(184j) Improving Numerical Methods for Bioreactor Process Simulation and Parameter Estimation

This abstract discusses methods to speed up numerical integration of Ordinary Differential Equations (ODEs) and optimization for Flux Balance Analysis (FBA) in bioreactor models, aiming to improve the numerical performance of search-based parameter estimation algorithms.

In silico mammalian cell culture bioreactor modeling platforms hold great promise for transforming bioprocess development. Simulation and optimization of biomanufacturing processes can reduce experimentation and enhance process efficiency, as well as product quality. Building a predictive dynamic model requires estimating parameters based on bioreactor experimental data. Parameter estimation can represent a significant computational challenge because it requires solving a high dimensional non-convex optimization problem to an acceptable local or global optimality. Performing a successful parameter estimation requires practitioners to carefully formulate the optimization problem and to select efficient numerical methods for integration and optimization. This poses a significant risk of identifying sub-optimal solutions if an inappropriate parameter estimation workflow is employed.

In this work, we present two approaches to significantly speeding up the numerical integration of ODEs, as well as the numerical optimization for solving FBA, involved in simulating in-house developed bioreactor models for describing cellular metabolisms. First, an idea of better scaling the problem has been explored. To do so, the underlying equations for a model with the cellular metabolism described with simple kinetic equations (e.g., see [1]) were nondimensionalized. Thanks to the normalization of the model variables and parameters, numerical solvers can take advantage of better scaling of the problem, thus resulting in a much better performance. To demonstrate this concept, we compare the numerical performance of the dimensional and dimensionless simulations of the simple kinetic model. Second, alternate formulations for FBA in a hybrid model (e.g., see [2]), as well as the corresponding convex optimization solvers from the CVXOPT library (see [3]), have been explored. Without loss of generality, FBA can be formulated either as a Quadratic Program (QP) or a Second Order Cone Program (SOCP). To test each solver's numerical performance, solution time and accuracy, and stability of the obtained solutions were compared within the hybrid model's context.

Since our model parameter estimation algorithm is based on a genetic algorithm, which couples an ODE solver with a search-based numerical optimization algorithm, speeding up the numerical integration of ODEs, as well as the numerical optimization for solving FBA, holds a promise in achieving a significant reduction of the model parameter estimation time.

[1] Kontoravdi, C, Pistikopoulos, E. N., and Mantalaris, A. Systematic development of predictive mathematical models for animal cell cultures. Computers & Chemical Engineering. 2010;34(8):1192–1198. doi:https://doi.org/10.1016/j.compchemeng.2010.03.012.

[2] Nolan, R. P. and Lee, K. Dynamic model of CHO cell metabolism. Metabolic Engineering. 2011;13(1):108–124. doi:https://doi.org/10.1016/j.ymben.2010.09.003.

[3] Andersen, M., Dahl, J., and Vandenberghe, L. CVXOPT: Python software for convex optimization, version 1.2. http://cvxopt.org/, February 2019.