Regional Fractal Dimension as a Complementary Morphometric Marker in Alzheimer's Disease

Fractal Dimension (FD) has been proposed as a marker of structural complexity in Alzheimer's Disease (AD), but its regional distribution and complementary value beyond conventional morphometry remain unclear. This study investigated whether regional FD captures AD-related structural alterations distinct from regional volume and thickness.

Using T1-weighted MRI from ADNI1, with external validation in MIRIAD and NACC, we extracted 79 cortical, subcortical, and CSF-related regions and computed volume, thickness, and FD for each region. We assessed covariate-adjusted disease-stage associations, residual FD after linear and nonlinear adjustment for morphometric and demographic factors, clinical associations, and classification performance using conventional features, FD alone, or their combination.

FD showed localized, region-dependent alterations, particularly in the hippocampus, ventricular structures, and caudate. In linear residual analysis, FD associations remained strongest in the bilateral inferior lateral ventricles and left caudate after morphometric and demographic adjustment. Nonlinear adjustment attenuated the ventricular associations, suggesting sensitivity to nonlinear size-shape effects, whereas the left caudate remained consistently associated with diagnostic stage. Adjusted FD also showed modest but significant associations with clinical measures. Combining FD with volume and thickness showed modest additive classification utility.

Regional FD captures selected aspects of structural complexity that are not fully represented by volume or thickness under the tested framework. Ventricular FD appears sensitive to nonlinear size-shape effects, whereas caudate FD may provide more stable residual information.

Regional FD provides complementary, region-dependent morphometric information in AD and should be interpreted as an additive descriptor rather than a standalone biomarker.