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

• Published in: Mathematical biosciences 2019-11, Vol.317, p.108258-108258, Article 108258
• Main Authors: Chen, C.Y., Tseng, Y.H., Ward, J.P.
• Format: Article
• Language: English
• Subjects: Accumulation; Advection; Alzheimer's disease; Amyloid β; Boundary conditions; Brain; Cerebrospinal fluid; Clustering; Computational fluid dynamics; Differential equations; Fluid flow; Interstitial fluid; Mathematical model; Mathematical models; Neurodegenerative diseases; Oligomers; Outflow; Partial differential equations; Plaque formation; Porous media; Senile plaques
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2019.108258

•Transport and distribution of amyloid β is highly influenced by ISF flow.•ISF flow promotes clearance of amyloid β in the brain.•Decline of ISF flow promotes the rate of plaque formation.•Clustering of amyloid β is affected by the drainage properties into the CSF.•Amyloid plaque acts as a localised sink to smaller amyloid β aggregates. 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 non-uniform 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.