Alterations of brain tissue structural complexity and disorder in Alzheimer's disease (AD): Fractal, multifractal, fractal transformation, and disorder strength analyses.

Alzheimer's disease (AD) is characterized by progressive microstructural deterioration in brain tissue, yet conventional imaging and histopathology often lack the sensitivity needed to detect subtle early-stage changes. Here, we present a multiparametric framework combining fractal and multifractal analysis and their distributions to quantify structural alterations in human brain tissue affected by AD. Moreover, from the fractal and multifractal formalism, we introduced an innovative fractal functional distribution method, a novel technique that transforms fractal distribution into a Gaussian form. Statistically, these distribution parameters are easy to interpret and can distinguish between control and diseased tissues. Across samples, we identify pronounced threshold-dependent behavior of fractal and multifractal parameters, reflecting the intrinsic sparsity and heterogeneous intensity landscape of brain tissue. These threshold-sensitive signatures provide a framework for quantitative stage detection and may serve as biomarkers for early pathological transitions. In addition, we studied structural disorder and complexity using our established light localization technique, inverse participation ratio (IPR) analysis. IPR-based analysis demonstrates that increasing IPR pixel size highlights the elevation of structural alterations with disease progression. Together, these integrative analyses establish a robust, multi-scale quantitative framework for detecting microstructural alterations in AD, providing a promising foundation for early diagnosis and improved pathological assessment.