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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\u2019s 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.<\/jats:p>","DOI":"10.1371\/journal.pone.0310157","type":"journal-article","created":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T17:24:54Z","timestamp":1726853094000},"page":"e0310157","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":8,"title":["Morphological multiparameter filtration and persistent homology in mitochondrial image analysis"],"prefix":"10.1371","volume":"19","author":[{"given":"Yu-Min","family":"Chung","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4476-7866","authenticated-orcid":true,"given":"Chuan-Shen","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9488-3750","authenticated-orcid":true,"given":"Emily","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Henry C.","family":"Tseng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2024,9,20]]},"reference":[{"issue":"1","key":"pone.0310157.ref001","doi-asserted-by":"crossref","first-page":"6427","DOI":"10.1038\/s41598-022-09464-7","article-title":"A multi-parameter persistence framework for mathematical morphology","volume":"12","author":"YM Chung","year":"2022","journal-title":"Scientific Reports"},{"key":"pone.0310157.ref002","doi-asserted-by":"crossref","DOI":"10.1017\/9781108975704","volume-title":"Topological data analysis with applications","author":"G Carlsson","year":"2021"},{"issue":"1","key":"pone.0310157.ref003","first-page":"2522","article-title":"Persistent homology analysis distinguishes pathological bone microstructure in non-linear microscopy images","volume":"13","author":"Y Pritchard","year":"2023","journal-title":"Scientific"},{"issue":"2","key":"pone.0310157.ref004","first-page":"183","article-title":"Persistent homology based characterization of the breast cancer immune microenvironment: a feasibility study","volume":"12","author":"A Aukerman","year":"2022","journal-title":"Journal of Computational Geometry"},{"key":"pone.0310157.ref005","article-title":"Topology-preserving deep image segmentation","volume":"32","author":"X Hu","year":"2019","journal-title":"Advances in neural information processing systems"},{"key":"pone.0310157.ref006","doi-asserted-by":"crossref","unstructured":"Gupta S, Hu X, Kaan J, Jin M, Mpoy M, Chung K, et al. 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