Some effective approaches to check the identifiability of uncontrolled nonlinear systems

Denis-Vidal, Lilianne; Joly-Blanchard, Ghislaine; Noiret, Céline

doi:10.1016/s0378-4754(01)00274-9

Cited by 76 publications

(71 citation statements)

References 12 publications

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“…Alternatively, following the approach taken by Evans et al [12], an output equation can be derived for the model, which only involves the output and its derivatives up to order n (the number of model variables). Then (following a similar approach as Denis-Vidal et al [17]) any indistinguishable parameter vector, p, must also satisfy the same equation with p replaced by p and a polynomial of the following form can be generated:…”

Section: Structural Identifiabilitymentioning

confidence: 99%

Modelling of tumour growth and cytotoxic effect of docetaxel in xenografts

Evans

Dimelow²,

Yates

2014

Computer Methods and Programs in Biomedicine

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One of the major sources of information on physiological and pathophysiological effects in pre-clinical oncology studies is the xenografted tumour animal model. However, measurement of tumour volume over time potentially masks a range of biological changes that the xenograft is undergoing. In this paper a mechanistic model of tumour growth in xenografts is presented that can be used to investigate the mode of drug action with respect to phenotypic changes. The model encapsulates key histological biomarkers and spatial constraints. The unknown model parameters are first shown to be uniquely identifiable from the proposed experimental studies, and then estimated from the resulting data using the anti-cancer agent docetaxel.

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Section: Structural Identifiabilitymentioning

confidence: 99%

Modelling of tumour growth and cytotoxic effect of docetaxel in xenografts

Evans

Dimelow²,

Yates

2014

Computer Methods and Programs in Biomedicine

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“…Denis-Vidal et al [14] proposed the following model to illustrate how the identifiability of uncontrolled models may depend on the initial conditions.…”

Section: Knowledge Of Additional Initial Conditions Can Increase Idenmentioning

confidence: 99%

Structural Properties of Dynamic Systems Biology Models: Identifiability, Reachability, and Initial Conditions

Villaverde

Banga

2017

Processes

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Dynamic modelling is a powerful tool for studying biological networks. Reachability (controllability), observability, and structural identifiability are classical system-theoretic properties of dynamical models. A model is structurally identifiable if the values of its parameters can in principle be determined from observations of its outputs. If model parameters are considered as constant state variables, structural identifiability can be studied as a generalization of observability. Thus, it is possible to assess the identifiability of a nonlinear model by checking the rank of its augmented observability matrix. When such rank test is performed symbolically, the result is of general validity for almost all numerical values of the variables. However, for special cases, such as specific values of the initial conditions, the result of such test can be misleading-that is, a structurally unidentifiable model may be classified as identifiable. An augmented observability rank test that specializes the symbolic states to particular numerical values can give hints of the existence of this problem. Sometimes it is possible to find such problematic values analytically, or via optimization. This manuscript proposes procedures for performing these tasks and discusses the relation between loss of identifiability and loss of reachability, using several case studies of biochemical networks.

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“…Among them, the methods based on an algebraic approach, such as power expansion ( [4]), differential algebra (see for instance [5]) and Gröbner basis (see [6,7]) proved to be a valuable tool. The analyses based on differential algebra investigate the parameters-toobservable by assuming that the measurements are not affected by noise.…”

Section: Introductionmentioning

confidence: 99%

An information-theoretic approach to assess practical identifiability of parametric dynamical systems

Pant

Lombardi

2015

Mathematical Biosciences

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Abstract.A new approach for assessing parameter identifiability of dynamical systems in a Bayesian setting is presented. The concept of Shannon entropy is employed to measure the inherent uncertainty in the parameters. The expected reduction in this uncertainty is seen as the amount of information one expects to gain about the parameters due to the availability of noisy measurements of the dynamical system. Such expected information gain is interpreted in terms of the variance of a hypothetical measurement device that can measure the parameters directly, and is related to practical identifiability of the parameters. If the individual parameters are unidentifiable, correlation between parameter combinations is assessed through conditional mutual information to determine which sets of parameters can be identified together. The information theoretic quantities of entropy and information are evaluated numerically through a combination of Monte Carlo and k-nearest neighbour methods in a non-parametric fashion. Unlike many methods to evaluate identifiability proposed in the literature, the proposed approach takes the measurement-noise into account and is not restricted to any particular noise-structure. Whilst computationally intensive for large dynamical systems, it is easily parallelisable and is non-intrusive as it does not necessitate re-writing of the numerical solvers of the dynamical system. The application of such an approach is presented for a variety of dynamical systemsranging from systems governed by ordinary differential equations to partial differential equations -and, where possible, validated against results previously published in the literature.

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Some effective approaches to check the identifiability of uncontrolled nonlinear systems

Cited by 76 publications

References 12 publications

Modelling of tumour growth and cytotoxic effect of docetaxel in xenografts

Modelling of tumour growth and cytotoxic effect of docetaxel in xenografts

Structural Properties of Dynamic Systems Biology Models: Identifiability, Reachability, and Initial Conditions

An information-theoretic approach to assess practical identifiability of parametric dynamical systems

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