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A mathematical model demonstrating the role of interstitial fluid flow on the clearance and accumulation of amyloid β in the brain

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journal contribution
posted on 16.09.2019, 08:37 authored by C.Y. Chen, Y.H. Tseng, John WardJohn Ward
A system of partial differential equations is developed to describe the formation and clearance of amyloid β (Aβ) and the subsequent buildup of Aβ plaques in the brain, which are associated with Alzheimer’s disease. The Aβ related proteins are divided into five distinct categories depending on their size. In addition to enzymatic degradation, the clearance via diffusion and the outflow of interstitial fluid (ISF) into the surrounding cerebral spinal fluid (CSF) are considered. Treating the brain tissue as a porous medium, a simplified two-dimensional circular geometry is assumed for the transverse section of the brain leading to a nonlinear, coupled system of PDEs. Asymptotic analysis is carried out for the steady states of the spatially homogeneous system in the vanishingly small limit of Aβ clearance rate. The PDE model is studied numerically for two cases, a spherically symmetric case and a more realistic 2D asymmetric case, allowing for nonuniform boundary conditions. Our investigations demonstrate that ISF advection is a key component in reproducing the clinically observed accumulation of plaques on the outer boundaries. Furthermore, ISF circulation serves to enhance Aβ clearance over diffusion alone and that non-uniformities in ISF drainage into the CSF can lead to local clustering of plaques. Analysis of the model also demonstrates that plaque formation does not directly correspond to the high presence of toxic oligomers.

Funding

MOST of Taiwan (MOST 106-2115-M-390-006)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Mathematical Biosciences

Publisher

Elsevier

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Mathematical Biosciences and the definitive published version is available at https://doi.org/10.1016/j.mbs.2019.108258.

Acceptance date

12/09/2019

Publication date

2019-09-25

Copyright date

2019

ISSN

0025-5564

Language

en

Depositor

Dr John Ward

Article number

108258