Florey Institute of Neuroscience and Mental Health, University of Melbourne, Parkville, Victoria, Australia.
The Australian e-Health Research Centre, CSIRO, Parkville, Victoria, Australia.
J Alzheimers Dis. 2024;97(1):89-100. doi: 10.3233/JAD-230938.
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.
淀粉样蛋白-β（Aβ）斑块在大脑中的积累被认为是阿尔茨海默病（AD）的标志。数学建模作为一种潜在的替代方法，可以预测 Aβ的运动和积累，因此越来越受到关注，可用于辅助 AD 的诊断和预测疾病预后。这些数学模型深入了解了 AD 的发病机制和进展，这是仅通过实验研究难以获得的。数学建模还可以模拟治疗对大脑 Aβ水平的影响，从而具有模拟药物疗效和优化个性化治疗方法的潜力。在这篇综述中，我们概述了用于模拟大脑 Aβ水平（寡聚体、原纤维和/或斑块）的数学模型。我们将这些模型分为五类：一般常微分方程模型、一般偏微分方程模型、网络模型、线性最优常微分方程模型和修正偏微分方程模型（即 Smoluchowski 方程模型）。讨论了这些模型的假设、优点和局限性。鉴于使用 Smoluchowski 方程模型来模拟大脑 Aβ水平的普及，我们的综述总结了这些模型的历史和主要进展（例如，它们在预测 AD 发病中的应用及其与网络模型的结合使用）。本综述旨在引起更多从事 AD 研究的科学家和临床研究人员对数学建模的关注，以促进跨学科研究。
