Modeling of Biopharmaceutical Processes—Part 1: Microbial and Mammalian Unit Operations

ABSTRACT

The scale-up of processes from bench to commercial scale is challenging because of uncertainties about the physiochemical environment experienced by the cells at large scale. Process modeling tools can be useful in facilitating the scale-up and technology transfer of microbial and mammalian processes by ensuring that the process requirements can be met by the facility capabilities.

Economics of scale and significant improvements made in the understanding of bioprocesses, design of equipment, and construction of facilities, have driven commercial production of biotech molecules to larger scales in the last decade. Microbial and mammalian commercial processes are routinely performed at 10,000 L or greater amongst the major biotech companies and contract manufacturing organizations. However, the scale-up of processes from bench to commercial scale is challenging, with uncertainties about the physicochemical environment experienced by the cells at large scale. Some of the scale-dependent bioreactor differences are not readily influenced. As such, these differences need to be fully understood to determine the potential impact on culture performance.

Avecia Biologics Limited

This article is the twelfth in the Elements of Biopharmaceutical Production series and focuses on process modeling tools that can be useful in facilitating the scale-up and technology transfer of microbial and mammalian processes. Issues addressed include mixing and gassing characteristics, pressure differences, and heat transfer rates (fermentation). The underlying principles are presented along with examples from existing biotech processes.

MIXING IN BIOREACTORS

Bioreactor mixing is required to deliver process requirements for mass transfer of dissolved oxygen and carbon dioxide (in cell culture), and to aid in convective heat transfer for control of temperature (in fermentation). In addition, mixing strives to achieve bioreactor liquid homogeneity with respect to cell density, gas dispersion, and chemical gradients (pH and nutrients). In the case of mammalian cells, however, excessive mixing by impeller agitation or gas sparging may result in cell damage because of mechanical hydrodynamic shear (e.g., microscale eddies) or interfacial shear by bubble bursting events.¹ As a result, a balance between cellular requirements, cellular sensitivities, and bioreactor capability is key to defining a comparable operating space that ensures consistent process performance between scales.

Anurag S. Rathore, PhD

The Impact of Mixing on pH Gradient

Gradients in pH are influenced by bulk mix times, the type and concentration of titrant used (acid or base), pH control strategy, pH probe location, and titrant addition location. To determine the impact of pH gradients on cell culture performance, it is important to understand the magnitude of the pH excursion with regard to deviation from set-point and the excursion duration. Once this is established, the potential impact on process performance can be evaluated and resolved as required. The magnitude and duration of the pH gradients can be measured directly by control simulations in buffer solutions at large scale.^2,3 However, this can be challenging with regard to pH probe location and probe response time.

Computational fluid dynamics (CFD) can be used to model pH gradients with bolus titrant additions, and reasonable agreement with wet testing has been observed for base addition at 2,000 L (Figure 1). Initial discrepancies in the magnitude of the pH deviations over the first 22 seconds between wet testing and CFD are attributed to differences in measured and assumed locations for base addition and pH probe placement. Although CFD can be applied to assess bioreactor design capability and process scale-up, care should be taken to assess CFD predictions against the model assumptions and verified with wet testing.

Figure 1. Comparison of transient pH profiles from the wet test and computational fluid dynamics (CFD) simulation

A solution to minimize pH gradients and prevent over-addition of titrant is to improve bulk mixing times by increasing the agitation speed in view of the cell sensitivities to hydrodynamic shear and foaming. Another best practice is to direct base addition to a well-mixed bioreactor location, ideally subsurface (adjacent to impellers) In large bioreactors, the distance between the online control probe (typically located in the impeller region) and base addition location (typically at liquid surface) can lead to differences in measured and actual pH values at the titrant addition. Optimization of the titrant addition strategy (pulse frequency and volume) with respect to bulk mix times may also be required. Finally, the pH control strategy in relation to pH "dead band" or "controller dead zone" implementation may require fine-tuning to prevent acid-base cycling. Some other important considerations with pH control are sample handling, offline pH measurement, and probe standardization. Inconsistent practices with scale-up and process transfer may contribute to differences in pH control and process performance.

Impact of Mixing on Oxygen Distribution

Although dissolved oxygen (DO) generally is kept constant between scales, attention to DO probe zero and span calibration are required to fully represent process conditions. The relationship between DO saturation (%) and partial pressure (mm Hg) should be taken into account between sites and scales. The impact of bioreactor hydrostatic pressure at large scale also needs to be considered on dissolved gasses (DO and pCO₂). Depending on the mixing characteristics, liquid height, and location of the controlling DO probe, the actual DO (and pCO₂) experienced by the cells will vary depending on their location in the bioreactor. In combination with agitation power input per unit volume (P/V), the superficial gas velocity will influence the oxygen mass transfer rate (k_La). At typical agitation speeds with nonclumping mammalian cells, cell culture processes are considered more sensitive to interfacial shear by bubble bursting events than bulk hydrodynamic shear or microscale turbulence (Kolmogorov eddy size). Superficial gas velocities should be modeled to provide sufficient kLa at the selected agitation speed but not so overly aggressive as to incur cell damage, excessive gas stripping, or foaming.

For high cell density microbial processes, additional concerns exist around oxygen consumption and heat removal. Oxygen uptake rate (OUR) has a strong correlation with the heat generation rate and carbon evolution rate (CER). This is because of the relationship between cellular respiration and metabolism in aerobic microorganisms and the high cell densities that allows these values to be accurately determined. These data are important whenever a process is transferred into a new facility or increased in scale so that the process requirements (peak OUR, peak heat generation rate) can be assessed against the facility capabilities (maximum oxygen transfer rate, maximum heat removal rate).

Calculation of Agitation Speed

As mentioned above, selection of appropriate mass transfer conditions is important to achieve consistent cell culture and fermentation performance across sites and scales. During scale-up, for most situations the tank geometry and hardware (impellers, sparger, baffles, etc.) are not subject to change. Therefore, the focus is on defining appropriate agitation and sparge gassing conditions to achieve consistent performance across sites and scales.^4–6

For industrial-scale cell culture bioreactors, mixing times are typically on the order of three minutes or less. Mixing times of this order of magnitude have been sufficient to achieve consistent performance across scales for many industrial cell culture fed-batch processes. They have historically been estimated from impeller discharge rates using an equation such as^7,8

in which θ_m is the mixing time, V is the liquid volume, N is the agitation speed, D is the impeller diameter, N_Q is the impeller flow number (provided by the impeller manufacturer), and k is a constant related to the number of volume turnovers required to achieve homogeneity. Typically, five volume turnovers are assumed to result in homogeneity, but the actual impeller pumping rate is higher than the impeller discharge rate because of momentum transfer to the surrounding fluid. Therefore a multiplier, k, of three is often used. More recently, it has been suggested, based on turbulence theory, that the mixing time should be independent of impeller type⁹

in which T is the tank diameter (m), D is the impeller diameter (m), P is the impeller power input (W), V is the liquid volume (m³), and ρ is the fluid density (kg/m³). More accurate mixing times can be calculated using more complex models, for example, those based on CFD as described earlier.

Shear rate is another agitation-related parameter that is often evaluated, especially for cell culture applications. Because mammalian cells lack a cell wall, they are more susceptible to shear damage than microbial cells. Impeller tip speeds can be correlated to maximum impeller shear rates, and therefore, constant tip speed has been suggested as a scaling criterion for mammalian cell culture agitation.¹⁰ However, it has been shown by multiple investigators that impeller shear rates commonly used for cell culture applications are orders of magnitude below the shear rates required to cause cell damage.¹¹ Therefore, use of tip speed as a primary agitation scaling parameter is not recommended.

Power input (P/V)or mean specific energy dissipation rate is a parameter that is more commonly used for scaling agitation across sites or scales. The mean energy dissipation can be calculated from:

in which ε-mean_T is the mean energy dissipation rate (W/kg), P is the power input (W), V is the liquid volume (m³) and N_p is the impeller power number. Mean impeller energy dissipation rates typically used for mammalian cell cultures range from 0.001 to 0.050 W/kg (1 to 50 W/m³).¹⁰ A consequence of scaling agitation at constant energy dissipation is that the length scale of turbulent eddies is expected to be constant. The Kolmogorov microscale of turbulence is related to energy dissipation through the following equation:

in which λ is the Kolmogorov length scale (cm), υ is the kinematic viscosity (cm²/s) and ε-mean_T is expressed as cm²/s³.

When the length scale for turbulent eddies approaches the length scale of the cells in culture, cell damage may occur. This theory has been applied to microcarrier cultures, in which cell death can be correlated to eddy lengths that are smaller than the microcarrier diameter, and to suspension cell cultures, where cell aggregate sizes were found to correlate with eddy length.^12,13 It should be noted that energy does not dissipate uniformly over the entire bioreactor volume, and that local energy dissipation rates may differ significantly compared to the mean energy dissipation rate. Despite this caveat, the mean energy dissipation rate is most often used in agitation scaling calculations.

Figure 2. Impact of agitation speed on product titer in a scale-down production bioreactor model

Case Study: Scale-Up of a Mammalian Cell-Culture Unit Operation

In a case study involving technology transfer of a biotech process, we evaluated the impact of agitation speed on cell culture performance. Agitation speed was varied in a small-scale model bioreactor over a range that encompassed both the tip-speed and energy dissipation rate calculated for the full-scale bioreactor. As shown in Figure 2, we found that product titer correlated with agitation speed across this range. The cause for the titer correlation was found to be specific productivity, rather than cell growth. When the small scale model data are compared to manufacturing scale data as shown in Figure 3, it is evident that the specific productivity matched across scales for the agitation scaled by energy dissipation (275 rpm), whereas the specific productivity was lower for the constant tip speed condition (500 rpm).

Figure 3. Cellular specific productivity at manufacturing scale compared to a scale-down model operated with tip-speed agitation scaling (500 rpm) and energy dissipation scaling (275 rpm). Statistical analysis by Dunnett's method shows that scaling by energy dissipation more accurately reflects the manufacturing scale performance versus scaling by tip speed.

Further, on visual observations of microscopic cell count images (Figure 4), cell clumping observed when agitation was scaled by constant mean energy dissipation (275 rpm) was more consistent with the manufacturing scale than when agitation was scaled by tip speed (500 rpm). These results are consistent with observations reported in the literature that the size of cell clumps is related to the Kolmogorov eddy length.¹⁵ The turbulent eddies serve to disrupt cell aggregates that are comparable in size to the turbulent length scale. Because the eddy length scale is a function of energy dissipation rate as described above, cell clumping is expected to correlate with energy dissipation rate. A possible explanation for the increased cellular specific productivity is that the cells in moderate sized clumps are more productive than individual cells. Another possibility is that cell counts are less accurate for the highly clumped cultures, and the apparent changes in cell-specific productivity could be related to changes in cell density. Regardless, it is clear from these results that the best match to the manufacturing scale data was achieved with a constant energy dissipation rate scaling strategy, rather than constant tip speed scaling.

Figure 4. The impact of agitation speed on harvest day cell aggregation. Cell clumping (middle figure) was more consistent with the manufacturing scale (left figure) when agitation was scaled by constant mean energy dissipation than when agitation was scaled by tip speed (right figure).

In addition to facilitating liquid/ liquid mixing, agitation conditions can impact gas/liquid mass transfer. Oxygen is supplied and carbon dioxide (CO₂) removed from most industrial cell cultures through sparging of gas bubbles through the bioreactor broth. The bubble gas/liquid mass transfer is a function of agitation conditions and the characteristics of the sparge gas inlet. The impact of these parameters on bubble gas/liquid mass transfer is most often described in terms of the mass transfer coefficient, k_La_B:

in which P/V is the impeller power input normalized to liquid volume, Q is the sparge gas flow rate and k, α, and β are empirically fitted parameters. The fitted parameters can vary as a function of the sparge inlet characteristics, the most important of which may be orifice size. The size and number of air inlet orifices determine the superficial gas velocity and the resulting bubble size. Bubble size impacts the surface area to volume ratio of the bubble, and consequently the mass transfer efficiency. Smaller bubbles have a greater surface area relative to volume and hence they lead to more efficient mass transfer per volume of gas. Despite their mass transfer efficiency, very small (" 1 mm) bubbles are not favored for use in industrial mammalian cell culture for multiple reasons. A significant problem associated with sparging of mammalian cell cultures is cell death because of high shear, which occurs primarily because of bubble rupture at the liquid surface.¹⁴ Surfactants such as Pluronic F-68 are typically added to cell culture media to prevent cells from sticking to bubbles as they rise through the liquid, but damage can still occur to cells in the vicinity of bubble ruptures.¹⁵ Larger bubbles have lower maximum energy dissipation rates associated with bubble ruptures, which is consistent with literature observations that larger bubbles are less damaging to cell cultures.¹¹ Further, small bubbles lead to less effective removal of carbon dioxide. Because of their high mass transfer efficiency, volumetric gas flow rates required to control dissolved oxygen at set-point are minimized, and hence, the bubbles saturate with a higher concentration of CO₂. Accumulation of carbon dioxide can have a negative impact on the cell culture.^16,17 By using larger bubbles, higher volumetric gas flows are required to control dissolved oxygen, and CO² is more effectively removed.¹⁷ Finally, smaller bubbles lead to generation of more stable foam layers, and hence higher concentrations of antifoam may be required. For these reasons, larger bubbles (on the order of 5 mm) are preferred for industrial cell culture.¹¹

HEAT AND OXYGEN TRANSFER IN BIOREACTORS FOR HIGH CELL DENSITY MICROBIAL PROCESSES

Oxygen update rate (OUR) is defined as the rate of oxygen that is consumed by a given volume of fermentation broth, and this variable fluctuates over the course of a fermentation process depending on many factors such as the metabolic state of the cells, the level of oxygen saturation in the culture, and the volume of the culture itself relative to the cell density. Carbon dioxide evolution rate (CER) is defined as the rate of CO₂ evolution from a carbon nutrient source (usually glucose in fermentation processes) and can be used to determine the level of glucose utilization in the culture relative to cell density and the state of cellular metabolism through comparison with OUR. For most fermentation processes, the desired ratio of CER to OUR (RQ) is approximately 1.0. This correlates to six CO₂ molecules produced for every six oxygen (O₂) molecules that are consumed during the aerobic metabolism of a six-carbon sugar such as glucose. An RQ value that is noticeably lower than 1.0 indicates that the cells are using a different nutrient source for energy. In most industrial fermentation situations, it is desirable to maintain the RQ above 0.75 for the duration of the culture to ensure that the metabolic state of the cells is consistent. OUR and CER can be readily calculated using the following expressions:^18–21

in which QO₂ is the volumetric flow rate of O₂ into the fermenter in standard liter per minute (SLPM); Q_Air is the volumetric flow rate of air into the fermenter in standard liter per minute (SLPM); V_O2 is the molar volume of O₂ in the inlet O₂ (L/mol); V_Air is the molar volume of Air in the inlet air (L/mol); X_O2,in is the mole fraction of O₂ in the inlet air (mmol_O2/mmol_Air); X_O2,out is the mole fraction of O₂ in the outlet gas (mmol_O2/mmol_Exhaust); X_N2,in is the mole fraction of N₂ in the inlet Air (mmol_N2/mmol_Air); X_N2,out is the mole fraction of N₂ in the Outlet Gas (mmol_N2/mmol_Exhaust); X_CO2,in is the mole fraction of CO₂ in the inlet air (mmol_CO2/mmol_Air); and X_CO2,out is the mole fraction of CO₂ in the outlet gas (mmol_CO2/mmol_Exhaust). The inlet gas flow rates and the molar concentrations of the outlet gases can be measured by a volumetric gas flow meter or an in-line mass spectrometer. Derivation of equations 6 and 7 is based on the assumption that the water content in the gas does not affect the composition of the gas or the accuracy of the mass spectrometer reading.

Total heat generation rate in a bacterial fermentation system is the sum of all of non-negligible sources of heat generation and heat loss that typically consist of cellular metabolism, agitator motion, evaporation, feed addition, and gas addition. The following formula can be used to calculate the net rate of heat generation (H_net) in a fermentation system:

in which H_metab is the heat generation because of cellular metabolism, H_agit is the heat generation because of mechanical motion of the agitator(s), H_evap is the heat loss due to evaporation, H_feed is the heat loss because of addition of feed held at room temperature, and H_gas is the heat loss because of addition of supply air/O₂ at room temperature.

The component H_metab can be directly correlated to OUR and has been shown to account for approximately 80% of the net heat generation (i.e., heat generation from agitator motion accounts for ~20% of heat generation). However, when all major sources of process-related heat loss are taken into account, H_net ≈ H_metab. Because culture temperature is typically controlled at a constant setpoint during a fermentation process, H_net = H_cooling. Hence, metabolic heat generation rate can be measured fairly accurately by calculating the amount of heat removed from the cooling jacket (H_metab ≈ H_cooling).

Rate of Heat Removal

The rate of heat removal through the cooling jacket and cooling coils can be determined from the outputs of the temperature control system on the fermenter. In a commonly used control configuration, the temperature of water recirculated through the jacket or coils is regulated by an incremental addition of chilled water. The water in the jacket is warmed up through contact with the fermenter wall, and after it exits the jacket, a regulated amount of chilled water is added to cool down the water. It then enters the jacket again through a loop, acting as a heat exchange fluid to remove as much heat as needed from the fermenter to control the temperature at the setpoint. Using this setup, the heat removal rate can be calculated using the following formula:

in which Q_water is the volumetric flow rate of the water in the jacket (L/min), ^ρwater is the density of water (kg/L), C_{p, water} is the mass heat capacity of water (kJ/kg–K), T^out is the temperature of the water in the jacket downstream of the fermenter (°C), T_in is the temperature of the water in the jacket upstream of the fermenter (°C), and m_culture is the mass of the culture in the fermenter (kg). By measuring the volumetric flow rate of the water in the jacket and the temperature of the water at both the inlet and the outlet of the jacket, one can determine the heat removal rate from the cooling jacket at any given moment over the course of a fermentation process.

OUR data have been shown to correlate well with the heat generation rate from cellular metabolism in bacterial fermentation processes, with 1 mole of oxygen being consumed during cellular metabolism to generate ~115 kcal of heat.²¹ The following heat-based OUR can be derived from the correlation and used for comparing to OUR determined from the mass spectrometer:

in which units for OUR are mmol/kg–hr and for H_metab, J/kg–hr.

Case Study: Scale-Up of a Microbial Fermentation Unit Operation

In a case study of microbial fermentation, inlet gas flow rates and the molar concentrations of the outlet gases were measured by a volumetric gas flow meter and an in-line mass spectrometer (Perkin-Elmer MGA1200). Data were captured continuously using the PI data historian software, and the heat generation rate profile from the bioreactor was calculated as described above and compared to the OUR profile. Relevant OUR and RQ profiles from three microbial runs performed in a 300-L production fermenter are shown in Figures 5 and 6, respectively. The peak OUR value from the spectrometer was found to be approximately 300 mmol/kg/hr (Figure 5), which matched the maximum value of the OUR based off the heat removal rate measurements. The RQ was found to be ~1.0 during the first half of the induction phase, which was also consistent with the target for an aerobic E.coli process.

Figure 5. Oxygen uptake rate (OUR) measurements using mass spectroscopy for a high-cell density microbial process for three runs at 2,000-L scale. The peak OUR is observed to be 300 mmol/kg/hr.

CONCLUSION AND RECOMMENDATIONS

There are a number of process modeling tools that can be useful in facilitating scale-up and technology transfer of microbial and mammalian processes. Application of scale-up predictors using empirical calculations should be used to assess large-scale bioreactor capability with respect to gas flows and agitation speeds in relation to constant agitation (P/V), tip speeds, superficial gas velocities, and predicted k^La. Information pertaining to integrated shear factors, shear rates, and Kolmogorov eddy size (B5m) also provides useful information when comparing bioreactor conditions at different scales. Calculations of oxygen uptake rate (OUR) and carbon dioxide evolution rate (CER) for high cell density microbial processes can be useful to ensure that the process requirements (peak OUR, peak heat generation rate) can be met by the facility capabilities (maximum oxygen transfer rate, maximum heat removal rate).

Figure 6. Ratio of CER to OUR (RQ) measurements using mass spectroscopy for a high-cell density microbial process. The RQ of ~1.0 is consistent with the target for an aerobic E.coli process.

Anurag S.Rathore, PhD, is the director of process development, Ken Green is a principal scientist, and Yas Hashimura is a senior engineer, all at Amgen,Inc., Thousand Oaks, CA, 805.447.1000, asrathore@yahoo.comGreg Nyberg is a principal scientist at Amgen,Inc., Boulder, CO.

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