考虑抑制剂作用的阿尔茨海默病最优控制模型分析  

Analysis of optimal control model for Alzheimer′s disease considering the role of inhibitors

作　　者：董明岩 张永鑫[1] 罗建锋 DONG Mingyan;ZHANG Yongxin;LUO Jianfeng(School of Mathematics,North University of China,Taiyuan,Shanxi 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《石河子大学学报（自然科学版）》2024年第6期786-792,共7页Journal of Shihezi University(Natural Science)

基　　金：国家自然科学基金项目(12201582);山西省基础研究计划项目(202203021212130)。

摘　　要：阿尔茨海默病的主要病理特征是脑内β淀粉样蛋白斑块沉积及Ca^(2+)稳态失衡。为此,不同的抑制剂被研发出来用于抑制β淀粉样蛋白和Ca^(2+)的浓度,以期减缓阿尔茨海默病的疾病进程。本文基于Ca^(2+)与β淀粉样蛋白之间的相互作用,构建并分析了一个考虑抑制剂作用的最优控制模型。首先,从理论层面给出了系统出现双稳现象的阈值条件;其次,利用Pontryagin极小值原理求得最优控制策略;最后,基于数值模拟结果探究不同控制策略的作用效果。研究结果表明相比较于单一类型抑制剂的使用,β淀粉样蛋白抑制剂和Ca^(2+)抑制剂的联合作用能够有效地降低β淀粉样蛋白水平,进而控制疾病进程。The main pathological characteristics of Alzheimer′s disease are the deposition ofβ-amyloid plaques in the brain and an im-balance of Ca^(2+)homeostasis.For this reason,several inhibitors have been developed to lowerβ-amyloid and Ca^(2+)concentrations with the aim of slowing down the disease process in Alzheimer′s disease.In this paper,based on the interaction between Ca^(2+)andβ-amy-loid,an optimal control model considering the effect of inhibitors is constructed and analyzed.First,the threshold conditions for the oc-currence of bistability in the system are given from the theoretical level;next,the Pontryagin Minimum Principle is used to find the op-timal control strategy;and last,the effects of different control strategies are investigated based on numerical simulation results.The re-sults showed that,in contrast to the use of a single type of inhibitor,the combination ofβ-amyloid inhibitor and Ca^(2+)inhibitor can ef-fectively reduce the level ofβ-amyloid,thus controlling the disease process.

关 键 词：CA^(2+) Β淀粉样蛋白 双稳态 抑制剂 最优控制 

分 类 号：O175[理学—数学] O232[理学—基础数学]