Mathematical modelling and inference for Alzheimer’s Disease

Thesis

Alzheimer’s disease is a devastating neurological condition characterised by the accumulation of two toxic proteins, amyloid-beta and tau, resulting in neurodegen- eration and cognitive decline. The aetiology of Alzheimer’s disease is multifaceted and complex, and there remain a limited number of treatment options available for patients. The mechanisms of Alzheimer’s are particularly challenging to probe due to the numerous difficulties in observing disease mechanisms in vivo in the human brain. Instead, researchers must investigate from afar, relying on macro-scale neuroimaging methods and animal models of disease mechanisms. In this work, we address these obstacles by employing physics-based models of Alzheimer’s pathology that can be paired with neuroimaging data to investigate disease mechanisms.

In Chapter 2, we introduce the two components necessary for modelling tau pathol- ogy: transport through axonal connections and production via prion-like replication. We show that a simple network-based reaction-diffusion model of tau and neurodegen- eration can be usefully applied to human neuroimaging data to identify mechanisms of disease propagation, namely accelerated production of tau. In Chapter 3, we intro- duce a novel model of tau progression that accounts for the regional heterogeneity in vulnerability to tau pathology. We show that regionally specific production rates of tau are necessary for the accurate prediction of regional tau data and that the model can identify differences in transport and production dynamics across the Alzheimer’s disease continuum. In Chapter 4, we use results from previous chapters to develop the first mechanistic model of the amyloid-tau-neurodegeneration pathway and apply it to multimodal longitudinal neuroimaging data. The model explains and predicts several aspects of Alzheimer’s disease, including the necessity of amyloid for the ac- celeration of tau pathology, amyloid-induced regional heterogeneity of tau deposition, and tau-induced atrophy progression. Furthermore, we show that the spatial depo- sition of amyloid imparts a particular vulnerability to the entorhinal cortex for the deposition of tau seeds, providing a novel theory of amyloid-induced tau seeding.

Overall, we provide a framework for how mechanism-based modelling of Alzheimer’s disease can aid investigation into Alzheimer’s disease pathology and provide valuable tools for application in clinical research.

Authors: Chaggar, P

• DOI: 10.5287/ora-eo9jdkr4r
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Subjects: Neurosciences; Mathematics