An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases

Meshkat, Nicolette; Eisenberg, Marisa C.; DiStefano, Joseph J.

doi:10.1016/j.mbs.2009.08.010

Cited by 82 publications

(112 citation statements)

References 15 publications

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“…There have been different approaches to determining whether a system is identifiable or not, where one has to distinguish between local and global identifiability, as defined in [BÅ70]. These methods include a Taylor series expansion approach [Poh78], a Laplace transform approach [BÅ70], a similarity transformation approach [CG85,YEC09] also known as exhaustive modeling, and a differential algebra approach [LG94,MED09]. A graph theoretical approach to parameter identifiability is described in [BHS14].…”

Section: Previous Workmentioning

confidence: 99%

“…This can be done using a reparametrization of the original system, which reduces it to a model having a parameter space of lower dimension. A procedure for finding such a reparametrization has been discussed for the differential algebra approach [LG94,MED09,MAD11], for the Taylor series approach [EC00], and for the similarity transformation approach [CG98,MTK15]. In [MTK15,YEC09] it is observed that non-identifiability of a system of ODE's is often due to Lie point symmetries.…”

Section: Previous Workmentioning

confidence: 99%

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On the Existence of Identifiable Reparametrizations for Linear Compartment Models

Baaijens¹,

Draisma

2016

SIAM J. Appl. Math.

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Abstract. The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case, one can search for an identifiable reparametrization of the model: a map which reduces the number of parameters, such that the reduced model is identifiable. We study a specific class of models which are known to be unidentifiable. Using algebraic geometry and graph theory, we translate a criterion given by Meshkat and Sullivant for the existence of an identifiable scaling reparametrization to a new criterion based on the rank of a weighted adjacency matrix of a certain bipartite graph. This allows us to derive several new constructions to obtain graphs with an identifiable scaling reparametrization. Using these constructions, a large subclass of such graphs is obtained. Finally, we present a procedure of subdividing or deleting edges to ensure that a model has an identifiable scaling reparametrization.

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Section: Previous Workmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

On the Existence of Identifiable Reparametrizations for Linear Compartment Models

Baaijens¹,

Draisma

2016

SIAM J. Appl. Math.

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“…In comparison, there are relatively few techniques available for nonlinear systems (the Taylor series approach [11], similarity transformation based approaches [12,13], and differential algebra techniques) [14,15] and significant computational problems can arise for these, even for relatively simple models [16,17].…”

Section: Structural Identifiabilitymentioning

confidence: 99%

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake

Grandjean¹,

Chappell²,

Yates³

et al. 2014

Computer Methods and Programs in Biomedicine

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a b s t r a c tIn this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available.

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“…The local and global structural identifiability of both linear and nonlinear systems with respect to the parameters (not including the inputs) has been exhaustively studied [12], [13] and references therein. One of them, that can be easily understood and extrapolated to unknown inputs identifiability is the Differential Algebra for Identifiability of SYStems method (DAISYS) for which a succinct and clear description can be found in [14]. The application of the DAISYS steps on model (13) is achieved as follows.…”

Section: A Structural Identifiabilitymentioning

confidence: 99%

Combined distributed parameters and source estimation in tokamak plasma heat transport

Mechhoud

Witrant

Dugard

et al. 2013

2013 European Control Conference (ECC)

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An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases

Cited by 82 publications

References 15 publications

On the Existence of Identifiable Reparametrizations for Linear Compartment Models

On the Existence of Identifiable Reparametrizations for Linear Compartment Models

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake

Combined distributed parameters and source estimation in tokamak plasma heat transport

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