Brain geometry persistent homology marker for Parkinson's disease

The geometry of the human brain changes due to age and neurodegeneration. The brain geometry is expected to undergo a similar change in shape with a normal aging, however such change may differ in patients suffering from neurodegenerative disorders. In the novel framework proposed in this work, we model the brain geometry as a 3D point cloud and study the algebraic topology features of this point cloud. Specifically, we compute the persistence timelines of a simplicial complex in a multiscale simplicial homology of the underlying topology space. Further, persistence landscape summary features are obtained from the timelines and studied for their difference between the two groups. The statistical significance obtained in a permutation testing experiments highlights the ability of the persistence landscape features to differentiate between the PD and healthy control brain geometry.