Multiscale optimization using hybrid PDE/kMC process systems with application to thin film growth

Varshney, Amit; Armaou, Antonios

doi:10.1016/j.ces.2005.05.055

Cited by 58 publications

(30 citation statements)

References 54 publications

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“…The second challenge is the integration of the MAPK signaling pathway model for a large number of cells (in the order of 10 6 ). We applied the in situ adaptive tabulation (ISAT) method 85,86 to remedy the difficulties associated with the large number of ODEs evaluations. The basic idea of this method is to approximate the integration of the MAPK signaling pathway model for a given initial condition using previously stored evaluations of a relatively close initial condition.…”

Section: Cell Phenotypementioning

confidence: 99%

Modeling the effect of chemotaxis on glioblastoma tumor progression

et al. 2011

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Tumor progression depends on the intricate interplay between biological processes that span the molecular and macroscopic scales. A mathematical agent-based model is presented to describe the 3-D (three-dimensional) progression of a brain tumor type (i.e., glioblastoma multiforme) as the collective behavior of individual tumor cells whose fate is determined by intracellular signaling pathways (i.e., MAPK pathway) that are governed by the temporal-spatial distribution of key biochemical cues (i.e., growth factors, nutrients). The model is used to investigate how tumor growth and invasiveness depend on the response of migrating tumor cells to chemoattractants. Simulation results suggest that individual cell sensitivity to chemical gradients is necessary to generate in silico tumors with the irregular shape and diffusive tumor-stroma interface characteristic of glioblastomas. In addition, vascular network damage influences tumor growth and invasiveness. The results quantitatively recapitulate the central role that nutrient availability and signaling proteins have on tumor invasive properties.

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Section: Cell Phenotypementioning

confidence: 99%

Modeling the effect of chemotaxis on glioblastoma tumor progression

et al. 2011

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“…The ISAT algorithm has also been applied to incorporate detailed chemical kinetics in the direct numerical simulation (DNS) of reactive flow [23,24]. Besides the wide applications in the field of combustion, the applications of ISAT in other areas have been reported in [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient implementation of combustion chemistry in parallel PDF calculations

Lantz

Ren

et al. 2009

Journal of Computational Physics

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“…[7][8][9]); and the algorithm has been incorporated into the ANSYS/FLUENT software [3,10]. ISAT has also been used in chemical engineering [11][12][13], in solid mechanics [14], control [15] and the study of thin films and surface reaction [16,17]. Several variants of ISAT have been proposed and investigated [18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%