An aggregated mathematical model for the progression of Alzheimer’s disease with treatment implications
Artykuł w czasopiśmie
MNiSW
140
Lista 2024
| Status: | |
| Autorzy: | Ledzewicz Urszula, Ratajczyk Elżbieta, Schättler Heinz |
| Dyscypliny: | |
| Aby zobaczyć szczegóły należy się zalogować. | |
| Rok wydania: | 2026 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Wolumen/Tom: | 114 |
| Numer artykułu: | 596 |
| Strony: | 1 - 17 |
| Impact Factor: | 6,0 |
| Web of Science® Times Cited: | 0 |
| Scopus® Cytowania: | 0 |
| Bazy: | Web of Science | Scopus |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | NIE |
| Abstrakty: | angielski |
| A phenomenological mathematical model for Alzheimer’s disease is formulated and analyzed as a dynamical system. In the model, the formation of amyloid-beta (A) proteins is aggregated into three compartments consisting of monomeres, proto-oligomeres, and polymeres, and the net-effect of stimulating and inhibiting feedback loops on the production of monomeres through pro- and anti-inflammatory cytokines is considered. The resulting 4-dimensional nonlinear dynamical system exhibits a uniform dynamical structure irrespective of the numerical values of the parameters with a region of attraction of the trivial equilibrium point (corresponding to no disease) and a region of divergence of the trajectories (corresponding to the presence of the disease) separated by a 3-dimensional stable manifold of a positive equilibrium point acting as stability boundary. Existence and location of this stability boundary are determined by a simple mathematical quantity which expresses the difference between stimulating and inhibiting parameters in the feedback loops and allows a direct interpretation in terms of current treatment approaches. |
