Morphological multiparameter filtration and persistent homology in mitochondrial image analysis.

The complexity of branching and curvilinear morphology of a complete mitochondrial network within each cell is challenging to analyze and quantify. To address this challenge, we developed an image analysis technique using persistent homology with a multiparameter filtration framework, combining image processing techniques in mathematical morphology. We show that such filtrations contain both topological and geometric information about complex cellular organelle structures, which allows a software program to extract meaningful features. Using this information, we also develop a connectivity index that describes the morphology of the branching patterns. As proof of concept, we utilize this approach to study how mitochondrial networks are altered by genetic changes in the Optineurin gene. Mutations in the autophagy gene Optineurin (OPTN) are associated with primary open-angle glaucoma (POAG), amyotrophic lateral sclerosis (ALS), and Paget's disease of the bone, but the pathophysiological mechanism is unclear. We utilized the proposed mathematical morphology-based multiparameter filtration and persistent homology approach to analyze and quantitatively compare how changes in the OPTN gene alter mitochondrial structures from their normal interconnected, tubular morphology into scattered, fragmented pieces.