Modeling of mass transfer and optimization of stirred bioreactors

Models of power input and mass transfer are synthesized in bioreactor. A new constructive parameter of bioreactor the eccentricity of stirrer towards its rotation axis is introduced and investigated. Obtained values of constructive and regime parameters allow the design of a bioreactor with improved mass transfer characteristics.     

Optimal fed batch experiment design for estimation of monod kinetics of Azospirillum brasilense: from theory to practice

In this paper the problem of reliable and accurate parameter estimation for unstructured models is considered. It is illustrated how a theoretically optimal design can be successfully translated into a practically feasible, robust, and informative experiment. The well-known parameter estimation problem of Monod kinetic parameters is used as a vehicle to illustrate our approach. As known for a long time, noisy batch measurements do not allow for unique and accurate estimation of the kinetic parameters of the Monod model. Techniques of optimal experiment design are, therefore, exploited to design informative experiments and to improve the parameter estimation accuracy. During the design process, practical feasibility has to be kept in mind. The designed experiments are easy to implement in practice and do not require additional monitoring equipment. Both design and experimental validation of informative fed batch experiments are illustrated with a case study, namely, the growth of the nitrogen-fixing bacteria Azospirillum brasilense.     

Scaling-down biopharmaceutical production processes via a single multi-compartment bioreactor (SMCB)

Biopharmaceutical production processes often use mammalian cells in bioreactors larger than 10,000 L, where gradients of shear stress, substrate, dissolved oxygen and carbon dioxide, and pH are likely to occur. As former tissue cells, producer cell lines such as Chinese hamster ovary (CHO) cells sensitively respond to these mixing heterogeneities, resulting in related scenarios being mimicked in scale-down reactors. However, commonly applied multi-compartment approaches comprising multiple reactors impose a biasing shear stress caused by pumping. The latter can be prevented using the single multi-compartment bioreactor (SMCB) presented here. The exchange area provided by a disc mounted between the upper and lower compartments in a stirred bioreactor was found to be an essential design parameter. Mimicking the mixing power input at a large scale on a small scale allowed the installation of similar mixing times in the SMCB. The particularities of the disc geometry may also be considered, finally leading to a converged decision tree. The work flow identifies a sharply contoured operational field comprising disc designs and power input to install the same mixing times on a large scale in the SMCB without the additional shear stress caused by pumping. The design principle holds true for both nongassed and gassed systems.     

Model-based workflow for scale-up of process strategies developed in miniaturized bioreactor systems

Miniaturized bioreactor (MBR) systems are routinely used in the development of mammalian cell culture processes. However, scale-up of process strategies obtained in MBR- to larger scale is challenging due to mainly non-holistic scale-up approaches. In this study, a model-based workflow is introduced to quantify differences in the process dynamics between bioreactor scales and thus enable a more knowledge-driven scale-up. The workflow is applied to two case studies with antibody-producing Chinese hamster ovary cell lines. With the workflow, model parameter distributions are estimated first under consideration of experimental variability for different scales. Second, the obtained individual model parameter distributions are tested for statistical differences. In case of significant differences, model parametric distributions are transferred between the scales. In case study I, a fed-batch process in a microtiter plate (4 ml working volume) and lab-scale bioreactor (3750 ml working volume) was mathematically modeled and evaluated. No significant differences were identified for model parameter distributions reflecting process dynamics. Therefore, the microtiter plate can be applied as scale-down tool for the lab-scale bioreactor. In case study II, a fed-batch process in a 24-Deep-Well-Plate (2 ml working volume) and shake flask (40 ml working volume) with two feed media was investigated. Model parameter distributions showed significant differences. Thus, process strategies were mathematically transferred, and model predictions were simulated for a new shake flask culture setup and confirmed in validation experiments. Overall, the workflow enables a knowledge-driven evaluation of scale-up for a more efficient bioprocess design and optimization.     

Simultaneous versus sequential optimal experiment design for the identification of multi-parameter microbial growth kinetics as a function of temperature

Optimal experiment design for parameter estimation (OED/PE) has become a popular tool for efficient and accurate estimation of kinetic model parameters. When the kinetic model under study encloses multiple parameters, different optimization strategies can be constructed. The most straightforward approach is to estimate all parameters simultaneously from one optimal experiment (single OED/PE strategy). However, due to the complexity of the optimization problem or the stringent limitations on the system's dynamics, the experimental information can be limited and parameter estimation convergence problems can arise. As an alternative, we propose to reduce the optimization problem to a series of two-parameter estimation problems, i.e., an optimal experiment is designed for a combination of two parameters while presuming the other parameters known. Two different approaches can be followed: (i) all two-parameter optimal experiments are designed based on identical initial parameter estimates and parameters are estimated simultaneously from all resulting experimental data (global OED/PE strategy), and (ii) optimal experiments are calculated and implemented sequentially whereby the parameter values are updated intermediately (sequential OED/PE strategy).This work exploits OED/PE for the identification of the Cardinal Temperature Model with Inflection (CTMI) (Rosso et al., 1993). This kinetic model describes the effect of temperature on the microbial growth rate and encloses four parameters. The three OED/PE strategies are considered and the impact of the OED/PE design strategy on the accuracy of the CTMI parameter estimation is evaluated. Based on a simulation study, it is observed that the parameter values derived from the sequential approach deviate more from the true parameters than the single and global strategy estimates. The single and global OED/PE strategies are further compared based on experimental data obtained from design implementation in a bioreactor. Comparable estimates are obtained, but global OED/PE estimates are, in general, more accurate and reliable.     

Use of computational fluid dynamics as a tool for establishing process design space for mixing in a bioreactor

The concept of "design space" plays an integral part in implementation of quality by design for pharmaceutical products. ICH Q8 defines design space as "the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality. Working within the design space is not considered as a change. Movement out of the design space is considered to be a change and would normally initiate a regulatory post-approval change process. Design space is proposed by the applicant and is subject to regulatory assessment and approval." Computational fluid dynamics (CFD) is increasingly being used as a tool for modeling of hydrodynamics and mass transfer. In this study, a laboratory-scale aerated bioreactor is modeled using CFD. Eulerian-Eulerian multiphase model is used along with dispersed k-ε turbulent model. Population balance model is incorporated to account for bubble breakage and coalescence. Multiple reference frame model is used for the rotating region. We demonstrate the usefulness of CFD modeling for evaluating the effects of typical process parameters like impeller speed, gas flow rate, and liquid height on the mass transfer coefficient (k(L)a). Design of experiments is utilized to establish a design space for the above mentioned parameters for a given permissible range of k(L)a.     

Characterization of a perfusion reactor utilizing mammalian cells on microcarrier beads

Our overall objective is to develop a cell culture analogue bioreactor (CCA) that can be used together with a corresponding physiologically based pharmacokinetic model (PBPK) to evaluate molecular mechanisms of toxicity. The PBPK is a mathematical model that divides the body into compartments representing organs, integrating the kinetic, thermodynamic, and anatomical parameters of the animal. The CCA bioreactor is a physical replica of the PBPK; where the PBPK specifies organs, the CCA bioreactor contains compartments with a corresponding cell type that mimics some of the characteristic metabolism of that organ. The device is a continuous, dynamic system composed of multiple cell types that interact through a common circulating cell culture medium. The CCA bioreactor and the model can be coupled to evaluate the plausibility of the molecular mechanism that is input into the model. This paper focuses on the design, development, and characterization of a CCA bioreactor to be used in naphthalene dose response studies. A CCA bioreactor prototype developed previously is improved upon by culturing the cells on microcarrier beads. Microcarrier beads with cells attached can form packed beds with cell culture medium perfusing the beds. In this study, two packed beds of cells, one with L2 cells (rat lung) and one with H4IIE cells (rat hepatoma), are linked in a physiologically relevant arrangement by a common recirculating cell culture medium. Studies of this CCA bioreactor presented here include mixing profiles, effect of reactor environment on cell viability and intracellular glutathione, naphthalene distribution profile, and initial naphthalene dosing studies. Unlike the prototype system there is no detectable response to naphthalene addition; in a companion paper we show that this discrepancy can be explained by differences in liquid residence times in the organ compartments. The perfusion reactor design is shown to have significant operating improvements over prototype designs.     

Engineering design methodology for bio-mechatronic products

Four complex biotechnology products/product systems (a protein purification system, a bioreactor system, a surface plasmon resonance biosensor, and an enzymatic glucose analyzer) are analyzed using conceptual design principles. A design model well-known in mechanical system design, the Hubka-Eder (HE) model, is adapted to biotechnology products that exemplify combined technical systems of mechanical, electronic, and biological components, here referred to as bio-mechatronic systems. The analysis concludes that an extension of the previous HE model with a separate biological systems entity significantly contributes to facilitating the functional and systematic analyses of bio-mechatronic systems.     

A simplified steady-state model of a hybrid bioreactor composed of a bubble column bioreactor and biofilter compartments

In a previous study, a hybrid bioreactor comprised of a bubble column bioreactor section and a biofilter section was successfully applied to the treatment of benzene. In order to design and optimize the bioreactor system for actual use in the field, simple but effective mathematical models of the two-stage system were required. Since the liquid phase in the bubble column bioreactor section was well mixed, a CSTR (continuously stirred tank reactor) model was adopted for this section, with benzene removal by both air stripping and biodegradation being considered in the model equations. The gaseous benzene degradation in the biofilter section was described using a PFR (plug flow reactor) model. The combined model was validated through independent experiments, and the simulation results were in a good agreement with measured data.     

Incorporating prior parameter uncertainty in the design of sampling schedules for pharmacokinetic parameter estimation experiments

An experiment design procedure is proposed for nonlinear parameter estimation studies that formally incorporates prior parameter uncertainty. The design criterion derives from information theory considerations and involves an asymptotic interpretation of the expected posterior information provided by an experiment. A pharmacokinetic sample schedule design problem is used to illustrate and evaluate this information theoretic design strategy. The model considered is commonly used to describe the plasma concentration of a drug following its oral administration. The limitations and advantages of the proposed design procedure are discussed in relation to other previously reported design techniques for incorporating parameter uncertainty.     

Quantifying the hydrodynamic stress for bioprocesses

Hydrodynamic stress is an influential physical parameter for various bioprocesses, affecting the performance and viability of the living organisms. However, different approaches are in use in various computational and experimental studies to calculate this parameter (including its normal and shear subcomponents) from velocity fields without a consensus on which one is the most representative of its effect on living cells. In this letter, we investigate these different methods with clear definitions and provide our suggested approach which relies on the principal stress values providing a maximal distinction between the shear and normal components. Furthermore, a numerical comparison is presented using the computational fluid dynamics simulation of a stirred and sparged bioreactor. It is demonstrated that for this specific bioreactor, some of these methods exhibit quite similar patterns throughout the bioreactor—therefore can be considered equivalent—whereas some of them differ significantly.     

Scale-up analysis of geometrically dissimilar single-use bioreactors

Cell culture scale-up is a challenging task due to the simultaneous change of multiple hydrodynamic process characteristics and their different dependencies on the bioreactor size as well as variation in the requirements of individual cell lines. Conventionally, the volumetric power input is the most common parameter to select the impeller speed for scale-up, however, it is well reported that this approach fails when there are huge differences in bioreactor scales. In this study, different scale-up criteria are evaluated. At first, different hydrodynamic characteristics are assessed using computational fluid dynamics data for four single-use bioreactors, the Mobius® CellReady 3 L, the Xcellerex™ XDR-10, the Xcellerex™ XDR-200, and the Xcellerex™ XDR-2000. On the basis of this numerical data, several potential scale-up criteria such as volumetric power input, impeller tip speed, mixing time, maximum hydrodynamic stress, and average strain rate in the impeller zone are evaluated. Out of all these criteria, the latter is found to be most appropriate, and the successful scale-up from 3 to 10 L bioreactor and to 200 L bioreactor is confirmed with cell culture experiments using Chinese Hamster Ovary cell cultivation.     

Numerical simulation of global hydro-dynamics in a pulsatile bioreactor for cardiovascular tissue engineering

Previous numerical simulations of the hydro-dynamic response in the various bioreactor designs were mostly concentrated on the local flow field analysis using computational fluid dynamics, which cannot provide the global hydro-dynamics information to assist the bioreactor design. In this research, a mathematical model is developed to simulate the global hydro-dynamic changes in a pulsatile bioreactor design by considering the flow resistance, the elasticity of the vessel and the inertial effect of the media fluid in different parts of the system. The developed model is used to study the system dynamic response in a typical pulsatile bioreactor design for the culturing of cardiovascular tissues. Simulation results reveal the detailed pressure and flow-rate changes in the different positions of the bioreactor, which are very useful for the evaluation of hydro-dynamic performance in the bioreactor designed. Typical pressure and flow-rate changes simulated agree well with the published experimental data, thus validates the mathematical model developed. The proposed mathematical model can be used for design optimization of other pulsatile bioreactors that work under different experimental conditions and have different system configurations.     

Identifiability and interval identifiability of mammillary and catenary compartmental models with some known rate constants

The identifiability problem is addressed for n-compartment linear mammillary and catenary models, for the common case of input and output in the first compartment and prior information about one or more model rate constants. We first define the concept of independent constraints and show that n-compartment linear mammillary or catenary models are uniquely identifiable under n-1 independent constraints. Closed-form algorithms for bounding the constrained parameter space are then developed algebraically, and their validity is confirmed using an independent approach, namely joint estimation of the parameters of all uniquely identifiable submodels of the original multicompartmental model. For the noise-free (deterministic) case, the major effects of additional parameter knowledge are to narrow the bounds of rate constants that remain unidentifiable, as well as to possibly render others identifiable. When noisy data are considered, the means of the bounds of rate constants that remain unidentifiable are also narrowed, but the variances of some of these bound estimates increase. This unexpected result was verified by Monte Carlo simulation of several different models, using both normally and lognormally distributed data assumptions. Extensions and some consequences of this analysis useful for model discrimination and experiment design applications are also noted.     

Efficient Optimization of Stimuli for Model-Based Design of Experiments to Resolve Dynamical Uncertainty

This model-based design of experiments (MBDOE) method determines the input magnitudes of an experimental stimuli to apply and the associated measurements that should be taken to optimally constrain the uncertain dynamics of a biological system under study. The ideal global solution for this experiment design problem is generally computationally intractable because of parametric uncertainties in the mathematical model of the biological system. Others have addressed this issue by limiting the solution to a local estimate of the model parameters. Here we present an approach that is independent of the local parameter constraint. This approach is made computationally efficient and tractable by the use of: (1) sparse grid interpolation that approximates the biological system dynamics, (2) representative parameters that uniformly represent the data-consistent dynamical space, and (3) probability weights of the represented experimentally distinguishable dynamics. Our approach identifies data-consistent representative parameters using sparse grid interpolants, constructs the optimal input sequence from a greedy search, and defines the associated optimal measurements using a scenario tree. We explore the optimality of this MBDOE algorithm using a 3-dimensional Hes1 model and a 19-dimensional T-cell receptor model. The 19-dimensional T-cell model also demonstrates the MBDOE algorithm’s scalability to higher dimensions. In both cases, the dynamical uncertainty region that bounds the trajectories of the target system states were reduced by as much as 86% and 99% respectively after completing the designed experiments in silico. Our results suggest that for resolving dynamical uncertainty, the ability to design an input sequence paired with its associated measurements is particularly important when limited by the number of measurements.     

Neural network models for biological waste-gas treatment systems

This paper outlines the procedure for developing artificial neural network (ANN) based models for three bioreactor configurations used for waste-gas treatment. The three bioreactor configurations chosen for this modelling work were: biofilter (BF), continuous stirred tank bioreactor (CSTB) and monolith bioreactor (MB). Using styrene as the model pollutant, this paper also serves as a general database of information pertaining to the bioreactor operation and important factors affecting gas-phase styrene removal in these biological systems. Biological waste-gas treatment systems are considered to be both advantageous and economically effective in treating a stream of polluted air containing low to moderate concentrations of the target contaminant, over a rather wide range of gas-flow rates. The bioreactors were inoculated with the fungus Sporothrix variecibatus, and their performances were evaluated at different empty bed residence times (EBRT), and at different inlet styrene concentrations (C(i)). The experimental data from these bioreactors were modelled to predict the bioreactors performance in terms of their removal efficiency (RE, %), by adequate training and testing of a three-layered back propagation neural network (input layer-hidden layer-output layer). Two models (BIOF1 and BIOF2) were developed for the BF with different combinations of easily measurable BF parameters as the inputs, that is concentration (gm(-3)), unit flow (h(-1)) and pressure drop (cm of H(2)O). The model developed for the CSTB used two inputs (concentration and unit flow), while the model for the MB had three inputs (concentration, G/L (gas/liquid) ratio, and pressure drop). Sensitivity analysis in the form of absolute average sensitivity (AAS) was performed for all the developed ANN models to ascertain the importance of the different input parameters, and to assess their direct effect on the bioreactors performance. The performance of the models was estimated by the regression coefficient values (R(2)) for the test data set. The results obtained from this modelling work can be useful for obtaining important relationships between different bioreactor parameters and for estimating their safe operating regimes.     

On-line optimization of recombinant product in a fed-batch bioreactor

In this paper, an efficient scheme for on-line optimization of a recombinant product in a fed-batch bioreactor is presented. This scheme is based on the parametrization of the system states and the elimination of a subset of the dynamic equations in the mathematical model of the fed-batch bioreactor. The fed-batch bioreactor considered here involves the production of chloramphenicol acetyltransferase (CAT) in a genetically modified E. coli. The optimal inducer and the glucose feed rates are obtained using the proposed optimization approach. This approach is compared with the traditional optimization approach, where all the states and the manipulated variables are parametrized. The approach presented in this paper results in a 5-fold improvement in the computational time for the recombinant product optimization. The optimization technique is employed in an on-line optimization scheme, when parametric drift and a disturbance in the manipulated variable is present. Feedback from the process is introduced through resetting the initial conditions of the model and through an observer for estimating the time varying parameter. The simulation results indicated improvement in the amount of product formed, when the optimal profile is regenerated during the course of the batch.     

Dynamic analysis of lactic acid fermentation in membrane bioreactor

In this paper, a mathematical model for the lactic acid fermentation in membrane bioreactor is investigated. This novel theoretical framework could result in an objective criterion on how to control the substrate concentration in order to keep a sustainable and steady output of lactic acid. Firstly, continuous input substrate is taken. The existence and local stability of two equilibria are studied. According to Poincaré-Bendixson Theorem, we obtain the conditions for the globally asymptotical stability of the equilibrium. Secondly, impulsive input substrate is also considered. Using Floquet's theorem and small-amplitude perturbation, we obtain the biomass-free periodic solution is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations.