Dreaming of Electrical Waves: Generative Modeling of Cardiac Excitation Waves using Diffusion Models.

Electrical waves in the heart form rotating spiral or scroll waves during life-threatening arrhythmias such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which describe reaction-diffusion dynamics in excitable media. More recently, data-driven generative modeling has emerged as an alternative to generate spatio-temporal patterns in physical and biological systems. Here, we explore denoising diffusion probabilistic models for the generative modeling of electrical wave patterns in cardiac tissue. We trained diffusion models with simulated electrical wave patterns to be able to generate such wave patterns in unconditional and conditional generation tasks. For instance, we explored the diffusion-based i) parameter-specific generation, ii) evolution and iii) inpainting of spiral wave dynamics, including reconstructing three-dimensional scroll wave dynamics from superficial two-dimensional measurements. Further, we generated arbitrarily shaped bi-ventricular geometries and simultaneously initiated scroll wave patterns inside these geometries using diffusion. We characterized and compared the diffusion-generated solutions to solutions obtained with corresponding biophysical models and found that diffusion models learn to replicate spiral and scroll waves dynamics so well that they could be used for data-driven modeling of excitation waves in cardiac tissue. For instance, an ensemble of diffusion-generated spiral wave dynamics exhibits similar self-termination statistics as the corresponding ensemble simulated with a biophysical model. However, we also found that diffusion models {produce artifacts if training data is lacking, e.g. during self-termination,} and `hallucinate' wave patterns when insufficiently constrained.

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.

Real-Time Optical Mapping of Contracting Cardiac Tissues With GPU-Accelerated Numerical Motion Tracking.

Optical mapping of action potentials or calcium transients in contracting cardiac tissues are challenging because of the severe sensitivity of the measurements to motion. The measurements rely on the accurate numerical tracking and analysis of fluorescence changes emitted by the tissue as it moves, and inaccurate or no tracking can produce motion artifacts and lead to imprecise measurements that can prohibit the analysis of the data. Recently, it was demonstrated that numerical motion-tracking and -stabilization can effectively inhibit motion artifacts, allowing highly detailed simultaneous measurements of electrophysiological phenomena and tissue mechanics. However, the field of electromechanical optical mapping is still young and under development. To date, the technique is only used by a few laboratories, the processing of the video data is time-consuming and performed offline post-acquisition as it is associated with a considerable demand for computing power. In addition, a systematic review of numerical motion tracking algorithms applicable to optical mapping data is lacking. To address these issues, we evaluated 5 open-source numerical motion-tracking algorithms implemented on a graphics processing unit (GPU) and compared their performance when tracking and compensating motion and measuring optical traces in voltage- or calcium-sensitive optical mapping videos of contracting cardiac tissues. Using GPU-accelerated numerical motion tracking, the processing times necessary to analyze optical mapping videos become substantially reduced. We demonstrate that it is possible to track and stabilize motion and create motion-compensated optical maps in real-time with low-resolution (128 x 128 pixels) and high resolution (800 x 800 pixels) optical mapping videos acquired at 500 and 40 fps, respectively. We evaluated the tracking accuracies and motion-stabilization capabilities of the GPU-based algorithms on synthetic optical mapping videos, determined their sensitivity to fluorescence signals and noise, and demonstrate the efficacy of the Farnebäck algorithm with recordings of contracting human cardiac cell cultures and beating hearts from 3 different species (mouse, rabbit, pig) imaged with 4 different high-speed cameras. GPU-accelerated processing provides a substantial increase in processing speed, which could open the path for more widespread use of numerical motion tracking and stabilization algorithms during routine optical mapping studies.

Direct optogenetic stimulation of smooth muscle cells to control gastric contractility.

Rationale: Antral peristalsis is responsible for gastric emptying. Its failure is called gastroparesis and often caused by dysfunction of enteric neurons and interstitial cells of Cajal (ICC). Current treatment options, including gastric electrical stimulation, are non-satisfying and may improve symptoms but commonly fail to restore gastric emptying. Herein, we explore direct optogenetic stimulation of smooth muscle cells (SMC) via the light-gated non-selective cation channel Channelrhodopsin2 (ChR2) to control gastric motor function. Methods: We used a transgenic mouse model expressing ChR2 in fusion with eYFP under the control of the chicken-ß-actin promoter. We performed patch clamp experiments to quantify light-induced currents in isolated SMC, Ca2+ imaging and isometric force measurements of antral smooth muscle strips as well as pressure recordings of intact stomachs to evaluate contractile responses. Light-induced propulsion of gastric contents from the isolated stomach preparation was quantified in video recordings. We furthermore tested optogenetic stimulation in a gastroparesis model induced by neuronal- and ICC-specific damage through methylene blue photo-toxicity. Results: In the stomachs, eYFP signals were restricted to SMC in which blue light (460 nm) induced inward currents typical for ChR2. These depolarizing currents led to contractions in antral smooth muscle strips that were stronger than those triggered by supramaximal electrical field stimulation and comparable to those evoked by global depolarization with high K+ concentration. In the intact stomach, panoramic illumination efficiently increased intragastric pressure achieving 239±46% (n=6) of the pressure induced by electrical field stimulation and triggered gastric transport. Within the gastroparesis model, electric field stimulation completely failed but light still efficiently generated pressure waves. Conclusions: We demonstrate direct optogenetic stimulation of SMC to control gastric contractility. This completely new approach could allow for the restoration of motility in gastroparesis in the future.

Rotor Localization and Phase Mapping of Cardiac Excitation Waves Using Deep Neural Networks.

The analysis of electrical impulse phenomena in cardiac muscle tissue is important for the diagnosis of heart rhythm disorders and other cardiac pathophysiology. Cardiac mapping techniques acquire local temporal measurements and combine them to visualize the spread of electrophysiological wave phenomena across the heart surface. However, low spatial resolution, sparse measurement locations, noise and other artifacts make it challenging to accurately visualize spatio-temporal activity. For instance, electro-anatomical catheter mapping is severely limited by the sparsity of the measurements, and optical mapping is prone to noise and motion artifacts. In the past, several approaches have been proposed to create more reliable maps from noisy or sparse mapping data. Here, we demonstrate that deep learning can be used to compute phase maps and detect phase singularities in optical mapping videos of ventricular fibrillation, as well as in very noisy, low-resolution and extremely sparse simulated data of reentrant wave chaos mimicking catheter mapping data. The self-supervised deep learning approach is fundamentally different from classical phase mapping techniques. Rather than encoding a phase signal from time-series data, a deep neural network instead learns to directly associate phase maps and the positions of phase singularities with short spatio-temporal sequences of electrical data. We tested several neural network architectures, based on a convolutional neural network (CNN) with an encoding and decoding structure, to predict phase maps or rotor core positions either directly or indirectly via the prediction of phase maps and a subsequent classical calculation of phase singularities. Predictions can be performed across different data, with models being trained on one species and then successfully applied to another, or being trained solely on simulated data and then applied to experimental data. Neural networks provide a promising alternative to conventional phase mapping and rotor core localization methods. Future uses may include the analysis of optical mapping studies in basic cardiovascular research, as well as the mapping of atrial fibrillation in the clinical setting.

Inverse mechano-electrical reconstruction of cardiac excitation wave patterns from mechanical deformation using deep learning.

The inverse mechano-electrical problem in cardiac electrophysiology is the attempt to reconstruct electrical excitation or action potential wave patterns from the heart's mechanical deformation that occurs in response to electrical excitation. Because heart muscle cells contract upon electrical excitation due to the excitation-contraction coupling mechanism, the resulting deformation of the heart should reflect macroscopic action potential wave phenomena. However, whether the relationship between macroscopic electrical and mechanical phenomena is well-defined and unique enough to be utilized for an inverse imaging technique in which mechanical activation mapping is used as a surrogate for electrical mapping has yet to be determined. Here, we provide a numerical proof-of-principle that deep learning can be used to solve the inverse mechano-electrical problem in phenomenological two- and three-dimensional computer simulations of the contracting heart wall, or in elastic excitable media, with muscle fiber anisotropy. We trained a convolutional autoencoder neural network to learn the complex relationship between electrical excitation, active stress, and tissue deformation during both focal or reentrant chaotic wave activity and, consequently, used the network to successfully estimate or reconstruct electrical excitation wave patterns from mechanical deformation in sheets and bulk-shaped tissues, even in the presence of noise and at low spatial resolutions. We demonstrate that even complicated three-dimensional electrical excitation wave phenomena, such as scroll waves and their vortex filaments, can be computed with very high reconstruction accuracies of about 95% from mechanical deformation using autoencoder neural networks, and we provide a comparison with results that were obtained previously with a physics- or knowledge-based approach.

Synchronization-based reconstruction of electromechanical wave dynamics in elastic excitable media.

The heart is an elastic excitable medium, in which mechanical contraction is triggered by nonlinear waves of electrical excitation, which diffuse rapidly through the heart tissue and subsequently activate the cardiac muscle cells to contract. These highly dynamic excitation wave phenomena have yet to be fully observed within the depths of the heart muscle, as imaging technology is unable to penetrate the tissue and provide panoramic, three-dimensional visualizations necessary for adequate study. As a result, the electrophysiological mechanisms that are associated with the onset and progression of severe heart rhythm disorders such as atrial or ventricular fibrillation remain insufficiently understood. Here, we present a novel synchronization-based data assimilation approach with which it is possible to reconstruct excitation wave dynamics within the volume of elastic excitable media by observing spatiotemporal deformation patterns, which occur in response to excitation. The mechanical data are assimilated in a numerical replication of the measured elastic excitable system, and within this replication, the data drive the intrinsic excitable dynamics, which then coevolve and correspond to a reconstruction of the original dynamics. We provide a numerical proof-of-principle and demonstrate the performance of the approach by recovering even complicated three-dimensional scroll wave patterns, including vortex filaments of electrical excitation from within a deformable bulk tissue with fiber anisotropy. In the future, the reconstruction approach could be combined with high-speed imaging of the heart's mechanical contractions to estimate its electrophysiological activity for diagnostic purposes.