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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.24714 |
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| _version_ | 1866911626998841344 |
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| author | Quiccione, Donato Pirashvili, Mariam Broomhead, Nathan Fallon, Sean J. |
| author_facet | Quiccione, Donato Pirashvili, Mariam Broomhead, Nathan Fallon, Sean J. |
| contents | Understanding the structure of the brain, and how it changes with time and disease, is a core goal of structural neuroimaging. Contemporary approaches to structural brain analysis are dominated by voxel-wise, mass-univariate methods such as voxel-based morphometry (VBM). However, these techniques require images to be normalized to a standard template, which can obscure subject-specific geometric features. Normalization to a common stereotactic space can also be problematic when comparing groups with substantial brain pathology, lesions, or other anatomical abnormalities.
Here, we introduce two complementary pipelines based on persistent homology (PH), a tool from topological data analysis, to quantify multiscale geometric features of structural T1-weighted MRI scans. Pipeline 1 quantifies regional thinning by applying the Euclidean distance transform to tissue masks in a slice-wise manner. Pipeline 2 uses \(α\)-filtrations to measure structural similarity between pairs of scans, capturing sulcal widening and ventricular enlargement.
Synthetic experiments with controlled induced lesions showed that Pipeline 1 is best suited to between-subject analyses, whereas Pipeline 2 is better suited to within-subject designs. Applied to real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), Pipeline 1 separated Alzheimer's disease (AD) from cognitively normal (CN) participants using single-modality T1-weighted MRI without nonlinear registration (ROC-AUC = 0.895), with peak effects localized to medial temporal regions. Pipeline 2 captured disease-related longitudinal change, with follow-up scans remaining closest to their own baselines and AD subjects showing greater short-interval change than CN subjects. Together, these pipelines provide interpretable topological biomarkers for cross-sectional group comparisons and longitudinal tracking. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24714 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homology-based Morphometry of Brain Atrophy: Methods and Applications Quiccione, Donato Pirashvili, Mariam Broomhead, Nathan Fallon, Sean J. Algebraic Topology Image and Video Processing Neurons and Cognition 55N31, 92C55 I.4; I.5.4; J.3 Understanding the structure of the brain, and how it changes with time and disease, is a core goal of structural neuroimaging. Contemporary approaches to structural brain analysis are dominated by voxel-wise, mass-univariate methods such as voxel-based morphometry (VBM). However, these techniques require images to be normalized to a standard template, which can obscure subject-specific geometric features. Normalization to a common stereotactic space can also be problematic when comparing groups with substantial brain pathology, lesions, or other anatomical abnormalities. Here, we introduce two complementary pipelines based on persistent homology (PH), a tool from topological data analysis, to quantify multiscale geometric features of structural T1-weighted MRI scans. Pipeline 1 quantifies regional thinning by applying the Euclidean distance transform to tissue masks in a slice-wise manner. Pipeline 2 uses \(α\)-filtrations to measure structural similarity between pairs of scans, capturing sulcal widening and ventricular enlargement. Synthetic experiments with controlled induced lesions showed that Pipeline 1 is best suited to between-subject analyses, whereas Pipeline 2 is better suited to within-subject designs. Applied to real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), Pipeline 1 separated Alzheimer's disease (AD) from cognitively normal (CN) participants using single-modality T1-weighted MRI without nonlinear registration (ROC-AUC = 0.895), with peak effects localized to medial temporal regions. Pipeline 2 captured disease-related longitudinal change, with follow-up scans remaining closest to their own baselines and AD subjects showing greater short-interval change than CN subjects. Together, these pipelines provide interpretable topological biomarkers for cross-sectional group comparisons and longitudinal tracking. |
| title | Homology-based Morphometry of Brain Atrophy: Methods and Applications |
| topic | Algebraic Topology Image and Video Processing Neurons and Cognition 55N31, 92C55 I.4; I.5.4; J.3 |
| url | https://arxiv.org/abs/2604.24714 |