Identifiability Analysis and Parameter Estimation of Microgel Synthesis: A Set-Membership Approach

Abstract

Functional microgels with tailored structure and specific properties are required for medical and technical applications, thus motivating model-based optimization of their fabrication processes. An important step in the creation of accurate models is parameter estimation. We present a methodology for a parameter identifiability analysis, which approximates the feasible parameter set as a box by solving a series of constrained dynamic optimization problems. The method is applied to the synthesis of microgels based on two monomers, N-vinylcaprolactam and N-isopropylacrylamide, and the cross-linker N,N-methylenebis(acrylamide). The results show that kinetic parameters corresponding to the reaction of the monomers are identifiable as are a subset of the kinetic parameters involving the cross-linker. The reaction kinetics of the cross-linking are faster in comparison to the main polymerization reaction for N-vinylcaprolactam; this allows for an improved understanding of the occurring reaction phenomena. The reaction kinetics of the cross-linking are not identifiable for N-isopropylacrylamide for the given experimental setup; model-based experimental design for parameter precision might enable their identification. The results also indicate potential for model simplification and allow us to make suggestions toward the enhancement of Raman spectroscopy measurements.

Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?

“…We determine these extreme values by solving a series of constrained dynamic optimization problems. For a vector p j that consists of K parameters, the optimization problem for parameter number k is formulated , and as follows [42], [45]: with and K = 6. We set ε to 20%, which means that the differences between model predictions for and , and optimal model predictions for fall within 20% of the optimal prediction values .…”

“…In the former analysis, one determines if a given structure of a model allows the realization of unique parameters when certain measured variables are provided [40]. However, it only provides necessary conditions for identifiability because it does not take into consideration parameters precision [42], [43]. In contrast, practical identifiability aims to predict confidence intervals for the estimated parameters [42], [44].…”

“…However, it only provides necessary conditions for identifiability because it does not take into consideration parameters precision [42], [43]. In contrast, practical identifiability aims to predict confidence intervals for the estimated parameters [42], [44]. It can be conducted locally (in the neighborhood of the estimated parameter values) or globally over the entire range of values.…”

“…We conduct the global practical identifiability analysis by determining the smallest box that contains the so-called feasible parameter set for each patient j , as suggested in [42]. This set includes all values of parameters in p j for which the differences between model predictions and optimal model predictions (determined by solving (OP1)) fall within certain defined bounds , that is where , ε is the percentage of deviation, and P j is the set of parameter values in p j bounded by the components of and defined in (OP1).…”

“…We determine these extreme values by solving a series of constrained dynamic optimization problems. For a vector p j that consists of K parameters, the optimization problem for parameter number k is formulated ∀j ∈ J, and ∀k ∈ K as follows [42], [45]:…”