| Abstract: |
| A wide variety of medical imaging methods exist for research and diagnostic procedures on the Central Nervous System (CNS), among them Magnetic Resonance Imaging (MRI) and Optical Imaging. Mathematical modeling and simulation contribute significantly to an improved understanding of image data and the intricate transport, diffusion, and metabolic processes in the brain. This is of particular importance in the study of pathologies such as Alzheimer`s Disease, which, 125 years after its description, remains poorly understood and for which only moderate success has been made in its treatment. In the first work to be presented, we investigate tracer diffusion and transport in the glymphatic system by combining optical imaging in rats with a partial differential equation of reaction-advection-diffusion type. In a second work, we collect observations on the accumulation of amyloid-$\beta$, changes in neuronal density, and a decline in cognitive performance in TgF344-AD and wild-type rats. We develop a compartmental ordinary differential equation model and determine its parameters by fitting the output to the experimental observations. In the long run, our mathematical modeling effort is intended to bridge AD research in rodent models and the human condition of AD. |
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