamics in Live Human Hearts: a Novel Reservoir Computing Approach
Predicting complex nonlinear time series is a challenging task made even more difficult with the inclusion of space, such as behavior of cardiac tissue during arrhythmias. Nevertheless, even relatively short-term predictions of complex cardiac electrical dynamics in space could be useful for improving existing treatments or developing new therapeutical approaches. In this talk, we demonstrate a novel method for predicting the spatiotemporal electrical dynamics of cardiac tissue using an echo-state network integrated with a convolutional autoencoder. We show that our approach can forecast complex spiral-wave-breakup several periods in advance for time series ranging from model-derived synthetic datasets to optical-mapping recordings of explanted human hearts.
Desmond Kabus (KU Leuven) - Creation of Predictive Cardiac Excitation Model at the Tissue Scale with Machine Learning
Electrical wave propagation in cardiac muscle tissue is often modelled as a reaction-diffusion system. The reaction term, the so-called in silico tissue model or cell model describes the ion dynamics in, around, and between cells. Tissue models are often fit on the single-cell level using few current or voltage traces from patch clamp recordings and restitution curves, i.e. a small amount of data. In this talk, I outline a novel data-driven approach to create tissue-based models from optical voltage mapping experiments of conditionally immortalized human atrial myocyte monolayers using machine learning. This is done by extracting features from the full spatiotemporal evolution of the optically recorded transmembrane potential. A neural network is then fit to these features. The trained neural network-based models are able to predict the spiral wave propagation even though they are only trained on waves from point sources. This project is one further step towards a fully patient-specific tissue model.
Cristian A. Barrios (KIT) - Enhancing Machine Learning Methods for Cardiac Electrophysiology Through the use of Eikonal Simulations
Machine learning (ML) methods can potentially improve diagnosis in different fields of medicine. Large numbers of clinical data are required to properly train these methods, which are often unavailable in the desired quantity and quality. On the other hand, in silico data can replace or extend clinical data to train ML methods. In three examples, eikonal model simulations were used for this purpose. First, a neural network was trained to quantify the percentage of fibrotic tissue in the atria by using simulated P waves. The fibrosis extent was estimated by a neural network with an absolute root mean square error of 8.78%. Second, a decision tree classifier with a hold-out classification approach was trained using a hybrid dataset of atrial flutter cases (1424 in silico ECGs and 345 clinical ECGs). The decision tree was able to predict the localization of atrial flutter outperforming previous methods. Finally, in an ongoing project, the eikonal model was combined with biophysical models to simulate complex cardiac arrhythmias more accurately. This method will be used to develop a ML method predicting the arrhythmogenicity of different patterns of fibrosis. These three studies are representative cases of how the eikonal model can be a powerful tool to enable or fuel the application of ML methods in cardiac research.
Nele Vandersickel (U Ghent) - Classifying Atrial Tachycardia Dynamics Using Machine Learning
In this talk, we will present a unique topological classification of atrial tachycardia (AT). We will demonstrate that is it possible for each different case to uniquely label the AT, and propose a novel optimal ablation strategy.\\In a first part, we will show how we extended our software tool, DGM or directed graph mapping, so it can uniquely classify a measured AT. DGM uses network theory to convert the AT into a single network. This network and the topology of the atrium are the building blocks of the classification. In a second part, we will demonstrate the classification with a series of over 1000 different simulations, which will represent a large variety of different ATs. We will show how this classification leads to an optimal ablation target, which is close to 100% successful in case of simulated ATs. In a third part, we will apply our classification on a database of 120 ATs and show that our ablation strategy is superior to the current ablation strategy. Finally, we will demonstrate how machine learning can automatize the classification even further. This research opens future perspectives for the analysis of atrial fibrillation. We will end with some ideas how the classification of AT can lead to a better understanding of AF.
Prasanth Ganesan (Stanford) - Machine Learning of Spatiotemporal Organization of Electrograms and Clinical Data Predicts Response to Atrial Fibrillation Ablation
This talk will cover approaches to quantify spatiotemporal dynamics of atrial fibrillation (AF) from clinical electrophysiological data such as intracardiac electrograms, patient characteristics etc. Specific focus will be on Machine Learning (ML) of such data to predict outcomes of AF ablation therapy. I will discuss both past studies in the literature and recently published methods such as REpetitive ACTivity (REACT) mapping for AF, which is a novel approach to identify regions of organization in AF atrium. Simulations of morphological and timing variations in AF electrograms showed high robustness of REACT method. Unsupervised Machine Learning of REACT and 50 clinical variables predicted AF termination by ablation. I will conclude with some thoughts on the future of ML for clinical cardiac electrophysiology applications including improving AF ablation outcomes.
