Publication# Simplified approaches to mid-infrared spectrometers calibration for bioprocess monitoring applications

Abstract

This thesis aimed at developing new, simple methods of calibration for on-line monitoring of bioprocesses by Fourier-transform mid-infrared spectroscopy (FTIR). The conventional calibration approach implies the preparation and measurement of a large number of standards, usually around 50, and involves advanced mathematical tools, such as Principal Component Regression or Partial Least Squares for data treatment. This procedure is time-consuming, and requires, in addition, a fair level of expertise in linear algebra. For these reasons, there is a big need for calibration approaches that can be performed rapidly, by non-experts, in order to allow a routine operation of mid-infrared spectroscopy for the on-line monitoring of cultures. Mid-infrared spectroscopy deals with the vibrational energy of molecules, which means that a vast majority of compounds can be detected in this wavelength range. Data treatment is therefore complex, due to strong peak overlapping, but also because of the low concentrations involved in culture media (< 3%) and unavoidable drift of the signal instrument. Multi-level calibration designs have been developed to tackle these problems, and they proved to achieve a robust process modeling. However, in the case where a method to correct for signal drift is available and compounds do not interact with each other –which is likely to happen in dilute solutions as such as culture media– multi-level calibration designs are clearly oversized, since a 2-level design provides the same quantity of information for a much lower work load. It was shown in this research project that, for most common substances found in culture media, the absorbance is linear with respect to concentration (i.e. that the Lambert-Beer law is followed) and that species do not significantly interact with each other in solution. Based on this evidence, a relatively simple calibration method has been developed, which consists in correcting for signal drift through an anchorage method, and calculating the concentration using a library of pure component spectra as calibration set. Pure component refers here to a single compound dissolved in water at a concentration around 0.1 mol L-1. Anchorage points were set in the spectra in regions where none of the compounds of interest absorb, but close enough from the calculation range to insure an appropriate correction. Batch cultures of the yeast S. cerevisiae were carried out to validate this approach, and it was shown that the results were as accurate and as robust as if they were found using the conventional approach (standard error of calibration of 0.86, 0.98, 0.15 g L-1 for glucose, ethanol and ammonium respectively). Pulse additions of compounds during the culture could be successfully monitored by the calibration, which therefore proved to be truly predictive. A second calibration approach was developed and tested with batch cultures of the bacteria E. coli. While a spectra library was also used in this method to calculate concentrations from process data, signal instabilities were corrected for by including in the library a few "drift spectra". These drift spectra were found by a Principal Component Analysis of water absorbance spectra, measured in aseptic conditions, every 5 minutes over a representative period of 24 hours. The least squares algorithm could therefore use the molar absorbance of the main metabolites as well as two drift spectra in order to calculate concentrations from process measurements. Rather than water, culture medium was used as reference intensity to calculate absorbances during the processes, which allows for including all compounds that present small concentration changes into a background that is eliminated by subtraction. Although this method led to concentration differences instead of absolute values, the same spectra library could be used to monitor different cultures, regardless of the medium composition, therefore saving additional time during calibration. A single library of 5 spectra, including three molar absorbances and two drift spectra, was able to monitor several batch cultures of E. coli performed in different media, with a precision similar to what could be expected from the conventional approach. The effect of temperature and pH on these new calibration approaches was also studied. It was shown that the pH does not directly affect infrared spectra, and that it only influences deprotonation equilibria of weak acids, which in turn induce changes in the absorbance spectra. Temperature also proved not to interfere with the proposed calibration approaches. The results presented in this thesis pave the way to the implementation of mid-infrared spectroscopy in a high-throughput platform for medium and strain screening. The calibration approaches that have been developed can certainly be easily automated, in order to provide a wealth of relevant information on the main metabolite concentration at a very low labour cost.

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Julien Léo Billeter, Dominique Bonvin, Sriniketh Srinivasan

Identification of kinetic models is an important task for monitoring, control and optimization of industrial processes. Kinetic models are often based on first principles, which describe the evolution of the states – numbers of moles, temperature and volume – by means of conservation and constitutive equations. Identification of reaction kinetics, namely, rate expressions and rate parameters, represents the main challenge in constructing first-principles models. Estimation of parameters is especially difficult for fluid-fluid reaction systems when chemical species transfer between phases and possibly react in the bulk of the two phases. The identification task is commonly performed in one step via a simultaneous method. In this approach, a dynamic model comprising all kinetic steps, whether physical or chemical, is postulated, and the corresponding model parameters are estimated by comparing measured and modeled concentrations. The procedure is repeated for all combinations of model candidates, and the combination with the best fit is selected. However, simultaneous identification can be computationally costly when many candidate rate laws are available. Furthermore, this method often leads to high parameter correlation, and thus any structural mismatch in the modeling of one part of the model leads to errors in all estimated parameters. Alternatively, model identification can be carried out over several steps via an incremental method. This way, the identification task is decomposed into sub-problems of lower complexity. Measured concentrations are transformed into extents, which can then be modeled individually [1-3]. This transformation reduces the dimensionality of the dynamic model since all redundant states (invariants) can be removed. More importantly, the remaining states (variants) represent the minimal set of states describing, individually, the effects of reaction, mass transfer and transport, inlets and outlets. Postulated rate expressions (and rate parameters) are validated and estimated – one at a time – by comparing the corresponding measured and modeled extents. This approach reduces significantly the computational effort and convergence problems. Since each kinetic step can be dealt with individually, there is no correlation between the parameters of the different physical and chemical phenomena. This presentation will briefly review the extent-based model identification and then illustrate it with the absorption of nitrous oxides in water, which represents an important step in the treatment of flue gas and constitutes a complex reaction system with multiple reactions in both the gas and liquid phases. [1] Bhatt et al., "Incremental Identification of Reaction and Mass-Transfer Kinetics Using the Concept of Extents", Ind. & Eng. Chem. Res. 50, 12960-12974, 2011 [2] Srinivasan et al., "Extent-based Incremental Identification of Reaction Systems Using Concentration and Calorimetric Measurements", Chem. Eng. J. 208, 785-793, 2012 [3] Billeter et al., "Extent-based Kinetic Identification using Spectroscopic Measurements and Multivariate Calibration", Anal. Chim. Acta 767, 21-34, 2013

2013Julien Léo Billeter, Dominique Bonvin, Sriniketh Srinivasan

The identification of kinetic models is an important step for the monitoring, control and optimization of industrial processes. This is particularly the case for highly competitive business sectors such as chemical and pharmaceutical industries, where the current trend of changing markets and strong competition leads to a reduction in the process development costs [1]. Moreover, the PAT initiative of the FDA advocates a better understanding and control of manufacturing processes by the use of modern instrumental technologies and innovative software solutions [2]. Reaction systems can be represented by first-principles kinetic models that describe the time evolution of states – numbers of moles, temperature, volume, pressure – by means of conservation and constitutive equations of differential and algebraic nature. These models are designed to include all kinetic phenomena, whether physical or chemical, involved in the reaction systems. Generally, such kinetic phenomena include the dynamic effects of reactions (stoichiometry and reaction kinetics), transfer of species between phases (mass-transfer rates), and operating conditions (initial conditions as well as inlet and outlet flows). The identification of reaction and mass-transfer rates as well as the estimation of their corresponding rate parameters represents the main challenge in building first-principles models. The task of identification is commonly performed in one step via ‘simultaneous identification’, in which a dynamic model comprising all rate effects is postulated, and the corresponding model parameters are estimated by comparing the measured and modeled concentrations [3]. This procedure is repeated for all combinations of model candidates, and the combination with the best fit is usually selected. The main advantage of this identification method lies in its capability to model complex dynamic effects in a concomitant way and thus to generate enough constraints in the optimization problem so that indirect measurements such as spectroscopic and calorimetric data can be modeled without the use of a calibration step [4, 5]. However, the simultaneous approach can be computationally costly when several candidates are available for each dynamic effect. Furthermore, this method often leads to high parameter correlation with the consequence that any structural mismatch in the modeling of one part of the model can result in errors in all estimated parameters and, in addition, convergence problems can arise from a poor choice of initial guesses [6, 7]. As an alternative, the incremental approach decomposes the identification task into a set of sub-problems of lower complexity [8]. The approach consists in transforming the measured concentrations into decoupled rates or extents, which can then be modeled individually. When needed, prior to the modeling step, the missing or unmeasured states can be reconstructed using the computed rates or extents. In the ‘rated-based incremental identification’ [9], rates are first obtained by differentiation of concentration measurements. Then, postulated rate expressions and rate parameters are estimated one at a time by comparing the measured and modeled rates. However, because of the bias introduced in the differentiation step, the rate parameters estimated by this method are not statistically optimal. That is why, another approach, termed ‘extent-based incremental identification’ [10], that is based on the integral method of parameters estimation has been introduced. In this approach, extents are first computed from measured concentrations, and then postulated rate expressions are integrated individually for each extent and the corresponding rate parameters estimated by comparing the measured and modeled extents. The extent-based identification can also be adapted to analyze calorimetric and spectroscopic data using a calibration step [11, 12]. The transformation to rates or extents reduces the dimensionality of the dynamic model since all redundant states (invariants) can be discarded. More importantly, the remaining states (variants) isolate the effects of the reactions, mass transfers and operating conditions, which can then be analyzed individually [13]. This allows substantially reducing the computational effort, the convergence problems and the correlation between the estimated rate parameters. Recently, the extent-based incremental identification has been extended to fluid-fluid reaction systems undergoing unsteady-state mass transfer and reactions at the interface of the two immiscible phases. This situation is commonly encountered in reaction systems that are limited by diffusion, such as CO2 post-combustion capture and nitration reactions. Such reaction systems can be modeled using the film theory, where the two bulks are separated by a spatially distributed film, located in either of the two phases, in which diffusing species can accumulate and react. In both bulks, the mass balance equations describing the dynamics of chemical species are expressed as ordinary differential equations (ODE) and serve as boundary conditions for the film. The dynamic accumulation in the film is described by Fick’s second law combined with a reaction term, thus leading to partial differential equations (PDE), which can be solved by appropriate spatial discretization and rearrangement in ODEs. The extent-based model identification of fluid-fluid reaction systems with unsteady-state mass transfer and reactions requires a large number of measurements for reconstructing all the states and modeling the dynamics of the film [14]. The difficulty lies in the fact that, with the current state of sensor technology, such measurements can only come from the two homogeneous bulks, which provide information from a well-mixed reactor region and consequently are resolved only in time and not in space. Nevertheless, extents of reaction and extents of mass transfer can be extracted from these bulk measurements. These extents of reaction represent the effect of slow reactions that take place in the bulks of the two phases and can be modeled as before. On the other hand, the extents of mass transfer represent now the combined effect of mass transfer by diffusion through the film and of fast reactions taking place at the interface or in the film. Hence, both the diffusion coefficients and the rate constants of the fast reactions can be estimated by comparing the measured extents of mass transfer and the extents obtained by solving the corresponding PDEs. In the absence of coupling terms in the PDEs due to interactive diffusion and/or reactions, the diffusion coefficients of each species transferring through the film can be estimated incrementally. However, in the case of interactive diffusion and/or reactions, the interdependence of species via the coupling terms of the PDEs calls for a simultaneous identification of the diffusion coefficients and rate constants within the film. This contribution extends the extent-based incremental identification to the analysis of reaction systems with dynamic accumulation and reactions in the film. In particular, the question of whether to use incremental or simultaneous estimation of the diffusion coefficients and rate constants within a diffusion layer will be addressed. [1] Workman et al., Anal. Chem. 83, 4557-4578, 2011 [2] Billeter et al., 100th AIChE Annual Meeting, Philadelphia, 2008 [3] Hsieh et al., Anal. Chem., http://dx.doi.org/10.1021/ac302766m, 2013 [4] Billeter et al., Chemom. Intell. Lab. Syst. 95(2), 170-187, 2009 [5] Zogg et al., Thermochimica Acta 419, 1-17, 2004 [6] Billeter et al., Chemom. Intell. Lab. Syst. 93(2), 120-131, 2008 [7] Billeter et al., Chemom. Intell. Lab. Syst. 98(2), 213-226, 2009 [8] W. Marquardt, Chem. Eng. Res. Des., 83(A6), 561–573, 2005 [9] Brendel et al., Chem. Eng. Sci. 61, 5404-5420, 2006 [10] Bhatt et al., Ind. Eng. Chem. Res. 50, 12960-12974, 2011 [11] Srinivasan et al., Chem. Eng. J. 207-208, 785-793, 2012 [12] Billeter et al., Anal. Chim. Acta 767, 21-34, 2013 [13] Srinivasan et al., IFAC Workshop TFMST, Lyon, 2013 [14] Billeter et al., 104th AIChE Annual Meeting, Pittsburgh, 2012

2013Identification of kinetic models is an important task for monitoring, control and optimization of industrial processes. Robust kinetic models are often based on first principles, which describe the evolution of states – number of moles, temperature and volume – by means of conservation and constitutive equations. Identification of reaction kinetics, namely, rate expressions and rate parameters, represents the main challenge in building first-principles models. Estimation of parameters is especially complex for fluid-fluid reaction systems where chemical species can transfer between phases. The identification task is commonly performed in one step via a simultaneous approach. In this approach, a dynamic model comprising all kinetic steps, whether physical or chemical, is postulated and the corresponding parameters are estimated by comparing the predicted and measured concentrations. The procedure is repeated for all combinations of model candidates and the combination with the best fit is selected. However, simultaneous identification can be computationally costly when several candidates are available and convergence problems can arise for poor initial guesses. Furthermore, this approach often leads to high parameters correlation, and any structural mismatch in the modeling of one part of the model leads to errors in all estimated parameters. In this contribution, the model identification over several steps via an incremental approach will be used. In this approach, the identification task is decomposed into sub-problems of lower complexity. Measured concentrations are first transformed to reaction rates or extents, which are fully decoupled from each other. Then, postulated rate expressions (and corresponding rate parameters) are estimated – one at a time – by comparing individually the predicted and experimental rate or extent of each kinetic step. This approach allows considerably reducing the computational effort and the convergence problems. Since each kinetic step is dealt individually, correlation between parameters of different physical and chemical kinetic steps disappears. The extent-based method of identification will be presented and the relevance of this incremental approach will be demonstrated via examples taken from homogeneous and heterogeneous chemistry.

2013