Parameter Estimation of Dynamic Beer Fermentation Models.

In this study, two dynamic models of beer fermentation are proposed, and their parameters are estimated using experimental data collected during several batch experiments initiated with different sugar concentrations. Biomass, sugar, ethanol, and vicinal diketone concentrations are measured off-line with an analytical system while two on-line immersed probes deliver temperature, ethanol concentration, and carbon dioxide exhaust rate measurements. Before proceeding to the estimation of the unknown model parameters, a structural identifiability analysis is carried out to investigate the measurement configuration and the kinetic model structure. The model predictive capability is investigated in cross-validation, in view of opening up new perspectives for monitoring and control purposes. For instance, the dynamic model could be used as a predictor in receding-horizon observers and controllers.

Dynamic modeling of Rhodospirillum rubrum PHA production triggered by redox stress during VFA photoheterotrophic assimilations.

Polyhydroxyalkanoates (PHA) represent an environmentally friendly alternative to petroleum based plastics for a broad range of applications from packaging to biomedical devices. In the prospect of an industrial PHA production, it is highly valuable to accurately control the incorporation of different repeating units into the polymer, to produce a polyester with specific material characteristics. In this study, we develop macroscopic dynamic models predicting the polymer production and composition when mixtures containing up to four volatile fatty acids (VFA) are used as substrates. These models successfully reproduce the sequential (and preferential) substrate consumption and polymer production/reconsumption patterns, experimentally observed during biomass growth, thanks to simple kinetic structures based on Monod and inhibition factors. These models can serve as a basis for numerical simulation and process analysis, as well as process intensification through model-based optimization and control.

Variable selection and parameter estimation of viral amplification in vero cell cultures dedicated to the production of a dengue vaccine.

In this study, a dynamic model of a Vero cell culture-based dengue vaccine production process is developed. The approach consists in describing the process dynamics as functions of the whole living (uninfected and infected) biomass whereas previous works are based on population balance approaches. Based on the assumption that infected biomass evolves faster than other variable, the model can be simplified using a slow-fast approximation. The structural identifiability of the model is analysed using differential algebra as implemented in the software DAISY. The model parameters are inferred from experimental datasets collected from an actual vaccine production process and the model predictive capability is confirmed both in direct and cross-validation. The model prediction shows the impact of the metabolism on virus yield and confirms observations reported in previous studies. Multi-modality and sensitivity analysis complement the parameter estimation, and allow to obtain confidence intervals on both parameters and state estimates. Finally, the model is used to compute the maximum infectious virus yield that can be obtained for different combinations of multiplicity of infection (MOI) and time of infection (TOI). © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 35: e2687, 2019.

On the derivation of a simple dynamic model of anaerobic digestion including the evolution of hydrogen.

Hydrogen has been found to be an important intermediate during anaerobic digestion (AD) and a key variable for process monitoring as it gives valuable information about the stability of the reactor. However, simple dynamic models describing the evolution of hydrogen are not commonplace. In this work, such a dynamic model is derived using a systematic data driven-approach, which consists of a principal component analysis to deduce the dimension of the minimal reaction subspace explaining the data, followed by an identification of the kinetic parameters in the least-squares sense. The procedure requires the availability of informative data sets. When the available data does not fulfill this condition, the model can still be built from simulated data, obtained using a detailed model such as ADM1. This dynamic model could be exploited in monitoring and control applications after a re-identification of the parameters using actual process data. As an example, the model is used in the framework of a control strategy, and is also fitted to experimental data from raw industrial wine processing wastewater.

Macroscopic Dynamic Modeling of Sequential Batch Cultures of Hybridoma Cells: An Experimental Validation.

Hybridoma cells are commonly grown for the production of monoclonal antibodies (MAb). For monitoring and control purposes of the bioreactors, dynamic models of the cultures are required. However these models are difficult to infer from the usually limited amount of available experimental data and do not focus on target protein production optimization. This paper explores an experimental case study where hybridoma cells are grown in a sequential batch reactor. The simplest macroscopic reaction scheme translating the data is first derived using a maximum likelihood principal component analysis. Subsequently, nonlinear least-squares estimation is used to determine the kinetic laws. The resulting dynamic model reproduces quite satisfactorily the experimental data, as evidenced in direct and cross-validation tests. Furthermore, model predictions can also be used to predict optimal medium renewal time and composition.

Dynamic metabolic flux analysis using a convex analysis approach: Application to hybridoma cell cultures in perfusion.

In recent years, dynamic metabolic flux analysis (DMFA) has been developed in order to evaluate the dynamic evolution of the metabolic fluxes. Most of the proposed approaches are dedicated to exactly determined or overdetermined systems. When an underdetermined system is considered, the literature suggests the use of dynamic flux balance analysis (DFBA). However the main challenge of this approach is to determine an appropriate objective function, which remains valid over the whole culture. In this work, we propose an alternative dynamic metabolic flux analysis based on convex analysis, DMFCA, which allows the determination of bounded intervals for the fluxes using the available knowledge of the metabolic network and information provided by the time evolution of extracellular component concentrations. Smoothing splines and mass balance differential equations are used to estimate the time evolution of the uptake and excretion rates from this experimental data. The main advantage of the proposed procedure is that it does not require additional constraints or objective functions, and provides relatively narrow intervals for the intracellular metabolic fluxes. DMFCA is applied to experimental data from hybridoma HB58 cell perfusion cultures, in order to investigate the influence of the operating mode (batch and perfusion) on the metabolic flux distribution.

Parameter identification of a dynamic model of CHO cell cultures: an experimental case study.

In this paper, we address the problem of parameter identification in dynamic models of animal cultures, and we propose a step-by-step procedure, which gradually considers more detailed models. This procedure allows subsets of parameters to be estimated at each step, which can be used in the initialization of the next identification step. Finally, the full parameter set can be re-estimated starting from the results of the last step. The efficiency of the procedure is illustrated with a simulation case study and with the identification of a dynamic model from experimental data collected in CHO cell culture.

Parameter identification of Droop model: an experimental case study.

Mathematical modeling and the development of predictive dynamic models are of paramount importance for the optimization, state estimation, and control of bioprocesses. This study is dedicated to the identification of a simple model of microalgae growth under substrate limitation, i.e., Droop model, and describes the design and instrumentation of a lab-scale flat-plate photobioreactor, the associated on-line and off-line instrumentation, the collection of experimental data, and the parameter identification procedure. In particular, a dedicated methodology for parameter identification is discussed, including the determination of an initial parameter set using an analytical procedure, the selection of a cost function, the evaluation of confidence intervals as well as direct and cross-validation tests.

Anaerobic biodegradability of fish remains: experimental investigation and parameter estimation.

The generation of organic waste associated with aquaculture fish processing has increased significantly in recent decades. The objective of this study is to evaluate the anaerobic biodegradability of several fish processing fractions, as well as water treatment sludge, for tilapia and sturgeon species cultured in recirculated aquaculture systems. After substrate characterization, the ultimate biodegradability and the hydrolytic rate were estimated by fitting a first-order kinetic model with the biogas production profiles. In general, the first-order model was able to reproduce the biogas profiles properly with a high correlation coefficient. In the case of tilapia, the skin/fin, viscera, head and flesh presented a high level of biodegradability, above 310 mLCH4gCOD⁻¹, whereas the head and bones showed a low hydrolytic rate. For sturgeon, the results for all fractions were quite similar in terms of both parameters, although viscera presented the lowest values. Both the substrate characterization and the kinetic analysis of the anaerobic degradation may be used as design criteria for implementing anaerobic digestion in a recirculating aquaculture system.

Design and test of a low-cost RGB sensor for online measurement of microalgae concentration within a photo-bioreactor.

In this study, a low-cost RGB sensor is developed to measure online the microalgae concentration within a photo-bioreactor. Two commercially available devices, i.e., a spectrophotometer for offline measurements and an immersed probe for online measurements, are used for calibration and comparison purposes. Furthermore, the potential of such a sensor for estimating other variables is illustrated with the design of an extended Luenberger observer.

Design, analysis and validation of a simple dynamic model of a submerged membrane bioreactor.

In this study, a simple dynamic model of a submerged membrane bioreactor (sMBR) is proposed, which would be suitable for process control. In order to validate the proposed model structure, informative data sets are generated using a detailed simulator built in a well-established environment, namely GPS-X. The model properties are studied, including equilibrium points, stability, and slow/fast dynamics (three different time scales). The existence of slow-fast dynamics is central to the development of a dedicated parameter estimation procedure. Finally, a nonlinear model predictive control is designed to illustrate the potential of the developed model within a model-based control structure. The problem of water treatment in a recirculating aquaculture system is considered as an application example.

A dynamical interpretation of strong observability and detectability concepts for nonlinear systems with unknown inputs: application to biochemical processes.

Determination of the observability/detectability properties of a nonlinear system is fundamental to assess the possibility of constructing observers and the properties that can be assigned to them, as e.g., the assignability of the convergence rate. For linear systems this task can be solved by well-known techniques, for the case without perturbations as much as for the perturbed case. However, for nonlinear systems this study is usually a very hard task, in particular, when unknown inputs and/or perturbations are present. In this paper a general method to study these properties will be described, and its capabilities and feasibility will be assessed by means of a few case studies related to the culture of phytoplankton in the chemostat.

Accelerating animal cell growth in perfusion mode by multivariable control: simulation studies.

This study considers the problem of manipulating in an optimal way the perfusion and bleed flow rates of a continuous culture of hybridoma cells, so as to achieve a fast transient start-up and reject potential disturbances. The proposed solution makes use of an analysis of the properties of the steady state solutions of the nonlinear dynamic model of the cell culture, and in particular the relationship between the two main limiting substrates, glucose and glutamine. The solution is implemented using extended prediction self-adaptive control. Simulation results demonstrate the approach potentiality.

Stoichiometric identification with maximum likelihood principal component analysis.

This study presents an effective procedure for the determination of a biologically inspired, black-box model of cultures of microorganisms (including yeasts, bacteria, plant and animal cells) in bioreactors. This procedure is based on sets of experimental data measuring the time-evolution of a few extracellular species concentrations, and makes use of maximum likelihood principal component analysis to determine, independently of the kinetics, an appropriate number of macroscopic reactions and their stoichiometry. In addition, this paper provides a discussion of the geometric interpretation of a stoichiometric matrix and the potential equivalent reaction schemes. The procedure is carefully evaluated within the stoichiometric identification framework of the growth of the yeast Kluyveromyces marxianus on cheese whey. Using Monte Carlo studies, it is also compared with two other previously published approaches.

Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection.

Several mathematical models have been developed in anaerobic digestion systems and a variety of methods have been used for parameter estimation and model validation. However, structural and parametric identifiability questions are relatively seldom addressed in the reported AD modeling studies. This paper presents a 3-step procedure for the reliable estimation of a set of kinetic and stoichiometric parameters in a simplified model of the anaerobic digestion process. This procedure includes the application of global sensitivity analysis, which allows to evaluate the interaction among the identified parameters, multi-start strategy that gives a picture of the possible local minima and the selection of optimization criteria or cost functions. This procedure is applied to the experimental data collected from a lab-scale sequencing batch reactor. Two kinetic parameters and two stoichiometric coefficients are estimated and their accuracy was also determined. The classical least-squares cost function appears to be the best choice in this case study.

An optimizing start-up strategy for a bio-methanator.

This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang-bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.

Model selection, identification and validation in anaerobic digestion: a review.

Anaerobic digestion enables waste (water) treatment and energy production in the form of biogas. The successful implementation of this process has lead to an increasing interest worldwide. However, anaerobic digestion is a complex biological process, where hundreds of microbial populations are involved, and whose start-up and operation are delicate issues. In order to better understand the process dynamics and to optimize the operating conditions, the availability of dynamic models is of paramount importance. Such models have to be inferred from prior knowledge and experimental data collected from real plants. Modeling and parameter identification are vast subjects, offering a realm of approaches and methods, which can be difficult to fully understand by scientists and engineers dedicated to the plant operation and improvements. This review article discusses existing modeling frameworks and methodologies for parameter estimation and model validation in the field of anaerobic digestion processes. The point of view is pragmatic, intentionally focusing on simple but efficient methods.

Dynamic modeling of complex biological systems: a link between metabolic and macroscopic description.

In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows an equivalent 'input-output' representation of the system to be derived. The procedure is illustrated with a few examples.