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

arXiv: https://arxiv.org/abs/2312.14830 · HTML: https://mlsanity.com/paper/2312.14830/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 26 of its 65 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [CNN-generated images are surprisingly easy to spot... for now](https://mlsanity.com/paper/1912.11035/) (2019)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [Calibrated Language Models Must Hallucinate](https://mlsanity.com/paper/2311.14648/) (2023)
- [Inverse Mechano-Electrical Reconstruction of Cardiac Excitation Wave Patterns from Mechanical Deformation using Deep Learning](https://mlsanity.com/paper/2008.01640/) (2020)
- [A study of deep perceptual metrics for image quality assessment](https://mlsanity.com/paper/2202.08692/) (2022)
- [Rotor Localization and Phase Mapping of Cardiac Excitation Waves using Deep Neural Networks](https://mlsanity.com/paper/2109.10472/) (2021)
- [Reconstruction of Three-dimensional Scroll Waves in Excitable Media from Two-Dimensional Observations using Deep Neural Networks](https://mlsanity.com/paper/2209.06860/) (2022)
- [An integrative smoothed particle hydrodynamics framework for modeling cardiac function](https://mlsanity.com/paper/2009.03759/) (2020)
- [Deep Learning-based Prediction of Electrical Arrhythmia Circuits from Cardiac Motion: An In-Silico Study](https://mlsanity.com/paper/2305.07822/) (2023)

## Abstract (arXiv)

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.