Deep-learning based extraction of circle of Willis topology with anatomical priors

This is the code repository of our paper Deep-learning based extraction of circle of Willis Topology with anatomical priors.

We extract a graph representation from the circle of Willis topology from 3D TOF-MRA scans. A complete circle of Willis is used as an anatomical prior of these graphs. Therefore, we connect automatically detected bifurcation points in these scans using a shortest path algorithm, that depends on a cost function $\mathcal{C}$ based on local artery orientations. These local artery orientations are obtained through a deep-learning based, scale-invariant, rotation-equivariant estimator that operates on local image data (SIRE).

Environment

The conda environment can be created through the environment.yml file:
conda env create -f environment.yml -n cow_extraction
In addition, we need the gauge-equivariant mesh convolution library (as SIRE depends on it):

git clone https://github.com/Qualcomm-AI-research/gauge-equivariant-mesh-cnn.git
cd gauge-equivariant-mesh-cnn
pip install .

If you get an error regarding OpenMesh, try

conda install -c conda-forge openmesh-python

then try to pip install again.

Data

Data is stored in the /data directory, with the following structure:

/data
    /scans
        /<Patient ID>.nii.gz
    /bifurcations
        /<Patient ID>.npy
    /sire-weights
        /model-weights.pt
        /train.yml

SIRE model weights and the parameters in /train.yml can be downloaded from here.

Usage

The code for automatic topology extraction is in /scripts/extract_topology.py. Patient ID and parameters are hardcoded in this script and can be changed there. The figure below gives an overview of the method. extract_topology.py saves both the paths found by Dijkstra's algorithm (as a dictionary where the world-coordinates can be accessed through the key 'world'). This script also saves the result of the SIRE preprocessing filter as a 9D vectorfield, with the following contents: $[D_1(x), D_1(y), D_1(z), D_2(x), D_2(y), D_2(z), \text{entropy}, \text{max activation}, \text{max scale}]$.

Results

Results are automatically saved in the /results folder after running /scripts/extract_topology.py. The SIRE vectorfields are saved as .npy files in /results/SIRE_filtered and a minimal intensity projection as well as the coordinates of the paths are saved as .png and .pkl files respectively under /results/paths.