Cross-section perimeter is a suitable parameter to describe the effects of different baffle geometries in shaken microtiter plates
- Clemens Lattermann†1,
- Matthias Funke†2,
- Sven Hansen3,
- Sylvia Diederichs1 and
- Jochen Büchs1Email author
© Lattermann et al.; licensee BioMed Central Ltd. 2014
Received: 7 May 2014
Accepted: 9 July 2014
Published: 15 July 2014
Biotechnological screening processes are performed since more than 8 decades in small scale shaken bioreactors like shake flasks or microtiter plates. One of the major issues of such reactors is the sufficient oxygen supply of suspended microorganisms. Oxygen transfer into the bulk liquid can in general be increased by introducing suitable baffles at the reactor wall. However, a comprehensive and systematic characterization of baffled shaken bioreactors has never been carried out so far. Baffles often differ in number, size and shape. The exact geometry of baffles in glass lab ware like shake flasks is very difficult to reproduce from piece to piece due to the hard to control flow behavior of molten glass during manufacturing. Thus, reproducibility of the maximum oxygen transfer capacity in such baffled shake flasks is hardly given.
As a first step to systematically elucidate the general effect of different baffle geometries on shaken bioreactor performance, the maximum oxygen transfer capacity (OTRmax) in baffled 48-well microtiter plates as shaken model reactor was characterized. This type of bioreactor made of plastic material was chosen, as the exact geometry of the baffles can be fabricated by highly reproducible laser cutting. As a result, thirty different geometries were investigated regarding their maximum oxygen transfer capacity (OTRmax) and liquid distribution during shaking. The relative perimeter of the cross-section area as new fundamental geometric key parameter is introduced. An empirical correlation for the OTRmax as function of the relative perimeter, shaking frequency and filling volume is derived. For the first time, this correlation allows a systematic description of the maximum oxygen transfer capacity in baffled microtiter plates.
Calculated and experimentally determined OTRmax values agree within ± 30% accuracy. Furthermore, undesired out-of-phase operating conditions can be identified by using the relative perimeter as key parameter. Finally, an optimum well geometry characterized by an increased perimeter of 10% compared to the unbaffled round geometry is identified. This study may also assist to comprehensively describe and optimize the baffles of shake flasks in future.
KeywordsShaken bioreactors Maximum oxygen transfer capacity (OTRmax) Degree of baffling Relative perimeter Out-of-phase phenomena
Shaken small scale bioreactors like shake flasks or microtiter plates are typically used for high throughput screening processes today. In the last years, many efforts have been made to characterize small scale bioreactors by describing and modeling liquid distribution, gas transfer, specific power input as well as mixing (reviewed in [1–7]). These efforts are motivated by the need to understand the yet insufficiently characterized screening systems in more detail. Furthermore, knowledge about important process parameters in an earlier stage of process development is desired [7, 8]. While shake flasks are already characterized to some extent, there are several open questions regarding microtiter plates. The small dimensions of these reactor systems result in specific problems like the influence of surface tension or the lack of space for on-line measurement equipment.
For successful screening processes, sufficient oxygen supply is mandatory . In shaken bioreactors higher maximum oxygen transfer capacities can be achieved by reducing the filling volume or increasing the shaking frequency, the vessel diameter or the shaking diameter. However, this approach has clear limits. Another possibility to enhance the maximum oxygen transfer capacity is the use of baffles inside the bioreactor. However, for shake flasks it is known that the reproducibility of oxygen transfer is poor between individual flasks if baffles are introduced [7, 9, 10]. This is due to the flow characteristics of molten pyrex glass which is very hard to control during the fabrication process of the baffles. As a result, it is nearly impossible to reproduce the exact geometries of the baffles. In most cases this can be proven even by the naked eye. Therefore, some authors even do not recommend the use of baffled shaken bioreactors at all [7, 11].
Fabrication of baffles in microtiter plates is much more accurate and reproducible if laser cutting or injection molding is used. A wide variety of different baffled microtiter plates were extensively studied by Funke et al. . An optimal geometry was found, considering different criteria. The best version is meanwhile commercially available. It shows reproducible oxygen transfer properties on an elevated level.
Up to now, no general method to predict the impact of baffles and its geometries on the maximum oxygen transfer capacity of shaken bioreactors is available. This is mainly caused by the problem to obtain a set of different baffled bioreactors with reproducible geometries made from glass. Therefore, in this work we utilized the results of Funke et al.  which were generated with the sulfite method for a wide variety of different reproducible geometries of 48-well microtiter plates as shaken model bioreactors. By using 48-well microtiter plates, an influence of surface tension which is quite prominent in 96-well microtiter plates is minimized [4, 13]. The absolute cross-section areas were consistently kept constant (112 mm2) among the different geometries. The relationship between the geometries of the wells and the maximum oxygen transfer capacities were derived and a respective mathematical correlation was developed. This correlation depends on the shaking frequency, the filling volume and the relative perimeter of the cross-section area of the wells as new geometric key parameter. In this equation, the relative perimeter is the only criterion reflecting the degree of baffling. Thereby, all important parameters of baffling like number, size and shape of the baffles are considered in one value. This work is deemed to be the first step in understanding and quantifying the impact of baffles on shaken bioreactor performance. In a future attempt the applicability of the developed approach has to be proven also for baffled shake flasks.
Results and discussion
Influence of baffling on oxygen transfer in microtiter plates
In Figure 3, the OTRmax is plotted as a function of the relative perimeter of all investigated geometries to systematically characterize the influence of baffles on the maximum oxygen transfer capacity. The smoothing splines between the measurement points were calculated by applying a modified L-curve criterion. As expected, the maximum oxygen transfer capacity increases with decreasing filling volume, as illustrated in Figure 3. This result agrees with the theory and literature, since the surface-to-volume ratio, and, thus, the oxygen transfer into the bulk liquid increases with decreasing filling volume in surface aerated bioreactors . The measured OTRmax value in general increases with increasing shaking frequency. This trend also agrees with literature . Furthermore, the shapes of the OTRmax curves over the relative perimeter for filling volumes of 200 - 400 μL equal each other. For example, looking at a specific shaking frequency, the OTRmax curves are merely shifted in their absolute height depending on the filling volume. For filling volumes of 500 μL and 600 μL the shape of the OTRmax curves seem to be smoother.
The most important result depicted in Figure 3 is the development of the OTRmax curves as a function of the relative perimeter. Starting at a relative perimeter of 1.0, up to a relative perimeter of approximately 1.05, a linear increase of the OTRmax values can generally be observed. Subsequently, always a maximum is reached at a relative perimeter of about 1.075 to 1.12. For even higher relative perimeters, the OTRmax values remain either constant (<700 rpm) or decrease (>700 rpm). Obviously, there is a common limit of the OTRmax for all applied shaking frequencies, filling volumes and well geometries. Expressed in other words, increasing the degree of baffling increases the maximum oxygen transfer capacity until an upper limit value is reached. This maximum is generally observed at baffled geometries with a perimeter 10% larger than the one of the unbaffled round geometry. The result is quite astonishing because it reflects the abstract character of the relative perimeter, taking number, size and shape of the baffles indirectly into account. According to Figure 1C, the maximum oxygen transfer capacity at a relative perimeter of 1.1 corresponds to a geometry between square (Ø2) and the 6-edged flower (Ø5). It is remarkable that this result excellently agrees with the qualitative observations made by Funke et al . It can now be quantitatively described by means of the relative perimeter.
Influence of baffling on liquid distribution in microtiter plates
The phenomenon of stagnant or decreasing OTRmax values at relative perimeters > 1.1 in Figure 3 has to be evaluated in detail to entirely explain the whole data. In order to understand the mass transfer data, the behaviour of the rotating liquid has to be considered. The bulk liquid in shaken bioreactors typically rotates inside the vessel if in-phase conditions exist. In contrast, at out-of-phase conditions the major part of the liquid remains on the bottom of the vessel and does not move anymore. Simultaneously, the maximum liquid height and the maximum oxygen transfer capacity into the liquid is reduced.
Three different reasons for inducing these unsuitable out-of-phase conditions in shake flasks were identified in literature . One effector is elevated viscosity. In this case, out-of-phase conditions are provoked, if the rotating centrifugal force is not strong enough to overcome the viscous forces . A new Phase-Number Ph was defined and concluded that Ph > 1.26 is the relevant constraint for desired in-phase operation . Another reason for out-of-phase conditions are unsuitable high ratios between the maximum diameter of the shaken bioreactors and the shaking diameter of the applied shaker, as shown for non-baffled large shake flasks by Büchs et al.  and for microtiter plate with round geometry by Kensy et al. . The third reason for unsuitable out-of-phase operating conditions in shake flasks is the introduction of baffles which are too in number large in size. Problems may already occure at water-like viscosities. The probability of out-of-phase conditions increases with decreasing shaking diameter [7, 15]. The undesired phenomenon appears if the rotating centrifugal force generated by the shaker is not strong enough to overcome the negative impact of the baffles preventing the bulk liquid from rotating in the flask. Although this third reason for out-of-phase conditions resembles the first reason, the above mentioned Phase-Number can not be used to evaluate the impact of baffles.
Considering the decreasing mass transfer at higher degrees of baffling (relative perimeter > 1.1) it can be speculated that out-of-phase conditions exist at relative perimeters higher than 1.1 in the investigated 48-well microtiter plates. Therefore, an experimental examination of the appearance of out-of-phase conditions has been conducted in this study. As mentioned above, the shaken liquid remains at the bottom of the well if out-of-phase conditions are present. This implies that the liquid height at the well center is elevated compared to in-phase conditions. Hence, an optical measurement of the liquid height provides further information about the flow conditions in the microtiter wells and, thus, may help to explain the observations of the mass transfer study.
The relative perimeter as integral parameter to calculate OTRmax in microtiter plates
Equation (2) represents a novel equation to pre-calculate the maximum oxygen transfer capacity OTRmax in baffled 48-well microtiter plates at in-phase operating condition. The OTRmax is calculated dependent on the relative perimeter of the well geometry (Peri), the shaking frequency (n) and the filling volume (VL). From literature it is known that the shaking diameter also has a strong influence on the oxygen transfer in shaken bioreactors . However, for optical on-line measurements in shaken microtiter plates using the BioLector technique, a constant shaking diameter of 3 mm is established . Therefore, the shaking diameter in this study was kept constant to 3 mm and the influence of the shaking diameter is not considered in Eq. (2). The constant second term in Eq. (2) is explained by the fact that a basal oxygen transfer is accomplished by sole diffusion at static condition (without any convective flow). This effect has originally been discovered by Hermann et al.  for 96-well plates and later been verified by Kensy et al. for 48-well plates .
Conclusion and outlook
In this work the influence of baffling on the maximum oxygen transfer capacity in 48-well microtiter plates has quantitatively been investigated. The relative perimeter of the cross-section area was chosen as geometric key parameter to correlate the maximum oxygen transfer capacity with the shaking frequency and filling volume. In agreement with the qualitative results of Funke et al , an optimum maximum oxygen transfer capacity could be found at a relative perimeter of 1.1. Furthermore, optical measurements of the liquid height at the center of the wells were conducted to obtain additional information about the prevailing operating condition. It could be shown that undesired out-of-phase conditions exist if the relative perimeter exceeds values of 1.1. With this investigation, a phenomenological explanation for the measured mass transfer values could be given. Finally, an empirical correlation was derived to calculate the maximum oxygen transfer capacity in baffled microtiter plates depending on the shaking frequency and filling volume. The relative perimeter as geometric key parameter includes the specific properties of the baffles. Therefore, the degree of baffling in microtiter plates can now quantitatively be described for new geometries if liquids with water-like viscosities are used and effects caused by surface tension are negligible. The obtained correlation is limited to microtiter plates shaken at a shaking diameter of 3 mm. Further investigations in other shaken bioreactors like shake flasks or large shaken barrels have to be carried out to extend the correlation to a more universal equation. The influence of specific effects in small scale bioreactors, e.g. caused by surface tension, could also be investigated in future studies.
Materials and methods
Baffled well geometries
A total of thirty different well geometries, varying in number, size and shape of the baffles, were investigated in this work. The baffled geometries shown in Figure 1 have been realized in the wells of 48-well microtiter plates by introducing rectangular or rounded wall structures. The dimensions of the wells were chosen as such that the cross sectional area is always equivalent (112 mm2) to the round reference geometry.
Prototypes of microtiter plate bodies were fabricated out of a 20 mm thick acrylic glass plate (polymethyl methacrylat, PMMA) with outer dimensions of 128 mm × 85 mm by laser cutting. To seal the bottom, a PMMA plate of 2 mm thickness was glued onto the bottom of the prototype bodies. As illustrated in Figure 1A, 3 different sets of well geometries represent a gradual transition from the most pronounced baffling (square and pentagon geometry, respectively) to the least pronounced baffling (round geometry). The transition was realized in 3 different ways. First, starting at square geometry, the number of edges is continuously increased. Second and third, starting at square and pentagon geometry, the edges are more and more rounded. Moreover, Figure 1B shows 3 groups of well designs attained by introducing different types of baffles in round or edges well geometries. For further details regarding the investigated well geometries refer to .
Optical measurement system
The BioLector technique was used to determine the liquid height at the well center of the microtiter plate as well as the maximum oxygen transfer capacity OTRmax of the different baffled geometries. This optical measurement system enables non-invasive fluorescence and scattered light measurements in shaken microtiter plates . The shaking process of the microtiter plate is not interrupted and, thus, disturbing influences during measurement are avoided. Thereby, a quasi-continuous measurement in shaken microtiter plates is realized. In this study, a slightly modified BioLector system was used which consists of an orbital shaker (based on Lab-Shaker LS-W, Kühner AG, Basel, Switzerland), a x-y linear drive (Bosch Rexroth AG, Lohr am Main, Germany), a custom-made filter fluorescence spectrometer (PreSens GmbH, Regensburg, Germany) and a computer. The orbital shaker was modified to realize a shaking diameter of 3 mm and shaking frequencies of up to 1000 rpm. A hood was placed above the microtiter plate on the shaker tray. The hood was continuously flushed with humidified air to reduce evaporation. To avoid the influence of a cover foil, no additional cover except the hood was used. For further information regarding the optical measurement device refer to .
Characterization of oxygen transfer with a 0.5 M sulfite system
Using Eq. (6), the maximum oxygen transfer capacity can now be obtained indirectly through measurement of the oxygen transfer rate.
Detection of out-of-phase conditions through liquid height measurements
The liquid height at the well center of the microtiter plate was determined by measuring the fluorescence intensity of a 1.25 · 10−6 M fluorescein solution (sodium salt, Fluka, Buchs, Switzerland) in 0.2 M sodium phosphate buffer (pH 7) (Roth, Karlsruhe, Germany). The fiber optics of the BioLector prototype was vertically installed underneath the wells. All experiments to determine the liquid height were conducted at a constant filling volume of VL = 500 μL and different shaking frequencies of 400 – 1000 rpm. The fluorescence was excited at 420 nm (bandpassfilter ± 10 nm) and detected above 515 nm (cut-of filter). For calibration, different filling volumes of the fluorescein solution were filled into the microtiter plate prototypes. The fluorescence signal was measured at a shaking frequency of 200 rpm, where no liquid movement occurs . Since the cross-section area for each geometry is constant (112 mm2), the liquid height can be calculated depending on the filling volume. The fluorescence signal of the fluorescein solution decreases with decreasing liquid height. Thus, a geometry-independent correlation of fluorescence signal and liquid height at the well center is obtained.
Fitting of measurement data by applying the L-curve criterion
Equations (7) to (9) were implemented into an algorithm and solved by applying the MATLAB software package (Version 7.8.0; The Mathworks, MA, USA).
Regularization parameter [-]
Oxygen concentration in the liquid [mol/L]
Oxygen concentration at the gas-liquid interface [mol/L]
Sulfite concentration [g/L]
First-order kinetic reaction constant [1/h]
Volumetric mass transfer coefficient [1/h]
Oxygen solubility in the liquid [mol/L]
Shaking frequency [1/min]
Oxygen transfer rate [mol/L/h]
Maximum oxygen transfer capacity [mol/L/h]
Oxygen partial pressure in the gas phase [bar]
Normalized perimeter of the baffled geometry [-]
Perimeter of the baffled geometry [mm]
Perimeter of the round reference geometry [mm]
Residual, representing the data error [-]
Regularized solution, representing the smoothness of the curve [-]
Reaction time [s]
Filling volume [μL]
Stoichiometric coefficient of oxygen [-]
Data point of measurement data [-], in this study substituted by measured data of OTRmax.
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