Updated guidelines on agitation and vessel volumes for linear speed and falling films (Generation R and S vessels)
Linear speed and falling film (FF) are two parameters associated with iCELLis™ 500+ single-use fixed-bed bioreactor vessels that can be utilized during process design, to ensure the cell environment and nutrient supply remains the same during process scale-up. Both parameters are directly correlated to agitation speed and liquid volume whereby:
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Agitation speed increases the linear speed within the bioreactor vessel.
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Liquid volumes determine falling films within the vessel (as does agitation speed).
Updates to both the vessels and system hardware have resulted in our new Generation R and Generation S vessels. Recognizing that these important parameters will have changed since our previous studies on Generation Q vessels, this application note provides data on characterization of the relationship between linear speed, falling film and liquid volume for Generation R and S.
By conducting expanded and more thorough tests, we have determined the new rpm, linear speed, liquid volume, and falling film height relationships in the iCELLis™ 500+ Generation R and Generation S vessels for all surface area offerings (66 to 500 m2).
From these experimental results we have created guidelines to help you during process design, and provided further knowledge on these important parameters that will allow you to confidently operate the iCELLis™ 500+ single-use fixed-bed bioreactor in ongoing and new bioprocesses.
Introduction
What is linear speed inside a bioreactor?
The linear speed (also commonly referred to as linear velocity or volumetric flow rate) inside the iCELLis™ 500+ bioreactor vessel is the velocity of liquid media flowing through the fixed bed. Flow is established inside the iCELLis™ 500+ bioreactor vessel via a built-in impeller, causing media to flow upward and through the fixed bed. The media then falls along the outer wall of the fixed bed, creating a waterfall flow pattern called falling film (FF). This facilitates media oxygenation and mixing (Figure 1). Linear speed is dependent on multiple variables including the impeller agitation speed (rpm), the total surface area of the carriers within the vessel, the physical geometry/design of the vessel, and the FF height (directly linked to the total liquid volume).
Fig 1. A cross section of the iCELLis™ 500+ bioreactor vessel with a media flow path shown by arrows. The colors represent the oxygenation of the media as it is absorbed by cells in the fixed bed, and subsequently the oxygenation is replenished as media falls over the edge and down the side of the fixed bed.
Linear speeds were previously measured on the Generation Q (Gen Q) version of the iCELLis™ 500+ bioreactor vessel design and published in the Instructions for Use (USD3312c). However, numerous improvements have been incorporated into both the Generation R (Gen R) and Generation S (Gen S) vessel versions. Table 1 outlines the design changes implemented in these vessels.
Table 1. Design changes implemented in Gen R and Gen S iCELLis™ 500+ bioreactor vessels
| Description of internal vessel design changes | Generation |
| Improved tubing layout | R |
| New lid design (integrated ribs for more rigidity) | R |
| Pump housing basket support (PHBS) now made of two separate parts | R |
| Addition of a 4” sample port (optional) | R |
| Lid and vessels closed by welding (previous versions closed by bolting lid to vessel) | R |
| Anchoring mechanism of the fixed bed | R |
| Improved biomass holder sealing (dovetail groove design) | R |
| Improved draining – extra drain tube to drain PHBS faster | S |
| Improved draining – added tube connector at main drain line (reduce residual volume) | S |
| Improved biomass sensor integration – portion of top mesh/net cut out | S |
Gen R and Gen S vessels differ in the tubing assemblies attached to the headplate which extend down into the vessel. For the purposes of linear speed testing they are functionally equivalent because the bioreactor headplate must be removed when performing linear speed testing. We expect any differences in linear speed to be negligible between these generations. Therefore, the vessel generation referenced throughout the rest of this document will be Gen R/S, to indicate the dual applicability of these linear speed correlations.
Unrelated to iCELLis™ 500+ bioreactor vessel improvements, we have developed an update to the iCELLis™ 500+ hardware system that results in more stable weight measurements called the iCELLis™ 500+ agitation cap. Over the course of a batch, a small amount of vessel deformation can occur, resulting in a changed distance between the magnets in the agitator shaft and the vessel impeller. In cases of high deformation, the vessel may come to rest partially on the agitator shaft, which is not on the load cells. The purpose of the agitation cap is to cover the agitator shaft and ensure that the magnets do not push together, allowing all the vessel weight to rest on the load cells. This improvement results in a reduction in weight measurement fluctuations, but there are other trickle-down effects as well:
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More consistent FF height and oxygen transfer rate.
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More stable biomass sensor measurements (the biomass probe electric field is very sensitive to small volume fluctuations).
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Less required user interventions to maintain consistent FF and bioreactor volume.
In this application note, new rpm, linear speed, liquid volume, and FF height relationships have been characterized using the Gen R and S vessels and the agitation cap.
Methods and materials
The objective of this experiment was to correlate the agitation speed (rpm), liquid volume, and bioreactor FF height to linear speed in the iCELLis™ 500+ Gen R/S bioreactor vessel and updated agitation cap assembly. All commercially available iCELLis™ 500+ bioreactor vessel surface area offerings, within the range 66 to 500 m2, were tested to measure linear speed. Linear speed was measured at four different rpm settings for each of the three FF heights tested: 2 cm, 6 cm, and 10 cm (Table 2).
The rpm settings and FF heights were chosen to cover a broad linear speed range. The linear speed was measured at four equally spaced positions around the circumference of the fixed bed, to account for any variability in fixed bed packing. In addition, the bioreactor vessel weight was recorded at each test condition as it was necessary to adjust the liquid volume within the vessel at each rpm setting to maintain the desired FF height. Vessel weights were then directly correlated with liquid volumes to provide for analysis of linear speed and vessel volume. The same iCELLis™ 500+ vessel shell was used during all testing with fresh folded carrier packing and plate/spacer changes made depending on the surface area being tested. It is assumed that the vessel changes made during testing will be the same as individually manufactured vessels.
Table 2. rpm settings evaluated at each FF height
| rpm / 2 cm FF height | rpm / 6 cm FF height | rpm / 10 cm FF height |
| 175 | 225 | 275 |
| 225 | 275 | 325 |
| 275 | 325 | 375 |
| 325 | 375 | 425 |
Linear speed testing was performed using de-ionized (DI) water containing 100 mL Antibiotic-Antimycotic at a 37°C setpoint (maintained using the temperature control unit, [TCU]). For linear speed measurement, the top lid of the vessel was removed to gain access to the fixed bed. A flow catcher was positioned on the outer edge of the vessel’s fixed bed such that any liquid exiting from the fixed bed at that position would enter the flow catcher. Tubing was placed into the flow catcher that was also attached on the other end to a flow meter and Levitronix pump. During testing, the flow rate of the water entering the flow catcher from the fixed bed was matched by the Levitronix pump such that the liquid level in the flow catcher remained constant. This steady state flow rate was recorded as a volumetric flow rate (L/min) and used to calculate the linear speed. This process was repeated at each rpm value tested, from lowest to highest RPM. Also, the water pumped out of the flow catcher and through the flow meter was immediately pumped back into the bioreactor vessel to maintain constant volumes during testing. Since it was necessary to remove the iCELLis™ 500+ bioreactor vessel top lid during testing, the inlet/drain tubing attached to the top lid were not present during testing. It is assumed that this difference would have a negligible effect on flow and therefore pose minimal impact to linear speed measurements.
Linear speed calculation
Linear speeds were calculated from the measured flow rate via the following formulae:
Linear speed (vL) is calculated by dividing the liquid flow rate out of the fixed bed (Q) by the cross-sectional area of the fixed bed (A) and the porosity of the carrier material (ϕ). Since the liquid flow rate was measured using a flow catcher during testing, the inner circumference of the flow catcher (1/18th of the fixed bed circumference) was used to calculate the variable A, a slice of the fixed bed area, in the equation. The porosity of the fixed bed (ϕ) only varied with the compaction of the fixed bed. Table 3 provides definitions of the linear speed calculation constants and variables.
Table 3. Linear speed constants and variables
| Constants and variables | Definition or value |
| vL | Linear speed for liquid flow through the fixed bed column (cm/s) |
| Q | Liquid flow rate out of fixed bed column (L/min) |
| A | Fixed bed horizontal cross-sectional area (m2) |
| ϕ | Porosity |
| Vm | Volume of media inside of the fixed bed column with carriers (L) |
| V | Volume of media inside of the fixed bed column without carriers (L) |
| C | Compaction of carrier (g/L or g/cm3) |
| ρPET | Density of carrier material PET (g/cm3) |
| ρPET | 1.38 g/cm3 |
| A |
Flow catcher measures flow from 1/18th of fixed bed (0.015 m2, used for calculations) Total horizontal cross section surface of the fixed bed is 0.264 m2 |
| C1 | 96 g/L (0.096 g/cm3) = compaction 1 (for 66 m2, 133 m2, 333 m2 vessels) |
| C2 | 144 g/L (0.144 g/cm3) = compaction 1.5 (for 100 m2, 200 m2, 500 m2 vessels) |
References
Results
Linear speed test replicates
Due to the complex nature of measuring linear speed in iCELLis™ 500+ bioreactors, the random orientation of carriers resulting from the packing processes, and bed hydration over time, it is important to consider test replicates and evaluate the standard deviation of the tests. The repeatability of linear speed is demonstrated in Figure 2 using a representative data set of 66 m2 and 6 cm FF height.
Fig 2. The results of 4 replicate tests for linear speed in a 66 m2 fixed bed and 6 cm FF height.
There is a small amount of variability in replicates, ranging approximately +/- 0.3 cm/s across rpm. The slope of each test is approximately the same, with some small changes in slope occurring at high rpm, as evidenced in replicate 3.
Linear speed standard deviation by vessel size and FF
To analyze how linear speed behaves during testing, the standard deviation was calculated for each individual vessel at each rpm (Figure 3).
Fig 3. The standard deviation of linear speed calculated across rpm, displayed by vessel size (n= 24).
Standard deviation is up to 0.30 cm/s for all scales, with some additional variability for small, less dense vessels at high rpm. In cell culture applications, a high rpm setting in a small vessel is unlikely to be used because the resulting linear speed does not scale to large vessels and the added gas transfer is not necessary to support the cell population. Excluding those values at 375 and 425 rpm, the average standard deviation for the data set is 0.20 cm/s.
Updated characterization of linear speed for Gen R/S
Although there is some variability in the data, the new linear speed test data is plotted to show the broader range of tested rpm and resulting linear speed (Figure 4).
Fig 4. Graph showing changes in Gen Q- vs R/S-measured linear speeds. Gen Q tests consisted of up to n=3 for each rpm and Gen R/S tests consisted of up to n=32 for each rpm.
Compared to Gen Q, the characterization of linear speed for Gen R/S vessels is more thorough, using a broader, consistent, representative rpm range for each FF, resulting in more replicates per rpm and less extrapolation in models and tools. There are also more than twice the data points in this new study (183 vs 384 total tests).
To achieve the same linear speed in a Gen Q and Gen R/S vessel, agitation must be 50 rpm higher in a Gen R/S vessel. This relationship is true for all sizes and FF heights (only 66 m2 and 500 m2 are shown in Figure 4). Updated rpm and linear speeds across 2, 6, 10 cm FF height for each vessel size are in the appendix.
The linear speed may vary according to the average standard deviation (Figure 3). For example, using 325 rpm in a Gen R/S 500 m2 vessel may produce a linear speed of 0.63 cm/s to 1.03 cm/s in the fixed bed. Conversely, a linear speed of 0.80 in the fixed bed can be produced by the rpm range of 295 to 350.
The previous average linear speed characterization of Gen Q is not significantly different than the new study for any vessel (for example, the 500 m2 vessel, two sample t-test, p=0.27). There is indeed a trend, but it is not yet significant with the number of tests performed in either data set. It is likely that more tests could show a significant difference.
Updated characterization of volumes for maintaining FF height
The updated volumes for falling film heights were recorded and analyzed.
Fig 5. The measured volume for a given rpm and FF height. Gen Q tests were n=6 and Gen R/S tests were n=32.
The average volume to maintain a FF height is slightly less than previously measured at a given rpm. It is approximately 0.5 to1.0 kg lower for FF heights than previously measured. Exact volumes for each vessel size and FF height are displayed in the appendix.
In process, if agitation is increased by 50 rpm to maintain the same linear speed in Gen R/S, then the liquid volume will likely remain the same to achieve the same falling film. If agitation is not increased, linear speed will decrease by ~0.25 cm/s, in turn requiring 0.5 to 1.0 kg less media in the vessel to maintain the same FF height.
It was established that average linear speeds vary in a range of rpm by ~50, then similarly the average liquid volume to maintain a FF height may span 1 kg, or +/-0.5 kg from the volume in Figure 5.
Discussion and conclusion
The present study represents a thorough characterization of linear speeds in the iCELLis™ 500+ bioreactor. Most importantly, the study provides a stronger basis for understanding the necessary rpm and volumes to achieve a target media linear speed through the fixed bed and target FF. Linear speed is an important and complicated parameter for designing and scaling processes in the iCELLis™ 500+ fixed bed bioreactor. Linear speed is also difficult to measure, and the tests are subject to some variability. The average standard deviation for linear speed in this study was +/- 0.20 cm/s and volume for FF height was +/- 0.5 L.
The required agitation rpm to maintain an average linear speed in Gen R/S vessels is trending to ~50 rpm higher than in our previous Gen Q vessels characterization, but it is not statistically significant (P>0.05 in two sample t-tests). Small changes to the vessel housing or reduced variation of load cell readings are plausible contributors to these observed changes. It is also possible that using a more thorough test method and updated hardware has increased the accuracy of linear speed data, and the average is lower than originally expected.
Use of the iCELLis™ 500+ agitation cap is recommended because it results in more stable weight measurements. Weight stability has several positive impacts, including better weight/volume control which determines FF height. Additionally, biomass sensor measurements are also improved, since the biomass probe electric field is very sensitive to small volume fluctuations. This cap is standard on all new skids and can also be ordered for older vessels.
This linear speed update may or may not be biologically relevant, however, if you notice yield changes in the iCELLis™ 500+ bioreactor following shifts to Gen R/S, it could be an indication that the process is sensitive to linear speed changes. In the event of this, it may be prudent to design a test to evaluate differences caused by 50 rpm higher agitation which mimics the linear speed previously reported from Gen Q. However, the updated dataset outlined here will be useful for understanding current processes and designing new processes in Gen R/S vessels.
While rpm and FF height are typically critical operating parameters in established processes, linear speed is inferred because it cannot be measured directly.
There are three suggested approaches to the updated characterization:
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No change to rpm or vessel volumes if your established processes have not observed biologically relevant changes when switching generations (the new characterization is not statistically significant).
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Established processes that have observed biologically relevant changes when switching vessel generations would benefit from investigating an increase in agitation of 50 rpm, which may mimic the linear speed reported from the Gen Q characterization.
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New processes being developed or scaled up to the iCELLis™ 500+ bioreactor should use the updated values for linear speed and volume.
a. Identify the process linear speed in small-scale iCELLis™ bioreactors. This will be the target linear speed for the iCELLis™ 500+ process.
b. Select the correct RPM for the target linear speed and FF height (see graphical data in the appendix).
c. Determine the target volume based on the rpm and FF height (see graphical data in the appendix).
These guidelines will help you during process design, and provided further knowledge on these important parameters that will allow you to confidently operate the iCELLis™ 500+ single-use fixed-bed bioreactor in ongoing and new bioprocesses.
For support in process development and technical support for the iCELLis™ single-use fixed-bed bioreactor and other upstream products please contact us.
Appendix
Fig 6. 66 m2 Linear speed plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 7. 66 m2 Volume plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 8. 100 m2 Linear speed plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 9. 100 m2 Volume plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 10. 100 m2 Volume plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 11. 133 m2 Volume plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 12. 200 m2 Linear speed plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 13. 200 m2 Volume plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 14. 333 m2 Linear speed plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 15. 333 m2 Volume plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 16. 500 m2 Linear speed plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Fig 17. 500 m2 Volume plotted against rpm for 2, 6 and 10 cm FF heights. Polynomial regressions of the data are also plotted.
Table 4. The regressions for determining rpm to linear speed, rpm to volume, and linear speed to rpm are listed in the table for each vessel and FF height. R2 values for regressions were >0.95
| Vessel (m2) | FF (cm) | rpm to linear speed (cm/s) regression (polynomial) | rpm to volume (L) regression (polynomial) | Linear speed (cm/s) to rpm regression (polynomial) |
| 66 | 2 | *0.0072 x -0.95 | 3 -0.0000226 x^2 + 0.023 x + 60.7146 | 15.6156 x^2 + 117.713 x + 134.368 |
| 66 | 6 | -0.00001 x^2 + 0.0146 x - 2.47375 | -0.00005 x^2 + 0.044248 x + 53.6883 | 11.8753 x^2 + 101.741 x + 188.609 |
| 66 | 10 | -0.00001 x^2 + 0.0148 x - 2.89875 | -0.0000813 x^2 + 0.071088 x + 44.2548 | 20.3242 x^2 + 85.756 x + 236.459 |
| 100 | 2 | -0.00001 x^2 + 0.0128 x - 1.71875 | -0.0000375 x^2 + 0.03 x + 60.5797 | 23.2318 x^2 + 94.3808 x + 151.186 |
| 100 | 6 | -0.00001 x^2 + 0.0146 x - 2.47375 | -0.0000475 x^2 + 0.04335 x + 54.2247 | 17.467 x^2 + 84.3607 x + 199.069 |
| 100 | 10 | -0.00002 x^2 + 0.0228 x - 4.4675 | -0.0001075 x^2 + 0.0901 x + 41.3009 | 7.42129 x^2 + 99.1725 x + 233.26 |
| 133 | 2 | -0.00001 x^2 + 0.0124 x - 1.56875 | -0.0000449 x^2 + 0.034356 x + 59.5708 | 18.2779 x^2 + 100.933 x + 142.386 |
| 133 | 6 | -0.00001 x^2 + 0.0146 x - 2.47375 | -0.0000525 x^2 + 0.047554 x + 52.7481 | 18.192 x^2 + 87.7556 x + 193.315 |
| 133 | 10 | -0.00001 x^2 + 0.0156 x - 3.12875 | -0.0000438 x^2 + 0.049788 x + 46.9426 | 7.42129 x^2 + 99.1725 x + 233.26 |
| 200 | 2 | -0.00002 x^2 + 0.018 x - 2.4375 | 7.5×10^-6 x^2 + 0.0075 x + 63.4141 | 26.0492 x^2 + 89.5996 x + 162.605 |
| 200 | 6 | -0.00001 x^2 + 0.015 x - 2.74375 | -0.0000225 x^2 + 0.02895 x + 56.1916 | 17.1068 x^2 + 87.1763 x + 213.119 |
| 200 | 10 | -0.00001 x^2 + 0.0156 x - 3.22875 | -0.0000675 x^2 + 0.0621 x + 46.1384 | 13.2457 x^2 + 85.4277 x + 249.554 |
| 333 | 2 | -0.00001 x^2 + 0.0116 x - 1.51875 | -0.0000175 x^2 + 0.0199 x + 61.7797 | 31.2075 x^2 + 99.6816 x + 157.736 |
| 333 | 6 | -0.00002 x^2 + 0.0204 x - 3.4575 | 0.0000125 x^2 + 0.00635 x + 59.5372 | 25.2417 x^2 + 84.7174 x + 211.766 |
| 333 | 10 | -0.00001 x^2 + 0.0156 x - 3.32875 | -0.00001 x^2 + 0.0261 x + 51.7337 | 20.5758 x^2 + 82.2976 x + 255.086 |
| 500 | 2 | -0.00001 x^2 + 0.0108 x - 1.46875 | -7.5×10^-6 x^2 + 0.0151 x + 61.7234 | 32.4307 x^2 + 117.577 x + 167.82 |
| 500 | 6 | *0.0072 x - 1.51 | -0.0000175 x^2 + 0.02515 x + 56.0659 | 38.4428 x^2 + 90.5862 x + 218.741 |
| 500 | 10 | -0.00002 x^2 + 0.0212 x - 4.2075 | -0.0000425 x^2 + 0.0474 x + 47.8553 | 44.6766 x^2 + 71.8955 x + 267.783 |
*In some cases, a coefficient is so small that is nearly zero, so it is not included in the equation.