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This dissertation investigates privacy-preserving federated learning for Alzheimer's disease classification using three-dimensional MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Existing methodologies often suffer from unrealistic data partitioning, inadequate privacy guarantees, and insufficient benchmarking, limiting their practical deployment in healthcare. To address these gaps, this research proposes a novel site-aware data partitioning strategy that preserves institutional boundaries, reflecting real-world multi-institutional collaborations and data heterogeneity. Furthermore, an Adaptive Local Differential Privacy (ALDP) mechanism is introduced, dynamically adjusting privacy parameters based on training progression and parameter characteristics, thereby significantly improving the privacy-utility trade-off over traditional fixed-noise approaches. Systematic empirical evaluation across multiple client federations and privacy budgets demonstrated that advanced federated optimisation algorithms, particularly FedProx, could equal or surpass centralised training performance while ensuring rigorous privacy protection. Notably, ALDP achieved up to 80.4% accuracy in a two-client configuration, surpassing fixed-noise Local DP by 5-7 percentage points and demonstrating substantially greater training stability. The comprehensive ablation studies and benchmarking establish quantitative standards for privacy-preserving collaborative medical AI, providing practical guidelines for real-world deployment. This work thereby advances the state-of-the-art in federated learning for medical imaging, establishing both methodological foundations and empirical evidence necessary for future privacy-compliant AI adoption in healthcare.