1. Introduction
Synthetic liquid perfluorochemicals (PFCs; synonym: perfluorocarbons), which dissolve gases according to Henry’s Law, have been adopted in medicinal liquid ventilation procedures [
1,
2] and bioprocess engineering. PFCs have been repeatedly applied as biochemically inert liquid carriers of respiratory gases in many cell culture systems during the past three decades [
3,
4,
5]. The gas transfer rate into PFCs increases linearly with the partial pressure of a component in the gaseous phase [
6,
7] in opposition to the sigmoid dissociation curve that is characteristic of biological oxygen carriers. The lack of chemical bonds between molecules of oxygen and PFC allows the efficient release of gas from layered or dispersed PFCs into the aqueous phase. Due to the physicochemical properties exhibited by liquid PFCs (i.e., immiscibility with aqueous media), some investigators recommend using them as efficient liquid gas carriers in bioprocesses with biomass of animal or plant cells/tissues performed in various bioreactor systems, as an additional liquid layer at the bottom of a bioreactor vessel [
8,
9,
10], or as dispersed droplets of utilized PFC [
11,
12,
13] in intensively agitated systems.
Currently, in addition to conventional stirred tank stainless steel bioreactors, disposable (i.e., single-use) bioreactors are recognized as suitable equipment for developing and scaling-up in vitro bioprocesses with animal cells maintained in both forms: suspended biomass and as biomass integrated with biomaterial-based constructs or microcarriers. The main systematic difference distinguishing disposable bioreactors from typical bioreactors is the pre-sterilized single-use container made of polymer-based multi-layer plastic, which is applied as a flexible-in-shape bag (i.e., pillow-like shape) for preparation of individual culture environment [
14,
15]. Shape and size (i.e., dimensions and volume) of the culture bag determine the possible mechanism of agitation, which may be applied for efficient mixing of liquid phase poured into such a pillow-shaped container.
Two independent systems of disposable bioreactors are recommended for performing and scaling-up cultures of fragile mammalian cells. The first is a group of single-use stirred tank bioreactors presenting similarity to conventional stirred tanks made of stainless steel typically applied in chemical engineering [
16,
17]. The second group is representing by mechanically driven oscillating systems characterized by mixing driven by sequential horizontal raising and lowering of the culture bag fixed on the oscillating platform of the bioreactor [
18,
19,
20,
21]. Depending on the intensity of the operational parameters (i.e., rocking angle and rate, filling volume, and fluid properties), the liquid phase closed inside the culture bag ripples, waves, or popples, which finally provides wave-induced mixing of the culture medium and its surface aeration [
22,
23].
The new and original bioprocessing concept enhances mass transfer effects inside the disposable culture bag by supplementing the waving culture system with a continuous layer of PFC-based oxygen carrier poured at the bottom of the disposable container. Accordingly, the primary aim of the study was to quantitatively recognize the oxygen transfer effects that occur under conditions of wave-assisted agitation in the system of aqueous phase supported with the perfluorinated gas carrier, which both were waved in a 2.0 liter disposable culture bag of a ReadyToProcess WAVETM 25 bioreactor (WAVE 25; Citiva, formerly GE Healthcare, US).
Pre-sterilized distilled water (dH2O) and phosphate-buffered saline (PBS) were used as two independent aqueous phases, and pre-sterilized perfluorodecalin (PFD) was examined as a liquid PFC-based oxygen carrier. The detailed influences of operational parameters, such as angle (α) and frequency (ω) of oscillations, in addition to volumetric gas flow through a culture vessel (QG), on oxygen mass transfer effects, were identified according to a methodology based on Design of Experiments (DoE). Furthermore, values of the volumetric liquid-side mass transfer coefficient (kLa) obtained independently in dH2O-PFD and PBS-PFD systems were also determined and mutually compared. Finally, the correlations predicting the relation of values of the kLa coefficient and presets of operation parameters in WAVE 25 for both of the studied aqueous phase-PFD systems were initially introduced.
3. Results
Based on the DoE-aided analysis introduced in
Table 1, three operational parameters, i.e.,
α,
ω and
QG, were introduced in the BBD, as previously recognized parameters influencing significantly on oxygen transfer the studied systems. In total, 104 runs of experiments (i.e., 23 typical runs with three extra center point runs for four different studied systems) are presented in
Table 2, as the BBD devised to recognize the influence of operating parameters on the values of the
kLa coefficient obtained for the studied systems under wave-induced mixing. According to this,
kLa values were determined for the minimal, center, and maximal values (i.e., introduced in BBD as −1, 0, and +1, respectively) of
α,
ω, and
QG, for four independent systems: dH
2O (i.e.,
), PBS (i.e.,
), dH
2O supplemented with PFD (i.e.,
), and PBS supplemented with PFD (i.e.,
).
As is commonly known, the
kLa coefficient consists of two factors: the liquid side mass transfer coefficient (
kL) and the interfacial area of mass transfer (
a). The
kL values can be approximated by the Higby penetration mass transfer model [
20,
23], which the following equation can represent:
where:
DL is coefficient of oxygen diffusivity in liquid phase (i.e.,
DL = 3.06
× 10
−9 m
2 s
−1) and
τ is contact time [s].
Based on the values of the
kLa coefficient determined for dH
2O and PBS presented in
Table 2, and values of
kL coefficient calculated from Equation (2), the value of
a can be simply estimated from the following equation:
The values of
a estimated from Equation (3) represent the real interface for oxygen transfer from the gas phase into the liquid phase, which can be compared with the physical interfacial area (
a’) estimated for non-mixed conditions. For example, based on the real geometry of the Cellbag, which contained 0.3 dm
3 of liquid phase (please see
Figure 1), the value of
a’ can be calculated from the following equation:
where:
F is the interfacial area between gas and liquid (i.e., 0.043 m
2), and
VL is the volume of the liquid phase (i.e., 3
× 10
−4 m
3).
To analyze the influence of operating parameters that characterize oscillatory-driven wave-type agitation in WAVE 25, i.e.,
α and
ω, on the value of
a, the interface development factor (
f) was proposed. The values of
f for both studied aqueous phases of dH
2O and PBS were calculated from the following equation:
Moreover, to quantitatively analyze the influence of PFD supplementation on the level of the
kLa coefficient obtained in the studied two-liquid systems (i.e., dH
2O-PFD and PBS-PFD), the enhancement factors
EdH2OPFD and
EPBSPFD were introduced as follows:
analogously to enhancement factors for CO
2 absorption with chemical reaction and without chemical reaction previously defined by DeCoursey [
24].
The values of four originally introduced factors—
,
,
and
—calculated for all runs of the evaluated BBD are shown in
Table 3.
The values of
and
estimated for the present systems reached values smaller than 1.0. It appears that supplementation of the aqueous phase with PFD resulted in lower values of the
kLa coefficient than
kLa noted for pure aqueous phases. A similar relationship was observed previously by Ju [
25] for the emulsion system of water and perfluorocarbon. Ju [
25] reported smaller values of
kLa coefficient for water-perfluorocarbon emulsions than for the perfluorocarbon-free system.
The relationships between values of the
f factor calculated for dH
2O and PBS, and various values of
α and
ω, are graphically presented in
Figure 3. It was found that the obtained values of both
and
monotonically increased for higher values of
α and
ω. Additionally, the observed relationships between the experimentally determined values of
against
α and
ω (
Figure 3A,B) revealed very similar effects to predicted values of
(
Figure 3C,D).
The relationships between values of the
EPFD factor calculated for dH
2O and PBS, and various values of
α,
ω, and
QG are graphically presented in
Figure 4. In the case of the influence of
α and
ω, the values of
and
increased monotonically according to the increase in these operating parameters. Otherwise, it was observed that the increase in the value of
QG resulted in a monotonical decrease in the noted values of both
and
. Furthermore, the presented relationships between the values of
calculated for various values of
α,
ω, and
QG, shown in
Figure 4A–C, revealed very similar effects, resulting from the values of
, which are presented in
Figure 4D–F.
4. Discussion
To date, liquid PFC-based oxygen carriers have been repeatedly applied in prototyped culture systems varying in the volume of vessels, i.e., from ca. 1.0 cm
3 to 100 cm
3. Some examples of two-liquid culture systems that integrated immiscible aqueous phases of culture media and liquid PFC in the forms of dispersed droplets or continuous layers are briefly presented in
Table 4. More examples have been frequently discussed, for example, in a number of previously published reviews [
4,
5,
26].
From the perspective of mass transfer characteristics, systems of two liquids containing aqueous phase and liquid PFC have not been thoroughly described, probably due to the lack of simply-applied practical methods of measuring respiratory gas levels, i.e., O2 and CO2, in the liquid phase of PFD. Additionally, the rarely available literature data focused on such issues may be interpreted as incoherent.
The physical absorption of oxygen in aqueous media has been studied by measuring the values of
kLa as the overall liquid-side mass transfer coefficient. Therefore, the mass transfer rate without chemical reaction was investigated. Both PBS and dH
2O are recommended media to investigate the physical absorption of oxygen, including in single-use bioreactors, and such systems are also suitable for practical approximation of culture conditions [
33]. To widen the applicability of the results presented in the current study, all experiments were performed at 37 °C (
tC), according to the physiological requirements of most certified lines of mammalian cells, which are commonly in vitro cultured in submerged forms in disposable bioreactor systems. Such an assumption allowed comparison of the results reported in the present study with the data obtained for a range of in vitro cultures of isolated mammalian cells performed in a WAVE 25 system equipped with a Cellbag.
In our opinion, to fully recognize the oxygen transfer phenomena that occurred in the rocked system of two immiscible liquids, i.e., aqueous phase and liquid perfluorochemical, we propose the introduction of two factors: f, dependent on a; and EPFD, dependent on kLa. These factors, i.e., f and EPFD, are not typically applied in bioprocess engineering. However, analysis of their values obtained in the studied system facilitated the understanding of observed relationships between the level of the obtained kLa coefficient and operational parameters, i.e., α and ω, defining conditions of wave-assisted agitation.
In the case of the
f factor, the dimensional exponential correlation methodology was proposed to generalize the obtained values of
f that can possibly be obtained under wave-assisted agitation conditions, and not only those restricted to the WAVE 25 bioreactor. Two similar forms of dimensional exponential correlations, which depend only on
α and
ω, for both studied aqueous phases, i.e., dH
2O (Equation (9)) and PBS (Equation (10)), were proposed with the following forms:
According to the multidimensional regression analysis, the values of all constants refining Equations (9) and (10) were found. The parity plots are shown in
Figure 5 in order to verify the correctness of both correlations. As can be easily seen, the values of
and
factors were predicted with the relative error at similar values, i.e., 23–24%, by the correlations (9) and (10).
Similarly, in the case of the
EPFD factor, the dimensional exponential correlation methodology was proposed for the generalized estimation of the values of
EPFD that can possibly be obtained under various conditions of wave-assisted agitation for a broader range of operating parameter values than those presented in
Table 3. Two similar forms of dimensional exponential correlations, which analogously depend on three operational parameters that significantly influence the
kLa level under wave-assisted agitation, i.e.,
α,
ω, and
QG, for both studied aqueous phases independently supplemented with PFD, i.e., for
(Equation (11)) and
(Equation (12)), were proposed in the following forms:
with the values of all constants found according to the multidimensional regression analysis.
The parity plots are shown in
Figure 6 to verify the correctness of both introduced dimensional correlations. As can be easily seen, the values of
and
factors were predicted by the correlations (11) and (12) with the relative errors of 15–17% and 23–26%, respectively.
Moreover, in the case of the
and
factors, it is worth noting that all levels of both factor values that were calculated and presented in
Table 3 were less than 1. These indicate that the addition of PFD reduced the values of the
kLa coefficient in comparison to values reached for aqueous phases (i.e., dH
2O or PBS) without PFD supplementation. Supposedly, supplementation of the studied systems with PFD hypothetically induced the changes in hydrodynamics inside the disposable bag-like container. The worsening of mass transfer in the two liquid systems was observed. This may be caused by the limitation of circulation in liquid phases at the interface of contacting immiscible dH
2O (or PBS) and PFD due to decreases in the local liquid velocity. Such a phenomenon might indicate that the investigated liquid phase was not mixed properly and that the oxygen transfer rate was limited in the total volume of the liquid phase. The waving two-liquid system containing aqueous phase (as the upper liquid phase) and PFD (as the lower liquid phase) is characterized by different hydrodynamics than the waving individual aqueous phase, i.e., dH
2O or PBS, without PFD. We hypothesize that in the case of PFD presence in the studied systems, the circulation of the aqueous phase was significantly less intensive. Similarly, the surface of the aqueous phase was renewed less intensively. These two effects may be interpreted as phenomena that have a strong negative influence on the
kLa values reached for the waving two liquid phase dH
2O-PFD and PBS-PFD systems compared to waving dH
2O or PBS without PFD. Therefore, a decrease in the value of the
kLa coefficient will not disturb oxygenation if oxygen is still available in a liquid PFD-based reservoir. Thus, all of this might hypothetically explain the values lower than 1, estimated for both
and
.
The correlations for
EdH2OPFD and
EPBSPFD introduced by Equations (11) and (12), respectively, are very similar in their forms. Only the value of the absolute term varied in proposed correlations, which may result from different values of the oxygen diffusion coefficient estimated for dH
2O and PBS, i.e., 3.06
× 10
−9 m
2 s
−1 vs. 2.50
× 10
−9 m
2 s
−1, respectively [
34]. The exact values of the other constants refining both discussed dimensional correlations (i.e., Equations (11) and (12)) allowed us to hypothesize that the hydrodynamics of wave-type mixing concerning both studied systems of two liquids—aqueous phase (i.e., dH
2O or PBS) and PFD—were identical.
In our opinion, characterization of mass transfer effects based on such atypical factors as
EPFD may be challenging or problematic to interpret and further discuss, due to the lack of available data in the literature concerning processes of aeration/oxygenation or mixing of two-liquid systems integrating immiscible aqueous phase and PFD. Correlations for predicting the
kLa values are significantly more appreciated and applicable due to commonly known quantitative characteristics of aeration conditions described by the
kLa coefficient. Thus, in the case of the considered aqueous phases not supported with PFD, the dimensional exponential correlation methodology may also be applied for estimation of the values of the
kLa coefficient that can be possibly obtained under various conditions of wave-assisted agitation defined by
α and
ω, and gas-phase flow characterized by
QG, as follows:
Therefore, to verify the correctness of dimensional correlations for predicting the values of the
and
coefficients, the parity plots are presented in
Figure 7. Values of
and
were predicted by the correlations (13) and (14) with similar relative error values not higher than 31% and 28%, respectively.
Finally, based on the above-presented correlations on the
kLa coefficients and the
E factors, i.e., Equations (11)–(14), respectively, dimension exponential correlation for prediction of values of the
kLa coefficient that can possibly be obtained in two-liquid systems containing aqueous phase and PFD (i.e., dH
2O-PFD and PBS-PFD) waving according to the operational parameters in WAVE 25, were proposed in the following forms:
The parity plots are shown in
Figure 8. The values of
and
were predicted with the relative errors of 23–31% and 27–34%, respectively.
The dimensional correlations (15) and (16) summarize the quantitative characterization of oxygen transfer effects in two-liquid systems of aqueous phase (i.e., dH2O or PBS-buffer) containing PFD applied as the gas carrier, and mixed under conditions of wave-assisted agitation performed in a bag-like disposable container (e.g., Cellbag) of a single-use bioreactor.