Speaker
Description
The extracellular amyloid plaques, whose primary component is the amyloid-beta peptide (A$\beta$), are a key hallmark of Alzheimer’s disease. A four-compartment mathematical model for the A$\beta$ movements and aggregation processes has been proposed in [1]. The growth of the amyloid plaques is assumed to depend on their surface area, using an area-to-volume shape index. In this talk, at first, we refine the model proposed in Ficiarà 2023. In particular, we assume that also the possible dissolution of amyloid plaques is surface-dependent, analogously to their formation. Then, we incorporate terms modeling possible treatment actions to enhance A$\beta$ disaggregation and reduce A$\beta$ aggregation. Specifically, we take into account that a low A$\beta$ level in the cerebrospinal fluid is considered a positive biomarker of Alzheimer’s disease. In addition, we assume that treatments become increasingly inefficient as the disease progresses. Finally, we reformulate the refined model as an optimal control problem to reduce the amyloid plaques and minimize treatment actions and costs.
Bibliography
Ficiarà, Eleonora, et al. «A Mathematical Model on Aβ Blood–Brain Transport: Simulations of Plaques’ Formation in Alzheimer’s Disease». Medical Hypotheses, vol. 181, dicembre 2023, p. 111194, https://doi.org/10.1016/j.mehy.2023.111194.
