A mathematical model on the propagation of tau pathology in neurodegenerative diseases.
Bifurcation analysis
Mathematical model
Neurodegenerative disease
Tauopathy propagation
Travelling wave analysis
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
15 May 2024
15 May 2024
Historique:
received:
28
09
2023
accepted:
12
04
2024
revised:
06
03
2024
medline:
16
5
2024
pubmed:
16
5
2024
entrez:
15
5
2024
Statut:
epublish
Résumé
A system of partial differential equations is developed to study the spreading of tau pathology in the brain for Alzheimer's and other neurodegenerative diseases. Two cases are considered with one assuming intracellular diffusion through synaptic activities or the nanotubes that connect the adjacent cells. The other, in addition to intracellular spreading, takes into account of the secretion of the tau species which are able to diffuse, move with the interstitial fluid flow and subsequently taken up by the surrounding cells providing an alternative pathway for disease spreading. Cross membrane transport of the tau species are considered enabling us to examine the role of extracellular clearance of tau protein on the disease status. Bifurcation analysis is carried out for the steady states of the spatially homogeneous system yielding the results that fast cross-membrane transport combined with effective extracellular clearance is key to maintain the brain's healthy status. Numerical simulations of the first case exhibit solutions of travelling wave form describing the gradual outward spreading of the pathology; whereas the second case shows faster spreading with the buildup of neurofibrillary tangles quickly elevated throughout. Our investigation thus indicates that the gradual progression of the intracellular spreading case is more consistent with the clinical observations of the development of Alzheimer's disease.
Identifiants
pubmed: 38750128
doi: 10.1007/s00285-024-02101-z
pii: 10.1007/s00285-024-02101-z
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
4Subventions
Organisme : National Science and Technology Council
ID : 111-2115-M-390-003
Organisme : London Mathematical Society
ID : 42257
Informations de copyright
© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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