Ioanna Stamati

Optimal experimental design for discriminating between microbial growth models as function of suboptimal temperature: From in silico to in vivo

Temperature is an important food preservation factor, affecting microbial growth. Secondary predictive models can be used for describing the impact of this factor on microbial growth. In other words, the microbial behavior can be described in a dynamic environment with the use of a primary and secondary model. Two models for describing the effect of temperature on the microbial growth rate are the cardinal temperature model with inflection (CTMI) (Rosso et al., 1993) and its adapted version (aCTMI) (Le Marc et al., 2002). Although Escherichia coli is commonly modeled using CTMI, there are indications that aCTMI may be more appropriate (Van Derlinden and Van Impe, 2012a). For clarifying this, the method of Optimal experiment design for model discrimination (OED/MD) will be used in this work (Donckels et al., 2009; Schwaab et al., 2008). Results from an in silico study point out the required direction. Whereas the results of the in vivo study give a more realistic answer to the research question. Finally, discrimination unravelled the appropriate model for the needed use.

On the effect of sampling rate and experimental noise in the discrimination between microbial growth models in the suboptimal temperature range

Abstract Biochemical and microbial processes benefit from mathematical models. Often microbial kinetics are described as a function of environmental conditions in models exploited in predictive microbiology. Based on the organism different model structures are available. However, the aim is to determine the model that describes the system best. This work deals with secondary models describing microbial kinetics in the suboptimal temperature range and their possibility to be discriminated. The used models are the cardinal temperature model with inflection and its adapted version. The method of Optimal Experiment Design for Model Discrimination is used to investigate the practical (in)feasibility of model discrimination given different noise and sampling frequency values. Results point out the required steps and the possibilities of the method for model discrimination. It has been observed that discrimination is possible at various noise and sampling frequency levels. Moreover, also the corresponding increase in required experimental effort has been obtained.

Optimal experimental design for discriminating between microbial growth models as function of suboptimal temperature

In the field of predictive microbiology, mathematical models play an important role for describing microbial growth, survival and inactivation. Often different models are available for describing the microbial dynamics in a similar way. However, the model that describes the system in the best way is desired. Optimal experimental design for model discrimination (OED-MD) is an efficient tool for discriminating among rival models. In this work the T12-criterion proposed by Atkinson and Fedorov (1975) [1] and applied efficiently by Ucinski and Bogacka (2005) [2] and the Schwaab-approach proposed by Schwaab et al. (2008) [3] and Donckels et al. (2009) [4] will be applied for discriminating among rival models for the microbial growth rate as a function of temperature. The two methods will be tested in silico and their performances will be compared. Results from a simulation study indicate that it is possible to validate the case that one of the proposed models is more accurate for describing the temperature effect on the microbial growth rate. Both methods are able to design inputs with a sufficient discrimination potential. However, it has been observed that the Schwaab-approach provides inputs with a higher discrimination potential in combination with more accurate parameter estimates.

Optimal Experiment Design for Model Discrimination using the Sigma Point Method

Abstract Bioprocesses can be controlled and optimised by dynamic process models. However, often different models are available for describing the dynamics in a similar way. In order to discriminate efficiently among rival models, optimal experiment design for model discrimination (OED-MD) has been developed. In this work the OED-MD method proposed by Schwaab et al. (2008) will be used for discriminating among dynamic models of microbial growth rate as a function of temperature. In this model discrimination procedurethe variance-covariance matrix of the parameters is needed, which is traditionally approximated by the inverse of the Fisher information matrix using the Cramer-Rao lower bound. For models nonlinear in the parameters, this can be a severe underestimation of the actual parameter uncertainty. A more accurate estimation of the variance-covariance matrix of the parameters can be obtained by using the so-called sigma point method ( Schenkendorf et al., 2009 ). The main contribution of this paper is that the sigma point method is used for accurately computing the variance- covariance matrix of the parameters. This matrix is subsequently employed in the procedure for discriminating between two possible models of microbial growth rate as a function of temperature. In addition, the sigma point method is compared with the classic Fisher information matrix approach on the level of discriminating potential.

Optimal experimental design for mechanistic nonlinear dynamic models using multisine inputs: Application to a Diesel engine

For many applications first-principles nonlinear dynamic models are preferred by practitioners. Parameter estimation for these models is often a non-trivial and time consuming task. The use of optimally designed dynamic inputs can reduce the experimental burden and increase the accuracy of the estimated parameters. Traditionally, piecewise polynomial input sequences are exploited for this purpose. In contrast, this paper proposes optimal experiment design with the use of random phase multisine inputs, which are typically used for black box model identification. The main motivations are (i) the practical requirement that the inputs have to be concentrated around an operating point, and (ii) the fact that fast dynamics have to be included in the input profile without introducing a large number of discretization parameters. Moreover, multisines can be designed to excite exclusively a specific frequency band of interest. As an illustration, optimal inputs are designed and validated experimentally for estimating the parameters important for the dynamical behaviour of a Diesel engine air path model.