A systematic approach to the scale separation problem in the development of multiscale models.

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' prob...

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Autores principales:	Pinaki Bhattacharya, Qiao Li, Damien Lacroix, Visakan Kadirkamanathan, Marco Viceconti
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/dc25b6fff05247bda48914c2c926d12c
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spelling	oai:doaj.org-article:dc25b6fff05247bda48914c2c926d12c2021-12-02T20:11:19ZA systematic approach to the scale separation problem in the development of multiscale models.1932-620310.1371/journal.pone.0251297https://doaj.org/article/dc25b6fff05247bda48914c2c926d12c2021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0251297https://doaj.org/toc/1932-6203Throughout 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.Pinaki BhattacharyaQiao LiDamien LacroixVisakan KadirkamanathanMarco VicecontiPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 5, p e0251297 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Pinaki Bhattacharya Qiao Li Damien Lacroix Visakan Kadirkamanathan Marco Viceconti A systematic approach to the scale separation problem in the development of multiscale models.
description	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.
format	article
author	Pinaki Bhattacharya Qiao Li Damien Lacroix Visakan Kadirkamanathan Marco Viceconti
author_facet	Pinaki Bhattacharya Qiao Li Damien Lacroix Visakan Kadirkamanathan Marco Viceconti
author_sort	Pinaki Bhattacharya
title	A systematic approach to the scale separation problem in the development of multiscale models.
title_short	A systematic approach to the scale separation problem in the development of multiscale models.
title_full	A systematic approach to the scale separation problem in the development of multiscale models.
title_fullStr	A systematic approach to the scale separation problem in the development of multiscale models.
title_full_unstemmed	A systematic approach to the scale separation problem in the development of multiscale models.
title_sort	systematic approach to the scale separation problem in the development of multiscale models.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/dc25b6fff05247bda48914c2c926d12c
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A systematic approach to the scale separation problem in the development of multiscale models.

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