Group Analysis

Overview

purple-mri supports statistical analysis at multiple spatial scales:

  1. Vertex-wise cortical analysis (surface-based)

  2. Voxel-based / deformation-based morphometry (DBM)

  3. ROI-wise regional analysis

All analyses are performed in a common coordinate system (template space or fsaverage space).

Vertex-Wise GLM (Surface-Based)

Cortical thickness and related surface measurements (thickness, curvature, area) are analyzed in fsaverage space using vertex-wise generalized linear modeling (GLM).

Typical model:

Cortical thickness (mm) ~ pathology + covariates

Where pathology variables may include:

  • Global amyloid-β (Aβ)

  • Braak staging

  • CERAD score

  • Medial temporal lobe (MTL) neuronal loss

  • Tau pathology

Covariates typically include:

  • Age at death

  • Sex

  • Postmortem interval (PMI)

Scripts are located in:

glm/

Step 1 — Warp to fsaverage

Warp subject-native measurements (thickness, curvature, area) to fsaverage space.

bash warp_to_template_space.sh

This produces VTK files in template space.

Step 2 — Prepare VTK files

Prepare VTK files for GLM compatibility:

python prepare_vtk_files_for_glm.py

This step:

  • Ensures consistent VTK format

  • Replaces invalid vertices with NaNs

  • Standardizes input for statistical modeling

Step 3 — Prepare Design Matrix and Contrasts

You must define:

  • sample_design_matrix.txt

  • contrast.txt

These encode:

  • Pathology variable of interest

  • Covariates (age, sex, PMI)

  • Desired statistical contrast

Customize these files according to your hypothesis.

Step 4 — Run Vertex-Wise GLM

The workflow uses the binaries:

  • mesh_merge_arrays

  • meshglm

Run:

bash glm.sh

This performs vertex-wise GLM across all subjects.

Outputs

Example outputs:

  • all_hemis.glm_merged_5mm_pial.vtk

  • all_hemis.glm_output_for_ABETA_5mm_pial.vtk

  • all_hemis.edges.glm_output_for_ABETA_5mm_pial.vtk

These files contain:

  • Beta coefficients

  • T-statistics

  • P-values

  • Cluster edges

Visualization

Load output VTK files into ParaView for visualization of significant clusters and spatial patterns.

Deformation-Based Morphometry (DBM)

Deformation-based morphometry is performed in template space using subject-to-template deformation fields.

Workflow:

  1. Register all subjects to the population template

  2. Compute Jacobian determinant maps

  3. Perform voxel-wise GLM on Jacobians

The statistical modeling follows the same structure as the vertex-wise surface analysis, including:

  • Pathology variables

  • Age, sex, PMI covariates

ROI-Wise Analysis

Region-of-interest analyses can be performed using:

  • Atlas-based volumes

  • Regional cortical thickness averages

  • Subcortical volumetry

Typical workflow:

  1. Extract regional measurements

  2. Assemble CSV table

  3. Fit linear models in Python (e.g., statsmodels, pingouin)

This enables:

  • Partial correlations

  • Multiple regression

  • Mixed-effects modeling

  • FDR correction

Scientific Rationale

High-resolution ex vivo MRI provides localized morphometric measures that are more sensitive to neuropathology than corresponding in vivo MRI measures.

By linking:

  • Surface-based thickness

  • Deformation-based morphometry

  • Atlas-derived volumetry

with gold-standard histopathology measures, purple-mri enables discovery of pathology-specific structural signatures.

Dependencies

  • meshglm binaries

  • mesh_merge_arrays

  • Python (for VTK preparation and statistical scripts)

  • ParaView (for visualization)