The Kinetics and Mechanism of Inhibitor Drugs in the Treatment of Alzheimer's Disease

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-08-18 DOI:10.1002/mma.70029

Yasser Alzahrani, Shantia Yarahmadian, Vaghawan Prasad Ojha, Trey Leonard

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引用次数: 0

Abstract

The etiology of Alzheimer's disease (AD) remains elusive. From a pathological point of view, several complex hypotheses, such as impaired neurotransmission, oxidative stress, and aggregation of amyloid- $β$ (A $β$ ), are considered crucial contributors to the pathophysiology of AD. Recent studies have primarily focused on AD treatment strategies targeting drugs that intervene in cerebral deposition of aggregated amyloid- $β$ (A $β$ ) polymers, often found in the form of amyloid plaques. In this paper, we present intuitive mathematical models that clarify the treatment of AD in the presence of inhibitory drugs. These models elucidate the intricate kinetics involved in A $β$ formation and the interaction of drugs with these processes. We discuss two categories of drugs: first, anti-inflammatory drugs (NSAIDs), which act as monomer inhibitors of A $β$ aggregation, and second, drugs that directly interact with A $β$ aggregated polymers. We initially analyze each drug independently and then assess their combined effects. Our numerical simulations demonstrate that the first type of drug reduces the equilibrium state value of aggregated filaments, whereas the second model of drug exhibits even greater efficacy in reducing the equilibrium state value of aggregated filaments. Furthermore, we conduct simulations of the simultaneous application of both drugs. The results are compared with the experimental data.

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抑制剂药物治疗阿尔茨海默病的动力学和机制

阿尔茨海默病（AD）的病因仍然难以捉摸。从病理学的角度来看，一些复杂的假设，如神经传递受损、氧化应激和淀粉样蛋白- β $$ \beta $$ （a β $$ \beta $$）聚集，被认为是AD病理生理的关键因素。最近的研究主要集中在针对干预脑沉积聚集的淀粉样蛋白- β $$ \beta $$ （A β $$ \beta $$）聚合物（通常以淀粉样斑块的形式存在）的药物的AD治疗策略上。在本文中，我们提出了直观的数学模型，阐明了在抑制药物存在下治疗AD的方法。这些模型阐明了A β $$ \beta $$形成的复杂动力学以及药物与这些过程的相互作用。我们讨论了两类药物：一类是抗炎药（NSAIDs），它作为A β $$ \beta $$聚集的单体抑制剂；另一类是直接与A β $$ \beta $$聚集的聚合物相互作用的药物。我们首先单独分析每种药物，然后评估它们的联合作用。我们的数值模拟表明，第一类药物降低了聚集丝的平衡状态值，而第二种药物模型在降低聚集丝的平衡状态值方面表现出更大的功效。此外，我们还进行了两种药物同时应用的模拟。计算结果与实验数据进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.