1,720,998 research outputs found
Optimal input design for identification of compartmental models. Theory and application to a model of glucose kinetics.
No full textThe optimal input design problem for the identification of linear compartmental models is studied. The optimality criterion consists in maximizing the achievable precision of parameter estimates. The rationale, theory, and computational methods for solving the problem for the scalar case are presented first. An application to a two-compartment model of glucose kinetics is then shown. The effect on parameter precision of the measurement error structure and of various design factors, such as an equienergy or equidose class of admissible inputs and the time interval for input and measurement, is discussed. The performance of standard classical inputs, e.g. an impulse or an infusion, is also evaluated
Generalized Sensitivity Functions in Physiological System Identification.
No full textParameters of physiological models are commonly associated in an input-output experiment with a specific pattern of the system response. This association is often made on an intuitive basis by traditional sensitivity analysis, i.e., by inspecting the variations of model output trajectories with respect to parameter variations. However, this approach provides limited information since, for instance, it ignores correlation among parameters. The aim of this study is to propose a new set of sensitivity functions, called the generalized sensitivity functions (GSF), for the analysis of input-output identification experiments. GSF are based on information theoretical criteria and provide, as compared to traditional sensitivity analysis, a more accurate picture on the information content of measured outputs on individual model parameters at different times. Case studies are presented on an input-output model and on two structural circulatory and respiratory models. GSF allow the definition of relevant time intervals for the identification of specific parameters and improve the understanding of the role played by specific model parameters in describing experimental data
On optimality of the impulse input for linear system identification.
No full textThe optimal input design for the identification of linear single input-single output systems is considered in the particular situation of continuous time measurement corrupted by white gaussian noise of constant variance. The optimality of the impulse among nonnegative equidose inputs is proven
Optimal equidose inputs and role of measurement error for estimating the parameters of a compartmental model of glucose kinetics from continuous- and discrete-time optimal samples.
No full textThe optimal input design for estimating all the parameters of a two-compartment model of glucose kinetics is studied. The problem is solved by simulation for the class of equidose rectangular-shaped inputs with both continuous- and discrete-time optimal samples. The important role of the measurement error in determining the optimal input is analyzed by examining four error structures. With continuous-time measurements the optimal input depends on the measurement error, but rather efficient suboptimal inputs can be obtained with small infusion periods. The impulse input is optimal among the considered error structures with discrete-time optimal samples
The minimal model of glucose disappearance: optimal input studies.
No full textThe “minimal model” of glucose disappearance provides noninvasive estimates of important metabolic parameters, among them the effect of insulin on glucose uptake. We study here the design of optimal inputs for the identification of the model, i.e., for estimating its parameters with maximum precision. The scalar case is examined first and solved via Pontryagin's maximum principle for two input classes: equienergy and equidose. For the equidose class the vector case is then studied by simulation for clinically realizable glucose inputs in both the normal and the diabetic case. Finally, recent experimental developments proposed for the identification of the model, i.e., a glucose input involving a concomitant drug stimulus and a tracer labeled glucose input, are examined in the context of optimal input design
New Perspectives and Practical Tools for Local Identifiability Analysis of Biomathematical Models.
No full textCalculating all multiple parameter solutions of ODE models to avoid biological misinterpretations
No full textBiological system's dynamics are increasingly studied with nonlinear ordinary differential equations, whose parameters are estimated from input/output experimental data. Structural identifiability analysis addresses the theoretical question whether the inverse problem of recovering the unknown parameters from noise-free data is uniquely solvable (global), or if there is a finite (local), or an infinite number (non identifiable) of parameter values that generate identical input/output trajectories. In contrast, practical identifiability analysis aims to assess whether the experimental data provide information on the parameter estimates in terms of precision and accuracy. A main difference between the two identifiability approaches is that the former is mostly carried out analytically and provides exact results at a cost of increased computational complexity, while the latter is usually numerically tested by calculating statistical confidence regions and relies on decision thresholds. Here we focus on local identifiability, a critical issue in biological modeling. This is the case when a model has multiple parameter solutions which equivalently describe the input/output data, but predict different behaviours of the unmeasured variables, often those of major interest. We present theoretical background and applications to locally identifiable ODE models described by rational functions. We show how structural identifiability analysis completes the practical identifiability results. In particular we propose an algorithmic approach, implemented with our software DAISY, to calculate all numerical parameter solutions and to predict the corresponding behaviour of the unmeasured variables, which otherwise would remain hidden. A case study of a locally identifiable HIV model shows that one should be aware of the presence of multiple parameter solutions to comprehensively describe the biological system and avoid biological misinterpretation of the results
Structural vs Practical Identifiability of Nonlinear Differential Equation Models in Systems Biology.
No full textLocal influence analysis when interfacing toxicokinetic and proportional hazard models
No full textWe present a local influence analysis to assigned model quantities in the context of a dose–response analysis of cancer mortality in relation to estimated absorbed dose of dioxin. The risk estimation is performed using dioxin dose as a time-dependent explanatory variable in a proportional hazard model. The dioxin dose is computed using a toxicokinetic model, which depends on some factors, such as assigned constants and estimated parameters. We present a local influence analysis to assess the effects on final results of minor perturbations of toxicokinetic model factors. In the present context, there is no evidence of local influence in risk estimates. It is however possible to identify which factors are more influential
Multiple imputation of missing values in a cancer mortality analysis with estimated exposure dose
No full textImputation of missing values in a cancer mortality analysis in relation to estimated dose of dioxin for a cohort of chemical workers is considered. In particular, some subjects of the cohort have the body mass index (BMI) missing. This quantity is an essential ingredient for a toxicokinetic model that gives the estimated absorbed dose, which is then used for risk estimation in a proportional hazards model. Imputation of BMI allows to recover information and to use the entire cohort for risk estimation. Both conditional mean imputation and multiple imputation are used. The latter is a simulation-based approach to the analysis of missing data which takes into account the uncertainty of the imputation process using several imputations for each missing value. In the present context, the two imputation methods gave similar results, both correcting for bias (although with some questions) and leading to increased efficiency with respect to the complete-case analysis that simply discards the partially unobserved individuals
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