A mathematical model of the impact of novel treatments on the A\03B2 burden in the Alzheimer's brain, CSF and plasma

With the advent of novel therapies for AD, there is a pressing need for biomarkers that are easy to monitor, such as the amyloid-beta levels in the cerebrospinal fluid (CSF) and plasma. To gain a better understanding of the explanatory power of these biomarkers, we formulate and analyze a compartmental mathematical model for the amyloid-beta accumulation in the brain, CSF and plasma throughout the course of Alzheimer's treatment. Our analysis reveals that the total amyloid-beta burden in the brain is dictated by a unitless quantity called the polymerization ratio, which is the product of the production and elongation rates divided by the product of the fragmentation and loss rates. In this ratio, the production rate and loss rate include a source and sink term, respectively, related to the intercompaxtmental transport. Our results suggest that production inhibitors are likely to reduce the amyloid-beta levels in all three compartments. In contrast, agents that ingest monomers off of polymers, or that increase fragmentation or block elongation, may also reduce amyloid-beta burden in the brain, but may produce little change in or even transiently increase CSF and plasma amyloid-beta levels. Hence, great care must be taken when interpreting these biomarkers. Keywords: amyloid beta, mathematical model.