Global identifiability of nonlinear models of biological systems

Audoly, S.; Bellu, Giuseppina; D’Angiò, Leontina; Saccomani, Maria Pia; Cobelli, Claudio

doi:10.1109/10.900248

Cited by 296 publications

(322 citation statements)

References 15 publications

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“…Different approaches have been proposed in literature [1,2,5,4,8,9,14] but, to the best of our knowledge, no general software tools currently exist to perform the identifiability analysis for a nonlinear dynamic model, despite the crucial importance of this step in the modelling process.…”

Section: Introductionmentioning

confidence: 99%

DAISY: A new software tool to test global identifiability of biological and physiological systems

Bellu

Saccomani

Audoly

et al. 2007

Computer Methods and Programs in Biomedicine

398

397

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A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.

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Section: Introductionmentioning

confidence: 99%

DAISY: A new software tool to test global identifiability of biological and physiological systems

Bellu

Saccomani

Audoly

et al. 2007

Computer Methods and Programs in Biomedicine

398

397

View full text Add to dashboard Cite

show abstract

“…The result is 100 pairs of identified parameters, which are summarized in Table 3. (20). There are also good separations in the 90% CI's.…”

Section: Healthy and Diseased Human With Noise-no Volume Measurementmentioning

confidence: 83%

“…The volume is approximately constant at this point, and therefore, the formula of Eq. (20) shows that t inflect,2 should be equal to . The maximum left ventricle pressure gradient, is also known to occur justbefore the aortic valve opens, which corresponds closely to t ao,min .…”

Section: Further Validation On An Animal Model and Clinical Implementmentioning

confidence: 99%

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Unique parameter identification for cardiac diagnosis in critical care using minimal data sets

Hann

Chase

Desaive

et al. 2010

Computer Methods and Programs in Biomedicine

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Lumped parameter approaches for modelling the cardiovascular system typically have many parameters of which a significant percentage are often not identifiable from limited data sets. Hence, significant parts of the model are required to be simulated with little overall effect on the accuracy of data fitting, as well as dramatically increasing the complexity of parameter identification. This separates sub-structures of more complex cardiovascular system models to create uniquely identifiable simplified models that are one to one with the measurements. In addition, a new concept of parameter identification is presented where the changes in the parameters are treated as an actuation force into a feed back control system, and the reference output is taken to be steady state values of measured volume and pressure. The major advantage of the method is that when it converges, it must be at the global minimum so that the solution that best fits the data is always found.By utilizing continuous information from the arterial/pulmonary pressure waveforms and the end-diastolic time, it is shown that potentially, the ventricle volume is not required in the data set, which was a requirement in earlier published work. The simplified models can also act as a bridge to identifying more sophisticated cardiac models, by providing an initial set of patient specific parameters that can reveal trends and interactions in the data over time. The goal is to apply the simplified models to retrospective data on groups of patients to help characterize population trends or un-modelled dynamics within known bounds. These trends can assist in improved prediction of patient responses to cardiac disturbance and therapy intervention with potentially smaller and less invasive data sets. In this way a more complex model that takes into account individual patient variation can be developed, and applied to the improvement of cardiovascular management in critical care. Keywords :Model-based cardiac diagnosis ; Cardiovascular system ; Integral-based parameter identification ; Pressure waveform ; ECG ; Intensive care unit IntroductionIn critical care, cardiovascular dysfunction can be easily misdiagnosed due to incomplete information and the complexities involved, leading to premature discharge or non-optimal treatment [1][2][3]. It is also a major cause of increased length of stay and death [4,5]. Demand for critical care is growing dramatically severely affecting healthcare delivery [6][7][8]. The overall goal of this research is to use computational cardiac models to better aggregate available clinical data in an intensive care unit (ICU) into a more readily understood physiological context for clinicians. The computational models can be used to reveal non-linear dynamics and interactions that are not readily apparent in the data.A major difficulty faced with cardiovascular modelling in general, is the level of detail these models typically include. For example multi-scale modelling approaches utilizing finite elements have successfully expl...

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“…Although a variety of methods have been proposed to test identifiability of nonlinear models [36][37][38], it remains a challenging mathematical problem. In this paper we present a full structural analysis of the linear RD elastic model, which is supported by MRE phantom experiments.…”

Section: Introductionmentioning

confidence: 99%

Non-identifiability of the Rayleigh damping material model in Magnetic Resonance Elastography

Petrov

Chase

Sellier

et al. 2013

Mathematical Biosciences

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Global identifiability of nonlinear models of biological systems

Cited by 296 publications

References 15 publications

DAISY: A new software tool to test global identifiability of biological and physiological systems

DAISY: A new software tool to test global identifiability of biological and physiological systems

Unique parameter identification for cardiac diagnosis in critical care using minimal data sets

Non-identifiability of the Rayleigh damping material model in Magnetic Resonance Elastography

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