Sensitivity analysis of ordinary differential equation systems—A direct method

Dickinson, Robert P.; Gelinas, Robert J.

doi:10.1016/0021-9991(76)90007-3

Cited by 240 publications

(142 citation statements)

References 4 publications

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“…Another way to compute the derivatives is the direct differential method, which solves the differential equations for the sensitivity coefficients [9,13]. These differential equations are differential output y i with respect to the model input parameter p over time.…”

Section: Direct Differential Methodsmentioning

confidence: 99%

Sensitivity analysis approaches applied to systems biology models

2011

IET Systems Biology

330

263

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With the rising application of systems biology, sensitivity analysis methods have been widely applied to study the biological systems, including metabolic networks, signalling pathways and genetic circuits. Sensitivity analysis can provide valuable insights about how robust the biological responses are with respect to the changes of biological parameters and which model inputs are the key factors that affect the model outputs. In addition, sensitivity analysis is valuable for guiding experimental analysis, model reduction and parameter estimation. Local and global sensitivity analysis approaches are the two types of sensitivity analysis that are commonly applied in systems biology. Local sensitivity analysis is a classic method that studies the impact of small perturbations on the model outputs. On the other hand, global sensitivity analysis approaches have been applied to understand how the model outputs are affected by large variations of the model input parameters. In this review, the author introduces the basic concepts of sensitivity analysis approaches applied to systems biology models. Moreover, the author discusses the advantages and disadvantages of different sensitivity analysis methods, how to choose a proper sensitivity analysis approach, the available sensitivity analysis tools for systems biology models and the caveats in the interpretation of sensitivity analysis results.

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Section: Direct Differential Methodsmentioning

confidence: 99%

Sensitivity analysis approaches applied to systems biology models

2011

IET Systems Biology

330

263

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“…Methods in the literature range from solving simple partial derivatives to spatial and temporal sensitivity analyses (Morisawa and Inoue, 1974;Atherton et al, 1975;Dickinson and Gelinas, 1976;Koda et al, 1979;Dunker, 1981;Gardner et al, 1981;Summers and McKellar, 1981;Koda, 1982;Helton et al, 1985;Iman and Helton, 1985;Helton et al, 1986;Iman and Helton, 1988;Helton et al, 1991;Zimmerman et al, 1991). A sensitivity coefficient is basically the ratio of the change in output to the change in input while all other parameters remain constant (Kfieger et al, 1977).…”

Section: Differential Sensitivity Analysismentioning

confidence: 99%

“…The Fourier amplitude sensitivity test (FAST) (Cukier et al 1973(Cukier et al , 1978 has been used to solve coupled nonlinear rate equations by Schaibly and Shuler (1973) and Cukier et al, (1975). FAST has also been used by Dickinson and Gelinas (1976) to study sensitivities of parameters used to model atmospheric chemical kinetics, by Koda et al (1979) to study atmospheric diffusion, and several others (Leipmann and Stephanopoulos, 1985;Kim etal., 1988). Theoretical aspects of a method using Green's functions are presented by Demiralp and Rabitz (1981).…”

Section: Introductionmentioning

confidence: 99%

A review of techniques for parameter sensitivity analysis of environmental models

Hamby

1994

Environ Monit Assess

1,533

852

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Abstract. Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a 'sensitivity analysis'. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.

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“…In these simulation conditions, formaldehyde is formed both from acetaldehyde, the initial product of ethyl nitrite photolysis, reaction (36), and by the sequence of reactions initiated by OH radical oxidation of MTA, reaction (20):…”

Section: Resultsmentioning

confidence: 99%

“…Reaction rate analysis for complex kinetic systems includes the solution of a mathematical model, i. e., a set of coupled kinetic ordinary differential equations, the study of the effects of parameter changes on the results and the exploration of important reaction pathways [19][20][21][22][23][24][25] . This information is important to decide which reactions should be included in a atmospheric photochemical mechanism and, also, which reactions should be experimentally studied.…”

Section: Introductionmentioning

confidence: 99%

Kinetic analysis of the gas-phase reactions of methacrolein with the OH radical in the presence of NOx

Pimentel¹,

Arbilla²

1999

J. Braz. Chem. Soc.

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Um mecanismo explícito para a reação da metacroleína (MTA) com radicais OH, numa mistura NOx -ar, foi simulado resolvendo as equações diferenciais ordinárias usando o método RungeKutta-4-semi-implícito. Os resultados simulados são consistentes com os dados experimentais publicados e o modelo explica as principais vias de reação para a oxidação da MTA com radicais OH na presença de NOx -ar. Usando uma análise dos autovetores e autovalores dos coeficientes de sensibilidade, para todas as espécies químicas envolvidas em diferentes tempos de reação, foi extraída informação cinética do sistema. Este método foi utilizado para reduzir o modelo cinético de forma objetiva. Foi utilizado, também, o método tradicional de análise de velocidade de produção (ROPA) para estudar a importância relativa das reações individuais. Usando a informação da análise de componente principal e da análise de velocidade de produção, foram identificadas as principais reações individuais.An explicit chemical mechanism for the reaction of methacrolein (MTA) with OH radicals in NOx-air systems, was simulated by solving the corresponding ordinary differential equations using Runge-Kutta-4-semi-implicit method. The simulated results are consistent with the published experimental data and the model accounts for all the major pathways by which MTA reacts in NOx-air systems. An eigenvalue-eigenvector analysis is used to extract meaningful kinetic information from linear sensitivity coefficients computed for all species of the chemical mechanism at several time points. This method is used to get an objective condition for constructing a minimal reaction set. Also, a classic method called rate of production analysis (ROPA) was used for the study of the reactions relevance. Using the principal component information as well as the rate of production analysis the main paths of reaction are identified and discussed.

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Sensitivity analysis of ordinary differential equation systems—A direct method

Cited by 240 publications

References 4 publications

Sensitivity analysis approaches applied to systems biology models

Sensitivity analysis approaches applied to systems biology models

A review of techniques for parameter sensitivity analysis of environmental models

Kinetic analysis of the gas-phase reactions of methacrolein with the OH radical in the presence of NOx

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