Functional Connectivity Assessment in Alzheimer's Disease: A Comparative Study of Linear and Non-linear fMRI Analysis Approaches

Purpose: Brain connectivity studies unveil the intricate interactions within neural networks. Various approaches exist to explore brain connectivity, yet the debate between the efficacy of linear versus non-linear methods remains unresolved due to the advantages and limitations of each. This study aims to provide a comprehensive evaluation of neuroimaging data analysis to gain insights into the functional aspects of the brain, particularly in the context of Alzheimer's Disease (AD). The objective is to identify potential pathways for early intervention and prevention, despite the controversies arising from diverse neuroimaging modalities and analytical techniques. Materials and Methods: Using fMRI data, both linear and non-linear approaches are investigated. The linear approach employs the Pearson Correlation Coefficient (PCC) to create whole-brain graphs. For non-linear approaches, Distance Correlation (DC) and the kernel trick are utilized. Functional brain networks are constructed and sparsified for each AD stage, followed by calculating global graph measures. Results: The findings indicate that non-linear approaches are more effective in distinguishing between different stages of AD. Among these, the kernel trick method performs better than the DC technique. Polynomial kernel (degree 3) showed better group separability, with significantly different graph measures such as clustering, transitivity, modularity, and small-worldness. Kernel analysis revealed that within-region connectivity was more disrupted in AD. Notably, the functional graphs of the brain are more significantly degraded in the early stages of AD. Conclusion: In the initial phases of AD, both functional integration and segregation of the brain are compromised, with a more pronounced decline in functional segregation as the disease progresses. The clustering coefficient, indicative of brain functional segregation, emerges as the most distinguishing feature across all stages of AD, highlighting its potential as a biomarker for early diagnosis.