\section{Discussion and Conclusion}
\label{sec:discussion}

%In this work, we introduced \textit{MORPHADE}, a framework that, to the best of our knowledge, is the first of its kind that uses deformations with unsupervised learning to enable the analysis of the severity and localization of atrophy at the patient-level due to Alzheimer's disease using 3D T1-weighted brain MRI.

%We found that our method was able to localize atrophy in clinically relevant brain regions, such as the hippocampus and amygdala, exhibiting higher mean anomaly scores in these regions for subjects with Alzheimer's compared to healthy controls. Crucially, our method was also able to generate anomaly maps with visual correspondence to medial temporal lobe atrophy scores assessed by an expert neuroradiologist. Finally, MORPHADE was able to identify AD with an AUROC of 0.80, demonstrating superior performance not only over other unsupervised methods, but also compared to several supervised approaches.

%Future research could integrate \textit{MORPHADE}'s deformation metrics with established AD biomarkers, such as tau protein accumulation, to gain a more nuanced understanding of AD progression.

%In conclusion, we demonstrated the excellent performance of our method not only in AD detection, but also in determining the location and severity of atrophy due to the disease. Our results show the potential for the use of our method as an insightful tool to aid in the study, early detection and monitoring of the progression of AD. 
In this work, we introduced MORPHADE, a novel framework leveraging 3D deformable AEs for the unsupervised analysis of Alzheimer's Disease using T1-weighted brain MRI. Our approach is unique in employing deformation fields within an unsupervised learning context to analyze, localize, and assess the severity of AD-related atrophy.

Our results demonstrate that MORPHADE can effectively identify and localize atrophy in clinically relevant brain regions, such as the hippocampus and amygdala, which aligns with clinical expectations of AD pathology. Furthermore, the anomaly maps generated by our method show strong visual correspondence with MTA scores, underscoring the potential of our method in clinical assessments. Lastly, MORPHADE achieved an AUROC of 0.80 in detecting AD, outperforming several supervised and unsupervised baselines. Our method thus identifies AD with high performance without requiring extensive labeled datasets, addressing a significant limitation in current diagnostic approaches.

Future work could explore integrating MORPHADE's deformation metrics with established AD biomarkers, such as tau protein accumulation and amyloid-beta levels, to enhance understanding of disease progression. Additionally, expanding our framework to other neurodegenerative diseases could further validate its versatility and clinical utility.

In conclusion, MORPHADE offers a promising tool for localization and severity assessment of AD-related atrophy, with potential to contribute valuable insights into the progression and diagnosis of neurodegenerative diseases. We believe our approach could enhance the non-invasive monitoring and understanding of AD, paving the way for improved patient outcomes.

% Acknowledgements
\subsubsection{\ackname} C.I.B. is funded via the EVUK program (“Next-generation Al for Integrated Diagnostics”) of the Free State of Bavaria and partially supported by the Helmholtz Association under the joint research school ‘Munich School for Data Science’. This work was also supported by the German Federal Ministry of Health on the basis of a decision by the German Bundestag, under the frame of ERA PerMed.
\subsubsection{\discintname}
The authors have no competing interests to declare that are relevant to the content of this article. 