Dreaming of Electrical Waves: Generative Modeling of Cardiac Excitation
  Waves using Diffusion Models
Tanish Baranwal Jan Lebert Jan Christoph
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
inpainting tasks, such as reconstructing three-dimensional wave dynamics from
superficial two-dimensional measurements, and evolving and generating
parameter-specific dynamics. We characterized and compared the
diffusion-generated solutions to solutions obtained with biophysical models and
found that diffusion models learn to replicate spiral and scroll waves dynamics
so well that they could serve as an alternative data-driven approach for the
modeling of excitation waves in cardiac tissue. For instance, we found that it
is possible to initiate ventricular fibrillation (VF) dynamics instantaneously
without having to apply pacing protocols in order to induce wavebreak. The VF
dynamics can be created in arbitrary ventricular geometries and can be evolved
over time. However, we also found that diffusion models `hallucinate' wave
patterns when given insufficient constraints. Regardless of these limitations,
diffusion models are an interesting and powerful tool with many potential
applications in cardiac arrhythmia research and diagnostics.