Dataset Information

Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models.

ABSTRACT: In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.

SUBMITTER: Villaverde AF

PROVIDER: S-EPMC6685009 | biostudies-literature | 2019 Jul

REPOSITORIES: biostudies-literature

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Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models.

Villaverde Alejandro F AF Tsiantis Nikolaos N Banga Julio R JR

Journal of the Royal Society, Interface 20190703 156

In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as ...[more]

PMID: 31266417

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Project description:Neural mass models (NMMs) are important for helping us interpret observations of brain dynamics. They provide a means to understand data in terms of mechanisms such as synaptic interactions between excitatory and inhibitory neuronal populations. To interpret data using NMMs we need to quantitatively compare the output of NMMs with data, and thereby find parameter values for which the model can produce the observed dynamics. Mapping dynamics to NMM parameter values in this way has the potential to improve our understanding of the brain in health and disease. Though abstract, NMMs still comprise of many parameters that are difficult to constrain a priori. This makes it challenging to explore the dynamics of NMMs and elucidate regions of parameter space in which their dynamics best approximate data. Existing approaches to overcome this challenge use a combination of linearising models, constraining the values they can take and exploring restricted subspaces by fixing the values of many parameters a priori. As such, we have little knowledge of the extent to which different regions of parameter space of NMMs can yield dynamics that approximate data, how nonlinearities in models can affect parameter mapping or how best to quantify similarities between model output and data. These issues need to be addressed in order to fully understand the potential and limitations of NMMs, and to aid the development of new models of brain dynamics in the future. To begin to overcome these issues, we present a global nonlinear approach to recovering parameters of NMMs from data. We use global optimisation to explore all parameters of nonlinear NMMs simultaneously, in a minimally constrained way. We do this using multi-objective optimisation (multi-objective evolutionary algorithm, MOEA) so that multiple data features can be quantified. In particular, we use the weighted horizontal visibility graph (wHVG), which is a flexible framework for quantifying different aspects of time series, by converting them into networks. We study EEG alpha activity recorded during the eyes closed resting state from 20 healthy individuals and demonstrate that the MOEA performs favourably compared to single objective approaches. The addition of the wHVG objective allows us to better constrain the model output, which leads to the recovered parameter values being restricted to smaller regions of parameter space, thus improving the practical identifiability of the model. We then use the MOEA to study differences in the alpha rhythm observed in EEG recorded from 20 people with epilepsy. We find that a small number of parameters can explain this difference and that, counterintuitively, the mean excitatory synaptic gain parameter is reduced in people with epilepsy compared to control. In addition, we propose that the MOEA could be used to mine for the presence of pathological rhythms, and demonstrate the application of this to epileptiform spike-wave discharges.

Project description:BackgroundDynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability.ResultsWe successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh-Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls.ConclusionsOur approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).

Dataset Information

Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models.

Publications

Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models.

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