Classification and analysis of integrating frameworks in multiscale modelling

Ingram, Gordon D.; Cameron, Ian; Hangos, Katalin M.

doi:10.1016/j.ces.2004.02.010

Cited by 124 publications

(36 citation statements)

References 25 publications

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“…This relation expresses that the density of the individuals in each step size i x  is same as the number of individuals in step size   . In addition, the ratio between the variable step size Δxi of the curve x and the time step   ( t  ) provides the slope of x(t,τ) that should be equal to g(x,t) defined in Equation (1). If the slopes of all characteristic curves are same such that the curve…”

Section: Transport Methods Formulationmentioning

confidence: 99%

“…Thus, if x is the characteristic of individuals then we get a family of curves x(t, τ), the characteristic curves, as shown in Figure 1. For each individual, and for a fixed τ, x(t,τ) is classically derived from a kinetic law: (1) This represents g(x,t) as the growth rate defined as the slope of internal variable x. Let us define the nucleation term as the source term ( , ) N x t , which varies between x to xx  within time t to tt  .…”

Section: Classical Pbe With Growth and Nucleationmentioning

confidence: 99%

“…We need a modelling technique that can work at both scales to provide a relation between both levels. [1,2] Population balance models (PBMs) have provided such an interface which connects the different scales and deals with several particulate processes simultaneously. [3,4] Population balance modelling is a very useful tool in chemical engineering.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

Ali

Elkamel

Gruy³

et al. 2016

Can J Chem Eng

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The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, mass, and protein concentration) is typically modelled by a population balance equation, a first-order linear hyperbolic partial differential equation that is shared by all T-cells is involved. At these crossing points, the linear advection equation is not possible by using the hyperbolic conservation laws in a classical way. Therefore, a new transport method is introduced in this article that is able to find the population density function for such processes. A multi-scale mathematical modelling framework is employed. At the first scale, two processes, which are termed as the activation and reaction terms (assimilated as nucleation and growth in chemical processes), are studied as independent processes. At the second scale, the dynamic variation in the population density of activated T-cells is investigated in the presence of activation and reaction terms. The newly-developed transport method is shown to work in the case of crossing and to provide a smooth solution at the crossing points in contrast to the classical PDF techniques.2

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Section: Transport Methods Formulationmentioning

confidence: 99%

Section: Classical Pbe With Growth and Nucleationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Population balances in case of crossing characteristic curves: Application to T‐cells immune response

Ali

Elkamel

Gruy³

et al. 2016

Can J Chem Eng

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“…There are many excellent papers that present multiscale models (including many with important biomedical applications; Noble 2002; Hunter & Nielson 2005), and some specialized journals exist (e.g. Multiscale Modeling and Simulation, International Journal on Multiscale Computational Engineering), but few methodological papers on multiscale modelling have appeared (Ingram et al 2004;Weinan et al 2007).…”

Section: Multiscale Modelling and Simulation In Biomedicinementioning

confidence: 99%

The application of multiscale modelling to the process of development and prevention of stenosis in a stented coronary artery

Evans

Lawford

Gunn

et al. 2008

Phil. Trans. R. Soc. A.

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The inherent complexity of biomedical systems is well recognized; they are multiscale, multiscience systems, bridging a wide range of temporal and spatial scales. While the importance of multiscale modelling in this context is increasingly recognized, there is little underpinning literature on the methodology and generic description of the process. The COAST (complex autonoma simulation technique) project aims to address this by developing a multiscale, multiscience framework, coined complex autonoma (CxA), based on a hierarchical aggregation of coupled cellular automata (CA) and agent-based models (ABMs). The key tenet of COAST is that a multiscale system can be decomposed into N single-scale CA or ABMs that mutually interact across the scales. Decomposition is facilitated by building a scale separation map on which each single-scale system is represented according to its spatial and temporal characteristics. Processes having wellseparated scales are thus easily identified as the components of the multiscale model. This paper focuses on methodology, introduces the concept of the CxA and demonstrates its use in the generation of a multiscale model of the physical and biological processes implicated in a challenging and clinically relevant problem, namely coronary artery in-stent restenosis.

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“…the widely used but certainly not universally adopted 'serial' versus 'concurrent' [24]). During the workshop, three different but partly overlapping classifications where introduced [4,[25][26][27][28] and others exist [12,24,29,30]. A shared view on multiscale modelling and a clear, all-inclusive, and universally adopted classification would be very beneficial to the field of multiscale modelling.…”

Section: What Is Multiscale Modelling?mentioning

confidence: 99%

Multiscale modelling and simulation: a position paper

Hoekstra

Chopard

Coveney

2014

Phil. Trans. R. Soc. A.

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One contribution of 13 to a Theme Issue 'Multi-scale systems in fluids and soft matter: approaches, numerics and applications' . We argue that, despite the fact that the field of multiscale modelling and simulation has enjoyed significant success within the past decade, it still holds many open questions that are deemed important but so far have barely been explored. We believe that this is at least in part due to the fact that the field has been mainly developed within disciplinary silos. The principal topics that in our view would benefit from a targeted multidisciplinary research effort are related to reaching consensus as to what exactly one means by 'multiscale modelling', formulating a generic theory or calculus of multiscale modelling, applying such concepts to the urgent question of validation and verification of multiscale models, and the issue of numerical error propagation in multiscale models. Moreover, we believe that this would, in principle, also lay the foundation for more efficient, well-defined and usable multiscale computing environments. We believe that multidisciplinary research to fill in the gaps is timely, highly relevant, and with substantial potential impact on many scientific disciplines.

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Classification and analysis of integrating frameworks in multiscale modelling

Cited by 124 publications

References 25 publications

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

Population balances in case of crossing characteristic curves: Application to T‐cells immune response

The application of multiscale modelling to the process of development and prevention of stenosis in a stented coronary artery

Multiscale modelling and simulation: a position paper

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