Constant-number Monte Carlo simulation of population balances

Smith, Matt; Matsoukas, Themis

doi:10.1016/s0009-2509(98)00045-1

Cited by 301 publications

(245 citation statements)

References 16 publications

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“…The first column of plots corresponds to simulating the hybrid system that consists of the ensemble model for the concentrations and the CPB for the volume (equations 54-57). The second column corresponds to the cell population Monte Carlo simulation where a maximum number of 100000 cells were used in a constant number simulation scheme, (see Smith and Matsoukas, 1998). The perfect agreement between the two simulations demonstrates computationally the equivalence of the two models, as theoretically predicted by Stamatakis (2010).…”

Section: Cell Population Simulationsmentioning

confidence: 89%

“…These simulations are performed for positive feedback architecture with a value of the dissociation constant α for which two stable steady states coexist. For the simulation of the full CPB model (equation 50) and the CPB part of the hybrid model (equation 54) KMC algorithms were used (Smith and Matsoukas, 1998;Mantzaris, 2006;Stamatakis and Zygourakis, 2010;Stamatakis and Zygourakis, 2011).…”

Section: Cell Population Simulationsmentioning

confidence: 99%

“…For solving the CPB equations (50) and (54) the constant-number KMC framework was used (Smith and Matsoukas, 1998;Mantzaris, 2006;Stamatakis and Zygourakis, 2010;Stamatakis and Zygourakis, 2011). Moreover, the solution of the ensemble equation (55) …”

Section: Accuracy and Computational Efficiency Of Hybrid Modelmentioning

confidence: 99%

“…Moving-boundary approaches have also been developed (Kavousanakis et al, 2009) to overcome the issue that the state space boundaries in which the cell population distribution is confined are not known a priori. As an alternative to solving the actual CPB equations, computational methods that employ kinetic Monte Carlo (KMC) simulation have also been developed (Smith and Matsoukas, 1998;Mantzaris, 2006). Finally, Stamatakis (2010) investigated a set of assumptions that allowed for the transformation of a CPB to hybrid models involving ensemble or continuum equations.…”

Section: Introductionmentioning

confidence: 99%

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Cell population balance and hybrid modeling of population dynamics for a single gene with feedback

Stamatakis¹

2013

Computers & Chemical Engineering

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Latest research on biological systems is steadily shifting from isolated single cells to entire cell populations. The latter are inherently heterogeneous, and their modeling requires approaches that explicitly account for this property. A comprehensive such approach is the cell population balance (CPB), which, however, is computationally expensive and becomes intractable for multivariable models.In this work, we demonstrate the use of model-reduction to efficiently simulate cell population heterogeneity in a genetic network of a single gene with feedback. Starting from a 4-species model we use singular perturbation analysis to derive a single equation for the intracellular protein concentration. We subsequently incorporate this equation to a hybrid model consisting of a CPB for the cell volume, and a continuum equation for the protein concentration. We finally compare the results obtained with the hybrid model with those of the full CPB, demonstrating the accuracy and computational efficiency of the hybrid methodology.

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Section: Cell Population Simulationsmentioning

confidence: 89%

Section: Cell Population Simulationsmentioning

confidence: 99%

Section: Accuracy and Computational Efficiency Of Hybrid Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cell population balance and hybrid modeling of population dynamics for a single gene with feedback

Stamatakis¹

2013

Computers & Chemical Engineering

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“…The combined quadrature method of moments -method of characteristics was a successful technique to solve full 1D PBE-s with nucleation and growth only (Aamir et al, 2009. The Monte Carlo simulations were successfully applied to solve PBE-s as well (Bárkányi et al, 2013;Irizarry, 2008;Smith and Matsoukas, 1988) but the computational costs are far too increased to be applicable in the majority of engineering problems. The method of classes is based on the discretization of internal variables but for the more complicated PBEs a large number of classes is required to maintain the accuracy (Valentas and Amundson, 1966).…”

mentioning

confidence: 99%

Graphical processing unit (GPU) acceleration for numerical solution of population balance models using high resolution finite volume algorithm

Szilágyi

Nagy

2016

Computers & Chemical Engineering

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Graphical Processing Unit (GPU) Acceleration for Numerical Solution of Population Balance Models Using High Resolution Finite Volume AlgorithmBotond Szilágyi 1 , Zoltán K. Nagy 2,3,* AbstractPopulation balance modeling is a widely used approach to describe crystallization processes.It can be extended to multivariate cases where more internal coordinates i.e. particle properties such as multiple characteristic sizes, composition, purity, etc. can be used. The current study presents highly efficient fully discretized parallel implementation of the high resolution finite volume technique implemented on graphical processing units (GPUs) for the solution of singleand multi-dimensional population balance models (PBMs). The proposed GPU-PBM is implemented using CUDA C++ code for GPU calculations and provides a generic Matlab interface for easy application for scientific computing. The case studies demonstrate that the code running on the GPU is between 2…40 times faster than the compiled C++ code and 50…250 times faster than the standard MatLab implementation. This significant improvement in computational time enables the application of model-based control approaches in real time even in case of multidimensional population balance models.

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