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)
]-\pi, \pi]
\pm2\pi

Graph Helmholtz Decomposition

 

  • Obtains gradient and curl edge weights of graph:
  • Curl component            associated with re-entry
W = W_G + W_C
W_C
W
W_G
W_C
+
=

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