homology-brain-atrophy

name	homology-brain-atrophy
description	Homology-based morphometry methods for analyzing brain atrophy using topological data analysis. Activation triggers: homology morphometry, brain atrophy, topological neuroimaging, persistent homology brain, TDA neuroimaging

Homology-based Morphometry of Brain Atrophy

Topological data analysis approach for subject-specific brain morphometry that avoids template normalization artifacts using persistent homology.

Metadata

• Source: arXiv:2604.24714v1
• Authors: Donato Quiccione, Mariam Pirashvili, Nathan Broomhead
• Published: 2026-04-27
• Category: math.AT (Algebraic Topology)

Core Methodology

Key Innovation

Traditional voxel-based morphometry (VBM) requires normalization to a standard template, which obscures subject-specific geometric features. This method uses persistent homology from topological data analysis (TDA) to analyze brain structure without template normalization, preserving individual anatomical characteristics.

Technical Framework

1. Persistent Homology Pipeline

Brain MRI → Segmentation → Point Cloud → Vietoris-Rips Complex 
→ Persistent Homology Computation → Persistence Diagrams → Statistical Analysis

2. Advantages Over VBM

Aspect	VBM	Homology Morphometry
Template	Required	Not required
Subject-specific features	Lost	Preserved
Geometric information	Limited	Rich
Group comparisons	Problematic	Natural

3. Applications

• Longitudinal atrophy tracking: Monitor disease progression
• Cross-sectional group comparisons: Compare patient populations
• Individual biomarker discovery: Subject-specific morphometric features
• Disease staging: Quantify atrophy patterns

Implementation Guide

Prerequisites

• Python 3.8+
• Packages: gudhi, ripser, scikit-tda, nibabel, scipy

Step-by-Step

1. Image Preprocessing

import nibabel as nib
from scipy.ndimage import gaussian_filter

def preprocess_mri(mri_path):
    img = nib.load(mri_path)
    data = img.get_fdata()
    # Smooth to reduce noise
    smoothed = gaussian_filter(data, sigma=1.0)
    return smoothed

2. Point Cloud Generation

def brain_to_pointcloud(seg_mask, voxel_size=1.0):
    """Convert segmentation mask to point cloud"""
    coords = np.argwhere(seg_mask > 0)
    # Scale by voxel size
    coords = coords * voxel_size
    return coords

3. Persistent Homology Computation

from ripser import ripser
from persim import plot_diagrams

def compute_persistence(point_cloud, max_dim=2):
    """Compute persistent homology"""
    diagrams = ripser(point_cloud, maxdim=max_dim)['dgms']
    return diagrams  # List of persistence diagrams for each dimension

4. Feature Extraction

def persistence_statistics(diagrams):
    """Extract statistical features from persistence diagrams"""
    features = {}
    for dim, dgm in enumerate(diagrams):
        if len(dgm) == 0:
            continue
        # Persistence (death - birth)
        persistences = dgm[:, 1] - dgm[:, 0]
        features[f'dim{dim}_mean_persistence'] = np.mean(persistences)
        features[f'dim{dim}_max_persistence'] = np.max(persistences)
        features[f'dim{dim}_count'] = len(persistences)
    return features

Applications

• Alzheimer's disease: Track hippocampal and cortical atrophy
• Multiple sclerosis: Monitor lesion evolution and brain volume changes
• Aging studies: Characterize normal aging patterns
• Clinical trials: Quantify treatment effects on brain structure

Pitfalls

• Computational cost: Persistent homology is expensive for high-resolution data
• Parameter sensitivity: Results depend on filtration parameters
• Interpretation: TDA features are less intuitive than voxel-wise measures
• Validation: Requires careful validation against established methods

Related Skills

• brain-higher-order-structures
• dgcl-brain-network-construction
• persistent-homology-brain
• neurodegenerative-4d-diffusion

References

• arXiv:2604.24714v1
• Edelsbrunner & Harer, "Computational Topology: An Introduction"
• Otter et al., "A roadmap for the computation of persistent homology" (2017)