Linear expandable bioreactor system

Abstract

A scalable single use bioreactor bag and system is provided for performing a scalable bio-manufacturing process. A small-scale system models a larger-scale system on the basis of shear / scalability / performance. The disclosed bioreactor system provides improved scalability by using the same or substantially the same container geometry ratio and maximum process parameters for small and large scale biofabrication.

Description

Technical Field

[0001] This disclosure relates to bioreactor systems and methods for processing biological materials. In some embodiments, the disclosed bioreactor systems include disposable components. Background Technology

[0002] Cell culture is an essential step in the manufacture of bioproducts. Bacterial, microbial, and mammalian cells are typically cultured to produce therapeutic proteins. Such proteins may include, for example, monoclonal antibodies (MAbs), erythropoietin (EPO), and interferon. These cells are also cultured to produce nucleic acids, viruses (for vaccines), and recombinant proteins (for pharmaceuticals).

[0003] In scale-up cultures, from laboratory benchtop bioreactors to larger commercial production bioreactors, it is important to consider changes in culture conditions as culture volume increases. In the biotechnology / pharmaceutical manufacturing industry, the “technology transfer” (hereinafter referred to as “techtransfer”) of biopharmaceutical processes (such as cell culture) from the research or development level (i.e., small-scale production) to large-scale commercial production is typically a complex, costly, and time-consuming process.

[0004] Related to the above, oxygen is a critical and often limiting substrate for growth, production, and maintenance activities in cell culture. Cells obtain oxygen from soluble oxygen in an elemental, non-compound form called "dissolved oxygen" (DO). One of the most important functions of a bioreactor is the continuous supply of dissolved oxygen to cells via aeration. Aeration in a bioreactor typically occurs through two gas supply modes: a) oxygen diffuses from a covering gas supplied above the liquid to dissolve at the cell culture-gas interface, and b) oxygen is supplied below the liquid surface, sometimes into bubble tubes or bubble elements. Bubble elements are designed to provide gas in bubble form to increase the surface area to volume contact ratio and residence time of the gas in the liquid, thereby promoting dissolution. Gas supplied below the liquid surface can be further dissolved into the cell culture or solution medium with the aid of agitation. Agitation disperses oxygen bubbles, increases the residence time of bubbles below the liquid surface, and promotes mass transfer of gas into the liquid. The oxygen transfer rate (OTR) from gaseous oxygen to soluble oxygen is a function of the physicochemical properties of the cell culture medium, the geometry and operating parameters of the bioreactor, and the presence of cells. Dissolved oxygen (DO) was monitored under various operating conditions—stirring, gas flow rate, culture medium, or culture medium mimicry solution—in the absence of cells to evaluate OTR. OTR is correlated with the oxygen mass transfer coefficient k. La (volume mass transfer coefficient, which describes the efficiency at which oxygen can be delivered to the bioreactor for a given set of operating conditions) is related to the oxygen concentration gradient in the liquid.

[0005] Due to the low solubility of oxygen in the liquid phase and the increasing metabolic consumption of cells over time, oxygen is continuously supplied to the cell culture. Oxygen supply is carefully controlled for optimal cell growth by manipulating gas supply, agitation, or culture medium addition, in response to DO readings from immersion sensors. During batch cell culture, oxygen utilization / uptake (OUR) is initially low during the lag phase, where cells divert energy to maintain internal cellular function, and there is little increase in cell doubling or overall culture cell density. Cell density increases during the subsequent phase (exponential phase), during which OUR increases until OTR (oxygen transfer rate) becomes limiting under these conditions. Therefore, OTR is determined by its relationship with k L The correlation of 'a' defines the theoretical maximum cell density achievable in cell cultures under OTR test conditions before oxygen supply becomes a limiting control parameter. Because of this correlation with cell density, k was obtained under various gas supply and agitation conditions. L The α-value can be particularly used to evaluate various bioreactor design features and the scalability within a bioreactor platform across possible bioreactor system sizes. Any variation in the process, engineering parameters, or geometry of the system tanks and components will affect k. L a has an impact and is therefore a good measure of the scalability of bioreactor design to scale to representative volumes on a bioreactor platform.

[0006] Mixing is used to maintain homogeneity and eliminate gradients in concentration (cells, gases, pH, culture medium, and nutrients), temperature, and other properties. Gas bubble size and residence time are highly dependent on a range of mixing conditions surrounding the stirrer design, including impeller type, speed, and location, as well as bubbler design, porosity, and gas flow rate performance. L The a value typically increases with increasing stirring speed. However, high stirring speeds can lead to increased shear forces at the blade tips, resulting in cell death.

[0007] Furthermore, higher oxygen supply concentrations and higher gas flow rates improve oxygen availability, which drives an increase in OTR. Increasing the oxygen supply to the bioreactor drives this availability by increasing the concentration gradient (depending on the fluid composition and related to potentially higher saturation values), and can be controlled by altering the oxygen concentration in the gas (air vs. O2 enrichment) and the volumetric flow rate. Despite high k LWhile the α value is ideal, it's important to consider actual operating conditions and its impact on cell viability and related process costs. For example, high airflow velocities can lead to cell damage due to shear forces. Excessive foaming may also occur, requiring high concentrations of defoamers, which can inhibit cell growth and potentially cause batch-to-batch variability in downstream process performance. Furthermore, higher airflow velocities necessitate larger exhaust filter areas to limit bioreactor overpressure, driving up consumable costs.

[0008] Therefore, traditional bioreactors are designed with different impeller types, bubblers, combinations, and positions to achieve target k. L The a-value is used to minimize harmful shear forces. However, these modifications are often difficult to scale up across bioreactors within a given platform because the key design parameters are not constant.

[0009] Therefore, there is a continued demand in biopharmaceutical development and manufacturing for easily scalable systems and process transfer technologies that provide easy, reliable, and reproducible technology transfer across bioreactor sizes for scale-up, scale-down, and lateral expansion. Regardless of the process-scale purpose—whether for process development, clinical manufacturing, or cGMP production—scaling requires robustness and consistency across bioreactor sizes, as well as reduced process evaluation, process operation changes, or validation testing requirements. Summary of the Invention

[0010] This invention provides scalable, single-use bioreactor systems and methods for performing scalable biomanufacturing processes that address many recognized problems in scaling up cell culture processes for commercial production or smaller-scale product / process evaluation. Using the disclosed systems and methods minimizes risk and helps ensure that the robustness, purity, and potency of the scaled-up process are comparable to the original process. Technology transfer and scaling using the disclosed systems provide optimal results, as well as safe and cGMP-compliant scaled-up manufacturing processes, while eliminating or reducing the need for extensive, costly, and time-consuming process and parameter evaluations. In summary, the disclosed small-scale (e.g., 50 L) bioreactor systems provide “linear scalability” by using the same or substantially similar container and bag geometries, gas bubbling systems, impeller shapes and types, and process control systems found in larger bioreactors (e.g., 200 L to 2000 L systems). This invention particularly includes, individually or in combination, the following.

[0011] In one aspect, the present invention relates to a scalable bioreactor system for performing a scalable biomanufacturing process, the system comprising: a bioprocessing bag having a flexible wall; a working volume adjustment ratio of approximately 5:1 (maximum working volume: minimum working volume); a liquid height to diameter ratio of approximately 1:1 to 2:1, preferably approximately 1.7:1, at the maximum working volume; an impeller mounted on an impeller plate attached to the bottom inner surface of the flexible wall; and a ratio of the impeller diameter Di to the diameter Dt of the mounted bioprocessing bag, equal to a value of approximately 0.3 to 0.5, preferably approximately 0.4.

[0012] The biotreatment bag further includes at least one bubbler attached to the bottom inner surface of a flexible wall for introducing gas into the biotreatment bag. In an embodiment, the at least one bubbler comprises a first bubbler and a second bubbler. The first bubbler has a bubble surface area ratio (bubble surface area / bag cross-sectional area) of about 0.023 to 0.068, preferably about 0.04. The second bubbler has a bubble surface area ratio (bubble surface area / bag cross-sectional area) of about 0.008 to 0.024, preferably about 0.02. The gas introduced through the first and second bubblers is controlled such that a maximum gas outlet velocity is controlled. For the first bubbler, the target linear velocity is about 12 to 60 m / s, preferably about 24 m / s, corresponding to a maximum gas flow rate of about 0.15 to 0.55 vvm (gas volumetric flow rate / container working liquid volume), preferably 0.2 vvm. For the second bubbling channel, the maximum gas outlet velocity of the second bubbler is approximately 36 to 60 m / s, preferably 36 m / s, and a maximum gas flow rate of approximately 0.05 to 0.18 vvm, preferably 0.1 vvm, is allowed. Additionally, the superimposed maximum gas flow rate can be kept constant and can be set to approximately 0.05 vvm.

[0013] Throughout this text, "bubble surface area" is defined as the total surface area of ​​the bubblers that introduce gas into the bioreactor bag. Additionally, "bag cross-sectional area" is defined as the maximum cross-sectional area of ​​the liquid surface in the bioreactor when the bioreactor bag expands in situ within the external container. In other words, the "bag cross-sectional area" is approximately the same as the cross-sectional area of ​​the internal volume of the external container in which the bioreactor bag is placed during use.

[0014] Furthermore, with respect to all values ​​provided herein, the term “about” includes values ​​that differ from the specified value by + / - 15%, including boundary values ​​of any and all ranges.

[0015] According to the implementation scheme, the first bubbler is used for dissolved oxygen control of the culture medium, and to do so, a mixture of air and oxygen can be delivered. The second bubbler can be used for carbon dioxide stripping (removal) and can deliver nitrogen or air. Maintaining the same bubbler surface area ratio across bioreactor scales helps ensure the same degree of gas dispersion, and therefore better scalability.

[0016] Furthermore, the distance between the bottom of the impeller blades and the gas-generating surface of the bubbling surface is approximately 8 to 24 mm, preferably approximately 16 mm. This distance is maintained to ensure scalable performance across bioreactor sizes, and may not be scalable or proportional depending on the bioreactor liquid height or impeller height. This distance can be fixed to ensure similar gas bubble collapse caused by the impeller across different scales.

[0017] The bioreactor system further includes a container for housing the biotreatment bag. Matching the maximum operating liquid volume, the container has a liquid height to diameter ratio of approximately 1:1 to 2:1, preferably approximately 1.7:1, for the jacket section of the system. The container may include multiple baffles having a height ratio (baffle height / container diameter) of approximately 1 / 10 to 1 / 12, preferably approximately 1 / 11, noting that the baffle height is the distance the baffle extends from the container perimeter to the container center.

[0018] Impeller power rating (N) p The impeller power number depends on the impeller shape, container geometry (baffle size, distance between impeller blades and container surface), and liquid (density, viscosity, and therefore aeration conditions). The impeller power number is approximately 0.8 to 3.9, preferably approximately 2.6, in downward pumping (e.g., impeller rotating clockwise from a top view), and approximately 0.8 to 2.5, preferably approximately 1.7, in upward pumping (e.g., counterclockwise from a top view).

[0019] In another aspect, the present invention relates to a linearly scalable bioreactor system for performing scalable biomanufacturing processes, the system comprising: A first biological treatment bag, having a first volume, a first flexible wall, and a liquid aspect ratio of the bag height to the bag diameter when the bag has a maximum working volume equal to the first H / D; a first impeller mounted on a first impeller plate, the first impeller plate being attached to the first inner surface of the first flexible wall, the ratio of the first impeller Di to the diameter Dt of the first biological treatment bag being equal to Di / Dt; and a first bubbler attached to the bottom inner surface of the flexible wall, the ratio of the bubble surface area As1 of the first bubbler to the cross-sectional area Ab of the first biological treatment bag (in the expanded state) being equal to As1 / Ab. A second biological treatment bag has a second volume greater than the first volume of the first biological treatment bag, a second flexible wall, and an aspect ratio of the second bag height to the second bag diameter equal to the second H / D when the second bag has a maximum working volume, wherein the first and second H / D are substantially equal to each other; a second impeller mounted on a second impeller plate, the second impeller plate being attached to the second inner surface of the second flexible wall, the ratio of the second impeller diameter D2i to the second biological treatment bag diameter D2t being equal to D2i / D2t, wherein Di / Dt = D2i / D2t; a second bubbler attached to the bottom inner surface of the second flexible wall, the ratio of the bubble surface area A2s1 of the second bubbler to the cross-sectional area A2b of the second biological treatment bag (in the expanded state) being equal to A2s1 / A2b, wherein As1 / Ab = A2s1 / A2b. (or approximately equal), wherein the first and second impellers are of the same type and are each positioned above the bubbling surface of the respective bubbler, the distance between the bottom of the impeller blades and the bubbling surface of each of the first and second biotreatment bags is approximately the same, and each is configured to operate separately within the first and second bags, such that in biotreatment operations using the same fluid within the first and second biotreatment bags under similar conditions, consistent and similar maximum oxygen k is achieved by controlling the stirring speed and gas flow rate while maintaining within acceptable shear rates and Kolmogorov Eddy lengths. L a.

[0020] According to certain embodiments, H / D = about 1-2, preferably about 1.7, Di / Dt = D2i / D2t = about 0.3 to 0.5, preferably about 0.4, As1 / Ab = A2s1 / A2b = about 0.023 to 0.068, preferably about 0.04.

[0021] In the implementation, each of the first and second biotreatment bags includes an additional bubbler attached to the bottom inner surface of the first and second flexible walls, respectively. The ratio of the bubble surface area As2 of the additional bubbler to the cross-sectional area Ab of the first biotreatment bag (in the inflated state) is equal to As2 / Ab. The ratio of the bubble surface area A2s2 of the additional bubbler to the cross-sectional area A2b of the second biotreatment bag (in the inflated state) is equal to A2s2 / A2b, where As2 / Ab = A2s2 / A2b (or approximately equal).

[0022] According to some implementations, As2 / Ab = A2s2 / A2b = about 0.008 to 0.024, preferably 0.02.

[0023] In addition, for the first and second biological treatment bags, the distance between the bottom of the impeller blades and the bubbling surface is about 8 to 24 mm, preferably 16 mm.

[0024] Furthermore, the gas introduced through the first and second bubblers of the first and second bioreactor bags is controlled such that the maximum gas outlet velocity and the maximum gas flow rate are the same relative to the nominal bioreactor volume. Similarly, the gas introduced through additional bubblers of the first and second bioreactor bags is controlled such that the maximum gas outlet velocity and the maximum gas flow rate are the same relative to each other, but different from the first and second bubblers.

[0025] In some embodiments, the maximum gas outlet velocity and corresponding maximum gas flow rate of the first and second bubblers are about 12 to 60 m / s, preferably 24 m / s and about 0.15 to 0.55 vvm, preferably about 0.2 vvm, and the maximum gas outlet velocity and corresponding maximum gas flow rate of the additional bubbler are about 36 to 60 m / s, preferably 36 m / s and about 0.05 to 0.18 vvm, preferably 0.1 vvm.

[0026] According to the implementation, the first and second bubblers provide dissolved oxygen into the culture medium, and to do so, a mixture of air and oxygen can be delivered. Additional bubblers can be used for carbon dioxide stripping (removal) and can also deliver nitrogen or air. Maintaining the same bubbler surface area ratio across scales helps ensure equal levels of gas dispersion, and therefore better scalability (e.g., control over scalable performance).

[0027] Furthermore, the power ratings of the first and second impellers are approximately the same. In some embodiments, the power ratings of the first and second impellers are 0.8 to 3.6, preferably about 2.6, during downward pumping (e.g., clockwise rotation of the impellers), and about 0.8 to 2.5, preferably 1.7, during upward pumping (e.g., counterclockwise rotation).

[0028] The first and second biotreatment bags can each be placed inside a container. The container containing each of the first and second biotreatment bags has a liquid height-to-diameter ratio of approximately H / D. The H / D values ​​of the two containers are the same. In a particular embodiment, the H / D of the containers is also approximately 1:1 to 2:1, preferably 1.7:1. Each container may include multiple baffles (e.g., 1-4), said baffles having a height ratio (baffle height / container diameter) Hb / D, note that the container height is the distance the baffle extends from the container perimeter to the container center. The Hb / D values ​​of the two containers are the same.

[0029] In some implementations, Hb / D = about 1 / 10 to 1 / 12, preferably about 1 / 11.

[0030] According to a further aspect of the invention, a method for extending a biomanufacturing process is described. The method includes providing a first bioprocessing bag having a first volume and a first flexible wall, the first bioprocessing bag including a first impeller mounted on a first impeller plate attached to a first inner surface of the first flexible wall, and a first bubbler attached to a bottom inner surface of the flexible wall, wherein when the first bioprocessing bag is in an inflated state, the ratio of the bubble surface area As1 of the first bubbler to the cross-sectional area Ab of the first bioprocessing bag is equal to As1 / Ab; performing a first biomanufacturing process in the first bioprocessing bag; providing a second single-use bioprocessing bag having a second volume greater than the first volume and a second flexible wall, the second bioprocessing bag including a second impeller mounted on a second impeller plate attached to a second inner surface of the second flexible wall, wherein when the second bioprocessing bag is in an inflated state, the ratio of the bubble area A2s1 of the second bubbler to the cross-sectional area A2b of the second bioprocessing bag is equal to A2s1 / A2b; and extending the first biomanufacturing process to a larger volume by performing a second biomanufacturing process in the second bioprocessing bag; wherein As1 / Ab is approximately equal to or equal to A2s1 / A2b.

[0031] In the implementation, As1 / Ab = A2s1 / A2b (or approximately equal) = about 0.023 to 0.068, and in a preferred implementation, As1 / Ab is about 0.04.

[0032] In one embodiment, the first and second biological treatment bags each include an additional bubbler attached to the bottom inner surface of the first and second flexible walls, wherein the ratio of the bubble surface area As2 of the additional bubbler to the cross-sectional area Ab of the first biological treatment bag is equal to As2 / Ab, and the ratio of the bubble surface area A2s2 of the additional bubbler to the cross-sectional area A2b of the second biological treatment bag is equal to A2s2 / A2b, where As2 / Ab = A2s2 / A2b (or approximately equal).

[0033] In the implementation, As2 / Ab = A2s2 / A2b = about 0.008 to 0.024, and in a preferred implementation, As2 / Ab is about 0.02.

[0034] The method may further include operating the first and second bioprocessing bags in the same (or similar) manner as described with respect to other aspects of the invention.

[0035] In any and all aspects and embodiments of the present invention, a linearly scalable bioreactor system and related methods for performing scalable biomanufacturing processes may include a process measurement system; a system of field actuators or field devices; and a local processing unit and related software logic configured to transform measurement system inputs and transmit measurement system inputs to a supervisory controller or human-machine interface for data manipulation and storage, and to convert measurement system inputs from the supervisory controller or human-machine interface into manipulations of the field actuators or field devices.

[0036] The scalable biological processing system may have a human-machine interface and associated software programming, including at least one of a computer mouse, keyboard and touch screen; and a supervisory controller and software programming that can command the system device to respond to specific configurable parameters using data from process inputs, sensor measurements, device status, setpoints, deviations from setpoints, alarm conditions and combinations thereof.

[0037] The disclosed scalable bioreactor system (which can be a single-use system) is designed to provide consistent and similar maximum oxygen mass transfer capabilities within the operating range and geometry of each bioreactor in the system, while remaining within acceptable volume fractions for the target cell type, including excessive shear rates and Kolmogorov Eddy lengths.

[0038] In any aspect and embodiment of the invention, a single-use bioprocessing bag is placed within a container (also referred to in the text as a “can”). The container may comprise a rigid or slightly rigid material and serves to support the bag placed therein. “Linear scalability,” as used herein, refers to relatively constant values ​​of one or more geometric and process parameters of the container or the bag placed therein, and the ability to achieve and maintain consistent and similar oxygen mass transfer between the various bioreactors in the system (e.g., from 50 L to approximately 2000 L). For the various bioreactors in the system, geometric similarity of the container or the bag placed therein, and consistent and similar maximum oxygen mass transfer, is maintained across a wide range of operating volumes. This linear scalability provides a means of performance modeling (scaling down) of large bioreactors in smaller bioreactors, or conversely, provides a development approach in relatively small bioreactors that can be easily scaled up for larger commercial-scale processes with minimal scheme variations.

[0039] The disclosed scalable single-use bioreactor system is designed so that its gas bubbling / aeration system remains substantially the same across sizes, allowing smaller bioreactors to simulate the performance (aeration and inflation performance) of larger systems. This additional feature of linear scalability provides a means of modeling the performance of large bioreactors in smaller bioreactors, or conversely, a development methodology for relatively small bioreactors that can be easily scaled up for larger commercial-scale processes with minimal scheme variations. Specifically, by keeping, for example, Di / Dt, power number, and bubbler surface area ratio constant across different volumes, stirring speed and bubbling rate can be varied across all bioreactor sizes within acceptable shear rates and Kolmogorov Eddy lengths, while maintaining substantially the same maximum k. L a.

[0040] In summary, the disclosed bioreactor system provides “linear scalability” by using the same or substantially similar bag and container geometries, gas bubbling systems, impeller shapes and types, and process control systems as those used in larger systems. The disclosed bioreactor system is well-suited for the culture of mammalian cells, microorganisms, bacteria, plants, insects, protozoa, organs, and / or fungal cells. Attached Figure Description

[0041] Figure 1 This is a schematic side elevation sectional view of a 50L bioreactor vessel according to an embodiment of the present invention, comprising a single-use flexible bag, an impeller, a magnetic impeller shaft, an impeller plate, and an external magnetic actuator disposed therein.

[0042] Figure 2 This is a top view of a bioreactor vessel with impeller plates and a bubbler according to an embodiment of the present invention.

[0043] Figure 3 This is a top view of a bioreactor vessel having the impeller plate, bubbler and impeller shown, according to an embodiment of the present invention.

[0044] Figure 4 This describes the empirical dissolved oxygen (k) in 50L and 200L bioreactors according to embodiments of the present invention. L Contour map of a. Detailed Implementation

[0045] The following is a description of preferred embodiments of the present invention. It will be understood that specific embodiments of the invention are shown by way of example and not by way of limitation. The invention will first be described in its broadest sense, followed by a more detailed description. Features and other details of the compositions and methods of the invention will be further pointed out in the claims.

[0046] Throughout the description and claims of this specification, the words “comprising” and “containing,” and variations thereof, mean “including but not limited to,” and are not intended (and do not) exclude other parts, additives, components, integers, or steps. Throughout the description and claims of this specification, the singular includes the plural unless the context requires otherwise. In particular, when the indefinite article is used, the specification should be understood to consider both the plural and singular unless the context requires otherwise.

[0047] The scalable single-use bioreactor system according to embodiments of the present invention is a small-scale bioreactor that provides linear scalability from small to large scale, for example from 50L single-use bioreactor bags to 2000L single-use bioreactor bags, on the same single-use platform across different families of bioreactors of various sizes.

[0048] Figure 1 This is a schematic side elevation sectional view of the disclosed bioreactor system 100, which includes a 50L bioreactor container or support structure 20 having a single-use flexible bag 30 placed therein; an impeller 22 attached to a magnetic shaft 24 at the bottom center inside the bag 30; an impeller plate 26 positioned on the bottom inside the bag and on which the magnetic shaft 24 rotates; and an external magnetic actuator 23.

[0049] Bioreactor system 100 has been designed to achieve high cell density culture conditions. In particular, small-scale (e.g., 50 L) bioreactor systems have been designed to include sufficient oxygen transfer capabilities without negatively impacting oxygen levels. L A bubbler with a bubble surface area of ​​a. Specifically, because the bubble surface area independently realizes oxygen k L (i.e., independent of stirring and flow conditions), thus small-scale bioreactor systems are designed such that the oxygen transferred to the cell culture can be maintained at a level sufficient to achieve high cell density culture conditions within maximum stirring and gas flow rate limits. The inventors have advantageously discovered that scalability is improved by maintaining the same (or substantially the same) bubble surface area ratio (bubble surface area / bag cross-sectional area in the expanded state within the container) across scales, along with other geometric parameters described in more detail below. Alternatively, by determining the bubble surface area providing sufficient oxygen transfer in the small-scale operation and maintaining the bubble surface area ratio based on this value across scales, culture conditions in each scale can be similar without exceeding maximum stirring and gas flow rates.

[0050] In addition to the bubble surface area, maintaining additional geometric parameters constant (or nearly constant) across scales further improves scalability by making the geometries of different scales the same (or substantially the same). For example, even greater similarity of culture conditions across scales can be achieved by fixing the aspect ratio H / D, the Di / Dt ratio (where Di is the impeller diameter and Dt is the container diameter), the impeller blade-bubbler distance, and / or the baffle height ratio (baffle height / container diameter).

[0051] Furthermore, limiting certain operating parameters across scales further improves scalability by avoiding operations of the bioreactor system in protocols detrimental to cell growth. For example, by limiting the maximum gas flow rate (and therefore the gas flow rate per minute) and the mixing contribution from the stirring rate (i.e., the power input to volume ratio (P / V)), cell culture conditions are kept within ideal limits across all scales (e.g., maintaining acceptable shear rates, dissolved oxygen and carbon dioxide concentrations, and Kolmogorov Eddy).

[0052] Although this invention relates to keeping certain geometric and process parameters constant, the range of values ​​for each of these parameters described below is within the scope of this invention. Specifically, any value within a given range may provide the advantages described herein, provided it is constant (or substantially the same) across scales. Furthermore, the ranges are based on mathematical calculations taking into account the overall design constraints of this bioreactor system. However, it should be noted that the specific values ​​recorded as preferred values ​​described herein represent optimal values ​​for scalable bioreactor systems. And the invention is explicitly not limited to these values, but includes all ranges described herein.

[0053] In the embodiment, the aspect ratio H / D of the liquid working volume height H to the diameter D of the bag 30 is about 1-2, preferably 1.7. The ratio of Di / Dt (where Di is the impeller diameter and Dt is the container diameter) is about 0.3 to 0.5, preferably about 0.4.

[0054] like Figure 2 Ideally, at least one bubbler is also present attached to the inner bottom of the bag 30. The at least one bubbler may be in the form of a set of bubble discs 27, 28 located on the impeller plate 26. In an embodiment, the at least one bubbler comprises two bubblers. The first bubbler 27, which... Figure 2 The described embodiment includes three bubbling discs having a ratio of approximately 0.023 to 0.068, preferably approximately 0.04, of the bubbling surface area to the cross-sectional area of ​​the bag (when the container is in an expanded state). A second bubbler 28, which... Figure 2The described embodiment includes a bubbling disc having a ratio of approximately 0.008 to 0.024, preferably approximately 0.02, of the bubbling surface area to the cross-sectional area of ​​the bag (when the container is in an expanded state). The gas introduced through the first and second bubblers 27, 28 is controlled such that the maximum gas outlet velocity of the first bubbler 27 is approximately 12-60 m / s, preferably 24 m / s, corresponding to a maximum gas flow rate of approximately 0.15 to 0.55 vvm (container volume / min), preferably 0.2 vvm, while the maximum gas outlet velocity of the second bubbler 28 is approximately 36 to 60 m / s, preferably 36 m / s, corresponding to a maximum gas flow rate of approximately 0.05 to 0.18 vvm, preferably 0.1 vvm. The combined maximum gas flow rate is approximately 0.05 vvm. Additionally, the maximum stirring rate (i.e., the power input to volume ratio (P / V)) is limited to approximately 150 W / m. 3 .

[0055] The reusable bioreactor vessel according to the disclosed system may include a reusable polymer or metal vessel platform, support or bracket 20 with an integrated external motor / stirring assembly 23, and a measurement and control system (not shown). The vessel platform, support or bracket may be composed of a mixture of materials, such as polymer and metal. The polymer or metal container may be of any shape or size, as long as it can support the disclosed stirred tank single-use flexible bioreactor bag 30 design. For example, according to one embodiment of the invention, the polymer or metal platform, support or bracket 20 is capable of receiving and supporting a 50L flexible or foldable bioreactor bag assembly 30.

[0056] The measurement and control system is built on a configurable software platform. The system operates in real time; it accepts process inputs (measurements) such as temperature, RPM, pH, DO, weight, pressure, etc.; and controls field devices such as mass flow controllers, pumps, solenoid valves, heating elements, etc. According to one embodiment, human interaction with the system is via a touchscreen-based interface on a desktop, laptop, or notebook computer, allowing for remote computer operation or remote control of devices via the internet. The interface allows users to access setpoints, manage gas bubbling, calibrate field devices, manage alarms, configure operator identities and access levels, and view process values ​​graphically over time. The measurement and control system may further include a server for storing current and historical data related to the cultivation process.

[0057] The scalability described above is a crucial factor, especially in the biotechnology / pharmaceutical manufacturing industry, as it allows for the easy and simple transfer of technology from the research level (small-scale) to large-scale production. Geometric similarity, such as aspect ratio (H / D), impeller geometry, bubbler geometry, and impeller power rating, as well as process similarity, such as bubbler gas inlet velocity and gas flow rate, are key factors in controlling and minimizing performance variations in bioreactor processes during scale-up.

[0058] In addition to the above, shear rate and Kolmogorov eddy length are parameters that must be considered. Specifically, shear rate and Kolmogorov eddy length act as limiting factors to avoid operating the bioreactor according to a protocol detrimental to cell growth for cell types suitable for growth in suspension cell culture. The aforementioned process parameters have been designed such that, based on the power density (W / m³) through the two bubbling components... 3 Static analysis of the system with the preferred target gas flow rate under maximum stirring was performed, and the bioreactor was designed for a shear rate not exceeding 2000 s⁻¹. -1 The Kolmogorov Eddy value is greater than 62 micrometers. It is acceptable for no less than 95% of the container volume to meet these two limits, meaning small localized areas exceeding these limits are permissible.

[0059] Tables 1 and 2 below provide an overview of the range of geometric and operating parameters within the scope of this invention. For all reactors, each bioreactor has the same or approximately the same H / D aspect ratio, impeller geometry, bubbler geometry, and impeller power number, as well as the same or similar operating constraints, such as bubbler gas inlet velocity. All ranges provided are approximate (i.e., each boundary is adjustable by up to 15%).

[0060] Tables 3 and 4 below provide an overview of preferred geometric and operational parameter values ​​and ranges within the scope of this invention. Specifically, for all reactors, each bioreactor has the same or approximately the same H / D aspect ratio, impeller geometry, bubbler geometry, and impeller power number, as well as similar operational constraints, such as bubbler gas inlet velocity. All values ​​are approximate (i.e., each boundary can be adjusted by up to 15%).

[0061] Maintaining these values ​​constant (or approximately the same) within the stated range between scales helps achieve linear scalability and highly predictable scaling-up condition modeling, while also preserving substantially consistent oxygen mass transfer (i.e., oxygen k). L a(+ / -30%)). Throughout this paper, the 50L, 200L, 500L, 1000L and 2000L single-use bioreactor bags disclosed herein are respectively named X-50, X-200, X-500, X-1000 and X-2000.

[0062] The data in Tables 1 through 4 above show some linear expansion factors for the disclosed single-use bioreactor. Assuming the entire working volume of the single-use bioreactor bag according to an embodiment of the invention is substantially cylindrical, the volume adjustment ratio, as the ratio of the maximum working volume to the minimum working volume, is approximately 5:1 for all bioreactor sizes. “H” is the height of the working volume in the single-use bag, and “D” is the diameter of the tank or the single-use bag placed within the support tank. For a range of maximum working volumes, the H / D ratio of the tank or the bag placed therein is substantially constant, having a value of approximately 1:1 to 2:1, preferably approximately 1.7. The impeller diameter “Di” is variable (i.e., increases with increasing container size), but the ratio of the impeller diameter Di to the container diameter Dt remains constant at a value of approximately 0.3-0.5, preferably approximately 0.4. In some embodiments, the impeller type of the invention is a 6-blade combination of Rushton 50-degree pitch blades, and is the same type in every system. The number of blades on the impeller can vary.

[0063] In one implementation, the impeller is mounted on an impeller plate and is magnetically driven by an external motor.

[0064] The impeller power number "N" is calculated according to the following formula. p ": (For both upward and downward pumping) is similarly constant across bioreactor sizes. Specifically, as shown, the upward pumping power is about 0.8–2.5, preferably about 1.7, and the downward pumping power is about 0.8–3.6, preferably 2.6.

[0065] Impeller blade – Bubbling distance, which is the vertical distance between the upper surface of the bubbler and the bottom surface of the impeller blade, is also constant and has a value of about 8-24 mm, preferably 16 mm.

[0066] The bioreactor bag of the present invention may include two types of bubblers 27, 28, for example in the form of bubble discs, located below the impeller (see example, Figure 2 and 3Bubble 1 (as provided in Tables 1 and 3), corresponding to Figure 2 Bubbler 27 is used for dissolved oxygen (DO) control and configured to deliver a mixture of nitrogen and oxygen. Bubbler 2 (as provided in Tables 1 and 3), corresponding to bubbler 28, is used for carbon dioxide (CO2) stripping (removal) and configured to deliver nitrogen and / or air. As shown in Tables 1 and 3, the total surface area of ​​the bubbling surface of each bubbler, divided by the cross-sectional area of ​​the container / bag, also remains constant (or approximately the same). Specifically, the bubbling surface area ratio of bubbler 1 is about 0.023 to 0.068, and in a preferred embodiment, 0.04, and the bubbling surface area ratio of bubbler 2 is about 0.008 to 0.024, and in a preferred embodiment, about 0.02. These values ​​are constant (or approximately the same) between scales.

[0067] A significant advantage of this invention is that it provides the same bubbling area ratio across all sizes of bioreactors. By keeping this ratio constant, equal amounts of gas dispersion are achieved, which greatly facilitates control over factors such as oxygen concentration. L a (and therefore oxygen mass transfer) and the extended processes related to dissolved CO2 stripping. More specifically, because the bubble surface area independently realizes oxygen k L a (i.e., independent of stirring and flow conditions), thus establishing an oxygen supply that is not limited by the required oxygen k L The constant bubbler surface area ratio of a provides a higher maximum k across scales. L a and a fixed geometric shape.

[0068] In addition to the geometric extension parameters, it was found advantageous to set operational constraints across all bioreactor scales. As provided in Tables 2 and 4, the same maximum gas inlet velocity and maximum gas flow rate of the bubbler are constant for all bioreactor scales. Bubbler 1 has a maximum gas inlet velocity of about 12–60 m / s, preferably about 24 m / s, and a maximum total gas flow rate of about 0.15–0.55 vvm, preferably about 0.2 vvm, while bubbler 2 has a maximum gas inlet velocity of about 36–60 m / s, preferably about 36 m / s, and a maximum total gas flow rate of about 0.05–0.18 vvm, preferably about 0.1 vvm. Furthermore, the maximum power input per unit volume (maximum P / V), which is the amount of power transferred to the culture working volume through impeller rotation, remains constant for nominal bioreactor volume across bioreactor scales, and has a maximum power input per unit volume of about 150 W / m³. 3 The value of . Ensuring that these operating parameters have a constant maximum value between scales helps in controlling, for example, with oxygen k. LThis involves extended processes related to CO2 stripping (and thus oxygen mass transfer), and ensuring that all bioreactors operate within specified shear rates and Kolmogorov eddy limits. Alternatively, this approach, making these operational constraints identical across scales, provides design space that delivers identical or similar performance at each scale. Furthermore, this design space allows for variations in the oxygen concentration in the feed stream and the use of bubblers 2 to attempt to match gas flow rates (in vvm) across scales, enabling similarity in pCO2 profiles while delivering similar oxygen k at a constant P / V. L a.

[0069] It may also be advantageous to control the maximum superimposed gas flow rate, which is the gas flow rate supplied to the top space of the bioreactor bag 30. As provided in Tables 2 and 4, this maximum value is constant across all scales and is set at 0.05 vvm.

[0070] In the implementation, the bags or containers use the same single-use or disposable structural materials and rigid plastic product contact components as in larger-scale bioreactors within the same system. Using the same structural materials or the same type of structural polymer eliminates the regulatory disconnect between small-scale optimization and large-scale implementation regarding extractable and leachable components, biocompatibility compliance, and regulatory testing. As a result, the 50L system models larger-scale systems not only on a scalability / performance basis but also on a regulatory compliance basis.

[0071] Some features of the stirred tank bioreactor in the disclosed system include: bottom-mounted or side-mounted impellers positioned close to and above substantially the same bubbling surface as described above; USP Class VI materials; full integration with the controller; biocompatible structural materials; and linear scalability in the same single-use bioreactor system across a wide range of working tank or bag volumes (e.g., 50 L to 2000 L) as described above.

[0072] Scale-up factors for single-use bioreactors Numerous parameters influence cell growth, and deviations from acceptable ranges are detrimental to health and growth. Therefore, maintaining these parameters within acceptable limits during scaling is critical and often challenging. As described above, this invention provides a highly scalable bioreactor. By fixing certain geometric properties and establishing the same operational constraints across scales, many fluid response parameters remain within acceptable ranges and, in some cases, can be kept constant, which greatly facilitates scaling across bioreactor sizes. This can be achieved, for example, by selecting a constant scaling-up basis, such as stirring power density (P / V). With this value constant, the same OTR can be achieved through a similar system k that is finely tunable across scales. LA delivery method (e.g., by adjusting the inlet oxygen concentration and by using a supplementary second bubbler that results in a similar pCO2 profile to match the overall gas flow rate based on VVM).

[0073] It is crucial to ensure sufficient oxygen mass transfer to the cell culture and CO2 stripping; otherwise, unnecessary cell death occurs, and cell proliferation is reduced or halted. Furthermore, mixing time also has a significant impact on cell health and proliferation, as slow mixing times prevent cells from receiving the necessary nutrients in a timely manner or may expose them to harmful concentration gradients.

[0074] Because each scaling-up parameter depends on another parameter, not all parameters can remain constant during scaling-up. For example, oxygen k L a. The stirring speed and gas flow rate cannot both be kept constant. Instead, two of these parameters can be kept constant, while a third parameter is varied to maintain the other two.

[0075] We have now discovered a system comprising two or more single-use bioreactor bags, each with one or more of the aforementioned geometric parameters and operational constraints fixed. By fixing these, other scale-up parameters can all be kept within ideal ranges, even if they cannot all remain constant.

[0076] Figure 4 Empirical dissolved oxygen (k) for 50L and 200L bioreactors is provided according to embodiments of the present invention. L The contour plot of a. As shown, and under the design constraints mentioned above, at the maximum P / V (150W / m 3 At 0.19 and 1 vvm of bubbler, the maximum oxygen k for a 50 L bioreactor is... L a (h -1 The value is approximately 45. Based on characterization data, each of these other scales (e.g., 100–2000 L) can achieve or exceed the same oxygen K0. L a, while still within the aforementioned operational limitations. For example, at 108 W / m 3 The maximum oxygen mass transfer coefficient (k) for a 200 L bioreactor at a nominal volume under a P / V ratio and a bubbling gas flow rate of 0.15 vvm. L a) Approximately 45 hours -1 In this way, it becomes apparent that sufficiently high oxygen k can be achieved at all scales within the same operational constraints. L a (for example, these k) L The a value allows for high cell densities (e.g., exceeding 100x10). 6 (cells / mL), which helps to scale up (or scale down).

[0077] Successful scale-up (SU) and / or scale-down (SD) of biopharmaceutical production requires performance equivalence across operating scales. The disclosed scalable, single-use bioreactor design for SU and SD platforms provides a unique system for achieving this. As shown in Table 3, the maximum oxygen kk across scales... L a and dissolved CO2 stripping are constant, which greatly helps ensure that cell cultures maintain adequate oxygen mass transfer and dissolved CO2 removal regardless of scale. Specifically, this design provides SU and SD platforms that offer a consistent maximum k across all scales within maximum permissible limits (e.g., maximum P / V, shear, eddy). L a. In this way, each bioreactor can consistently provide sufficient dissolved oxygen and CO2 stripping by adjusting the stirring speed and / or bubbling rate without causing toxic conditions (e.g., unacceptably high shear rates) within the cell culture.

[0078] Accessories are added to the bag to enable the functionality required in a bioreactor, such as permeators and filters that allow fluid and gas transfer, mixing interfaces, sensors, and bubbling surfaces for controlling bubble size. Various bubbling surfaces and options are available in different embodiments of the invention. Bubbling surfaces may be attached to the bioreactor bag as adapters or partition accessories, designed to connect hoses or tubing, such as oxygen supply tubing, to the bag. The porosity and area of ​​the bubbling surface can vary (within the foregoing limitations). In one embodiment, the bubbling surface may be a single or multiple pores configured to introduce oxygen or air into the bioreactor bag. At least some bubbling surfaces may be located below the impeller (e.g., a bubbler for DO control) to allow efficient gas circulation through the culture medium within the bag, and their location and type are substantially the same as those of larger 50L-5000L systems.

[0079] A linearly scalable bioreactor system according to an embodiment of the invention may include a temperature controller and at least one sensor and / or probe (not shown). To eliminate the utilities required for temperature control via a heat exchanger, heating may be provided via a closed-loop water jacket for heating and / or cooling by a control system mounted on the bioreactor system, or via an electric heating blanket or a Peltier heater. The heating blanket may include thermocouples for sensing the temperature of the contents of the biotreatment bag, which work in conjunction with the temperature controller to control the set temperature of the contents of the biotreatment bag. If desired, a temperature-conducting material may be embedded in the surface of the biotreatment bag to counteract the insulating effect of the plastic.

[0080] Cooling can also be provided by a closed-loop water jacket that heats and / or cools the bio-treatment bag via a control system mounted on the bag, or by a standard heat exchanger on a lid or sleeve on the tank supporting the bio-treatment bag. Cooling can also be provided by a Peltier cooler. For example, a Peltier cooler can be applied to the exhaust duct (e.g., a chamber similar to the small bag, with a large volume to slow the air, and a large surface area located in the heat exchanger) to condense gases in the exhaust air to help prevent the exhaust filter from becoming wet. Alternatively, the exhaust filter can be heated by a filter heater to help prevent moisture condensation from the exhaust duct. This heat source can also be waste heat from the active cooling side of the Peltier unit, which guides the hot airflow through ducts and supports for the exhaust filter.

[0081] The bioprocessing bag, including all accessories, perforators, sensors, etc., can be sterilized before use (e.g., by gamma radiation). After sterilization, the interior of the bag, tubing, and components can be considered sterile, providing a "sterile barrier" that protects the contents of the container from airborne external contaminants.

[0082] It should also be understood that the stirred tank bioreactor uses at least three basic operating modes, and the disclosed bioreactor system includes a bioreactor that can be easily modified to operate in any of the three modes. The three modes are as follows.

[0083] Semi-continuous, continuous, or perfusion modes: In semi-continuous, continuous, or perfusion modes, nutrients and supporting process fluids are continuously added to the system; waste is continuously or periodically removed (“drain and refill”); and the product is harvested intermittently or throughout the culture period. In continuous mode, it is generally acknowledged that achieving sufficiently high product titers is consistently difficult. In addition to low titers, it is necessary to concentrate the product in continuous mode.

[0084] Batch mode: In batch mode, all nutrients are added at the beginning and the product is not removed until the batch is finished. Waste accumulates during operation, and nutrients are depleted, making the batch process inefficient for many applications. However, its simplicity makes it ideal for seed culture amplification.

[0085] Fed-batch mode: The fed-batch mode is similar to the batch mode in that the product is only removed at the end of the run, but the difference is that nutrients are added at multiple intervals during the process. Many biotherapeutic drugs and most viruses are produced using microcarrier cultures after infection in a fed-batch process.

[0086] Features, integers, properties, compounds, chemical parts, or groups described in connection with a particular aspect, embodiment, or example of the invention should be understood to be applicable to any other aspect, embodiment, or example described herein, unless incompatible therewith. All features disclosed in this specification (including any appended claims and abstract), and / or all steps of any disclosed method or process, may be combined in any combination, unless at least some of such features and / or steps are mutually exclusive in the combination. The invention is not limited to the details of any of the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification (including any appended claims and abstract), or any novel step or any novel combination of steps of any disclosed method or process.

Claims

1. A bioreactor system for performing a scalable biomanufacturing process, the system comprising: Biological treatment bags with flexible walls; An impeller mounted on an impeller plate, the impeller plate being attached to the inner surface of a flexible wall; and A first bubbler is attached to the inner surface of a flexible wall, wherein when the biotreatment bag is in an inflated state, the ratio of the bubbling surface area of ​​the first bubbler to the cross-sectional area of ​​the bag is about 0.023 to 0.

068.

2. The bioreactor system according to claim 1, wherein the ratio of the bubbling surface area of ​​the first bubbler to the cross-sectional area of ​​the bag is approximately 0.

04.

3. The bioreactor system according to claim 1 or 2, further comprising a second bubbler attached to the inner surface of the flexible wall, wherein when the bioreactor bag is in an inflated state, the ratio of the bubbling surface area of ​​the second bubbler to the cross-sectional area of ​​the bag is about 0.008 to 0.

024.

4. The bioreactor system according to claim 3, wherein the ratio of the bubbling surface area of ​​the second bubbler to the cross-sectional area of ​​the bag is approximately 0.

02.

5. The bioreactor system according to any one of claims 1-4, wherein the ratio of the impeller diameter Di to the bioreactor bag diameter Dt is equal to about 0.3 to 0.

5.

6. The bioreactor system according to claim 5, wherein the ratio of the impeller diameter Di to the bioreactor bag diameter Dt is approximately 0.

4.

7. The bioreactor system according to any one of claims 3-6, wherein the first bubbler is configured to introduce oxygen and / or air into the bioreactor bag, and wherein the second bubbler is configured to introduce nitrogen and / or air into the bioreactor bag.

8. The bioreactor system according to any one of claims 1-7, wherein the distance between the impeller blades of the impeller and the bubbling surface of the first bubbler is about 8 to 24 mm, preferably about 16 mm.

9. A bioreactor system for performing a scalable biomanufacturing process, the system comprising: A first biological treatment bag having a first volume and a first flexible wall; A first impeller is mounted on a first impeller plate, the first impeller plate being attached to a first inner surface of a first flexible wall; A first bubbler attached to the inner surface of a flexible wall, wherein when the first biological treatment bag is in an inflated state, the ratio of the bubble surface area As1 of the first bubbler to the cross-sectional area Ab of the first biological treatment bag is equal to As1 / Ab. A second single-use bio-processing bag having a second volume and a second flexible wall, wherein the second volume is larger than the first volume; The second impeller is mounted on the second impeller plate, which is attached to the second inner surface of the second flexible wall. When the second biological treatment bag is in an expanded state, the ratio of the bubbling surface area D2s1 of the second bubbler to the cross-sectional area A2b of the second biological treatment bag is equal to A2s1 / A2b. Where As1 / Ab is approximately equal to or equal to A2s1 / A2b.

10. The bioreactor system of claim 9, wherein the As1 / Ab ratio is from about 0.023 to 0.

068.

11. The bioreactor system according to claim 9 or 10, wherein the As1 / Ab ratio is about 0.

04.

12. The bioreactor system according to any one of claims 9-11, wherein the first bioreactor bag and the second bioreactor bag each include additional bubblers attached to the inner surfaces of the first and second flexible walls, respectively, wherein the ratio of the bubble surface area As2 of the additional bubbler to the cross-sectional area Ab of the first bioreactor bag is equal to As2 / Ab, and the ratio of the bubble surface area A2s2 of the additional bubbler to the cross-sectional area A2b of the second bioreactor bag is equal to A2s2 / A2b, wherein As2 / Ab is approximately equal to or equal to A2s2 / A2b.

13. The bioreactor system of claim 12, wherein the As2 / Ab ratio is from about 0.008 to 0.

024.

14. The bioreactor system according to claim 13, wherein the As2 / Ab ratio is about 0.

02.

15. The bioreactor system according to claim 9, wherein the ratio of the diameter Di of the first impeller to the diameter Dt of the first biological treatment bag is equal to Di / Dt, and the ratio of the diameter D2i of the second impeller to the diameter D2t of the second biological treatment bag is equal to D2i / D2t, wherein Di / Dt is equal to or approximately equal to D2i / D2t.

16. A method for scaling up a biomanufacturing process, comprising: A first biological treatment bag is provided having a first volume and a first flexible wall. The first biological treatment bag includes a first impeller mounted on a first impeller plate attached to a first inner surface of the first flexible wall and a first bubbler attached to the inner surface of the flexible wall, wherein when the first biological treatment bag is in an inflated state, the ratio of the bubble surface area As1 of the first bubbler to the cross-sectional area Ab of the first biological treatment bag is equal to As1 / Ab. The first biomanufacturing process is carried out in the first bioprocessing bag; A second single-use bio-treatment bag is provided, having a second volume greater than a first volume and a second flexible wall. The second bio-treatment bag includes a second impeller mounted on a second impeller plate attached to a second inner surface of the second flexible wall. When the second bio-treatment bag is in an inflated state, the ratio of the bubbling area A2s1 of the second bubbler to the cross-sectional area A2b of the second bio-treatment bag is equal to A2s1 / A2b. The first biomanufacturing process is expanded to a larger volume by carrying out a second biomanufacturing process in a second bioprocessing bag. Where As1 / Ab is approximately equal to or equal to A2s1 / A2b.

17. The method of claim 16, wherein As1 / Ab is about 0.023 to 0.

068.

18. The method of claim 17, wherein As1 / Ab is about 0.

04.

19. The method according to any one of claims 16-18, wherein the first bio-treatment bag and the second bio-treatment bag each include an additional bubbler attached to the inner surfaces of the first and second flexible walls, wherein the ratio of the bubble surface area As2 of the additional bubbler to the cross-sectional area Ab of the first bio-treatment bag is equal to As2 / Ab, and the ratio of the bubble surface area A2s2 of the additional bubbler to the cross-sectional area A2b of the second bio-treatment bag is equal to A2s2 / A2b, wherein As2 / Ab is approximately equal to or equal to A2s2 / A2b.

20. The method of claim 19, wherein As2 / Ab is about 0.008 to 0.

024.

21. The method of claim 20, wherein As2 / At is about 0.02.

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