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During the past 10 years, single-use bioreactors have been well accepted in modern biopharmaceutical production processes targeting high-value products. Up to now, such processes have mainly been small- or medium-scale mammalian cell culture-based seed inoculum, vaccine or antibody productions. However, recently first attempts have been made to modify existing single-use bioreactors for the cultivation of plant cells and tissue cultures, and microorganisms. This has even led to the development of new single-use bioreactor types. Moreover, due to safety issues it has become clear that single-use bioreactors are the "must have" for expanding human stem cells delivering cell therapeutics, the biopharmaceuticals of the next generation. So it comes as no surprise that numerous different dynamic single-use bioreactor types, which are suitable for a wide range of applications, already dominate the market today. Bioreactor working principles, main applications, and bioengineering data are presented in this review, based on a current overview of greater than milliliter-scale, commercially available, dynamic single-use bioreactors. The focus is on stirred versions, which are omnipresent in R&D and manufacturing, and in particular Sartorius Stedim's BIOSTAT family. Finally, we examine development trends for single-use bioreactors, after discussing proven approaches for fast scaling-up processes.
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Dynamic Single-Use Bioreactors Used
in Modern Liter- and m
3
- Scale
Biotechnological Processes: Engineering
Characteristics and Scaling Up
Christian Löffelholz, Stephan C. Kaiser, Matthias Kraume,
Regine Eibl and Dieter Eibl
Abstract During the past 10 years, single-use bioreactors have been well
accepted in modern biopharmaceutical production processes targeting high-value
products. Up to now, such processes have mainly been small- or medium-scale
mammalian cell culture-based seed inoculum, vaccine or antibody productions.
However, recently first attempts have been made to modify existing single-use
bioreactors for the cultivation of plant cells and tissue cultures, and microorgan-
isms. This has even led to the development of new single-use bioreactor types.
Moreover, due to safety issues it has become clear that single-use bioreactors are
the ‘‘must have’’ for expanding human stem cells delivering cell therapeutics, the
biopharmaceuticals of the next generation. So it comes as no surprise that
numerous different dynamic single-use bioreactor types, which are suitable for a
wide range of applications, already dominate the market today. Bioreactor working
principles, main applications, and bioengineering data are presented in this review,
based on a current overview of greater than milliliter-scale, commercially avail-
able, dynamic single-use bioreactors. The focus is on stirred versions, which are
omnipresent in R&D and manufacturing, and in particular Sartorius Stedim’s
BIOSTAT family. Finally, we examine development trends for single-use biore-
actors, after discussing proven approaches for fast scaling-up processes.
Keywords Computational fluid dynamics Engineering characteristics Main
applications Scale-up Single-use bioreactor types
C. Löffelholz (&)S. C. Kaiser R. Eibl D. Eibl
School of Life Sciences and Facility Management, Institute of Biotechnology,
Zurich University of Applied Sciences (ZHAW), 8820 Wädenswil, Switzerland
e-mail: christian.loeffelholz@zhaw.ch
M. Kraume
Department Chemical and Process Engineering, Technische Universität Berlin,
Straße des 17. Juni 135, 10623 Berlin, Germany
Adv Biochem Eng Biotechnol
DOI: 10.1007/10_2013_187
ÓSpringer-Verlag Berlin Heidelberg 2013
Abbreviations
1-D 1-dimensional
2-D 2-dimensional
3-D 3-dimensional
A
o,G
Interfacial area of gas bubbles
aSpecific interfacial area
BWidth of the bag
Bo Bond number
c
m
Dimensionless mixing number
c
o2
Actual concentration of the oxygen in the liquid
c
o2
*
Saturation concentration of the oxygen in the liquid
c
s
Distance between stirrers
c
s
/d
s
Ratio of stirrer distance to stirrer diameter
cv Culture volume
CCorrelation factor
CFD Computational fluid dynamics
CHO Chinese hamster ovary cells
d
0
Shaking diameter
d
32
Sauter diameter
d
B
Bubble diameter
d
m,SF
Maximal shake flask diameter
d
s
Stirrer diameter
d
s
/DRatio of the stirrer and bioreactor diameter
d
SF
Diameter shake flask
d
x
Cell diameter
DVessel diameter
D
I
Inner diameter of the container
DO Dissolved oxygen
Do
2
Diffusion coefficient of oxygen
FDA Food and Drug Administration
Fr Froude number
FVM Finite volume method
hMSC Human mesenchymal stem cells
hStirrer height
h/DRatio of stirrer height and bioreactor diameter
h/HRatio of stirrer and liquid height
HHeight of the liquid
Ha Hatta number
HCD High cell density
H/DRatio of liquid height and bioreactor diameter
HTS High-throughput screening
kRocking rate
k
H
Henry coefficient
k
L
Mass transfer coefficient
C. Löffelholz et al.
k
a
LVolumetric mass transfer coefficient
k
n
Reaction coefficient
LLength of the bag
LBM Lattice–Boltzmann method
LDA Laser–Doppler anemometry
mSlope in (26)
MTorque
M
d
Dead weight torque (measured without liquid, representing
only the bearing torque)
nReaction order
Ne Newton number
N
S
Rotation frequency
OD Optical density
OTR Oxygen transfer rate
OUR Oxygen uptake rate
PPower input
P/VSpecific power input
PIV Particle image velocimetry
PMP Plant-made protein
p
O2
Oxygen partial pressure
PTV Particle tracking velocimetry
q
02
Specific oxygen uptake rate
Re Reynolds number
Re
crit
Critical Reynolds number
RT Rushton turbine
S.U.B. Single-use bioreactor from ThermoFisher scientific
SBI Segment blade impeller
Sc Schmidt number
tTime
u
G
Superficial gas velocity
u
max
Maximum velocity
u
Tip
Tip speed
VWorking volume
WIM Wave-induced motion
XLiving cell density
xRadial coordinate
x
1
and x
2
Empirical constants
XD Extreme density
aVolume fraction
bCoefficient
c
NT
Local shear gradients
c
NT, m
Mean local shear gradients
e
T
Local energy dissipation rate
gViscosity
Dynamic Single-Use Bioreactors
h
m
Mixing time
kKolmogorov length scale
qDensity
Contents
1 Introduction..............................................................................................................................
2 Single-Use Bioreactor Types ..................................................................................................
2.1 Current Overview ...........................................................................................................
2.2 Scale-Dependent, Potential Fields of Application.........................................................
3 Bioengineering Characterization of Single-Use Bioreactors: Methods and Parameters ......
3.1 Fundamental Engineering Characterization...................................................................
3.2 Advanced Engineering Characterization........................................................................
4 Bioengineering Data of the UniVessel SU and BIOSTAT CultiBag STR...........................
4.1 Fluid Flow Pattern and Velocity Distribution ...............................................................
4.2 Power Input.....................................................................................................................
4.3 Mixing Time ............................................................................................. ......................
4.4 Mechanical Stress ...........................................................................................................
4.5 Volumetric Mass Transfer Coefficient ..........................................................................
5 Scale-up of single-use bioreactors ..........................................................................................
6 Conclusions and Outlook ........................................................................................................
References......................................................................................................................................
1 Introduction
The term ‘‘single-use’’ bioreactor (or ‘‘disposable’’ bioreactor) refers to the fact
that the cultivation container is made of FDA-approved plastics (e.g., polyethylen,
ethylenevinylacetate, polycarbonate, polystyrene) [1], and is only used once [2].
The cultivation container is typically provided in a sterile state and already pre-
assembled, so that it can be used directly without further preparation. After fin-
ishing the bioprocess it is decontaminated and discarded. The resulting absence of
sterilization and cleaning procedures allows products to be changed and new
production campaigns to be started very quickly [3]. This finally leads to higher
process flexibility, savings in time and costs, improvements in biosafety, and
reduced environmental impact and waste, as has already been demonstrated in
different studies with single-use bioreactors [46]. Sensor techniques [2], leach-
ables/extractables (which can be secreted from plastic material and decrease
product quality) [7], stability of the plastic material, and vendor dependence are
among the main drawbacks of single-use bioreactors [8].
Nevertheless, advantages prevail, and single-use bioreactors have reached
annual growth rates of 11 % [8] during recent years. This continuous growth can
be ascribed to the international demand for rapid development, increased
C. Löffelholz et al.
manufacturing of new biotherapeutics (such as antibodies, hormones, enzymes,
and vaccines), and an up to tenfold increase in the quantities of product titers that
can be reached in these types of bioreactors [9,10]. This last achievement explains
the reduction of bioreactor size from 20 and 10 m
3
to 2 and 1 m
3
respectively, and
the availability of single-use bioreactors in these smaller sizes.
Whereas single-use cultivation containers up to 50-L culture volume are rigid
plastic vessels, cultivation containers for larger culture volumes are flexible, multi-
layered plastic bags. These bags differ in their shapes and are 2-D pillowlike, 3-D
cylindrical, 3-D cubes, 3-D with asymmetrical geometry or 3-D U-shaped. It is
worth mentioning that trouble-free use of a flexible bag always requires a support
container (dike or vessel often made from stainless steel) which supports the bag
and keeps it in shape.
With the exception of single-use bioreactors developed for high-throughput
screening (HTS), such as the Advanced MicroBioReactor System from TAP
Biosystems [11,12] or the Biolector from m2p-labs [13], and hollow fiber-based
stem cell bioreactors such as the Quantum Cell Expansion System from Cari-
dianBCT [14,15], single-use bioreactors for milliliter-scale applications are nor-
mally not instrumented. These types of single-use bioreactors are not included in
this chapter. In contrast, liter- and cubic meter-scale single-use bioreactors are
equipped with standard or single-use sensors (installed either in situ or ex situ) to
measure and control main process parameters such as pH and DO [16,17].
However, single-use bioreactors are characterized by a lower level of instrumen-
tation in comparison to reusable versions. In single-use bioreactors standard sen-
sors are only regarded as a compromise inasmuch as their application requires the
availability of 12-mm ports and aseptic connectors, or other special solutions. In
addition, standard sensors need to be calibrated and sterilized before use,
increasing the contamination risk. For this reason, single-use noninvasive and
optical sensors are preferred by the majority of users.
2 Single-Use Bioreactor Types
The way for single-use bioreactors was paved by Fenwal‘s invention of the plastic
blood bag in 1953 [18]. The first hollow fiber reactor was developed by Knazek
et al. [19] in the early 1970s, followed by the replacement of CellFactories [20]
and roller flasks. However, the development of further single-use bioreactors
finally led to wave-mixed bioreactors [21,22], which have increasingly displaced
spinner flasks in seed inoculum productions since the early 2000s. Today the user
can choose among a multitude of single-use bioreactors provided by different
vendors. A systematization of single-use bioreactors that is analogous to that of
their reusable counterparts was recommended by Eibl et al. [23,24] and is based
on the type of power input. Due to improved energy and mass transfer, dynamic
single-use bioreactors have gained importance as scale has increased.
Dynamic Single-Use Bioreactors
2.1 Current Overview
It can be clearly seen from Table 1, which summarizes commercially available
liter- and cubic meter-scale dynamic single-use bioreactors, that mechanically
driven wave-mixed and stirred systems represent the largest groups among the
listed types. This development can be explained by the long-term experience of
using stirred reusable bioreactors and the available knowledge in this area. The
Wave was the first scalable single-use system that became accepted, despite its
new mixing principle, wave-induced motion (WIM).
The WIM is caused by rocking or raising the platform containing the differently
shaped single-use bags and is dependent on the bioreactor type (e.g. BIOSTAT
CultiBag RM or AppliFlex). To date, six single-use bioreactor configurations from
different vendors (the Wave Bioreactor, the BIOSTAT CultiBag RM, the Smart-
Bag, the AppliFlex, the CELL-tainer and the XRS Bioreactor System) are in use
for a wide range of production organisms including microorganisms [25], algae
[26], plant cells [27], animal cells [2830], bioactive T-cells [31,32] and human
mesenchymal stem cells (hMSCs) [33,34]. As described by Ref. [27], power input
and mass transfer are mainly influenced by the rocking rate, rocking angle, culture
volume, culture broth viscosity and aeration rate. Along with WIM, bubble-free
surface aeration in wave-mixed bioreactors results in more homogeneous energy
dissipation and reduced foaming and flotation compared to stirred cell culture
bioreactors. This is particularly the case for 1-D moving bags, which (in contrast to
2-D or 3-D moving bags) can exhibit limited power input and oxygen transfer for
non-Newtonian fluids (e.g., plant cell suspensions) and aerobic microbial high cell
density (HCD) cultivations. However, this problem is of less significance in animal
cell-derived productions, where Newtonian fluid flow behavior is assumed. Scaling
up of geometrically dissimilar wave-mixed single-use bioreactors (see also Sect. 5)
is more problematic (maximum scale is limited; less knowledge of scale-up cri-
teria exists), despite the fact that the sales literature highlights easy scalability as
one advantage of this type of bioreactor.
As with wave-mixed bioreactors, mechanically driven, rotatory oscillating
(BayShake Bioreactor [35]) and orbitally shaken single-use bioreactors (Current
Bioreactor, OrbShake Bioreactor) contain no moving parts in the bag. They are
surface-aerated and characterized by homogeneous energy dissipation and negli-
gible foaming or flotation. Because they only recently entered cell culture labs,
there are fewer application data available, even though bioengineering data have
been determined and scale-up criteria proposed [4,34,3638].
In Meissner‘s mechanically driven, oscillating, single-use Saltus Bioreactor
(formerly VibroMix), the power input is adjustable through regulation of the motor
amplitude and frequency [39]. An axial flow that mixes and aerates the cells in a
cylindrical bag is caused by the movement of one or more perforated disks, which
are fixed to an oscillating hollow shaft. The Saltus Bioreactor can generate high
local power inputs and is designed for applications that are suited to medium to
high shear conditions and culture broths with high viscosity. This means that this
C. Löffelholz et al.
Table 1 Current overview of commercially available liter- and cubic meter-scale single-use bioreactors
Working principle Bioreactor brand Max. cv Vendor References
Mechanically driven, oscillating movement, wave-mixed
1-D WIM by rocking a
pillowlike 2-D culture bag
Wave Bioreactor 500 L GE Healthcare [22,4449]
BIOSTAT CultiBag RM 300 L Sartorius Stedim Biotech [2528,
5058]
SmartBag 25 L Finesse [59]
1-D WIM by rocking a 3-D culture bag AppliFlex 25 L Applikon Biotech [54,60,61]
2-D WIM by rocking a 3-D culture bag CELL-tainer 125 L Cellution Biotech [56,6264]
3-D WIM by rocking a 3-D culture bag XRS Bioreactor System 25 L Pall Life Sciences [65]
Mechanically driven, rotatory oscillating
3-D culture bag (cube-shaped) BayShake Bioreactor 1 m
3
Bayer Technology Services [4,35,66]
Mechanically driven, oscillation motion
3-D culture bag with one or more vibrating
disks
Saltus Bioreactor (in the past
VibroMix)
100 L Meissner Filtration Productions,
Incorporation
[24,39]
Mechanically driven, orbitally shaken
3-D culture bag CURRENT Bioreactor 300 L AmProtein [6769]
OrbShake Bioreactor 250 L Satorius Stedim Biotech/Kühner [36,7073]
Mechanically driven, stirred
Rotating stirrer, magnetically coupled, 3-D
culture bag
XDR 2 m
3
Xcellerex (now part of GE Healthcare) [7478]
Mobius CellReady 200 L Merck Millipore [7981]
BIOSTAT CultiBag STR 1 m
3
Sartorius Stedim Biotech [57,8286]
Rotating stirrer, mechanically coupled, rigid
cylindrical vessel
UniVessel SU 2 L Sartorius Stedim Biotech [87,88]
Mobius CellReady 2.4 L Merck Millipore [21,34,89,
90]
CelliGEN BLU Single-Use
Bioreactor
50 L Eppendorf [91]
Rotating stirrer, mechanically coupled, 3-D
culture bag
Single-Use Bioreactor (S.U.B.) 2 m
3
Thermo Fisher Scientific [54,64,92
94]
(continued)
Dynamic Single-Use Bioreactors
Table 1 (continued)
Working principle Bioreactor brand Max. cv Vendor References
Tumbling stirrer, magnetically coupled, 3-D
culture bag (cube-shaped)
Nucleo Bioreactor 1 m
3
ATMI [93,95,96]
Pneumatically driven
Air Wheel design, 3-D culture bag
(U-shape)
PBS Bioreactor 2 m
3
PBS Biotech [40,97]
Bubble column type,
3-D culture bag (asymmetrical geometry)
CellMaker Regular 8 L Cellexus [4143]
Pneumatically driven and mechanically driven (hybrid)
Combination of bubble column and stirred
type, 3-D culture bag (asymmetrical
geometry)
CellMaker Plus 50 L Cellexus [41]
Hydraulically driven
Fixed bed type, 3-D culture bag iCELLis 55 L &666 m
2
ATMI [98101]
Remark If not specially specified, the bag is cylindrical
cv culture volume
C. Löffelholz et al.
single-use bioreactor is not recommended for animal cell cultivations and pro-
cesses with shear-sensitive plant cells.
Aeration and mixing in stirred single-use bioreactors, for which animal and
microbial versions exist, is ensured by the aeration device (which is in most cases
static) and rotating or tumbling stirrer(s) installed in the bag. A stirrer must be
aseptically sealed, if it is not magnetically coupled, as is the case in the Mobius
CellReady 3 L from Merck Millipore and the S.U.B. versions from ThermoFisher
Scientific. Nevertheless, scaling-up of stirred single-use bioreactors is easier due to
the geometrical similarity within a bioreactor family, which is normally based on
reusable stirred cell culture bioreactors (compare also Sects. 3 and 4).
Pneumatically driven single-use bioreactors (Table 1) are applied for animal
[40] and microbial [4143] cultivations. They operate on the bubble column
principle and provide homogeneous energy dissipation and high-efficiency mass
transfer.
Disadvantages of bubble column bioreactors principally include bubble coa-
lescence, strong foaming, and flotation. The currently available single-use, pneu-
matically driven bioreactors differ mainly in bag scale, shape and method of
bubble generation. More detailed information about their working principles and
characteristics are provided by Refs. [24 and 39].
Bubble column and stirring principles are combined in Cellexus‘s CellMaker
Plus, a hybrid, single-use bioreactor, suitable for microorganisms, algae, and
animal cells [41,102]. The first hydraulically driven bioreactor with a bag is the
ATMI‘s iCELLis, a single-use fixed bed bioreactor. The iCELLis uses medical-
grade polyester microfiber macrocarriers, which provide capacity for HCDs,
leading to high product titers in mammalian cell-based vaccine productions [98,
99]. As described by Prieels and Hambor [100,101], this single-use bioreactor also
allows successful expansion of hMSCs, where the scale is defined by the height of
the bed.
2.2 Scale-Dependent, Potential Fields of Application
If focusing on potential fields of application for the previously described dynamic,
single-use bioreactors, seven scale- and production-organism-dependent fields
become evident (see Fig. 1). Production organisms are either grown as free or
immobilized (bound to a carrier) cells. In most cases the bioreactors produce
animal cell-derived products used in prophylaxis, diagnosis and therapy on a
medium volume scale. They are mainly operated in fed batch (feeding) mode or, if
HCDs and high-level protein titers are required, in perfusion mode [103]. For
example, DSM Biologic’s XD process [104] is a perfusion process that guarantees
cell densities of around 1 910
8
cells/mL and antibody titers of around 25 g/L.
In seed inoculum productions, the wave-mixed BIOSTAT CultiBag RM and
Wave Bioreactor have become widely accepted, whereas stirred, single-use bio-
reactors up to 1 m
3
are the systems of choice if mammalian cell-derived
Dynamic Single-Use Bioreactors
therapeutics are the targeted products. Even though stirred single-use systems are
already available up to 2 m
3
, they have rarely been used. This is closely related to
the more extensive operating procedures and training for staff, which both increase
as culture volumes in single-use bioreactor bags rise.
If shear-sensitive cells (such as T-cells, bone marrow, or adipose tissue derived
hMSCs) need to be grown, or if processes have to be realized, in which extensive
foaming can occur (e.g., insect cell-based processes, where no chemically defined
culture medium exists), wave-mixed single-use bioreactors should be chosen. As
already mentioned in Sect. 2.1, they are characterized by homogeneous energy
dissipation and low foam formation.
Wave-mixed bag bioreactors (up to a culture volume of 300 L) are also suc-
cessfully used for the commercial production of plant-cell-derived secondary
metabolites for cosmetics. Prominent product examples include the PhytoCELL-
Tec products (Malus domestica Uttwiler Spätlauber, Vitis vinifera Gamay Tein-
turier Fréaux Grap, and Arganium spinosum) from Mibelle Biochemistry [105] and
RESISTEM from Sederma [106]. As described by [26], existing photobioreactor
versions are also suitable for microalgae cultivations. For the manufacturing of so-
called plant-made proteins (PMPs) single-use bioreactors have rarely been used.
Nevertheless, there will be a demand in the future for single-use bioreactors for
plant and microbial cell-derived high-value products that are not limited by mass
transfer (energy and oxygen). Specially designed microbial versions of the CELL-
Fig. 1 Potential fields of application for dynamic single-use bioreactors exceeding mL-scale
C. Löffelholz et al.
tainer and the XDR have proven themselves for HCD cultivations of Escherichia
coli, Pichia pastoris and Aspergilli [63,75]. ODs between 100 and 140 are also
achievable for microorganisms grown in standard versions of the BIOSTAT
CultiBag RM, as demonstrated by different groups [25,82,107]. In these cases
there was either a low culture volume of 20 % or special feeding strategies were
applied.
3 Bioengineering Characterization of Single-Use Bioreactors:
Methods and Parameters
Knowledge of principal single-use bioreactor engineering parameters (such as
mixing time, mass transfer coefficient, power input, fluid flow etc.) enables fast
process optimization, scaling-up, and comparison of different types of bioreactors.
The same methods were used to determine the bioengineering characteristics of
the single-use bioreactors as for their reusable counterparts. Taking this into
account, there is a differentiation between fundamental and advanced engineering
methods. Methods that have been established and proven for single-use bioreactors
and their resulting parameters are subsequently summarized and discussed.
3.1 Fundamental Engineering Characterization
In general, the flow regime in bioreactors can be characterized as laminar, tran-
sitional, or turbulent, depending on the dominance of viscous or inertial forces.
This is characterized by the Reynolds number (Re), which is defined for stirred
systems by (1) and depends on the stirrer diameter (d
S
), speed (N
S
) and liquid
properties: liquid density (q
L
) and viscosity (l
L
). It is well-known that the flow
becomes fully turbulent above a critical Reynolds number that was found to be in
the order of 1–10 910
4
for small- and medium-scale stirred bioreactors [88,90,
108,109], which is comparable to standard stirrer systems [59].
Re ¼NSdSqL
lLð1Þ
Similar relationships were introduced for orbitally shaken (e.g., shake flasks)
[111] and rotatory oscillating bioreactors (i.e., the BAYSHAKE bioreactor) [35,
66], where Re is determined using the averaged rotational frequency and the
maximum diameter of the mixing device. For shake flasks a critical Reynolds
number of Re [6910
4
was found [112]. Wave-mixed systems with 2-D motion
can be characterized by a modified Reynolds number given by (2), which is
determined by the working volume (V), the width of the culture bag (B), the liquid
level (H), the rocking rate (k) and an empirical constant that depends on the bag
Dynamic Single-Use Bioreactors
type (C). This definition was derived from channel flows, providing a critical Re
(Re
crit
) of 1,000 [29].
Remod ¼VkCqL
lL2HþBðÞ ð2Þ
In addition to turbulence, the fluid flow in orbitally shaken bioreactors can be
described by the ‘‘in-phase’’ and ‘‘out-of-phase’’ phenomenon, where the latter is
characterized by liquid not moving in phase with the rotation of the shaker table
[111]. A further parameter, which can often be easily related to the stirrer or vessel
dimensions, is the maximum observable fluid velocity (u
max
). Although, signifi-
cantly higher tangential peak velocities were found in the stirrer wake region of
Rushton turbines [113,114] with regard to conventional stirrers, the maximum
velocity in a number of different stirred single-use systems was found to corre-
spond well to the stirrer tip speed (u
Tip
) defined by (3)[90,108,109,115].
utip ¼pdSNSð3Þ
Furthermore, the tip speed of stirred systems is directly related to the impeller
Reynolds number (4), which provides a first approximation of the maximum
velocity at a desired turbulence. Because of shear sensitivity, a critical value of
1.0–2.0 m/s has been proposed [102].
Re /uTip dSð4Þ
In addition to these general criteria, the most important parameter for an
engineering characterization is the volume-specific power input (P/V). Two
approaches were developed for its determination: the torque method and the
temperature method. The torque method, where the effective stirrer torque (dif-
ference in torque for stirring with liquid Mand dead torque, M
d
) is determined
using a torque sensor (5), has become the standard method for conventional stirred
vessels [116]. Consequently, this method was used for the measurement of the
power input in the small-scale Mobius CellReady 3 L [90] as well as in the
medium-scale BIOSTAT CultiBag STR 50 L [85,86] and the S.U.B. Hyclone
[108,109]. The torque measurement was also shown to be feasible for shake flasks
[117] and orbitally shaken cylindrical vessels [118,119]. Therefore, the highest
local energy input e
max
, which is often related to mechanical stress, is proportional
to the specific power input under turbulent conditions (6).
P=V¼MMd
ðÞ2pNS
VLð5Þ
P=V/emax /u3
Tip
dSð6Þ
As an alternative, the temperature method was developed, where the power
input is obtained from the heat balance given by (7), where c
P
wdT
F
/dt,UA(T
F
-
C. Löffelholz et al.
T
0
) and dQ
0
/dtrepresent the change in temperature, the overall heat transfer rate
through the vessel walls, and the heat-generating rate by the power consumption,
respectively.
cpwdTF
dt¼UATFT0
ðÞ
dQ0
dtð7Þ
Although the torque method was expected to provide greater accuracy in terms
of power consumption [118], because the power consumption can be obtained
directly from the measured torque, results from both methods correlated reason-
ably well [119]. However, it should be emphasized that the power inputs inves-
tigated in these studies were in the range of 0.5 and 8 kW/m
3
, which is much
higher than typical values used for cell cultures in stirred systems, which are
typically in the range of 0.01–0.25 kW/m
3
[120]. Thus, the temperature method
may not be feasible for stirred or wave-mixed single-use systems, because of the
much lower power input. Furthermore, when measuring the power consumption in
small vessels, heat insulation is required, inasmuch as the temperature change from
heat loss is relatively quick and leads to higher inaccuracies [118].
The power input of pneumatically driven bioreactors can be estimated from the
superficial gas velocity (u
g
) according to (8) if the isothermal expansion of gas is
the predominant source of power [121]. However, no published data about specific
power inputs for the pneumatically driven bioreactors were found.
PG
VL¼qLguGð8Þ
Based on the power input, mixing and oxygen mass transfer can be estimated.
Mixing (h
m
) is mostly characterized by the mixing time, defined as the duration
required to achieve a defined degree of homogeneity after disturbance of the
system (e.g., by change of temperature, concentration, conductivity, color, and/or
density). In the majority of cases, 95 % homogeneity is accepted as adequate
mixing performance. To determine mixing times two main approaches were
applied: (de-)colorization methods and sensor methods.
Although the latter have the drawback of only measuring the mixing at specific
locations, potentially leaving dead and rest zones hidden, these methods have been
used to characterize different single-use bioreactors from benchtop to large-scale
[80,97,122125]. The advantages of the sensor methods are the precise data they
deliver, reducing interobserver differences, and the fact that no optical accessibility
is required, as is the case for (de-)colorization methods [116]. The main disad-
vantage of colorimetric methods is their inherent subjectivity, due to the personal
view of the investigator. This may be overcome by automated image analysis,
which has been used in mixing analysis of stirred single-use bioreactors [126].
For standard stirred bioreactors, it is well-known that the dimensionless mixing
number (c
m
), which represents the stirrer rotations required for the desired
homogeneity (9), becomes constant under fully turbulent conditions [110]. It is not
entirely surprising that the same relationship was confirmed for small- and
Dynamic Single-Use Bioreactors
medium-scale single-use stirred vessels [90,115]. Typical mixing numbers (c
m
)
for those systems are in the range of 20–40, leading to mixing times below 30 s for
meaningful stirrer speeds in mammalian cell cultures.
cm¼NShmð9Þ
Based on turbulence theory, it was found that mixing time is inversely pro-
portional to the third root of the specific power input under turbulent flow con-
ditions. Furthermore, the mixing time is related to geometrical parameters leading
to (10) which is valid for bioreactors where H=D[120,127].
hm/P
V

1=3
dS
D

1=3
D2=3ð10Þ
For bioreactors with higher aspect ratios (H/D[1), an additional term is
introduced [i.e. (H/D)
2.43
], which was originally developed for multiple impellers
but has been shown also to take the influence of the filling height in single impeller
systems into account [120]. This is represented by (11), which was shown to
correlate well with mixing times in stirred single-use bioreactors predicted by CFD
[115].
hm/P
V

1=3
dS
D

1=3
H
D

2:43
D2=3ð11Þ
Mixing in orbitally shaken bioreactors was found to be scalable by keeping the
ratio of the inner diameter of the container (D
I
) to the shaking diameter (d
SF
) and
the Froude number (Fr), defined by (12), constant [73]. Depending on the shaking
speed, shaking amplitude, filling volume and vessel diameter, mixing numbers are
between 5 and 80 for vessels of up to 1,500 L [73].
Fr ¼2pNDIþdSF
ðÞ=2
ffiffiffiffiffiffiffiffiffiffiffi
gDI
pð12Þ
In addition to mixing, oxygen mass transfer is considered to be the most
important process during aerobic cultivation. The overall oxygen demand of the
cells throughout the cultivation (OUR) must be met by the oxygen transfer rate
(OTR). This demand is influenced by the specific oxygen uptake rate (q
o2
) and
increases as long as the number of viable cells (X) is also increasing, where c
o2
and
c
o2
*
represent the actual and the saturated oxygen concentration respectively (13).
qo2X¼kLac
o2co2
 ð13Þ
Oxygen transfer is mostly characterized by the overall volumetric mass transfer
coefficient (k
L
a), which represents the product of the liquid mass transfer coeffi-
cient (k
L
) and the specific interfacial area (a). For submerged aerated systems, the
interfacial area depends on the local gas volume fraction (a) and the local bubble
size represented by the Sauter mean diameter (d
32
;14).
C. Löffelholz et al.
a¼Ao;G
VL¼6a
1aðÞd32 ð14Þ
An approximate estimate of the gas–liquid interfacial area in surface-aerated,
circular or cube-shaped vessels may be obtained from (15):
a¼pD2
VL
or a¼LB
VLð15Þ
However, it is notable that the bioreactor or surface motion will increase the
interfacial area. For shake flasks, the interfacial area has been predicted to follow
(16) for a fixed shaking diameter [128].
a/N0:6ð16Þ
Although separate determination of the interfacial area in surface aerated sys-
tems was performed by image analysis [129], using an estimation of the evapo-
ration rate [130], a chemical model system [131], and computational fluid
dynamics (CFD) [128,132], this remains difficult for submerged aeration because
of the various factors affecting the local bubble size (aeration system, gas dis-
persion, media properties, etc.). Therefore, usually the k
L
avalue is measured using
either the gassing-out method or the sulphite method. Other methods, such as the
respiratory gassing-out method, are of minor importance for engineering charac-
terization in single-use bioreactors and are, therefore, not discussed in detail here
(for more information please refer to Ref. [133]).
According to the definition, given in [116], in the gassing-out method the
oxygen in the liquid is depleted by the introduction of nitrogen. After complete
depletion, air is introduced leading to an increase in the oxygen concentration,
where the rate of the concentration increase is determined by the k
L
a. Thus, the
k
L
acan be obtained from the oxygen mass balance in the liquid (dc
o2
/dt), which
may be written for a totally mixed system by (17).
dco2
dt¼kLac
o2co2
 ð17Þ
The gassing-out method is most often used in single-use systems above mL-
scale independent of the type of power input (see Table 2). Typical k
L
avalues
achieved in stirred single-use bioreactors from benchtop to large scale are in the
order of 5–40 1/h, depending on the scale, aeration rate and agitation. For
example, k
L
avalues of up to 35 1/h were achieved at typical cell culture agitation
rates in the Mobius CellReady 3 L bioreactor with the microsparger [90,134].
Similar values were found for the medium-scale BIOSTAT CultiBag STR 50 L at
specific power inputs of 90 W/m
3
and an aeration rate of 0.1 vvm (see Sect. 4.5).
In general, the k
L
avalues in stirred bioreactors can be calculated by (18), where x
1
,
x
2
and C are bioreactor-dependent empirical constants. For the above-mentioned
bioreactors, it was found that the influence of the superficial gas velocity was more
pronounced than the specific power input P/V(i.e. x
1
\x
2
). This is clearly
Dynamic Single-Use Bioreactors
different from standard bioreactors used for microbial fermentations [135] and
may be explained by the low gas dispersion capacities of the stirrers operated
under typical cell culture conditions.
kLa¼CP=VðÞ
x1ux2
Gð18Þ
Lower k
L
avalues of between 4 and 20 1/h were reported in rocker-type wave-
mixed systems with water and cell culture medium using typical process param-
eters for mammalian cells (6–10°rocking angle, 25–30 rpm, 0.25 vvm, 40–50 %
filling level) [29]. In contrast, much higher k
L
avalues of up to 700 1/h were
reported for the CELLtainer, which is characterized by an additional horizontal
displacement enabling much higher specific power inputs of up to 3.8 kW/m
3
[63].
As a result of such high oxygen transfer capacities, the cultivation of high oxygen
demanding cultures may be realized without oxygen limitation.
However, it should be emphasised that results in surface-aerated systems
obtained by the classical gassing-out method should be treated with caution
because of the significant effect of the headspace gas composition. After intro-
duction of nitrogen, the headspace is (nearly) free of oxygen, then increases
continuously as the air supply is switched on again. During this process, the liquid
saturation concentration changes with time according to Henry’s Law
(po
2
=k
H
*c
o2
*
). Assuming a time-independent c
o2
*
, as given in (17), may lead to
k
L
abeing affected and to an erroneous effect of the aeration rate, which was
confirmed by our own measurements [136] and is supported by data given in [137].
In the sulphite method, the depletion of oxygen is achieved by oxidation of
sulphite ions to sulphate ions in the presence of a catalyst, such as copper, ferric,
cobalt or manganese ions (19).
2SO2
3þO2!
Co2þ;Fe;Mnþ;Cuþ2SO2
4ð19Þ
Because the mass transfer phenomenon is coupled with a chemical reaction
when using the dynamic sulphite method, the different sulphite oxidation regimes
should be taken into account [138]. These can be classified by the Hatta number
(Ha) defined by (20), where n,k
n
and D
O2
denote the reaction order for oxygen, the
reaction constant, and the diffusion coefficient in the solution.
Ha ¼reaction rate
mass transfer rate ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
nþ1knc
o2

n1DO2
qkLð20Þ
Catalyst concentration, pH, temperature, and even light irradiation are the
primary parameters that influence the reaction rate [139]. By using the film model,
a reasonable approximation of the exact solution of the stationary mass balance
can be derived for the absorption process (21)[140]. Measurements of the
k
L
ahave to be conducted in a nonaccelerated sulphite oxidation reaction regime,
where Ha \0.3 and the term ain (21;[131]) can be neglected [131].
C. Löffelholz et al.
OTR ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
nþ1knc
o2

n1DO2
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
a
þk2
L
|{z}
b
v
u
u
u
tac
o2co2

ð21Þ
The sulphite method was primarily used in noninstrumented, small-scale sys-
tems, such as microtiter plates [131,138], Tubespin reactors [141], shake flasks
[142], and the BioLector [143]. Volumetric oxygen transfer coefficients of up to
200 1/h have been observed in 96-well microplates operated at high shaking
frequencies (n
SF
) of over 1000 rpm [130]. Correlating k
L
aby dimensionless
groups, (22) was obtained, where Sc and Bo denote the Schmidt number
l=qDðÞðÞand the Bond number ðqd2g=rÞrespectively, and xand yare
dependent on the microplate geometry.
Table 2 Overall oxygen mass transfer coefficients obtained by gassing-out method in different
selected single-use bioreactor systems
System Scale
[L]
Agitation Aeration rate
[vvm]
k
a
L[1/
h]
References
Mechanically driven, stirred
Mobius CellReady 3
a
250 rpm 0.25 35 [90]
200
a
140 rpm 0.05 60 [80]
BIOSTAT UniVessel SU 3
a
435 W/m
3
0.2 100 [146]
BIOSTAT CultiBag STR 50
b
240 rpm 0.1 47 [85,86]
200
b
240 rpm 0.1 37 [86]
Hyclone S.U.B. 50
b
200 rpm 0.1 8.3 [125]
200
b
100 rpm 0.01 15 [23]
XDR-1000 1000
a
132 rpm 0.015 9 [147]
Mechanically driven, oscillation motion
BayShake Bioreactor 32
b
120°, 210 W/
m
3
n.a. 20 [35]
Pneumatically driven
PBS bioreactor n.a. 20 [148]
Mechanically driven, oscillating movement, wave-mixed
AppliFlex Bioreactor 2.5
b
6°, 24 rpm 0.5 14.6 [61]
5
b
11°, 25 rpm 0.5 24 [61]
10
b
4°, 20 rpm 0.025 4.4 [29]
Biostat CultiBag RM 1
b
n.a. n.a. 22 [57]
10
b
n.a. n.a. 6 [57]
BioWave Bioreactor 1
b
6°, 30 rpm 0.25 10 [29]
10
b
5°, 30 rpm 0.25 9.3 [29]
100 L
b
10°, 24 rpm 0.25 5.6 [29]
CELL-tainer 10
b
20°
c
n.a. &700 [63]
Mechanically driven, orbitally shaken
OrbShake bioreactor
SB200-X
100
b
70 rpm n.a. 27 [70]
a
total volume,
b
working volume,
c
20-cm displacement, n.a. not available
Dynamic Single-Use Bioreactors
kLa¼31:35 DO2aRe0:68 Sc0:36 FrxBoyð22Þ
Lower values for k
L
aof up to 104 1/h were found for shake flasks with 200 mL
working volumes at agitation rates of 210 rpm [141]. Comprehensive investiga-
tions of oxygen mass transfer have been carried out by Büchs and his co-workers,
who found that the ‘‘out-of-phase’’ phenomenon (see above) has an adverse effect
on the oxygen mass transfer [144]. The data could be correlated to the maximum
oxygen transfer capacity (mmol/L/h) by (23), where the rotational speed n is given
in rpm, the shaking diameter d
0
and the flask diameter in cm and the working
volume in mL [142].
OTRmax /n0:84
SF V0:84
Ld0:27
0d1:25
m;SF ð23Þ
Further engineering characterization, such as determination of residence time
[29,145] and heat transfer [118], are of minor importance for single-use biore-
actors and only few reports are available in the literature. This may be explained
by the fact, that single-use bioreactors are primarily used for cell culture appli-
cations, where low feeding rates are used, leading to significantly longer residence
times compared to mixing time, and almost no heating or cooling limitations.
Nevertheless, heating and cooling may become problematic in a microbial process
performed in single-use bioreactors.
3.2 Advanced Engineering Characterization
Advanced engineering methods are applied to gain local and instantaneous values
for the fluid flow, which, in addition to the previously described criteria that are
considered as volume-averaged parameters, can be used for bioreactor charac-
terization and scaling-up. Keeping in mind that the fluid flow in bioreactors can be
very heterogeneous, the ‘‘global’’ parameters may not be sufficient for an advanced
characterization. For example, it is well-known that the stirrer power is only
dissipated in a small fraction of the bioreactors and the maximum dissipation rate
is 100–200 times higher than the volume-average [149]. This may have an intrinsic
effect on shear-sensitive organisms.
Some attempts have been made to characterize local fluid flow in single-use
bioreactors by measuring fluid velocities using particle image velocimetry (PIV)
[108], particle tracking velocimetry (PTV) [150], laser Doppler anemometry
(LDA) [109], and hot-film anemometry [151]. The latter method has the drawback
of affecting the flow, because the probe must be positioned inside the liquid.
Therefore, the contactless, laser-based PIV and PTV methods are preferred.
However, although these experimental methods are reliable, they are too time
consuming to characterize the complete 3-D fluid flow within a typical bioreactor
[152]. Thus, numerical methods are used to overcome this limitation and, of these
methods, CFD has become the most important approach in recent years.
C. Löffelholz et al.
The fundamentals of CFD are based on mass, momentum and energy conser-
vation equations, which are second-order partial differential equations that, for the
most part, cannot be solved analytically. Thus, different numerical methods, such
as the finite volume method (FVM) or the Lattice–Boltzmann method (LBM) are
used to render the flow field. In each case, the fluid domain is divided into a
discrete number of elements and the conservation equations are solved for each
volume element. Details of the numerical basics and the algorithms used are
provided elsewhere [153157].
CFD has been applied for characterization of fluid flows in different stirred [88,
90,108,109,158] and wave-mixed bioreactors [29,151], orbitally shaken flasks
[128], microtiter plates [159], the rotatory oscillating BayShake Bioreactor [35],
and the pneumatically driven PBS Bioreactor [109]. The main advantage of CFD
is that local and time-resolved data about the fluid flow (e.g., pressure, turbulence,
shear stress) as well as physical and chemical properties (e.g., concentrations,
viscosity, density, gas hold-up) can be obtained.
The local specific energy dissipation rate (e) is considered to be an important
parameter that can be predicted using CFD. This can be used to calculate the
Kolmogorov micro-scale of turbulence (k) in turbulent flows defined by (24). The
turbulence micro-scale defines the size of the smallest turbulent eddies. Various
studies have proposed that cell damage occurs in bioreactors, if the size of these
eddies is comparable to the biological entity (i.e. k=dX1) [160162]. However,
this theory is yet to be proven and there are some doubts inasmuch as it does not
take the physical properties of the cells into account [120,127].
k¼l3
q3
Le

1=4
ð24Þ
Furthermore, eis often used to predict oxygen mass transfer, based on Higbie’s
penetration theory [163,164]. Here, the liquid oxygen mass transfer coefficient is
related to the surface renewable rate resulting in (25).
kL¼2ffiffiffi
p
pffiffiffiffiffiffiffiffi
DO2
peqL
lL

1=4
ð25Þ
Together with the specific surface area a, the k
L
a, which has been shown to be
spatially heterogeneous, not only in large-, but also in small-scale bioreactors, can
be predicted using CFD [88,90]. However, special two-phase models that are not
discussed here in detail, which take momentum exchange of the continuous and
dispersed phases into account, are required. Detailed information is provided in
Ref. [156].
Dynamic Single-Use Bioreactors
4 Bioengineering Data of the UniVessel SU and BIOSTAT
CultiBag STR
The following case study presents a possible approach for the engineering char-
acterization of small- to medium-scale, stirred, single-use bioreactors. For this
purpose, the two single-use bioreactor systems UniVessel SU and BIOSTAT
CultiBag STR from Sartorius Stedim Biotech were chosen because they are as
close as possible to the design and instrumentation of conventional glass or
stainless steel cell culture bioreactors. The rigid UniVessel SU (Fig. 2a) is
equipped with two-stage segment blade impellers with a blade angle of 30°. The
impellers have a diameter of 0.055 m and are mounted with an impeller distance
(c
s
) of 0.07 m. The diameter of the cylindrical vessel (D) increases towards the top
(from 0.118 to 0.126 m), caused by the validated manufacturing process. The ratio
of liquid height to vessel diameter (H/D) is 1.3 and ensures a maximum working
volume of 2 L. The bioreactor can be equipped either with conventional probes or
optical sensors and is unbaffled.
In the case of the BIOSTAT CultiBag STR product line, the cultivation vessel is
a flexible 3-D bag, which has to be mounted in a stainless steel support housing
(Fig. 2b). Two different top-driven stirrer configurations are available: a combi-
nation of a Rushton turbine (RT) and SBI or two SBIs. Irrespective of the con-
figuration, the stirrer diameters are 0.37, 0.23, 0.31, and 0.38 m for the
corresponding working volumes of 50, 200, 500, and 1,000 L, respectively.
However, the BIOSTAT CultiBag STR line primarily differs from the smaller-
scale series in the differently shaped bottoms of the cultivation vessels. The other
geometric parameters (e.g. d
s
/D,H/D,c
s
/d
s
etc.) are similar for all the different size
bags in the unbaffled BIOSTAT CultiBag STR line (for details see Refs. [85,86])
and, therefore, fulfill the scale-up criteria. The measurement of pH and dissolved
oxygen are realized using small optical sensors, which have no significant influ-
ence on the fluid flow, and no additional elements are installed.
In order to characterize the UniVessel SU and the BIOSTAT CultiBag STR line
using CFD, the ANSYS Fluent commercial software package was used.
Fig. 2 The stirred single-use cell culture bioreactors from Sartorius Stedim with the UniVessel
SU (a) and the BIOSTAT CultiBag STR with a working volume of 50 L (b)
C. Löffelholz et al.
Depending on the maximum working volume, the fluid domains of the nine dif-
ferent bioreactor configurations were divided into unstructured, body-fitted grids
with up to approximately 5-mio volume elements. PIV was used for experimental
measurement of the fluid flow in a 50 L vessel. In the systems with volumes of up
to 200 L, the power input was determined using the torque method and the mixing
time was predicted by the decolorization method.
4.1 Fluid Flow Pattern and Velocity Distribution
In Fig. 3, the ungassed fluid flow pattern obtained using CFD and PIV are com-
pared for the mid-vessel plane (xy-plane). The velocity components in the x- and
y-directions are considered and the values are normalized by the tip speed (u
Tip
).
The highest fluid velocity magnitudes are found near the impeller tips and cor-
respond well with the calculated tip speed (u
Tip
) of 1.05 m/s using (3) (data not
shown), which creates fully turbulent conditions (see Sect. 4.2).
In the BIOSTAT CultiBag STR 50 L with two SBIs (Fig. 3a, b), the highest
relative velocity of 0.45 u
Tip
occurs at the outer blade edges. Along the blade
discharge the relative velocities decrease down to 0.3 u
Tip
and a swirl in the axial
direction can clearly be seen. This results in fluid recirculation along the vessel
wall towards the fluid surface and the stirrer shaft. Here, the relative velocities
range between 0.03 and 0.15 u
Tip
. Due to prevailing axial swirls next to the
impeller discharge of the two segment blade impellers, an axial fluid flow pattern
and a similar velocity distribution can be observed for both the numerical and
experimental methods. In summary, the CFD model can be considered as valid,
because the numerically and experimentally obtained results visually agree
[165167]. Furthermore, the obtained fluid flow pattern corresponds well to pat-
terns seen for conventional stirrers.
In the case of the RT ?SBI stirrer configuration (Fig. 3c, d), the upper SBI
clearly shows an axial flow profile in down-pumping mode with a maximum
velocity of 0.45 u
Tip
, whereas the lower RT discharges the fluid radially towards
the vessel wall. The CFD simulation shows a maximum relative velocity of 0.51
u
Tip
(x- and y-direction), which develops close to the impeller. In the predicted
fluid flow pattern, the upward-forming loop represents the major flow, caused by
the downward-inclining blade discharge. This results in a less pronounced swirl
along the bottom wall. The experimental investigations reveal that the fluid is
discharged radially, impinges on the outer wall, splits, and moves up and down,
forming two recirculating loops in each vessel half. The interaction of the two
impellers can be ignored if the c
s
/d
s
ratio exceeds 1.25 [110], which is true in the
present case. In contrast, a slight downward tendency in the impeller discharge was
observed in different experimental [168,169] and numerical investigations [170]
using RT in fully baffled and unbaffled vessels under turbulent conditions.
A more quantitative analysis is given in Fig. 3e, where radial profiles of
the normalized fluid velocities for different heights in the BIOSTAT CultiBag STR
Dynamic Single-Use Bioreactors
50 L with RT and SBI (Fig. 3e) are presented. Almost identical velocity distri-
butions were found a third and half-way up the vessel height (h/H=0.33; h/
H=0.5), with deviations towards the vessel walls. This may be explained by both
numerical and experimental uncertainties resulting from optical distortions. The up
to 60 % lower relative velocities were obtained in the experimental approach.
However, the maximum and minimum velocities that were predicted for the
impeller discharge and the point of flow reversal (where up- and downward flow
meet) were well captured by PIV, with deviations below 10 %. For the rest of the
velocity profile, the two different methods correlate sufficiently, with a maximum
deviation of 10 %. However, the two graphs do not correlate if h/His 0.5 or x/Dis
0.35 (Fig. 3e). This inconsistency is based on the experimental measurement
technique where the SBI covers the fluid and thus prevents determination. The
above-mentioned deviating circulation flow is clearly shown in the velocity dis-
tribution profile of h/H=0.2. Here, the maximum relative velocity of 0.51 u
Tip
decreases similarly along the blade discharge towards the vessel wall (0.1 \d
s
/
D\0.3 and 0.7 \x/D\0.9). Compared to the experimental investigation, the
CFD simulation predicts a 0.05 x/Dreduced discharge, causing a downward fluid
flow (Fig. 3e). In addition, the velocities near the vessel wall differ by up to 45 %
Fig. 3 Evaluation of the BIOSTAT CultiBag STR 50 L for both stirrer configurations. The
numerical and experimental fluid flow patterns for the 2 9SBI configuration is shown in aand b,
and for the RT ?SBI configuration in cand d. A quantitative analysis of the relative velocity as
a function of dimensionless diameter is provided in efor different dimensionless heights (mid-
plane of RT and SBI as well as in the middle of both stirrers)
C. Löffelholz et al.
when comparing the two methods. However, further experimental investigations
of power input and mixing times are recommended in order to compare the
methods and assess the influence of different fluid flows on biochemical engi-
neering parameters.
4.2 Power Input
The power input represents the most important criterion for scaling-up of biore-
actor systems [171]. Consequently, determining this was one of the major tasks of
this case study to characterize and compare the UniVessel SU and the BIOSTAT
CultiBag STR versions. By using CFD, the power input (P) in the BIOSTAT
CultiBag STR 50 L was determined by the torque at the stirrer elements (1and 5).
It was demonstrated that, while exceeding a critical Reynolds number (Re
crit
)of
10
4
, a turbulent flow regime is reached when the Newton number (Ne) becomes a
constant with values of 1.1 for the 2 9SBI configuration and 3.1 for the
RT ?SBI configuration [88]. Thus, the values obtained for Re
crit
and Ne are
comparable to those for conventional glass or stainless steel bioreactors [110,172,
173]. Furthermore, the CFD predicted and experimentally determined power
inputs were very similar [85,86] with a maximum deviation below 15 %.
The tip speed was increased up to a maximum u
Tip
of 1.8 m/s, which has been
proposed as the maximum tolerable fluid velocity for mammalian cells [160]. At
such high tip speeds, the maximum P/Vof about 86 and 240 W/m
3
were obtained
for the 2 9SBI configuration and the RT ?SBI configuration, respectively
(Fig. 4a). Henzler and Eibl and Eibl propose a maximum specific power input of
100 W/m
3
to avoid any cell damage [102,174], although, a higher range of up to
250 W/m
3
is suggested by Nienow [120].
An additional analysis of the power input was carried out for aerated conditions.
Although the effect of aeration is normally negligible, due to the low gassing rates
used for mammalian cell cultures, the total power input (P/V) is usually applied to
make a comparison or to scale up bioreactors [120,175]. For the two stirrer
configurations, the determined aerated P/Vvalues obtained for an aeration rate of
0.02 vvm follow the same trend as the unaerated power input (see Fig. 4a), with a
mean increase of 15 %. This could be verified by experimental data (not shown).
The numerically and experimentally obtained results for the BIOSTAT CultiBag
STR 50 L correlated well, therefore determination of P/V was also carried out for
the UniVessel SU and the BIOSTAT CultiBag STR 200, 500 and 1000 L, for both
stirrer configurations. In Fig. 4b the results are presented as a function of u
Tip
.If
u
Tip
is used as a scale-up or scale-down criterion, P/Vincreases significantly for
smaller volumes, but decreases for large volumes and is described by the relation
in (6). Therefore, in the UniVessel SU the maximum P/Vis about 435 W/m
3
,
which is unreasonably high for cell culture applications, but sufficient for micro-
bial fermentations. Reasonable power inputs for cell culture applications of up to
150 W/m
3
have already been achieved with medium values of u
Tip
in the range of
Dynamic Single-Use Bioreactors
0.5–1.25 m/s. For these values, Re is between 0.8 and 2 910
4
, indicating tur-
bulent fluid flow, for a constant Newton number of 1.5.
In the case of the BIOSTAT CultiBag STR with working volumes of 200, 500,
and 1,000 L (Fig. 4b), the P/Vbehaves according to (6). Considering the maxi-
mum P/Vfor the 50 L bioreactor with *86 W/m
3
(2 9SBI) and *240 W/m
3
(RT ?SBI), the power inputs in the 200-L bioreactors are only *48 W/m
3
(2 9SBI) and 133 W/m
3
(RT ?SBI). P/V decreases even further in the 1,000-L
bioreactors so that *28 W/m
3
(2 9SBI) and *73 W/m
3
(RT ?SBI) are
achieved. The numerically determined Ne numbers of 1.1 and 2.8 (2 9SBI/
RT ?SBI) diverge only slightly from the values for the 50-L bioreactors, which
can be explained by the minor differences of the dimensionless ratios of the reactor
geometry for the various sizes.
In summary, it could be demonstrated that the numerically determined engi-
neering parameters (Re
crit
, Ne, P/Vrange) agree excellently with the experimen-
tally obtained results. Furthermore, it could be shown that the characteristics of the
investigated single-use bioreactors are comparable to those of conventional cell
culture bioreactors.
4.3 Mixing Time
The characterization of the mixing behavior in the investigated single-use biore-
actors was performed dependent on u
Tip
using an identical range of up to 1.8 m/s
(see Sect. 4.2). For this purpose, the concentration was determined, after addition
of an inert tracer with identical fluid properties to the vessel contents. The tracer
concentration was predicted transiently using a numerical method, however, the
flow field of the steady simulation was ‘‘frozen’’. The CFD predicted mixing times
were validated by comparing experimental data. The iodometrical decolorization
Fig. 4 Comparison of numerical and experimental investigations of the specific power input as a
function of tip speed in the BIOSTAT CultiBag STR 50 L under unaerated and sparged
conditions (a). Comparison of the CFD-predicted specific power input as a function of tip speed
for all bioreactor sizes and configurations (b)
C. Löffelholz et al.
[116] (UniVessel SU) and conductivity methods [85] (BIOSTAT CultiBag STR)
were applied, and 95 % mixing was assumed.
Figure 5a depicts the experimentally and numerically obtained mixing times
(h
m
) for the UniVessel SU and the BIOSTAT CultiBag STR 50 and 200 L, which
are presented as a function of P/V. Turbulence increases as power input rises,
therefore this directly leads to a decrease in the mixing time [172]. Although about
100 s are required to achieve the desired 95 % homogeneity in the UniVessel SU
at lowest power input (0.5 W/m
3
), only about 3 s are required at the maximum
power input (435 W/m
3
). In the BIOSTAT CultiBag STR (2 x SBI), the numerical
mixing times range between 10 and 60 s for the 50-L bioreactor (0.8–86 W/m
3
),
and between 20 and 60 s for the 200-L scale (1.5–49 W/m
3
). Therefore, the
mixing times of the BIOSTAT CultiBag STR are in the same range as for the
UniVessel SU. Although it was found that fluctuations in the tracer concentrations
were underpredicted by the applied RANS approach using the k-eturbulence
model, the mixing times correlate fairly well [176,177]. Comparison of the
numerically and experimentally determined mixing times (Fig. 5a) shows a
maximum deviation below 4 % for the UniVessel SU. Higher deviations were
found for the BIOSTAT CultiBag STR systems, where mixing times differ by up
to 18 %, which can be ascribed to uncertainties in both experimental and CFD
predicted data.
Based on similar results obtained for the UniVessel SU, the mixing times in the
BIOSTAT CultiBag STR line with RT ?SBI (Fig. 5b) and SBIs (data not shown)
were analyzed. As shown in Fig. 5b, the mixing time decreases with increasing
working volume and decreasing specific power input. This results in a mixing time
ranging between 13 s (50 L; 240 W/m
3
) and 200 s (1,000 L; 0.05 W/m
3
) for the
stirrer configuration of RT ?SBI. However, in cell culture processes a power
input in the range of 1 up to 150 W/m
3
is required and here the mixing times are
between 15 and 75 s. The numerically determined mixing number (c
m
) specifies
the number of rotations required to achieve the desired homogeneity and is
29 ±5. In addition, the exponent of -0.32 of the regression line (Fig. 5B) is
roughly equivalent to the theoretically cited exponent of -0.33, which is obtained
under turbulent flow conditions [178]. In the BIOSTAT CultiBag STR (2 9SBI),
the determined mixing times are on average 30 % higher considering the entire
operation range. According to this, the homogenization number is 34 ±1, whereas
the exponent of the regression line is identical to the theoretical value (data not
shown). In summary, the comparison of the results from the CFD simulation and
the experimental measurements agree well (c
H
[95 %, 80 % \h
m
\100 %).
4.4 Mechanical Stress
The spatially resolved data obtained by CFD can also be used to evaluate
mechanical stress that can potentially damage cells. The turbulence, the formation
of eddies [179,180], and velocity gradients [160,181] are considered potential
Dynamic Single-Use Bioreactors
sources of mechanical stress. In the following sections, methods to determine
mechanical stress for the UniVessel SU are discussed. The maximum power input
is proportional to the mechanical stress (24).
4.4.1 Kolmogorov Length Scale
According to the theory that cells are damaged by eddies of comparable size, the
size of the smallest turbulent eddies (k), also referred to as the Kolmogorov
microscale of turbulence, was determined assuming local isotopic turbulence
according to (24). Smaller eddies do not possess the energy to harm the cells, and
cells follow larger eddies convectively. The volume-averaged turbulence micro-
scales predicted for the UniVessel SU are summarized in Fig. 6a, where the static
fluid zone, the rotating zone of the stirrer, and the stirrer surface are shown.
The investigation of the volume-weighted averaged Kolmogorov length scale in
the fluid domain and in the stirrer zone revealed values of between 50 and 400 lm.
The minimum Kolmogorov length scales are determined directly at the stirrer sites
and range between 32 and 9 lm (0.4 W/m
3
\P/V\435 W/m
3
). Furthermore, it
was found that k(24) correlates well with P/Vas follows (26):
k/P=VðÞ
mð26Þ
where m is 0.2 ±0.01, a value that is near the theoretical value of 0.25 provided
by (24). This agrees well with the literature and is almost identical to other single-
use bioreactors [108]. Comparable values were also obtained for the BIOSTAT
CultiBag STR product line, where the regions close to the stirrer and the rotating
stirrer zone (as well as in the fluid zone, data not shown) were investigated
(Fig. 6b). In addition, the Kolmogorov length scale increases if the scale increases,
and thus the power input declines.
Fig. 5 Comparison of numerical and experimental mixing times as a function of specific power
input in the UniVessel SU and the BIOSTAT CultiBag STR 50 L and 200 L (a). The error bars
indicate the simple standard deviation of the mixing times. Additionally, the mixing time as a
function of specific power input for the BIOSTAT CultiBag STR (RT ?SBI) is shown (b)
C. Löffelholz et al.
When considering the size of CHO cells (10 lm\d\20 lm), no cellular
damage is expected for either bioreactor type at meaningful power inputs, because
the smallest eddies are significantly larger than the cells and, therefore, the cells
will follow the eddies in a convective manner. In contrast, exceeding a P/Vof
10 W/m
3
is expected to damage the cells in the region close to the stirrer,
Fig. 6 Numerically predicted Kolmogorov length scale for the overall fluid domain, the rotating
stirrer zone, and close to the stirrer surface as a function of specific power input in the UniVessel
SU (a). The length scale close to the stirrer surface and in the rotating zone for all bioreactor sizes
and configurations is shown in (b). The stirrer zone comprises the fluid that is directly in contact
with the stirrer surface, whereas the rotating stirrer zone is made up of the stirrer movement
volume. For all scales, the rotating stirrer volume is approximately 7 % of the total volume. The
fluid domain represents the overall fluid without the rotating stirrer zones
Dynamic Single-Use Bioreactors
inasmuch as the minimum Kolmogorov length scale is below 20 lm. However,
this theory has not been proven thus far and describes a hypothesis (see Sect. 3.2).
4.4.2 Velocity Gradients
In addition to turbulence, cells are thought to be affected by velocity gradients,
where shear and normal gradients (experimentally and numerically determined)
can be distinguished [88,108,114]. Shear gradients were found to be dominant in
stirred bioreactors [88,114], and predominantly responsible for cell damage [181],
therefore normal gradients have not been considered in the present study. The
shear stress distribution, as given in (Fig. 7a), was obtained by discretizing the
shear stress values into 250 bins and summing the volume elements where the
shear stress occurred.
This volume-weighted distribution can be described by a logarithmic normal
function, providing a maximum volume fraction of about 4.7 % in the UniVessel
SU, irrespective of the specific power input (Fig. 7a). The local shear gradients
(c
NT
) obtained for a maximum volume fraction (median value), increase propor-
tionally to the third root of P/V from 2.4 up to 28 1/s [see (27); Fig. 7b]. The
resultant exponent of 0.33 has already been published for the Single-Use Biore-
actor (S.U.B.) and the BIOSTAT CultiBag STR 50 L (both stirrer configurations)
in earlier experiments [108].
cNT /P=VðÞ
1=3ð27Þ
For the maximum P/V (&435 W/m
3
), a maximum local shear gradient of
*1,000 1/s was determined. According to Yim and Shamlou [182], the range of
local shear gradients affecting the physiological state of the cells is between 500 and
5,000 1/s. Taking this into consideration, damage to the cells cultivated in the
UniVessel SU at a maximum P/V cannot be excluded. Nevertheless, the numerically
obtained mean and maximum shear gradient values are far beyond the critical values
of 1–3 910
5
1/s which are known to damage the cells irreversibly [160].
4.5 Volumetric Mass Transfer Coefficient
The investigation of the volumetric mass transfer coefficient k
L
awas performed
numerically using the Euler–Euler approach. As mentioned above, the k
L
adepends
on, among other things, the (local) gas-holdup, the properties of the medium, and the
size of the gas bubbles. These factors are primarily affected by the sparger and
influenced by bubble coalescence and break-up processes. The experimental
determination of the size of the gas bubbles was performed using photography [88]
and sophisticated Shadowgraphy (Fig. 8a) as described in Ref. [207]. In the CFD
models, a unique bubble size was assumed, although the prediction of bubble size
C. Löffelholz et al.
distribution by population balance equation models has been shown to improve the
accuracy of k
L
adetermination. However, these models result in much higher
computational demands. Depending on the cell line, high aeration rates or strong
sparging can immediately damage the cells, however, this can be prevented if the
aeration rate is below 0.1 vvm [183]. CHO cells, which represent the most often
used production organism in the modern biopharmaceutical industry, have specific
oxygen uptake rates on the order of 0.25–0.35 910
-12
mol/cell/h [38,184]. More
detailed data for specific oxygen uptake rates of various cell lines is provided in Refs.
[185,186]. Due to the low oxygen requirements, k
L
avalues on the order of 2–37 1/h
are mostly sufficient to reach medium to high cell densities, as shown in Ref. [187].
In the UniVessel SU two-phase simulations were performed for P/Vs from 0.4
to 435 W/m
3
, assuming an air bubble size of 1 mm. In order to analyze the
k
L
a(18), superficial gas velocities of 2.8 910
-4
and 5.7 910
-4
m/s (corre-
sponding to 0.1 and 0.2 vvm) were used (Fig. 8b). According to Zhu, the flow
regimes resulting from these aeration rates and bubble diameters are not signifi-
cantly altered [188]. The numerically determined k
L
avalues (14 and 25) for the
UniVessel SU at maximum working volume were plotted as a function of P/
V(Fig. 8b). Depending on the aeration rate, k
L
avalues ranging from 10–60 1/h
(0.1 vvm) and 20–100 1/h (0.2 vvm) were found. Comparing the experimental
results to the numerically obtained results, the latter deliver lower k
L
avalues,
which are, nevertheless, on the same order of magnitude [189]. However, these
values are very high, meaning they are sufficient for aerobic microbial fermen-
tations, requiring higher specific power inputs and aeration rates.
Increasing the P/Vresults in lower oxygen transfer resistance, due to the higher
surface renewal rate of the bubbles [190] and, therefore, leads to higher mass
transfer coefficient values of k
L
and k
L
a, respectively. In both bioreactor types, the
liquid mass transfer coefficient k
L
ranges from 1.25–2.65 910
-4
m/s (25). Based
on these results, the maximum required k
L
aof 37 1/h mentioned above, has
Fig. 7 Evaluation of the frequency distribution for the local shear gradients as a function of
volume fraction in the UniVessel SU for a specific power input of 0.4 and 435 W/m
3
(a).
Comparison of the mean local shear gradients as a function of specific power input in the
UniVessel SU under transient (0.4 \P/V\34 W/m
3
) and turbulent (34 \P/V\435 W/m
3
)
flow conditions (b)
Dynamic Single-Use Bioreactors
already been achieved with a P/Vof 90 W/m
3
at an aeration rate of 0.1 vvm, and
an even lower P/Vof 10 W/m
3
at 0.2 vvm. In the BIOSTAT CultiBag STR 50 L
(both configurations; Fig. 8a), the mean bubble diameter was 5 mm and was
measured using the Shadowgraphy technique at a P/V of 1.05 W/m
3
and an aer-
ation rate of 0.02 vvm. In this case, a maximum k
L
avalue of 35 1/h was deter-
mined at an aeration rate of 0.1 vvm [88] using the gassing-out method.
Using the correlation suggested by van’t Riet in (18), which represents the k
L
a
as a function of the specific power input and the superficial gas velocity, the
coefficients C,x
1
, and x
2
were found to be 0.4, 0.25, and 0.78, respectively (28).
Here, the superficial gas velocity has a strong influence on the k
L
avalue, whereas
the specific power input is of only minor importance. This may be explained by the
low dispersion capacity of the stirrer when operated at low agitation rates. These
results were also found for other single-use bioreactors such as the Mobius Cell-
Ready 3 L bioreactor or a prototype of the UniVessel SU with a Rushton turbine
and a segment blade impeller [88,90].
kLa¼0:4P=V
ðÞ
0:25u0:78
Gð28Þ
5 Scale-up of single-use bioreactors
A key element in the biopharmaceutical industry is the transfer of the cultivation
process from lab to production scale (scale-up), while ensuring identical process
characteristics [191]. The most often applied scale-up approach is based on geo-
metric similarity (height to diameter ratio) and/or engineering parameters (e.g.,
u
Tip
,P/V,h
m
,k
L
a,k,c
NT
) of the bioreactor [171,172,183,192].
Fig. 8 Determination of the mean bubble diameter in the BIOSTAT CultiBag STR (RT ?SBI)
50 L using Shadowgraphy (a). Experimentally and numerically-predicted volumetric oxygen
mass transfer coefficients as a function of specific power input for the aeration rates of 0.1 and
0.2 vvm in the UniVessel SU (b)
C. Löffelholz et al.
In order to determine a bioreactor’s engineering parameters, a fundamental
engineering characterization is required (see Sect. 3), where the specific power
input, mixing time, and volumetric mass transfer coefficient represent the most
often used scale-up criteria [192,193]. For microbial fermentations, the heat
exchange surface has proven itself as a reliable scale-up factor [120] whereas in
microcarrier-based stem cell cultivations the suspension criterion, where the mi-
crocarriers are homogeneously dispersed, has been successfully introduced [33,
194]. However, it is not possible to keep all parameters constant when scaling up
[38,192] and, therefore, a compromise must often be found under consideration of
critical process parameters (e.g., oxygen transfer or specific power input), which
have to be identified in advance [178].
The impeller speed, which is often used for scaling up in the pharmaceutical
industry [88] is not a major parameter for scaling up [120,172] and results in a
decreasing of the specific power input. Based on a tip speed of 0.9 m/s, the specific
power input is 118 W/m
3
in the UniVessel SU and decreases in the BIOSTAT
CultiBag STR 1,000 L to 5 W/m
3
. For bioreactors larger than benchtop scale, this
leads to decreased mixing and mass transfer and results in unacceptable cell growth.
To prevent the formation of concentration gradients, mixing time represents a
further criterion that can cause issues when scaling up. A relationship between the
mixing time and bioreactor/stirrer type is provided in Eq. (11), based on the
specific power input and the reactor as well as the stirrer geometry [120,127,195].
As shown in Fig. 9, the mixing times predicted for the different single-use bio-
reactors and sizes investigated in this study were well correlated by this single
equation (with R
2
=0.97). The determined proportional factor is 3.5, which is in
the same range as the predicted value of 5.9 [195].
hm¼3:5P=VðÞ
1=3ds=DðÞ
1=3H=DðÞ
2:43D2=3ð29Þ
Especially at larger scales, inhomogeneous mixing contributes to the formation
of pH and nutrient gradients as a result of local hydrodynamics [196], which may
result in a reduction of cell growth and protein expression [127,197,198].
However, keeping mixing time constant when scaling up leads to a significant
increase in the specific power input at larger scales [178,199]. If the mixing time
in the UniVessel SU is estimated to be 34 s (approximately 1 W/m
3
), specific
power inputs of 22 W/m
3
for the BIOSTAT CultiBag STR (2 9SBI) 500 L and
28 W/m
3
for the 1,000-L scale are required. According to (24), the Kolmogorov
length scale in the stirrer zone and close to the stirrer decreases to 89 and 16 lm,
respectively. In addition, an increase in the shear gradients can be observed due to
the rising specific power input. When considering the working volume
(c
NT
µV
-0.16
) and the ratio of impeller diameter to vessel diameter (c
NT
µd
s
/
D
-2.7
) (data generated by own studies, but not shown), correlation (30) results,
showing a linear graph with a single proportional factor Cfor the UniVessel SU
and the BIOSTAT CultiBag STR across the different scales (see Fig. 10). In the
present study, Cwas found to be 0.05 (31). Considering the mixing time, as
mentioned above, the mean local shear gradients are approximately 1.5 1/s (500 L,
Dynamic Single-Use Bioreactors
21 W/m
3
) and 1.4 1/s (1,000 L, 28 W/m
3
), respectively. The maximum local shear
gradients are below a value of 1,000 1/s (data not shown) and the Kolmogorov
microscale is in a typical range for cell culture processes where no cell damage is
expected (see Sect. 4.1,[160,182]).
cNT;m¼CP=VðÞ
1=3V0:16 ds=DðÞ
2:7ð30Þ
cNT;m¼0:05 P=VðÞ
1=3V0:16 ds=DðÞ
2:7ð31Þ
Specific power input has the largest influence on mass transfer and represents a
successful compromise for scaling-up a bioreactor according to the Büche theorem
[172]. Therefore, it is suggested that specific power input should be kept constant
during scale-up, a technique that has been successfully applied in microbial fer-
mentations and animal cell cultivations [38]. However, the scale-up with a con-
stant specific power input results in an increase in mixing time, the Reynolds
number and tip speed, whereas the stirrer speed, Froude number, and shear gra-
dient, are decreased under turbulent flow conditions. In contrast, the eddy length
scale remains constant according to (24).
In addition to the power input, oxygen mass transfer is a further scale-up
criterion for aerobic processes. As already mentioned, animal cells have lower
metabolic rates and oxygen demands than yeast and bacteria, but in high cell
density processes, or in cases where aeration is limited by lack of mechanical
stress tolerance, oxygen mass transfer can become a limiting factor [200]. If direct
bubble aeration is applied, the risk of damaging the cells as a result of the bubbles
bursting increases [160,201203,147]. This risk also increases as the bubble
diameter decreases [120].
The difficulty in scaling-up cell culture-based processes results from a lack of
preservation of local flow structures as the reactor vessels are scaled-up [193]. It is
Fig. 9 Comparison of the CFD-predicted mixing times correlated by (11) for all bioreactor
configurations investigated
C. Löffelholz et al.
well known that highly localized regions of high-energy dissipation exist and that
local flow structures strongly depend on the vessel geometry and operating con-
ditions. These local flow characteristics cannot be described adequately by global
scale-up parameters. Therefore, engineering characterization is required, which
consists of spatially resolved data obtained from experimental [193] and numerical
methods. In order to turn the scaling-up of single-use bioreactors into a describable
and understandable process, numerical techniques are increasingly being intro-
duced in scale-up studies [204]. However, scaling up of bioreactors and processes
remains a challenge and is ‘‘as much an art as a science’’ [205] and therefore,
extensive know-how is presupposed [206].
6 Conclusions and Outlook
In this review, instrumented, commercially available single-use bioreactors from
benchtop up to m
3
scale have been presented. Single-use bioreactors with entirely
new working and aeration principles, such as wave-mixed, orbitally shaken,
vibrating disk and rotatory oscillating systems, have established themselves during
the past decade. However, the trend is moving more towards the development of
bioreactors that are similar to conventional glass or stainless steel bioreactors and
take mass transfer and power input from stirrers into account. This trend is
independent of application and includes cell expansions, antibody and vaccine
production, and manufacturing of secondary metabolites used in cosmetics.
The availability of bioengineering data speeds up the processes of selecting the
most suitable single-use bioreactor type, defining process optimization parameters
and scaling-up. In addition, it makes comparison with other single-use bioreactors
Fig. 10 Mean local shear gradients as a function of (30) for all single-use bioreactors
investigated
Dynamic Single-Use Bioreactors
and their traditional counterparts possible, as shown for the UniVessel SU and the
BIOSTAT CultiBag STR versions. In addition to established experimental methods,
modern techniques such as CFD and PIV have become increasingly important. Their
application has led to a reduction in experimental effort, time, and costs as well as
ultimately contributing to more rapid product development and manufacturing.
Acknowledgments The results presented are part of a PhD thesis. The authors are grateful to
Dipl.-Ing. Ute Husemann, Dr. Gerhard Greller, Dipl.-Ing. Jacqueline Herrman and Dr. Alexander
Tappe, from Sartorius Stedim Biotech for providing geometric details for the bioreactors under
investigation and experimental results for the BIOSTAT CultiBag STR, as well as for their
participation in many helpful discussions.
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