Development and application of methods for complexity reduction, metamodelling and optimal experimental design based on global sensitivity analysis

Model based simulation of complex processes is an efficient approach to explore and study systems whose experimental analysis is costly or time-consuming. Modern mathematical models of real systems often have high complexity with hundreds of variables. Straightforward modelling using such models can be computationally costly or even intractable. Good modelling practice requires sensitivity analysis (SA) to ensure the model quality by analysing the model structure, selecting the best type of model and effectively identifying the important model parameters. Global SA is superior to other SA methods. It can be applied to any type of model for quantifying and reducing problem complexity without sacrificing accuracy and it is not dependent on a nominal point like local SA methods. We propose the development of a number of advanced model analysis and complexity reduction techniques based on global SA and efficient high dimensional Monte Carlo (MC) and Quasi MC methods. In particular, we will develop high dimensional Sobol' sequence generators with improved uniformity properties. It will allow increasing the efficiency of global SA and Quasi MC methods in general. The Sobol' method of global sensitivity indices is superior to other global SA methods. However, it has been applied only to low scale models because of the computational limitations of the existing technique. We propose a number of techniques which will improve the efficiency of the Sobol' method. We also propose a set of new global SA measures which are much less computationally demanding than variance based methods. By combining approaches based on the Fisher information matrix and GSA, we will develop a new technique for parameter estimation and optimal experimental design for model validation which would dramatically reduce experimental cost. One of the very promising developments of model analysis is the replacement of complex models and models which need to be run repeatedly on-line with equivalent operational meta models. Sampling efforts of the existing approaches grow exponentially with the number of input variables which makes them impractical in high dimensional cases. We will develop a novel approach to metamodelling using quasi random sampling - high dimensional model representation method (QRS-HDMR) which renders the original exponential difficulty to a problem of only polynomial complexity. We propose to solve optimization problems with high dimensional and computationally expensive objective functions by building QRS-HDMR meta models for the objective functions and set of constraints. Such meta models based optimization problems can be orders of magnitude cheaper to solve compared to the original models. The application of these methods to bioprocessing will involve the development of high-fidelity models for mammalian cell cultures, which produce high-value biological drugs, such as monoclonal antibodies. High-profile examples include the breast cancer drug Herceptin and blockbuster cancer drug Avastin. However, the production of such drugs often relies on manual control and optimisation, which increase cost and time-to-market. On the other hand, the implementation of modern model-based methodologies for optimisation and control necessitates predictive, computationally tractable models, which usually involve numerous parameters and require a high volume of expensive measurements for their validation. In order to address these issues and minimise the cost and time of experimentation, GSA and optimal experimental design will be used to formulate a state-of-the art model of mammalian cell cultures for in silico experimentation, system analysis and derivation of a metamodel for online applications. The validity of this approach will be demonstrated through a case study on antibody-producing CHO cells supplied by Lonza Biologics.

Beneficiaries ------------------ Our primary beneficiaries will be in the mathematical modelling community, particularly those associated in the engineering, process and pharmaceutical-related sectors (industrial and academic) who deal with large-scale, complex models. The tools we shall develop for sensitivity analysis, experiment design, complexity reduction and meta-model generation are generic in nature and will be of great value to this potential user base. Our immediate collaborators, Lonza and EdF will benefit directly from their involvement and we shall similarly benefit from the close involvement of potential users. Our strategy involves both methodological development and experimental verification. This will allow us to develop prototype tools and methods that can then be made available to other researchers in industry, academia and research institutes. The domain-specific research outcomes from the application part of the programme will benefit the wider systems and synthetic biology communities, who deal with highly complex systems. Mathematical modelling is integral to these areas of research, so we intend to make the advanced, computationally efficient techniques for sensitivity analysis, experiment design and model reduction available to these communities. Advanced models of animal cell culture systems will constitute a significant improvement to current (empirical) practice, hence the interest of Lonza Biologics in this project. Benefits ----------- The generic benefits relate to improved efficiency of modelling through the lifecycle from model development (global sensitivity analysis), model verification and improvement (experiment design) and model use (complexity reduction and metamodelling). Many complex engineered systems rely on models for effective design and operation and we anticipate widespread use of the techniques developed. This will then widen the scope of modelling and lead to improvements in complex system design and operation. Domain-specific benefits are expected in the area of biological systems modelling where improved models will be made available and the power of modelling will be demonstrated. Moreover, the PhD student involved in this project will receive high-quality interdisciplinary training, making his/her skills in both modelling and experimentation invaluable for the biotechnological sector. Engagement, communication and exploitation ------------------------------------------------------------------ Our ultimate objective is to disseminate our methods and tools widely, both through the publication of results in learned journals and conferences and through formal exploitation of the intellectual property. Our primary engagements during the project will be with our two industrial collaborators; they will support the research with data, models and cell lines and we shall solicit feedback on our methods and results from them. This will inform our wider communication and engagement strategy, starting with the CPSE industrial consortium (we have 20 years' experience of running an industrial consortium with a report series, specialist web site, dissemination meetings, technical workshops, software evaluation exercises, briefing sessions etc). CPSE also has a good track record in exploiting modelling-related technology (evidenced by a Queen's Anniversary Award for CPSE and a Queen's Award for Enterprise and the MacRobert Award for its spin-off company). We will be supported by Imperial Innovations PLC who are very experienced in the protection and exploitation of intellectual property. We shall also work with the Chemistry Innovation KTN to make the results available to their members.