Optimal experimental design based on global sensitivity analysis (original) (raw)
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Improved efficiency in sensitivity calculations for bioreactor models
Computers & Chemical Engineering, 2009
Sensitivity functions are a basic tool in the parametric identification of models. They can be used to obtain the gradient needed by optimization algorithms in the estimation of parameters and to calculate the Fisher information matrix in experimental design. In addition to systems identification, sensitivity functions are also used in robustness analysis, robust design, and robust control for batch and semi-batch processes. This paper shows that, for certain types of bioreactor models, there is a fixed relation between certain sensitivity functions. This property allows the computational load of the numerical calculation of the sensitivity trajectories to be reduced.
2008
Wastewater treatment plant control and monitoring can help to achieve good effluent quality, in a complex, highly non-linear process. The Benchmark Simulation Model no. 2 (BSM2) is a useful tool to competitively evaluate plant-wide control on a long-term basis. A key component to characterise the system for control is outputparameter sensitivity. This paper brings the results of a global sensitivity analysis performed on the BSM2 model in its open loop version, by means of Monte Carlo (MC) experiments and linear regression. This study presents methods that were applied to make computationally demanding MC experiments on such a complex model feasible, by reducing the computation time for a single simulation and by setting low but sufficient number of runs for the MC experiments; it was found that 50 times the number of uncertain parameters was necessary. The most sensitive parameters turned out to be the design and operation parameters, followed by the wastewater treatment model parameters, while the adopted BSM2 evaluation criteria are rather insensitive to variations in sludge treatment models parameters. The results are verified on a closed loop version of BSM2, and allow future uncertainty analysis studies on BSM2 to be conducted on a smaller set of parameters and to focus the attention on the most critical parameters.
Biotechnology Progress, 2008
Global sensitivity analysis (GSA) can be used to quantify the importance of model parameters and their interactions with respect to model output. In this study, the Sobol′ method for GSA is applied to a dynamic model of monoclonal antibody-producing mammalian cell cultures in order to identify the parameters that need to be accurately determined experimentally. Our results show that most parameters have low sensitivity indices and exhibit strong interactions with one another. These parameters can be set at their nominal values and unnecessary experimentation can therefore be avoided. In contrast, certain parameters are identified as sensitive, necessitating their estimation given sufficiently rich experimental data. Moreover, parameter sensitivity varies during culture time in a biologically meaningful manner. In conclusion, GSA can serve as an excellent precursor to optimal experiment design.
Optimal parametric sensitivity control for the estimation of kinetic parameters in bioreactors
Mathematical Biosciences, 2002
In this paper the well-known problem of optimal input design is considered. In particular, the focus is on input design for the estimation of kinetic parameters in bioreactors. The problem is formulated as follows: given the model structure (f,g), which is assumed to be affine in the input, and the specific parameter of interest theta;(k) find a feedback law that maximizes the sensitivity of the model output to the parameter under different flow conditions in the bioreactor and, possibly, minimize the input or state costs. Analytical solutions to these problems are presented. As an example a bioreactor with a biomass that grows according to the well-known Monod kinetics is considered.
Optimal Experiment Design in Bioprocess Modeling: From Theory to Practice
IFAC Proceedings Volumes, 2006
In this paper the problem of parameter identification for the Monod model is considered. As known for a long time, noisy batch measurements do not allow unique and accurate estimation of the kinetic parameters of the Monod model. Techniques of optimal experiment design are, therefore, addressed to design informative experiments and improve the parameter estimation accuracy. During the design process, practical feasibility has to be kept in mind. In this paper it is demonstrated how a theoretical optimal design can successfully be translated to a feasible optimal design. Both design and validation of informative fed batch experiments are illustrated with a case study that models the growth of the nitrogen fixing bacteria Azospirillum brasilense.
Global Sensitivity Analysis Challenges in Biological Systems Modeling
Industrial & Engineering Chemistry Research, 2009
Mammalian cell culture systems produce high-value biologics, such as monoclonal antibodies, which are increasingly being used clinically. A complete framework that interlinks model-based design of experiments (DOE) and model-based control and optimization to the actual industrial bioprocess could assist experimentation, hence reducing costs. However, high fidelity models have the inherent characteristic of containing a large number of parameters, which is further complicated by limitations in the current analytical techniques, thus resulting in the experimental validation of merely a small number of parameters. Sensitivity analysis techniques can provide valuable insight into model characteristics. Traditionally, the application of sensitivity analysis on models of biological systems has been treated more or less as a black box operation. In the present work, we elucidate the aspects of sensitivity analysis and identify, with reasoning, the most suitable group of sensitivity analysis methods for application to highly nonlinear dynamic models in the context of biological systems. Specifically, we perform computational experiments on antibody-producing mammalian cell culture models of different complexities and identify, as well as address, problems associated with such "real life" models. In conclusion, a novel global screening method (derivative based global sensitivity measures, DGSM) is proven to be the most time-efficient and robust alternative to the established variance-based Monte Carlo methods.
Response surface analysis and simulation as a tool for bioprocess design and optimization
Process Biochemistry, 2000
In the present work, factorial design and response surface techniques were used in combination with modeling and simulation to design and optimize an industrial bioprocess. Alcoholic fermentation process with multiple stages was considered. The fermentation system is composed of four ideal continuous-stirred tank reactors (ICSTR), linked in series, with cell recycling. Operational conditions for maximal yield and productivity were determined with ten parameters under consideration: temperature (four stages), residence time for each stage, cell recycling concentration, and the fraction of fresh medium fed into the second fermentation stage. Initially, screening design methodology was used to evaluate the process variables which were relevant in relation to yield and productivity. Five statistically significant parameters for each response were selected and utilized in factorial design in order to optimize the process. With the models obtained from the factorial design, response surfaces were generated, and the productivity improved to 12 g/l·h (an increase of 52% in relation to the control version of the bioprocess), while maintaining the high yield of 86.28% (99.1% conversion).
Model-driven design based on sensitivity analysis for a synthetic biology application
2011
Synthetic biology, which involves the design of genetic circuits, has been valuable for understanding and engineering biological systems. Such genetic circuits could be valuable in metabolic engineering applications, where the goal is to manipulate the machinery of the organism in order to force or improve the bioengineering objective (which is typically in conflict with the organism's objective governed by evolution, i.e. to optimally allocate the resources for growth).
Experimental Design and Process Optimization
CRC Press eBooks, 2014
A systematic technique for experimental design is important for the optimization of products and processes in various areas. This book introduces the methodology of factorial design associated with response surface analysis, which is a statistical theory-based experimental design and process optimization method. With this book, the authors wish to transmit their experience using these methodologies to assist others in solving the challenges of process or product research and development. The authors try to make the book practically useful to those who consider statistics an indispensable tool for developing products and processes. With this objective, the book starts by presenting the motivation for using experimental design, and explains the importance of integrating process, statistics, and common sense. Chapter 2 presents some fundamental statistics at an introductory level and covers descriptive statistics, probability and mathematical statistics, statistical inference, and the simple linear regression. Chapter 3 presents some basic concepts of experimental design (e.g. factorial design, fractional factorial, and central composite designs) for understanding the following chapters (4-7). To demonstrate the advantages of applying factorial design, Chapter 4 compares the factorial design method with the 'one factor at a time' method. Chapter 5 presents the full factorial design and fractional factorial design-based sequential experimental design techniques through informative case studies. This chapter involves a comprehensive investigation of experimental design with various numbers of factors, from 3-8. Chapter 6 discusses the Plackett and Burman design method for addressing the initial selection of factors when the total number is large (i.e. greater than eight). Chapter 7 presents several interesting applications of the factorial design-based sequential design method. These cases include good problem summary, methodology description, result analysis, and conclusions, which helps readers understand the motivation and the procedure of the major techniques introduced by the book. This book is organized in a way that is appropriate for practitioners who want to immediately use the methodologies to help solve problems. The authors acknowledge that the direct use of user-friendly software without prior knowledge of the fundamentals of a methodology can be a major risk, and can cause the user to make misguided interpretations. Based on such considerations, the book presents some fundamental statistics and experimental design knowledge at a reasonable level, although the book does not comprehensively cover all the theories, such as effect calculation and model adequacy checking. Overall, the book is a handy reference for those who seek direct and immediate applications of factorial design and response analysis methods for optimizing process or product development. From the reviewer's view, the book may be suitable as a supplementary reference book for university-level courses. Case studies from the book can be used as effective demonstrations of the theories. It can also be a valuable reference book for any practitioner of experimental design.
Biotechnology and Applied Biochemistry, 2008
The present paper describes the application of GSA (Global Sensitivity Analysis) techniques to mathematical models of bioprocesses in order to rank inputs such as feed titres, flow rates and matrix capacities for the relative influence that each exerts upon outputs such as yield or throughput. GSA enables quantification of both the impact of individual variables on process outputs, as well as their interactions. These data highlight those attributes of a bioprocess which offer the greatest potential for achieving manufacturing improvements. Whereas previous GSA studies have been limited to individual unit operations, this paper extends the treatment to an entire downstream process and illustrates its utility by application to the production of a Fab-based rattlesnake antivenom called CroFab TM [(Crotalidae Polyvalent Immune Fab (Ovine); Protherics U.K. Limited]. Initially, hyperimmunized ovine serum containing rattlesnake antivenom IgG (product), other antibodies and albumin is applied to a synthetic affinity ligand adsorbent column to separate the antibodies from the albumin. The antibodies are papain-digested into Fab and Fc fragments, before concentration by ultrafiltration. Fc, residual IgG and albumin are eliminated by an ion-exchanger and then CroFab-specific affinity chromatography is used to produce purified antivenom. Application of GSA to the model of this process showed that product yield was controlled by IgG feed concentration and the synthetic-material affinity column's capacity and flow rate, whereas product throughput was predominantly influenced by the synthetic material's capacity, the ultrafiltration concentration factor and the CroFab affinity flow rate. Such information provides a rational basis for identifying the most promising strategies for delivering improvements to commercial-scale biomanufacturing processes.