Castilho Leda R., Moraes Angela Maria (Ed.) Animal Cell Technology: From Biopharmaceuticals to Gene Therapy

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The terminal settling velocity (v

) of a spherical particle under laminar

ﬂow can be described by Stokes equation (Equation 1):

 r) bd

18

(1)

where r

and r are the particle (cell) density and the ﬂuid (medium)

density, respectively; b is the force ﬁeld intensity (b ¼ g for a gravitational

ﬁeld or b ¼ ø

r for a centrifugal ﬁeld); d is the particle (cell) diameter; 

is the ﬂuid viscosity; g is the acceleration due to gravity (9.81 m s

2

); ø is

the angular velocity; and r is the radial distance of the particle (cell) from

the rotation axis.

Terminal settling velocities decrease with cell concentration. Therefore,

for cell suspensions with concentrations higher than 1% by volume

(around 6 3 10

cells mL

–1

for cells with 15 m diameter), the terminal

settling velocity given by Equation (1) should be corrected using Equation

(2). This equation is valid under laminar ﬂow (Stokes region):

¼ v

1  c

ðÞ

4:65

(2)

where c

is the concentration by volume; v

is the terminal settling

velocity of the cell at a given concentration c

, and v

is the terminal

settling velocity of the cell given by equation (1).

This chapter describes the main unit operations employed for animal

cell separation. These are gravity settlers, centrifuges, hydrocyclones,

ﬁlters, and ultrasonic separators.

11.2 Separation efﬁciency

Monitoring the separation efﬁciency is an important way to evaluate the

performance of a given separator. The efﬁciency concepts described in this

section apply not only to animal cell separation, but also to the separation

of any particles and bioparticles, such as microorganisms, cellular debris,

nuclei, etc. These concepts apply to any separation device whose perform-

ance remains constant if the operational conditions do not change. This

happens, for instance, in gravity settlers, centrifuges, and hydrocyclones.

Batch cell

culture

Cell retention

device

End of the

batch culture

Cell suspension

from the bioreactor

Extracellular

product

Cells

Figure 11.2

Cell separation device as the ﬁrst step of the downstream processing in a batch

culture.

274 Animal Cell Technology

Two kinds of separation efﬁciency may be deﬁned when dealing with

separation devices: the total and the grade efﬁciency. The total efﬁciency is

a global efﬁciency and the grade efﬁciency is the efﬁciency attained for a

given cell size. To obtain the grade efﬁciency it is necessary to know the

cell size distributions. These distributions may be presented either as

frequency x or as cumulative distributions (undersize y or oversize z).

Figure 11.3 shows the frequency plot (Figure 11.3A) and the cumulative

plots (Figure 11.3B) of HeLa cells cultivated in a stirred bioreactor, in a

serum-free medium (Luebberstedt, 2000).

These three forms of presenting the cell size distribution are inter-

related through Equations (3) and (4).

x ¼

(3)

y ¼ 1  z (4)

(A)

Cell diameter ( m)µ

Frequency (%)

(B)

100

Cumulative distribution (%)

Figure 11.3

Cell size distribution o f HeLa cells grown in serum-free culture medium

(Luebberstedt, 2000), presented as (A) frequency and (B) cumulative undersize (y)

and oversize (z) distributions.

Animal cell separation 275

A given separator has three main streams: the feed, which carries the

cells to be separated, the stream concentrated in cells (underﬂow), and the

diluted stream (overﬂow), containing the cells that the separator was not

able to capture. These three streams are shown in Figure 11.4.

The total separation efﬁciency E is the cell fraction recovered in the

concentrated stream, as given by Equation (5).

E ¼

(5)

where Q and Q

are the ﬂow rates and X and X

are the cell concentra-

tions, as cell number per unit volume, of the feed and concentrated

streams, respectively.

The ﬂuid fraction discharged in the concentrated stream is known as the

ﬂow ratio R

. For diluted suspensions like the ones usually found in cell

cultures, R

may be expressed by Equation (6). Some separators operate

with R

¼ 0 and some with R

. 0. Because the ﬂuid leaving the separator

in the concentrated stream drags some particles with it, these particles are

separated not due to the separation power of the separator but due to the

drag force. This bypass is normally considered to be equal to the ﬂow ratio

(Medronho, 2003). Hence, R

also represents the lowest separation efﬁ-

ciency at which the separator will operate.

(6)

The reduced total efﬁciency E9 (Equation 7) is normally used for

separators that operate with R

. 0. This gives the separation efﬁciency of

the particles that are separated in the concentrated stream only due to the

separating power of the separator. Therefore, E9 does not consider the

particles that reach the underﬂow due to drag.

E9 ¼

E  R

1  R

(7)

Feed

,,Q X y

Diluted

stream

Concentrated

stream

QXy

,,Xy

Figure 11.4

Schematic drawing of a separator showing the ﬂow rates Q,thecell

concentrations X, and the cumulative undersize distributions y .

276 Animal Cell Technology

Based on Equations (5), (6), and (7) and in material balances for the

liquid and for the cells, it is possible to obtain Equation (8).

E9 ¼ 1 

(8)

The deﬁnition of the grade efﬁciency (Equation 9) is similar to the total

efﬁciency deﬁnition, but it applies only to a given bioparticle size. Figure

11.5 shows a typical grade efﬁciency curve:

G ¼

(9)

where G is the grade efﬁciency, and X

and X

are the concentrations of

cells of size d in the concentrated and feed streams, respectively.

Based on Equations (3) and (5), it is possible to rewrite Equation (9) as:

G ¼ E



(10)

Particle size

(A)

(B)

100

Grade efficiency (%)

100

Grade efficiency (%)

Figure 11.5

GradeefﬁciencycurveforR

equal to 0% (A) and greater than 0% (B).

Animal cell separation 277

Equation (11) represents a global mass balance for the cells of diameter d.

¼ Q

þ Q

(11)

Based on Equations (9) and (11), it is possible to write:

G ¼ 1 



(12)

Therefore, based on Equations (3) and (5):

G ¼ 1  1  E

ðÞ

(13)

From Equation (11), it is possible to write:



¼ Q



þ Q



(14)

Dividing Equation (14) by QX and using Equation (10):

¼ 1 þ

 1



(15)

Through Equations (10), (13), and (15), it is possible to obtain the grade

efﬁciency curve based on the total efﬁciency E and the size distributions

of two out of three streams (y, y

and y

The cell size that is separated with 50% grade efﬁciency (d

) is usually

accepted as the cut size (Figure 11.5). This is an indirect measure of the

separation power of a separator device. A better designed separator will

give a lower cut size. A high proportion of the cells smaller than d

will

leave the separator in the diluted stream while the majority of those greater

than d

will leave it in the concentrated stream.

For separators which operate with R

. 0, the grade efﬁciency curve

does not start at G ¼ 0% (Figure 11.5B). This is because the separator

operation always gives a minimum efﬁciency almost equal to the ﬂow

ratio R

. The reduced grade efﬁciency G9 may be obtained in the same

way as the reduced total efﬁciency E9:

G 9 ¼

G  R

1  R

(16)

A chart showing the reduced grade efﬁciency versus cell size starts in

the origin, and the cell size corresponding to 50% reduced grade efﬁciency

is known as the reduced cut size d9

(Figure 11.6).

Equation (17), obtained from Equation (10), shows that it is possible to

estimate the total efﬁciency of cell separation when the curves of grade

efﬁciency and feed size distribution are known. Based on Equations (16)

and (17), it is possible to obtain a similar result for the reduced total

efﬁciency (Equation 18).

E ¼

Gdy (17)

278 Animal Cell Technology

E9 ¼

G9dy (18)

If a separator, used as a cell retention device in a perfusion bioreactor, is

operating with E , 100%, some of the cells are lost in the perfusate. In

such a situation, the apparent speciﬁc cell growth rate 

is given by

Equation (19).



(19)

Equation (20) gives a global cell balance in a bioreactor of volume V

operating with a perfusion rate D and using a cell retention device that

gives a cell retention efﬁciency E.

¼ V  1  E

ðÞ



X (20)

Based on Equations (19) and (20), it is possible to write:



¼   (1  E)D (21)

The maximum operational perfusion rate D

max

is thus just marginally

lower than that which results in cell wash-out. Therefore, when working

with D

max

, the cell loss in the perfusate is totally compensated by the cell

growth. In this situation, the apparent speciﬁc cell growth rate 

is zero.

Hence, from Equation (21):

max



1  E

(22)

Consequently, the maximum perfusion rate possible that can be used in

a perfusion bioreactor is a function of both the speciﬁc cell growth rate

and the cell retention efﬁciency.

100

Particle size

Reduced grade efficiency (%)

d⬘

Figure 11.6

Reduced grade efﬁciency curve and reduced cut size (d9

Animal cell separation 279

11.3 Gravity settling

Cells are separated in a gravity settler due to the action of a gravitational

ﬁeld. This type of equipment operates with ﬂow ratios greater than zero.

As animal cells have low densities and diameters, their settling velocities

are very low. For instance, the values in an aqueous medium at 378C are in

the 1–15 cm h

–1

range (Castilho and Medronho, 2002). Therefore, the

separator settling area has to be large enough to avoid losing cells through

the diluted stream, since it would decrease separation efﬁciency.

There are two main types of gravity settlers, the vertical and the

lamellar (Figure 11.7). In the latter, a great number of inclined plates,

named lamellas, are packed into the settler in a such a way that the plate

distance is very small. Gravity drives the cells to settle over the lamella

immediately below them. The cells slide down the plate to the bottom of

the apparatus, forming a concentrated stream. Theoretically, the total

settling area of a lamella settler is the sum of the surface area projection of

all lamellas in a horizontal plane. However, according to Svarovsky

(2000), due to inefﬁciencies in the settling process, only around 50% of

this area is really effective. Even so, this separator is much more compact

than a vertical settler, whose settling area is the cross-sectional area of its

cylindrical part.

Gravity settlers are usually designed based on a desired 100% cell

separation efﬁciency. To obtain such efﬁciency, the terminal settling

velocity of the smallest cell (v

min

) should be higher than the ascending

velocity of the liquid (u). At the limiting condition (u ¼ v

t ,

min

), the

minimum required settling area (A

min

) will be given by Equation (23). The

recommended working area for the settler should then be three times this

minimum required settling area.

min

t, min

(23)

(B)

(A)

Figure 11.7

Settlers usually employed in cell separations: (A) vertical settler; (B) lamella settler

(adapted from Henzler et al., 2003 ).

280 Animal Cell Technology

Settlers are simple devices and present no moving parts, facilitating

operations under aseptic conditions. However, they present operational

problems because of the high residence time of the cells in an environment

that presents suboptimal conditions of oxygenation and temperature

(Woodside et al., 1998). They also present difﬁculties for scale-up since

the required settling area is directly proportional to the ﬂow rate to be

treated (Equation 23), which increases with bioreactor volume. Lamella

settlers are also prone to cell adhesion on the lamella surface. This problem

may be diminished by using a special coating on the plates or by installing

a vibration system to vibrate the whole settler (Castilho and Medronho,

2002). This implies an increase in the complexity of the device. Despite

these considerations, Henzler et al. (2003) have successfully employed a

lamella settler as the cell retention device in perfusion bioreactor systems.

According to the authors, the high cell retention efﬁciencies obtained with

their specially designed lamella settlers allow using perfusion rates as high

as 15 d

1

11.4 Centrifugation

Centrifugation is based on particle settling in a centrifugal ﬁeld. This

centrifugal ﬁeld is created when applying a centrifugal acceleration to a

suspension, through a rotational movement. In a general way, particles

more dense than the liquid will attain an outward radial movement and

particles less dense will attain an inward radial movement.

The main types of industrial centrifuges used for bioparticle separations

are the tubular, the multi-chamber, and the disc centrifuges (Figure 11.8).

The disc centrifuge may have nozzles to allow continuous exit of the

concentrated suspension. The nozzles allow operation in a continuous

mode, with R

. 0. Tubular and multi-chamber centrifuges operate with

¼ 0.

The settling velocity of bioparticles in centrifuges is given by Equation

(1). In this equation, the angular velocity ø is in rad s

–1

. Equation (24)

converts angular velocity expressed in rotations per minute (rpm) to

rad s

–1

½

rad=s



½

rpm

(24)

When expressing operational conditions of centrifuges, it is advisable to

give the centrifugal acceleration (ø

R) rather than angular velocity (ø),

since the latter does not properly describe the centrifugal ﬁeld intensity,

which is a function of the radius of the centrifuge rotor. Thus, it is usual to

use the g-factor concept, also known as RCF (relative centrifugal force).

This is obtained by dividing the bioparticle settling velocity under a

centrifugal ﬁeld by the bioparticle settling velocity under the gravitational

ﬁeld (Equation 25).

g-factor ¼

(25)

Animal cell separation 281

Centrifuges give high separation efﬁciencies for animal cells and may be

used either in batch processes (Kempken et al., 1995; Tebe et al., 1997) or

as cell retention devices in bioreactors operating in perfusion mode

(Johnson et al., 1996; Takamatsu et al., 1996). However, centrifuges are

complex devices, with moving parts, of relatively high cost, and the cells

are submitted to shear stresses that may reach relatively high levels.

Bjorling et al. (1995) observed cell adhesion problems and clogging of the

exit channels when using a disc centrifuge as a cell retention device in a

perfusion culture.

In an attempt to eliminate some of these problems, a new centrifuge

(Centritech

) was specially designed for mammalian cell separation

(Johnson et al., 1996). This centrifuge operates with R

. 0 and generates

a centrifugal ﬁeld intensity up to 320 g. It operates in a closed system and

contains a presterilized and disposable plastic insert, which eliminates the

(A) (B) (C)

Figure 11.8

Schematic drawing of centrifuges: (A) tubular, (B) multi-chamber, (C) disc centrifuge.

282 Animal Cell Technology

necessity for CIP (cleaning in place) and SIP (sterilization in place). The

available models may be employed for cell separation of batch processes

dealing with volumes from 5 to 600 L, or in perfusion processes coupled

to 5–3000 L bioreactors (Centritech

, 2006).

11.5 Hydrocyclones

Hydrocyclones are very simple devices and always operate with a ﬂow

ratio R

. 0. They may be easily designed to give a desired separation

efﬁciency (Castilho and Medronho, 2000), and their performance may also

be easily predicted (Coelho and Medronho, 2001). In the last few years, it

has been shown either theoretically or experimentally that hydrocyclones

may be used in animal cell separations (Luebberstedt et al., 2000; Medron-

ho et al., 2005; Elsayed et al., 2006; Pinto et al., 2007) aimed mainly at

mammalian cell retention in perfusion bioreactors (Jockwer et al., 2001;

Elsayed et al., 2005).

Hydrocyclones are similar to centrifuges in that they use cell settling

in a centrifugal ﬁeld as the principle of separation. A hydrocyclone

(Figure 11.9 ) consists of a conical section joined to a cylindrical portion,

Overflow

(diluted)

Underflow

(concentrated)

Feed

Vortex finder

Primary vortex

Secondary vortex

Figure 11.9

Perspective view of a hydrocyclone showing the liquid ﬂow path.

Animal cell separation 283