A systematic approach to the scale separation problem in the development of multiscale models.
A systematic approach to the scale separation problem in the development of multiscale models.
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DOI：
10.1371/journal.pone.0251297
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发表时间：
2021
期刊：
影响因子：
3.7
通讯作者：
Viceconti M
中科院分区：
文献类型：
--
作者：
Bhattacharya P;Li Q;Lacroix D;Kadirkamanathan V;Viceconti M
在整个工程中，存在这样的问题：需要根据另一个量的测量来预测一个量，但是这两个量在截然不同的时间和空间范围内具有特征变化。在此类“多尺度”问题带来的众多挑战中，定义“尺度”的问题仍然没有得到很好的解决。这个基本问题尤其在生物医学工程领域导致了很多混乱。本研究根据现有仪器的测量限制、可用的计算能力以及感兴趣的数量特征变化的时间和空间范围提出了尺度的定义。该定义用于从头到尾构建多尺度建模方法，从系统的描述（感兴趣的现实部分）开始，到系统内不同尺度的数学模型的算法编排结束。该方法针对一个具体但经过充分研究的问题进行了说明。尺度的概念和引入的多尺度建模方法被证明可以很容易地适应其他密切相关的问题。尽管超出了本文的范围，但我们相信所提出的方法可以广泛应用于整个工程。
Throughout engineering there are problems where it is required to predict a quantity based on the measurement of another, but where the two quantities possess characteristic variations over vastly different ranges of time and space. Among the many challenges posed by such ‘multiscale’ problems, that of defining a ‘scale’ remains poorly addressed. This fundamental problem has led to much confusion in the field of biomedical engineering in particular. The present study proposes a definition of scale based on measurement limitations of existing instruments, available computational power, and on the ranges of time and space over which quantities of interest vary characteristically. The definition is used to construct a multiscale modelling methodology from start to finish, beginning with a description of the system (portion of reality of interest) and ending with an algorithmic orchestration of mathematical models at different scales within the system. The methodology is illustrated for a specific but well-researched problem. The concept of scale and the multiscale modelling approach introduced are shown to be easily adaptable to other closely related problems. Although out of the scope of this paper, we believe that the proposed methodology can be applied widely throughout engineering.
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影响因子：
3.9
作者：
Hamed, Elham;Jasiuk, Iwona;Liszka, Tadeusz
通讯作者：
Liszka, Tadeusz
DOI：
10.1016/j.ijengsci.2020.103244
发表时间：
2020-04-01
影响因子：
6.6
作者：
Dyskin, A., V;Pasternak, E.
通讯作者：
Pasternak, E.
DOI：
10.1146/annurev-bioeng-071910-124729
发表时间：
2011-08-15
影响因子：
9.7
作者：
Deisboeck TS;Wang Z;Macklin P;Cristini V
通讯作者：
Cristini V
DOI：
10.1243/pime_proc_1991_205_258_02
发表时间：
1991-01-01
期刊：
Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine
影响因子：
--
作者：
Anderson, D D;Brown, T D;Radin, E L
通讯作者：
Radin, E L
DOI：
10.1115/1.4025390
发表时间：
2013-12-01
影响因子：
1.7
作者：
Gilchrist, Seth;Guy, Pierre;Cripton, Peter A.
通讯作者：
Cripton, Peter A.