Reconstruction of Three-dimensional Scroll Waves in Excitable Media from Two-Dimensional Observations using Deep Neural Networks (2209.06860v2)

Abstract: Scroll wave chaos is thought to underlie life-threatening ventricular fibrillation. However, currently there is no direct way to measure action potential wave patterns transmurally throughout the thick ventricular heart muscle. Consequently, direct observations of three-dimensional electrical scroll waves remains elusive. 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.

• The paper demonstrates that deep CNNs accurately reconstruct 3D scroll wave dynamics from limited 2D observations.
• The methodology employs encoding-decoding architectures evaluated on anisotropic cardiac tissue models, revealing key depth-encoding features.
• Results indicate robust performance under noise and varying tissue properties, offering promising insights for imaging arrhythmic events.

Reconstruction of Three-Dimensional Scroll Waves in Excitable Media Using Deep Neural Networks

This paper addresses a challenging problem in computational cardiology: reconstructing three-dimensional electrical scroll wave dynamics from two-dimensional surface observations within excitable media, with a direct application to cardiac tissue such as ventricular fibrillation. The authors explore the feasibility of using deep learning techniques, specifically convolutional neural networks (CNNs), to solve this problem.

The paper is predicated on the difficulty of directly imaging transmembrane potential patterns throughout the depth of the heart muscle, which is significant for understanding arrhythmic events such as ventricular fibrillation. Three-dimensional scroll waves are a key feature of such dynamics, but direct experimental measurement and visualization remain elusive, particularly in large, opaque cardiac tissues.

Methods and Innovations

The authors leveraged a computational approach by simulating three-dimensional scroll waves within excitable media, utilizing the well-established Aliev-Panfilov model. They employed CNNs, specifically encoding-decoding architectures, to predict the wave dynamics within these media from limited two-dimensional data. Multiple configurations were tested, including single-surface, dual-surface, and projected observations, each providing different glimpses into the underlying three-dimensional activities.

The core method involves feeding the neural network a sequence of five temporal two-dimensional observations and predicting the corresponding three-dimensional wave structure. This method's robustness was evaluated against various factors such as medium anisotropy and thickness, noise, and opacity. Importantly, the paper navigates through different levels of model complexity, contrasting simpler Encoder-Decoder networks against more sophisticated architectures like U-Net, TransUNet, and MIRNet.

Key Findings

1. Reconstruction Accuracy: The deep learning models demonstrated a strong capability to reconstruct scroll wave dynamics in transparent, anisotropic media. In these scenarios, the anisotropy appears to encode depth information, potentially due to variations in wave alignment, which the network effectively decodes to reconstruct the three-dimensional structure.
2. Properties Affecting Reconstruction: Thickness versus wave size emerges as a crucial factor; accurate reconstruction is feasible when scroll waves are larger or comparable to the medium thickness. The opacity of the medium presents additional challenges, with projection methods performing better with transparency.
3. Dual-Surface Observations: While dual-surface input showed improvements in the reconstruction of simple scroll wave dynamics, particularly in thinner media, it did not significantly enhance the performance in rendering complex scroll wave chaos dynamics.
4. Robustness to Noise: The reconstruction robustness to noise was evident, with CNNs maintaining a reconstruction error below 10% (RMSE) under various noise levels, which has practical implications for real-world applications where measurement noise is inevitable.

Implications and Future Directions

This research provides a foundational step towards non-invasively imaging the intricate dynamics of cardiac tissues, potentially offering new insights into arrhythmia mechanisms and better guiding therapeutic strategies. It suggests significant capabilities of neural networks in dealing with the data extrapolation challenges inherent in observing volumetric data through surface measurements. However, the technique's applicability to biological tissues, especially non-transparent cardiac ones, remains limited, highlighting areas for further advancements.

Future work might explore integrating more biologically realistic models and bridging simulations with experimental data on transparent or semi-transparent biological tissues like zebrafish or using emerging modalities like photoacoustic imaging. Additionally, incorporating more sophisticated architectures and interpretative frameworks could enhance accuracy and applicability, particularly for complex chaotic dynamics.

In conclusion, this paper demonstrates the potential of applying deep learning approaches in reconstructing three-dimensional electrophysiological phenomena from limited observations, pointing towards innovative pathways in computational biophysics and electrophysiology.