Bulletin of Mathematical Biology

, Volume 64, Issue 5, pp 1011-1031

First online:

A mathematical model of the impact of novel treatments on the Aβ burden in the Alzheimer’s brain, CSF and plasma

  • David L. CraftAffiliated withOperations Research Center, MIT
  • , Lawrence M. WeinAffiliated withSloan School of Management, MIT Email author 
  • , Dennis J. SelkoeAffiliated withCenter for Neurologic Diseases, Harvard Medical School, Brigham and Women’s Hospital

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With the advent of novel therapies for Alzheimer’s disease, there is a pressing need for biomarkers that are easy to monitor, such as the amyloid-beta (Aβ) 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 Aβ accumulation in the brain, CSF and plasma, throughout the course of Alzheimer’s treatment. Our analysis reveals that the total Aβ 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 intercompartmental transport. Our results suggest that production inhibitors are likely to reduce the Aβ levels in all three compartments. In contrast, agents that ingest monomers off of polymers, or that increase fragmentation or block elongation, may also reduce Aβ burden in the brain, but may produce little change in—or even transiently increase—CSF and plasma Aβ levels. Hence, great care must be taken when interpreting these biomarkers.