(523c) A Framework for Development of Integrated and Computationally Feasible Models of Large-Scale Mammalian Cell Bioreactors
Mammalian cell cultures have become responsible for half of the annual revenue earned by the biotechnology industry. Vulnerability of cells to physical environmental stimuli and spatial heterogeneity in industrial scale bioreactors demand a modeling framework which captures both biology and hydrodynamics of the system and their interactions. Existing cell culture models, in which hydrodynamics is often excluded, usually consider all causes of cell loss in one parameter, e.g. growth rate. The accuracy of these models deteriorates when process conditions change as their parameters are highly dependent on strain, cultivation medium and fermentation conditions . In addition to narrow confidence intervals, often achieving a satisfactory fit of experimental data requires considering extra terms, which are theoretically difficult to explain. Overall, despite the practical and commercial applications of CHO cells there are only few reports on their kinetics of growth and production. More specifically there is no literature on the kinetic parameters of CHO cell batch culture related to mAb production .
In this work we propose a framework for modeling of bioreactor operation integrating biological and physical phenomena which maintains computational feasibility and permits linking the model to nonlinear solvers for optimization . Biological processes are captured by modeling relevant portions of the cellular activities that control the product of interest. Unstructured modeling utilizes a reduced number of reactions to capture cellular metabolism macroscopically. Computational fluid dynamics (CFD) simulation is employed for prediction of flow characteristics inside the reactor. The main attributes of the flow are velocity fields, gas hold up, rate of dissipation of energy and gas-liquid mass transfer. Bubbles and turbulent eddies have been recognized to directly affect viable cell density . To include their interactions with cells the parameters of damaging threshold of mechanical shear and critical distance of interaction with bubbles are introduced into the model. Computing the evolution of the system requires dynamic multi-phase CFD simulation, which demands many CPU hours to simulate processing time of few seconds. For computational tractability the metabolic model is solved dynamically while hydrodynamics switches between defined steady states. This is based upon the assumption that the time for the flow to reach a new steady state in response to change in operational conditions is negligible compared to the total processing time. Operating conditions are described by process parameters of impeller rotation speed, gas sparging flowrate, and liquid fill level. A set of admissible operating states is defined by discretization of process parameters. The steady state solutions are obtained in advance from CFD simulations. Further model reduction is achieved by time-space decomposition through dividing the reactor into compartments small enough to be assumed homogenous. It provides the necessary formulation and modeling environment for coupling the model with nonlinear programming solvers and optimize bioreactor operation. There are two basic categories of optimization algorithms that use reduced models. Those are differentiated based on their dependencies on the original detailed model for calculation of gradients . For the proposed formulation most of the evaluations and construction of the reduced models are done before starting the optimization since minimal communication between the optimization algorithm and the original model is preferred.
Development of a surrogate model for hydrodynamics is investigated to exploit data obtained from CFD simulations and replace some of the discrete variables. To use large datasets generated by the simulations, first a sampling method based on Latin hypercube design is implemented. It accounts for spatial dependency of data and improves the uniformity of spread of samples. The surrogate model consists of a linear regression term and a stochastic error which follows a Gaussian process. Simultaneous estimation of coefficients in both terms improves the predictive power of the surrogate. This is achieved through maximizing a penalized likelihood function with spatial dependence incorporated into the penalty term. To reduce the computational burden on the solver an iterative method based on local linear approximation of the penalty term is used. With careful initial guess and choice of regularization parameter for the penalty term, one step of iteration has been shown to provide a statistically efficient approximation of the coefficients.
Quantification of the extent of effects of mechanical shear and bubble interactions on viability of cells is a valuable outcome which is achievable through integrated modeling, experimental design, and parameter estimation. Integration also gives better estimations of cellular growth and death rates as functions of metabolites concentrations. It addresses lack of universality of cell culture models, which is a major hindrance towards implementation of mechanistic models in biotechnology industry. Additionally a well-posed model which captures interactions of system components and is coupled with optimization solvers can recommend substantial improvements for bioreactor operations.
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