Toward predictive food process models: A protocol for parameter estimation.

Mathematical models, in particular, physics-based models, are essential tools to food product and process design, optimization and control. The success of mathematical models relies on their predictive capabilities. However, describing physical, chemical and biological changes in food processing requires the values of some, typically unknown, parameters. Therefore, parameter estimation from experimental data is critical to achieving desired model predictive properties. This work takes a new look into the parameter estimation (or identification) problem in food process modeling. First, we examine common pitfalls such as lack of identifiability and multimodality. Second, we present the theoretical background of a parameter identification protocol intended to deal with those challenges. And, to finish, we illustrate the performance of the proposed protocol with an example related to the thermal processing of packaged foods.

Quantitative image analysis to characterize the dynamics of Listeria monocytogenes biofilms.

This work shows that the combination of two-dimensional (2D) and three-dimensional (3D) analyses of images acquired by confocal laser scanning microscopy facilitates the quantitative spatiotemporal characterization of architectures formed by Listeria monocytogenes biofilms. In particular, the analysis of structural features such as maximum thickness, biovolume, areal porosity and maximum diffusion distance allowed elucidating differences in biofilm formation of three L. monocytogenes strains (L1A1, CECT5873 and CECT4032). The analysis showed a common sequence for all strains. In the first phase, independent clusters evolve to interconnected clusters and honeycomb-like structures. Flat biofilms characterized the second phase. The structures disappear in the third phase. Nevertheless, the duration of the phases differed from strain to strain. L1A1 strain exhibited the slowest dynamics and the thickest biofilms while the strain CECT4032 presented the faster dynamics and the thinnest biofilms. Also, the number of dead cells varies significantly from strain to strain. From the results of the analysis, it can be concluded that 2D parameters are critical to differentiating morphological features while 3D parameters ease the interpretation and comparative study of the different phases during the life cycle of biofilms.

Numerical spatio-temporal characterization of Listeria monocytogenes biofilms.

As the structure of biofilms plays a key role in their resistance and persistence, this work presents for the first time the numerical characterization of the temporal evolution of biofilm structures formed by three Listeria monocytogenes strains on two types of stainless-steel supports, AISI 304 SS No. 2B and AISI 316 SS No. 2R. Counting methods, motility tests, fluorescence microscopy and image analysis were combined to study the dynamic evolution of biofilm formation and structure. Image analysis was performed with several well-known parameters as well as a newly defined parameter to quantify spatio-temporal distribution. The results confirm the interstrain variability of L. monocytogenes species regarding biofilm structure and structure evolution. Two types of biofilm were observed: homogeneous or flat and heterogeneous or clustered. Differences in clusters and in attachment and detachment processes were due mainly to the topography and composition of the two surfaces although an effect due to motility was also found.

Generic parameterization for a pharmacokinetic model to predict Cd concentrations in several tissues of different fish species.

In the present work, a set of generic parameters was proposed for a pharmacokinetic model, with the objective of predicting Cd concentration in the tissues of diverse fish species under different environmental conditions. Cd concentrations in a number of tissues of Oncorhynchus mykiss and Cyprinus carpio were estimated by a structurally identifiable multicompartmental model (unique solution). The 13 generic parameters of the model comprised exchange rates, tissue-blood partition coefficients, and weight-corrected elimination rate constants accounting for the routes of water respiration, excretion and egestion. On the other hand, absorption efficiencies from water and food were considered to be condition-specific and estimated for each experiment. These two parameters reflected the differences in fish exposure to diet (food type and metal concentration) or water (water chemistry and bioavailable metal concentration). A data set of 27 experiments of Cd bioaccumulation in fish tissues was compiled for model calibration. The selected dynamics on trout and carp were performed under very different experimental conditions, involving water and/or food exposure, different fish weights and exposure concentrations and the presence/absence of depuration periods. Model predicted, for most compartments and experiments, the tendency of Cd dynamics. However, accumulation in liver and kidney was underestimated in approximately a half of the experiments, due mainly to a rapid metallothionein (MT) sequestration phenomena and subsequent saturation on liver and kidney produced under high exposure concentrations. On the other hand, both generic and condition-specific parameter values were in accordance with the values reported in literature when available. Therefore, the results obtained in this work are an initial step indicating that a generic global input parameter set could be applied to physiology-based pharmacokinetic (PBPK) models for estimating Cd accumulation in fish in different types of scenarios.

Computational procedures for optimal experimental design in biological systems.

Mathematical models of complex biological systems, such as metabolic or cell-signalling pathways, usually consist of sets of nonlinear ordinary differential equations which depend on several non-measurable parameters that can be hopefully estimated by fitting the model to experimental data. However, the success of this fitting is largely conditioned by the quantity and quality of data. Optimal experimental design (OED) aims to design the scheme of actuations and measurements which will result in data sets with the maximum amount and/or quality of information for the subsequent model calibration. New methods and computational procedures for OED in the context of biological systems are presented. The OED problem is formulated as a general dynamic optimisation problem where the time-dependent stimuli profiles, the location of sampling times, the duration of the experiments and the initial conditions are regarded as design variables. Its solution is approached using the control vector parameterisation method. Since the resultant nonlinear optimisation problem is in most of the cases non-convex, the use of a robust global nonlinear programming solver is proposed. For the sake of comparing among different experimental schemes, a Monte-Carlo-based identifiability analysis is then suggested. The applicability and advantages of the proposed techniques are illustrated by considering an example related to a cell-signalling pathway.