Processes 2018, 6,82
report on the kinetic parameters for Chinese hamster ovary (CHO) cell batch culture related to mAb
production [32]. Therefore, in this work, instead of final protein concentration, the time-integrated
value of biomass is the subject of maximization. The specific attributes of large-scale mammalian cell
cultures, e.g., high level of spatial heterogeneity and sensitivity of organisms to physical environmental
stimuli, demand a modeling framework that captures both the biology and the hydrodynamics of the
system and also their interactions. This work aims to improve on the current state of lumped-parameter
bioreactor modeling by capturing the interactions of system components. The selection of components
is based on experimental observations. The formulation is devised in order to take into account
the inherent dynamics of the system, maintain computational tractability, and couple the model
with optimization solvers. In the next section, the modeling and integration of hydrodynamics and
biological processes are discussed and the application of compartmental modeling for maintaining
computational feasibility is explained. In Section 3, the integrated model is used to find a near-optimal
operation scenario. Section 4 is a discussion of the challenges and potential in the area of modeling
and the optimization of a bioreactor operation.
2. Development of a Dynamic, Integrated, and Computationally Feasible Bioreactor Model
This work seeks to improve the reliability of bioreactor models by capturing the effects of
hydrodynamics on the performance of a bioreactor. Computational Fluid Dynamics (CFD) simulation
is employed to calculate the attributes of flow required for this purpose. Biological processes are
inherently dynamic; therefore, solving the problem requires dynamic CFD simulations. Dynamic CFD
simulations demand the discretization of time using step sizes in the range of 0.01 to 0.1 s [33–37],
even for a small reactor. A CPU time of 12 s per CPU for each time step has been reported [34], and
0.5 to 2 s per CPU has been observed for every iteration [36]. Considering the reported CPU times
and the fact that bioreactors are usually operated in fed-batch mode for up to two weeks, dynamic
CFD simulation of the entire operation is computationally unfeasible. To tackle this problem, in our
earlier work a two-step framework was developed [38]. This method is based on the assumption that
the effects of metabolic activities on hydrodynamics are negligible [18,39]. The simulation is run in
two steady-state and dynamic steps. First the steady state of the two-phase flow inside the bioreactor
for specific values of impeller rotation speed and gas sparging flowrate is calculated. At this stage
cells are considered merely components of the liquid phase without any biological function. Then
the problem is solved dynamically to obtain the evolution of biophase over time. In the dynamic
phase of the simulation only species conservation is considered. During the dynamic run, the process
parameters of impeller rotation speed and gas sparging flowrate are fixed and the flow remains at its
fully developed steady-state condition. Therefore the values of velocity, gas volume fraction, kinetic
energy, and energy dissipation rate remain approximately constant. Obtaining the solution in two
stages replaces the problem with two smaller systems of equations. This allows for the specification of
larger time step sizes and improves the convergence of the simulation.
Deconstructing the problem into steady-state flow and dynamic metabolism problems and
solving them sequentially seems to successfully address the batch operation with constant process
parameters [38]. Although this simulation procedure exploits off-the-shelf software packages, it is
still limited to simple case studies. The improvement in computational feasibility in order to simulate
fed-batch operation and study effects of composition and schedule of feeding on the performance of
bioreactor is achieved through the development of a compartmental model. Compartmental modeling
facilitates time–space decomposition, which significantly reduces computation. Therefore, it has been
widely used for modeling the hydrodynamics of stirred tanks [40–43]. In this methodology the reactor
is divided into well-mixed zones that do not contain segregated regions. Then fluxes between the zones
are calculated based on the expected flow patterns resulting from CFD simulations or experimental
data [18,40,41,44]. A number of states of operation are defined by discretizing the process parameters
of impeller rotation speed, gas sparging flow rate, and operating volume. Data on fully developed
steady state flow under all pre-defined operation states are obtained and stored in flow matrices.
117
report on the kinetic parameters for Chinese hamster ovary (CHO) cell batch culture related to mAb
production [32]. Therefore, in this work, instead of final protein concentration, the time-integrated
value of biomass is the subject of maximization. The specific attributes of large-scale mammalian cell
cultures, e.g., high level of spatial heterogeneity and sensitivity of organisms to physical environmental
stimuli, demand a modeling framework that captures both the biology and the hydrodynamics of the
system and also their interactions. This work aims to improve on the current state of lumped-parameter
bioreactor modeling by capturing the interactions of system components. The selection of components
is based on experimental observations. The formulation is devised in order to take into account
the inherent dynamics of the system, maintain computational tractability, and couple the model
with optimization solvers. In the next section, the modeling and integration of hydrodynamics and
biological processes are discussed and the application of compartmental modeling for maintaining
computational feasibility is explained. In Section 3, the integrated model is used to find a near-optimal
operation scenario. Section 4 is a discussion of the challenges and potential in the area of modeling
and the optimization of a bioreactor operation.
2. Development of a Dynamic, Integrated, and Computationally Feasible Bioreactor Model
This work seeks to improve the reliability of bioreactor models by capturing the effects of
hydrodynamics on the performance of a bioreactor. Computational Fluid Dynamics (CFD) simulation
is employed to calculate the attributes of flow required for this purpose. Biological processes are
inherently dynamic; therefore, solving the problem requires dynamic CFD simulations. Dynamic CFD
simulations demand the discretization of time using step sizes in the range of 0.01 to 0.1 s [33–37],
even for a small reactor. A CPU time of 12 s per CPU for each time step has been reported [34], and
0.5 to 2 s per CPU has been observed for every iteration [36]. Considering the reported CPU times
and the fact that bioreactors are usually operated in fed-batch mode for up to two weeks, dynamic
CFD simulation of the entire operation is computationally unfeasible. To tackle this problem, in our
earlier work a two-step framework was developed [38]. This method is based on the assumption that
the effects of metabolic activities on hydrodynamics are negligible [18,39]. The simulation is run in
two steady-state and dynamic steps. First the steady state of the two-phase flow inside the bioreactor
for specific values of impeller rotation speed and gas sparging flowrate is calculated. At this stage
cells are considered merely components of the liquid phase without any biological function. Then
the problem is solved dynamically to obtain the evolution of biophase over time. In the dynamic
phase of the simulation only species conservation is considered. During the dynamic run, the process
parameters of impeller rotation speed and gas sparging flowrate are fixed and the flow remains at its
fully developed steady-state condition. Therefore the values of velocity, gas volume fraction, kinetic
energy, and energy dissipation rate remain approximately constant. Obtaining the solution in two
stages replaces the problem with two smaller systems of equations. This allows for the specification of
larger time step sizes and improves the convergence of the simulation.
Deconstructing the problem into steady-state flow and dynamic metabolism problems and
solving them sequentially seems to successfully address the batch operation with constant process
parameters [38]. Although this simulation procedure exploits off-the-shelf software packages, it is
still limited to simple case studies. The improvement in computational feasibility in order to simulate
fed-batch operation and study effects of composition and schedule of feeding on the performance of
bioreactor is achieved through the development of a compartmental model. Compartmental modeling
facilitates time–space decomposition, which significantly reduces computation. Therefore, it has been
widely used for modeling the hydrodynamics of stirred tanks [40–43]. In this methodology the reactor
is divided into well-mixed zones that do not contain segregated regions. Then fluxes between the zones
are calculated based on the expected flow patterns resulting from CFD simulations or experimental
data [18,40,41,44]. A number of states of operation are defined by discretizing the process parameters
of impeller rotation speed, gas sparging flow rate, and operating volume. Data on fully developed
steady state flow under all pre-defined operation states are obtained and stored in flow matrices.
117