Generalization of a parameter set selection procedure based on orthogonal projections and the <i>D</i>‐optimality criterion

Chu, Ying‐Hao; Hahn, Juergen

doi:10.1002/aic.12727

Cited by 20 publications

(19 citation statements)

References 42 publications

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“…(19) can be approximated by ൣH ୧୩୦ ൧ ିଵ (as shown in Table 1). Hereafter we refer to this simplified version as Tikhonov regularization ("Reg"="Tikh").…”

mentioning

confidence: 99%

Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

López

Barz

Körkel

et al. 2015

Computers & Chemical Engineering

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“…(19) can be approximated by ൣH ୧୩୦ ൧ ିଵ (as shown in Table 1). Hereafter we refer to this simplified version as Tikhonov regularization ("Reg"="Tikh").…”

mentioning

confidence: 99%

Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

López

Barz

Körkel

et al. 2015

Computers & Chemical Engineering

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“…We propose a novel definition of identifiability of individual parameters in multi-parameters models. It is widely recognised that lack of identifiability can arise from two sources: lack of sensitivity, or compensation of a parameter by remaining model parameters [ 7 – 10 , 12 , 27 – 30 ]. A definition that quantifies this intuition has been missing.…”

Section: Methodsmentioning

confidence: 99%

“…The identifiable subset can be then estimated jointly with the remaining parameters assumed fixed. The determinant of the FIM and its least eigenvalue are used to measure optimality [ 7 – 10 ] of the selected set. Pairwise clustering has also been proposed to reduce the number of parameters [ 9 ].…”

Section: Introductionmentioning

confidence: 99%

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Clustering reveals limits of parameter identifiability in multi-parameter models of biochemical dynamics

et al. 2015

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BackgroundCompared to engineering or physics problems, dynamical models in quantitative biology typically depend on a relatively large number of parameters. Progress in developing mathematics to manipulate such multi-parameter models and so enable their efficient interplay with experiments has been slow. Existing solutions are significantly limited by model size.ResultsIn order to simplify analysis of multi-parameter models a method for clustering of model parameters is proposed. It is based on a derived statistically meaningful measure of similarity between groups of parameters. The measure quantifies to what extend changes in values of some parameters can be compensated by changes in values of other parameters. The proposed methodology provides a natural mathematical language to precisely communicate and visualise effects resulting from compensatory changes in values of parameters. As a results, a relevant insight into identifiability analysis and experimental planning can be obtained. Analysis of NF- κB and MAPK pathway models shows that highly compensative parameters constitute clusters consistent with the network topology. The method applied to examine an exceptionally rich set of published experiments on the NF- κB dynamics reveals that the experiments jointly ensure identifiability of only 60 % of model parameters. The method indicates which further experiments should be performed in order to increase the number of identifiable parameters.ConclusionsWe currently lack methods that simplify broadly understood analysis of multi-parameter models. The introduced tools depict mutually compensative effects between parameters to provide insight regarding role of individual parameters, identifiability and experimental design. The method can also find applications in related methodological areas of model simplification and parameters estimation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0205-8) contains supplementary material, which is available to authorized users.

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“…The challenges arise from two sources, namely the uncertainty of the model parameters and the computational burden of exploring the influence of a large number of parameters and their correlations. To overcome these challenges, large-scale ODE models have to employ supplementary tools like sensitivity and uncertainty analysis, model identifiability analysis and parameter set reduction in the modeling loop (Chu and Hahn, 2012; Jayaraman and Hahn, 2009; Kiparissides et al, 2011; Vodovotz et al, 2009). …”

Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis of a mathematical model of acute inflammation identifies nonlinear dependence of cumulative tissue damage on host interleukin-6 responses

Mathew

Bartels

Banerjee

et al. 2014

Journal of Theoretical Biology

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The precise inflammatory role of the cytokine interleukin (IL)-6 and its utility as a biomarker or therapeutic target have been the source of much debate, presumably due to the complex pro- and anti-inflammatory effects of this cytokine. We previously developed a nonlinear ordinary differential equation (ODE) model to explain the dynamics of endotoxin (lipopolysaccharide; LPS)-induced acute inflammation and associated whole-animal damage/dysfunction (a proxy for the health of the organism), along with the inflammatory mediators tumor necrosis factor (TNF)-α, IL-6, IL-10, and nitric oxide (NO). The model was partially calibrated using data from endotoxemic C57Bl/6 mice. Herein, we investigated the sensitivity of the area under the damage curve (AUCD) to the 51 rate parameters of the ODE model for different levels of simulated LPS challenges using a global sensitivity approach called Random Sampling High Dimensional Model Representation (RS-HDMR). We explored sufficient parametric Monte Carlo samples to generate the variance-based Sobol' global sensitivity indices, and found that inflammatory damage was highly sensitive to the parameters affecting the activity of IL-6 during the different stages of acute inflammation. The AUCIL6 showed a bimodal distribution, with the lower peak representing healthy response and the higher peak representing sustained inflammation. Damage was minimal at low AUCIL6, giving rise to a healthy response. In contrast, intermediate levels of AUCIL6 resulted in high damage, and this was due to the insufficiency of damage recovery driven by anti-inflammatory responses and the activation of positive feedback sustained by IL-6. At high AUCIL6, damage recovery was interestingly restored in some population of simulated animals due to the NO-mediated anti-inflammatory responses. These observations suggest that the host's health status during acute inflammation depends in a nonlinear fashion on the magnitude of the inflammatory stimulus, on the host's propensity to produce IL-6, and on NO-mediated downstream responses.

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Generalization of a parameter set selection procedure based on orthogonal projections and the D‐optimality criterion

Cited by 20 publications

References 42 publications

Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

Clustering reveals limits of parameter identifiability in multi-parameter models of biochemical dynamics

Global sensitivity analysis of a mathematical model of acute inflammation identifies nonlinear dependence of cumulative tissue damage on host interleukin-6 responses

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