EP-PINNs: Cardiac Electrophysiology Characterisation Using Physics-Informed Neural Networks

Reconstruction of excitation waves from mechanical deformation using physics-informed neural networks

Non-invasive assessment of the electrical activation pattern can significantly contribute to the diagnosis and treatment of cardiac arrhythmias, due to faster and safer diagnosis, improved surgical planning and easier follow-up. One promising path is to measure the mechanical contraction via echocardiography and utilize this as an indirect way of measuring the original activation pattern. To solve this demanding inversion task, we make use of physics-informed neural networks, an upcoming methodology to solve forward and inverse physical problems governed by partial differential equations. In this study, synthetic data sets were created, consisting of 2D excitation waves coupled to an isotropic and linearly deforming elastic medium. We show that for both focal and spiral patterns, the underlying excitation waves can be reconstructed accurately. We test the robustness of the method against Gaussian noise, reduced spatial resolution and projected tri-planar data. In situations where the data quality is heavily reduced, we show how to improve the reconstruction by additional regularization on the wave speed. Our findings suggest that physics-informed neural networks hold the potential to solve sparse and noisy bio-mechanical inversion problems and may offer a pathway to non-invasive assessment of certain cardiac arrhythmias.

Super-resolution Left Ventricular Flow and Pressure Mapping by Navier-Stokes-Informed Neural Networks

Intraventricular vector flow mapping (VFM) is a growingly adopted echocardiographic modality that derives time-resolved two-dimensional flow maps in the left ventricle (LV) from color-Doppler sequences. Current VFM models rely on kinematic constraints arising from planar flow incompressibility. However, these models are not informed by crucial information about flow physics; most notably the pressure and shear forces within the fluid and the resulting accelerations. This limitation has rendered VFM unable to combine information from different time frames in an acquisition sequence or derive fluctuating pressure maps. In this study, we leveraged recent advances in artificial intelligence (AI) to develop AI-VFM, a vector flow mapping modality that uses physics-informed neural networks (PINNs) encoding mass conservation and momentum balance inside the LV, and no-slip boundary conditions at the LV endocardium. AI-VFM recovers the flow and pressure fields in the LV from standard echocardiographic scans. It performs phase unwrapping and recovers flow data in areas without input color-Doppler data. AI-VFM also recovers complete flow maps at time points without color-Doppler input data, producing super-resolution flow maps. We show that informing the PINNs with momentum balance is essential to achieving temporal super-resolution and significantly increases the accuracy of AI-VFM compared to informing the PINNs only with mass conservation. AI-VFM is solely informed by each patient's flow physics; it does not utilize explicit smoothness constraints or incorporate data from other patients or flow models. AI-VFM takes 15 minutes to run in off-the-shelf graphics processing units and its underlying PINN framework could be extended to map other flow-associated metrics like blood residence time or the concentration of coagulation species.

Simultaneous data assimilation and cardiac electrophysiology model correction using differentiable physics and deep learning

Modelling complex systems, like the human heart, has made great progress over the last decades. Patient-specific models, called 'digital twins', can aid in diagnosing arrhythmias and personalizing treatments. However, building highly accurate predictive heart models requires a delicate balance between mathematical complexity, parameterization from measurements and validation of predictions. Cardiac electrophysiology (EP) models range from complex biophysical models to simplified phenomenological models. Complex models are accurate but computationally intensive and challenging to parameterize, while simplified models are computationally efficient but less realistic. In this paper, we propose a hybrid approach by leveraging deep learning to complete a simplified cardiac model from data. Our novel framework has two components, decomposing the dynamics into a physics based and a data-driven term. This construction allows our framework to learn from data of different complexity, while simultaneously estimating model parameters. First, using in silico data, we demonstrate that this framework can reproduce the complex dynamics of cardiac transmembrane potential even in the presence of noise in the data. Second, using ex vivo optical data of action potentials (APs), we demonstrate that our framework can identify key physical parameters for anatomical zones with different electrical properties, as well as to reproduce the AP wave characteristics obtained from various pacing locations. Our physics-based data-driven approach may improve cardiac EP modelling by providing a robust biophysical tool for predictions.

Animal Disease Models and Patient-iPS-Cell-Derived In Vitro Disease Models for Cardiovascular Biology-How Close to Disease?

Currently, zebrafish, rodents, canines, and pigs are the primary disease models used in cardiovascular research. In general, larger animals have more physiological similarities to humans, making better disease models. However, they can have restricted or limited use because they are difficult to handle and maintain. Moreover, animal welfare laws regulate the use of experimental animals. Different species have different mechanisms of disease onset. Organs in each animal species have different characteristics depending on their evolutionary history and living environment. For example, mice have higher heart rates than humans. Nonetheless, preclinical studies have used animals to evaluate the safety and efficacy of human drugs because no other complementary method exists. Hence, we need to evaluate the similarities and differences in disease mechanisms between humans and experimental animals. The translation of animal data to humans contributes to eliminating the gap between these two. In vitro disease models have been used as another alternative for human disease models since the discovery of induced pluripotent stem cells (iPSCs). Human cardiomyocytes have been generated from patient-derived iPSCs, which are genetically identical to the derived patients. Researchers have attempted to develop in vivo mimicking 3D culture systems. In this review, we explore the possible uses of animal disease models, iPSC-derived in vitro disease models, humanized animals, and the recent challenges of machine learning. The combination of these methods will make disease models more similar to human disease.

Reconstruction of three-dimensional scroll waves in excitable media from two-dimensional observations using deep neural networks

Scroll wave dynamics are thought to underlie life-threatening ventricular fibrillation. However, direct observations of three-dimensional electrical scroll waves remain elusive, as there is no direct way to measure action potential wave patterns transmurally throughout the thick ventricular heart muscle. Here we study whether it is possible to reconstruct simulated scroll waves and scroll wave chaos using deep learning. We trained encoding-decoding convolutional neural networks to predict three-dimensional scroll wave dynamics inside bulk-shaped excitable media from two-dimensional observations of the wave dynamics on the bulk's surface. We tested whether observations from one or two opposing surfaces would be sufficient and whether transparency or measurements of surface deformations enhances the reconstruction. Further, we evaluated the approach's robustness against noise and tested the feasibility of predicting the bulk's thickness. We distinguished isotropic and anisotropic, as well as opaque and transparent, excitable media as models for cardiac tissue and the Belousov-Zhabotinsky chemical reaction, respectively. While we demonstrate that it is possible to reconstruct three-dimensional scroll wave dynamics, we also show that it is challenging to reconstruct complicated scroll wave chaos and that prediction outcomes depend on various factors such as transparency, anisotropy, and ultimately the thickness of the medium compared to the size of the scroll waves. In particular, we found that anisotropy provides crucial information for neural networks to decode depth, which facilitates the reconstructions. In the future, deep neural networks could be used to visualize intramural action potential wave patterns from epi- or endocardial measurements.

A Review of Healthy and Fibrotic Myocardium Microstructure Modeling and Corresponding Intracardiac Electrograms

Computational simulations of cardiac electrophysiology provide detailed information on the depolarization phenomena at different spatial and temporal scales. With the development of new hardware and software, in silico experiments have gained more importance in cardiac electrophysiology research. For plane waves in healthy tissue, in vivo and in silico electrograms at the surface of the tissue demonstrate symmetric morphology and high peak-to-peak amplitude. Simulations provided insight into the factors that alter the morphology and amplitude of the electrograms. The situation is more complex in remodeled tissue with fibrotic infiltrations. Clinically, different changes including fractionation of the signal, extended duration and reduced amplitude have been described. In silico, numerous approaches have been proposed to represent the pathological changes on different spatial and functional scales. Different modeling approaches can reproduce distinct subsets of the clinically observed electrogram phenomena. This review provides an overview of how different modeling approaches to incorporate fibrotic and structural remodeling affect the electrogram and highlights open challenges to be addressed in future research.