The graph Helmholtz decomposition for the detection of cardiac arrhythmia

Sebastiaan Lootens

Overview

• Methods

  • Graph building

  • Existing: Phase Mapping and Cycle Search

  • New: Graph Helmholtz Decomposition

• Results

  • Functional re-entry (simulation and rat VF)

  • Anatomical re-entry (AT simulation and human clinical case)

• Possible improvements

• Conclusion

Methods: Graph building

Algorithm:

1. Input:
   • Electroanatomical map of LATs
2. Preprocessing:
   • Mesh Smoothing 
   • Point Sampling
   • Point Smoothing
3. Edge building:
   • Connect neighboring Voronoi cells
4. Edge filtering:
   • CVmin < CV < CVmax
   • Largest weakly connected component
5. Graph merging:
   • Combine Graph(t) with Graph(t + period/2)

Step 1

Step 2

Step 3 to 5

Phase Mapping and Cycle search

Phase Mapping:

1. Input: undirected graph
2. Calculate and sort i-th nearest neighbors  
3. Calculate phase differences restricted to
4. Phase Singularity (PS): ring sum =

Cycle Search:

1. Input: directed graph
2. Calculate directed cycles (BFS)

Graph Helmholtz Decomposition

Results: Simulated Rotors

Results: Experimental Rat VF

Results: Simulated AT

Results: Clinical Human AT

Results: Performance Comparison

Weighted relative distance of detections to closest ground truth

Possible improvements

• PM:
  • Limited circular ring shape
  • Expensive to search all rings
  • FPs for noisy data
• Cycle search:
  • Fast conduction or LAT errors can break cycles
  • Cannot find incomplete loops
• Helmholtz curl:
  • Abstract interpretation
  • Improve precision

Conclusion

• The Helmholtz decomposition for directed graphs shows promising potential for re-entry localization in diverse datasets

• The agreement of multiple methods increases confidence of re-entry detections