A novel mathematical and computational framework of amyloid-beta triggered seizure dynamics in Alzheimer's disease

TL;DR

This work introduces a multiscale computational framework that embeds amyloid-β–induced calcium dysregulation into a Barreto-Cressman–based ionic model and couples it to a monodomain description of brain tissue. A PolyDG discretization on polytopal meshes enables efficient, high-order simulations of sharp electrical wavefronts and accommodates tissue geometry and PET-derived amyloid distributions. Sensitivity analyses and 2D simulations reveal how progressive Aβ accumulation creates Ca2+ overload, hyperexcitability, and spatially heterogeneous seizure propagation, with high-A regions acting as autonomous epileptogenic drivers. The study provides mechanistic insight into the interplay between neurodegeneration and epilepsy in Alzheimer's disease and offers a scalable framework for patient-specific, anatomically realistic modeling.

Abstract

The association of epileptic activity and Alzheimer's disease (AD) has been increasingly reported in both clinical and experimental studies, suggesting that amyloid-$β$ accumulation may directly affect neuronal excitability. Capturing these interactions requires a quantitative description that bridges the molecular alterations of AD with the fast electrophysiological dynamics of epilepsy. We introduce a novel mathematical model that extends the Barreto-Cressman ionic formulation by incorporating multiple mechanisms of calcium dysregulation induced by amyloid-$β$, including formation of $\mathrm{Ca}^{2+}$-permeable pores, overactivation of voltage-gated $\mathrm{Ca}^{2+}$ channels, and suppression of $\mathrm{Ca}^{2+}$-sensitive potassium currents. The resulting ionic model is coupled with the monodomain equation and discretized using a $p$-adaptive discontinuous Galerkin method on polytopal meshes, providing an effective balance between efficiency and accuracy in capturing the sharp spatiotemporal electrical wavefronts associated with epileptiform discharges. Numerical simulations performed on idealized and realistic brain geometries demonstrate that progressive amyloid-\textbeta{} accumulation leads to severe alterations in calcium homeostasis, increased neuronal hyperexcitability, and pathological seizure propagation. Specifically, high amyloid-$β$ concentrations produce secondary epileptogenic sources and spatially heterogeneous wavefronts, indicating that biochemical inhomogeneities play a critical role in shaping seizure dynamics. These results illustrate how multiscale modeling provides new mechanistic insights into the interplay between neurodegeneration and epilepsy in Alzheimer's disease.

Figures (13)

• Figure 1: Schematic model of the pathological modifications induced by the A peptides.
• Figure 2: Effects of A accumulation with membrane potential with $\mathrm{K}_\mathrm{bath}=8\ \mathrm{mM}$. Evolution over $60 \text{s}$ of $[\mathrm{Ca}^{2+}]_i$ (first row), $[\mathrm{K}^+]_o$ (second row), $u$ (third row) and $J_{A\beta}$ (fourth row) for different values of $[A\mathrm{\beta}]$.
• Figure 3: Effects of A accumulation with membrane potential with $\mathrm{K}_\mathrm{bath}=8\ \mathrm{mM}$. Evolution of $[\mathrm{Ca}^{2+}]_i$ (first row), $[\mathrm{K}^+]_o$ (second row), $u$ (third row) for different values of $[A\mathrm{\beta}]$ and on different time scales $(0\,\mathrm{ms},100\,\mathrm{ms})$ (left), $(0\,\mathrm{s},10\,\mathrm{s})$ (center), $(15\,\mathrm{s},45\,\mathrm{s})$ (right).
• Figure 4: Stable attractor of the ODE system in the 3D space $([\mathrm{Ca}^{2+}]_i,[\mathrm{K}^+]_o,[\mathrm{Na}^+]_i)$. Sensitivity plot of the attractor with the projection on the three planes (a), attractor colored with $u$-values for $[A\mathrm{\beta}]=10\,\mu\mathrm{M}$ (b), and three details zoomed in the $([\mathrm{Ca}^{2+}]_i,[\mathrm{Na}^+]_i)$ plane (c).
• Figure 5: (a) Computational mesh; (b) Different pathological values of A concentration; (c) initial condition for the transmembrane potential.

Theorems & Definitions (2)

• Remark 1: Calcium dynamics
• Remark 2: Calcium-sensitive potassium current