Alterations of brain tissue structural complexity and disorder in Parkinson disease (PD): Fractal, multifractal, fractal transformation, and disorder strength analyses

Abstract: Parkinson disease (PD) is marked by progressive neurodegeneration, yet early and subtle structural alterations in brain tissue remain difficult to detect with conventional imaging and analytical methods. Fractal and multifractal frameworks offer a principled way to quantify complex biological architecture, but their diagnostic utility in PD has been largely unexplored. In this study, we investigated the fractal and multifractal characteristics of human brain tissues to identify structural alterations associated with PD. Alongside conventional fractal and multifractal analysis, we employed a recently developed fractal functional distribution method that transforms distributions into a Gaussian form, thereby enhancing quantification. Using this combined approach, we found notable deviations across multiple distribution metrics in PD samples, offering potential for quantitative staging and diagnostic applications. The multifractal analysis revealed threshold-dependent variations in intensity-based measures, which are linked to the sparsity and heterogeneity of neural tissue and suggestive of potential biomarker value. Additionally, we applied inverse participation ratio (IPR) analysis to assess structural disorder, demonstrating that larger IPR pixel sizes correlate with increased structural complexity during disease progression. These complementary analyses outline a multi-layered quantitative profile of PD-related tissue disruption, offering a foundation for earlier, objective assessment of disease-associated microstructural change.