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WIREs Syst Biol Med
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Multiscale modeling methods in biomechanics

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More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space–time continuum. We are forced to consider multiple space–time continua, each representing the phenomenon of interest at a characteristic space–time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: ‘causal confirmation,’ where multiscale models are used as materializations of the causation theories; ‘predictive accuracy,’ where multiscale modeling is aimed to improve the predictive accuracy; and ‘determination of effect,’ where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space–time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
Establishing ‘determination of effect’ of RBC membrane microstructural details on tank‐treading dynamics of RBC in shear flow. ‘Simulation’ refers to the multiscale model and ‘single‐layer model’ refers to a single‐scale model. The multiscale model simulation with zero membrane viscosity (vb = vs = 0) retrieves the single‐scale model result. With a nonzero membrane viscosity, the multiscale model compares better with the experimental results. (Reprinted with permission from Ref . Copyright 2011 Cambridge University Press)
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Basic topological interactions composing the multilevel model of endotoxin induced human inflammation. (Reprinted with permission from Ref . Copyright 2009 Wolters Kluwer Health, Inc.)
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Multiscale model of a red blood cell: (a) complete cell model; (b) molecular‐detailed junctional complex model; and (c) spectrin (Sp) model. (Reprinted with permission from Ref . Copyright 2010 American Physical Society)
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Multiscale model of cardiopulmonary bypass. (Reprinted with permission from Ref . Copyright 2014 Elsevier)
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Complete model of the muscle exhibits three blocks. (Reprinted with permission from Ref . Copyright 2011 Springer‐Verlag)
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Micromechanical representation of bone material by means of a five‐step homogenization procedure. (Reprinted with permission from Ref . Copyright 2007 Elsevier)
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Model hierarchy of MTLT (CIR and INT) tissues. (Reprinted with permission from Ref . Copyright 2014 Springer‐Verlag)
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Incidence of multiscale papers indexed in PubMed from 1991 to 2015. Incidence is obtained by dividing for each year the number of papers retrieved with the search ‘Multiscale [ALL]’ by the total number of papers indexed in that year.
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Multiscale modeling of lymphatic drainage. (Reprinted with permission from Ref . Copyright 2012 Elsevier)
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Different spatial scales identified in the modeling of the gastrointestinal system. (Reprinted with permission from Ref . Copyright 2010 Wiley)
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Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
Models of Systems Properties and Processes > Mechanistic Models
Analytical and Computational Methods > Computational Methods

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