Mixed-Effects Shape Models for Estimating Longitudinal Changes in Anatomy

Area of Science:

• Biomedical Engineering
• Medical Imaging Analysis
• Statistical Shape Analysis

Background:

• Longitudinal shape analysis is crucial for understanding biological processes like growth and disease progression.
• Existing methods often struggle with simultaneously modeling shape variation and establishing accurate correspondences over time.
• Hierarchical modeling offers a powerful framework for capturing population-level and individual-specific changes.

Purpose of the Study:

• To develop a new statistical method for longitudinal shape analysis that integrates correspondence optimization with linear mixed-effects modeling.
• To provide robust statistical significance testing for estimated shape trends.
• To enable comparative analysis of shape trends between different populations.

Main Methods:

• A linear mixed-effects model is fitted to anatomical shape data, incorporating fixed effects for global trends and random effects for individual variations.
• Correspondence optimization is performed simultaneously with model fitting to ensure accurate shape comparisons across time points.
• Permutation tests, including one based on the Hotelling T-squared statistic, are developed for statistical significance evaluation and population comparison.

Main Results:

• The proposed method effectively models hierarchical shape changes in longitudinal data.
• Statistical significance of shape trends can be reliably assessed using the developed permutation tests.
• The Hotelling T-squared based permutation test allows for effective comparison of average shape trends between two populations.

Conclusions:

• The new method provides a robust and statistically sound approach for longitudinal shape analysis.
• It enhances the understanding of shape dynamics in developmental studies and other biomedical applications.
• The simultaneous optimization of correspondences and statistical modeling offers significant advantages over existing techniques.