Sensitivity analysis of initial value problems with mixed odes and algebraic equations

Caracotsios, M.; Stewart, W. D. P.

doi:10.1016/0098-1354(85)85014-6

Cited by 377 publications

(178 citation statements)

References 9 publications

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“…For this reason, continuous efforts have been made to develop efficient and robust integration algorithms for solving sensitivity analysis problems in biological systems. 9,17,[19][20][21][22][23][24][25] As sensitivity analysis describes the importance of the model parameters to the measurement variables, it plays an important role in biological model development in an iterative cycle between data analysis, identifiability assessment, measurement set selection, parameter estimation, model validation and experimental design. One crucial issue relating to parameter estimation is identifiability analysis, and this is closely related to parametric sensitivity analysis.…”

Section: Introductionmentioning

confidence: 99%

Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-κB signalling pathway

et al. 2006

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This version is available at https://strathprints.strath.ac.uk/5175/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-kB signalling pathway{ Mathematical modelling offers a variety of useful techniques to help in understanding the intrinsic behaviour of complex signal transduction networks. From the system engineering point of view, the dynamics of metabolic and signal transduction models can always be described by nonlinear ordinary differential equations (ODEs) following mass balance principles. Based on the statespace formulation, many methods from the area of automatic control can conveniently be applied to the modelling, analysis and design of cell networks. In the present study, dynamic sensitivity analysis is performed on a model of the IkB-NF-kB signal pathway system. Univariate analysis of the Euclidean-form overall sensitivities shows that only 8 out of the 64 parameters in the model have major influence on the nuclear NF-kB oscillations. The sensitivity matrix is then used to address correlation analysis, identifiability assessment and measurement set selection within the framework of least squares estimation and multivariate analysis. It is shown that certain pairs of parameters are exactly or highly correlated to each other in terms of their effects on the measured variables. The experimental design strategy provides guidance on which proteins should best be considered for measurement such that the unknown parameters can be estimated with the best statistical precision. The whole analysis scheme we describe provides efficient parameter estimation techniques for complex cell networks.

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Section: Introductionmentioning

confidence: 99%

Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-κB signalling pathway

et al. 2006

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“…In TPLUG, the governing equations are discretized in the spatial (axial) direction, and the resulting differential-algebraic system is integrated in time with the DASAC software [32]. The set of governing equations consists of an overall continuity equation for the gas, material balances for all of the gas-phase and surface species, an ideal gas equation of state, and flux balances for the gas-phase boundary layer.…”

Section: Simulation Detailsmentioning

confidence: 99%

Microkinetic Modeling of Lean NO<sub>x</sub> Trap Storage and Regeneration

Larson

Chakravarthy

Pihl

et al. 2011

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A microkinetic chemical reaction mechanism capable of describing both the storage and regeneration processes in a fully formulated lean NO x trap (LNT) is presented. The mechanism includes steps occurring on the precious metal, barium oxide (NO x storage), and cerium oxide (oxygen storage) sites of the catalyst. The complete reaction set is used in conjunction with a transient plug flow reactor code (including boundary layer mass transfer) to simulate not only a set of long storage/regeneration cycles with a CO/H 2 reductant, but also a series of steady flow temperature sweep experiments that were previously analyzed with just a precious metal mechanism and a steady state code neglecting mass transfer. The results show that, while mass transfer effects are generally minor, NO x storage is not negligible during some of the temperature ramps, necessitating a re-evaluation of the precious metal kinetic parameters. The parameters for the entire mechanism are inferred by finding the best overall fit to the complete set of experiments. Rigorous thermodynamic consistency is enforced for parallel reaction pathways and with respect to known data for all of the gas phase species involved. It is found that, with a few minor exceptions, all of the basic experimental observations can be reproduced with the transient simulations. In addition to accounting for normal cycling behavior, the final mechanism should provide a starting point for the description of further LNT phenomena such as desulfation and the role of alternative reductants. 4 ACKNOWLEDGMENTSThe authors thank Dr. Andrew Lutz, formerly of Sandia, for initial development of the Chemkinbased transient plug flow reactor code (TPLUG).

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“…In TPLUG, the governing equations are discretized in the spatial (axial) direction, and the resulting differential-algebraic system is integrated in time with the DASAC software (Caracotsios and Stewart, 1985). The set of governing equations consists of an overall continuity equation for the gas, material balances for all of the gas-phase and surface species, and an ideal gas equation of state.…”

Section: Simulation Detailsmentioning

confidence: 99%

Simulation of lean NOx trap performance with microkinetic chemistry and without mass transfer.

Larson¹,

Daw

Pihl

et al. 2011

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A microkinetic chemical reaction mechanism capable of describing both the storage and regeneration processes in a fully formulated lean NO x trap (LNT) is presented. The mechanism includes steps occurring on the precious metal, barium oxide (NO x storage), and cerium oxide (oxygen storage) sites of the catalyst. The complete reaction set is used in conjunction with a transient plug flow reactor code to simulate not only conventional storage/regeneration cycles with a CO/H 2 reductant, but also steady flow temperature sweep experiments that were previously analyzed with just a precious metal mechanism and a steady state code. The results show that NO x storage is not negligible during some of the temperature ramps, necessitating a re-evaluation of the precious metal kinetic parameters. The parameters for the entire mechanism are inferred by finding the best overall fit to the complete set of experiments. Rigorous thermodynamic consistency is enforced for parallel reaction pathways and with respect to known data for all of the gas phase species involved. It is found that, with a few minor exceptions, all of the basic experimental observations can be reproduced with these purely kinetic simulations, i.e., without including mass-transfer limitations. In addition to accounting for normal cycling behavior, the final mechanism should provide a starting point for the description of further LNT phenomena such as desulfation and the role of alternative reductants. 4 ACKNOWLEDGMENTSThe authors thank Dr. Andrew E. Lutz, formerly of Sandia, for initial development of the Chemkin-based transient plug flow reactor code (TPLUG). The efforts at Oak Ridge were sponsored by the U.S.

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Sensitivity analysis of initial value problems with mixed odes and algebraic equations

Cited by 377 publications

References 9 publications

Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-κB signalling pathway

Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-κB signalling pathway

Microkinetic Modeling of Lean NO<sub>x</sub> Trap Storage and Regeneration

Simulation of lean NOx trap performance with microkinetic chemistry and without mass transfer.

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