IntroductionMathematical models play a crucial role in investigating complex biological systems, enabling a comprehensive understanding of interactions among various components and facilitating in silico testing of intervention strategies. Alzheimer's disease (AD) is characterized by multifactorial causes and intricate interactions among biological entities, necessitating a personalized approach due to the lack of effective treatments. Therefore, mathematical models offer promise as indispensable tools in combating AD. However, existing models in this emerging field often suffer from limitations such as inadequate validation or a narrow focus on single proteins or pathways.MethodsIn this paper, we present a multiscale mathematical model that describes the progression of AD through a system of 19 ordinary differential equations. The equations describe the evolution of proteins (nanoscale), cell populations (microscale), and organ-level structures (macroscale) over a 50-year lifespan, as they relate to amyloid and tau accumulation, inflammation, and neuronal death.ResultsDistinguishing our model is a robust foundation in biological principles, ensuring improved justification for the included equations, and rigorous parameter justification derived from published experimental literature.ConclusionThis model represents an essential initial step toward constructing a predictive framework, which holds significant potential for identifying effective therapeutic targets in the fight against AD.

中文翻译：

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纳米、微观和宏观尺度上阿尔茨海默病的计算模型

简介数学模型在研究复杂的生物系统中发挥着至关重要的作用，可以全面理解各个组成部分之间的相互作用并促进计算机模拟测试干预策略。阿尔茨海默病 (AD) 的特点是多因素病因和生物实体之间复杂的相互作用，由于缺乏有效的治疗方法，需要采取个性化的治疗方法。因此，数学模型有望成为对抗 AD 不可或缺的工具。然而，这个新兴领域的现有模型经常受到验证不足或只关注单一蛋白质或途径等局限性。方法在本文中，我们提出了一个多尺度数学模型，通过 19 个常微分方程组描述 AD 的进展。这些方程描述了 50 年寿命中蛋白质（纳米尺度）、细胞群（微观尺度）和器官水平结构（宏观尺度）的演化，因为它们与淀粉样蛋白和 tau 蛋白积累、炎症和神经元死亡有关。结果区分我们的模型是生物学原理的坚实基础，确保改进所包含方程的合理性，以及从已发表的实验文献中得出的严格参数合理性。结论该模型代表了构建预测框架的重要第一步，该框架在识别有效治疗靶标方面具有巨大潜力对抗AD。