How Can We Use Mathematical Modeling of Amyloid-β in Alzheimer’s Disease Research and Clinical Practices?

Article type: Review Article

Authors: Chu, Chenyin^a | Low, Yi Ling Clare^a | Ma, Liwei^a | Wang, Yihan^a | Cox, Timothy^b | Doré, Vincent^b | Masters, Colin L.^a | Goudey, Benjamin^{a; c} | Jin, Liang^{a; d; *} | Pan, Yijun^{a; d; e; *}

Affiliations: [a] Florey Institute of Neuroscience and Mental Health, University of Melbourne, Parkville, Victoria, Australia | [b] The Australian e-Health Research Centre, CSIRO, Parkville, Victoria, Australia | [c] ARC Training Centre in Cognitive Computing for Medical Technologies, University of Melbourne, Carlton, Victoria, Australia | [d] Drug Delivery, Disposition and Dynamics, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, Victoria, Australia | [e] Department of Organ Anatomy, Graduate School of Medicine, Tohoku University, Sendai, Miyagi, Japan

Correspondence: [*] Correspondence to: Dr. Liang Jin, Florey Institute of Neuroscience and Mental Health, University of Melbourne, Parkville, Victoria 3010, Australia. Tel.: +61 3 8344 3627; E-mail: [email protected]. and Dr Yijun Pan, Florey Institute of Neuroscience and Mental Health, University of Melbourne, Parkville, Victoria 3010, Australia. Tel.: +61 3 8344 3451; E-mail: [email protected].

Abstract: The accumulation of amyloid-β (Aβ) plaques in the brain is considered a hallmark of Alzheimer’s disease (AD). Mathematical modeling, capable of predicting the motion and accumulation of Aβ, has obtained increasing interest as a potential alternative to aid the diagnosis of AD and predict disease prognosis. These mathematical models have provided insights into the pathogenesis and progression of AD that are difficult to obtain through experimental studies alone. Mathematical modeling can also simulate the effects of therapeutics on brain Aβ levels, thereby holding potential for drug efficacy simulation and the optimization of personalized treatment approaches. In this review, we provide an overview of the mathematical models that have been used to simulate brain levels of Aβ (oligomers, protofibrils, and/or plaques). We classify the models into five categories: the general ordinary differential equation models, the general partial differential equation models, the network models, the linear optimal ordinary differential equation models, and the modified partial differential equation models (i.e., Smoluchowski equation models). The assumptions, advantages and limitations of these models are discussed. Given the popularity of using the Smoluchowski equation models to simulate brain levels of Aβ, our review summarizes the history and major advancements in these models (e.g., their application to predict the onset of AD and their combined use with network models). This review is intended to bring mathematical modeling to the attention of more scientists and clinical researchers working on AD to promote cross-disciplinary research.

Keywords: Alzheimer’s disease, amyloid-β, disease progression, mathematical modeling, Smoluchowski equation

DOI: 10.3233/JAD-230938

Journal: Journal of Alzheimer's Disease, vol. 97, no. 1, pp. 89-100, 2024