Bubble-column design for growth of fragile insect cells

Bioprocess Engineering

Bioprocess Engineering 3 (1988) 37-41

© Springer-Verlag 1988

Bubble-column design for growth of fragile insect cells J. Tramper, D. Smit, J. Straatman and J.M. Vlak, Wageningen, The Netherlands

Abstract. A mathematical model for the design of bubblecolumns for growth of shear-sensitive insect cells is presented. The model is based on two assumptions. First, the loss of cell viability as a result of aeration is a first-order process. Second, a hypothetical volume X, in which all viable cells are killed, is associated with each air bubble during its lifetime. The model merely consists of an equation for kd, the first-order death-rate constant, and Amin, the minimum specific surface area of the air bubbles to supply sufficient oxygen. In addition to X, the equation for kd contains the air flow F, the air-bubble diameter db, the diameter D and the height H of the bubble column. This equation has been experimentally validated. Comparison of the equations for kd and Amin shows that especially H is the key parameter to manipulate in bubble-column design in order to meet the demands set by Amin and kd < kg, the first-order growth-rate constant. It is concluded that net growth of cells is enhanced as size and height of the bubble column increase.

1 Introduction

Animal cell technology is currently a rapidly growing area of research aiming at the production of valuable biological compounds of medical, pharmaceutical and agricultural interest. One of the problems in the scale-up of suspension cultures of animal cells is the fragility or shear sensitivity of most of these cells. This is the result of their large size (radius 10 µm) and their lack of a cell wall; they only have a cell membrane. This fragility of animal cells limits the supply of sufficient oxygen by sparging the solution. Therefore, the oxygen demand and the shear sensitivity of these cells may require special bioreactor designs. Rational design is difficult, as little quantitative data on the fragility of animal cells in suspension cultures are available. An analysis of the hydrodynamic effects on microcarrier-supported vertebrate cells in agitated tissue culture reactors was made by Cherry and Papoutsakis [I]. They concluded that the primary mechanisms of cell damage appear to result from direct interaction between microcarriers and turbulent eddies, collisions between microcarriers in turbulent flow, and collisions against the

impeller or other stationary surfaces. Recently, Croughan et al. [2] reported new concepts and theoretical models which explain new experimental data as well as previously published data on growth of animal cells in agitated microcarrier cultures. They found good correlations between cell growth and the following three fluid dynamic parameters: an integrated shear factor, average shear rate and Kolmogorov eddy length. Together with their Eddylegnth Model, they provided for the first time a fundamental approach to the design, scale-up and operation of microcarrier-based bioreactors. The fragility of hybridoma, myeloma and BHK cells in aerated suspension cultures has been investigated in a quantitative fashion by Emery et al. [3] and Handa et al. [4]. They reported experimental evidence for their hypothesis that cell death in sparged systems is associated only with the region of bubble disengagement from the free liquid surface. Our own data on the quantitative description of the shear sensitivity of insects cells in suspension [5- 7] indicated that loss of cell viability may occur in the region of air injection as well. In this paper we introduce a model describing cell death in a bubble-column and discuss the relation of cell death with oxygen supply in these columns. In addition, the experimental validation of our model on laboratory scale is reported. The design equations thus obtained indicate that growth of insect cells is facilitated as size and height of the bubble-column bioreactor increase up to the point where exhaustion of the air bubbles starts to limit oxygen supply.

I. I Hypothesis

Fragility or shear-sensitivity of cells and oxygen supply are keywords in designing bioreactors for growth of animal cells. In order to be able to find correlations between bioreactor design parameters and death rate of the cells, we have derived a model on the basis of the following two assumptions:

38

Bioprocess Engineering 3 (1988)

i) The loss of viability of the cells is a first-order process:

(1)

with C1 and C0 being the concentration of viable cells at time t = t and t = 0, respectively (cells/m 3), and kd the first-order death-rate constant (s- 1). ii) Associated with each air-bubble, during its lifetime, is a hypothetical volume X(m 3) in which all viable cells are killed: dC1 6F V-=¢·C ·X=--·C ·X dt t 7t . dg t ,

(2)

where Vis the volume of the bubble-column (m 3), ¢ the number of air-bubbles generated per second, and db the diameter of the air-bubbles (m). Separation of variables, integration between C1 = C0 and C1 = C 1 , and t = b and t = t, and assuming X to be constant in time, yields: _/ 6F·X

t)

C 1 =Co·e ~ .

(3)

Combining (1) and (3) gives: 6F·X

kd=--1t.

(4)

db. v

or

kd =

24F·X

~----c--

7t2.

db. D2. H

'

(5)

with D being the diameter (m) and H the heigh (m) of the bubble-column. In order for this equation to be useful, the dependence of X on F, db, D and H was experimentally determined.

2 Materials and methods A cell line (IPLB-Sf-21) from pupal ovaries of the fall armyworm Spodoptera frugiperda, originally isolated by Vaughn et al. [8] was used in the experiments described here. The cells were maintained on plastic tissue culture flasks [6], in Erlenmeyers [6] or in a continuous suspension culture. The cells used in the bubble-column experiments were harvested from a 1 dm 3 round-bottomed fermentor (Applikon) equipped with a marine impeller, and operated as described previously [6]. To test the hypothesis describing the effects on cell viability of air bubbles rising through a cell suspension, the following experiments were performed. A bubblecolumn with an inner diameter of 0.036 m was filled with a suspension of 10 12 cells/m 3 in TNM-FH medium [9] containing 0.1 % methylcellulose and 0.02% silicon antifoam. The experiments in which the air flow F and the height H of the suspension in the bubble-column were varied, have been reported earlier [5, 6]. The effect of

bubble-column diameter was tested in bubble-columns with diameters of 0.036, 0.052, 0.062 and 0.08 m, filled with 0.12, 0.25, 0.36 and 0.6 dm 3 cell suspension, respectively, to accomplish the same height H. The columns were equipped with the same air-injector providing one air bubble at a time. A constant air flow of 7 dm 3/h prevented settling of the cells during the experiments, even in the larger columns. The effects of air-bubble diameter db was investigated in the bubble-column with the smallest inner diameter of 0.036 m and equipped during the various runs with a different nozzle diameter (0.1, 0.15, 0.20, 0.25, 0.30 1, 0.30 2, 0.50, 0.70, 1.0, 1.5, 2.0 mm, respectively). The size of the air bubbles was determined photographically several times during the experiment by means of a special set-up consisting of an optical bank with a camera situated at one side of the bubble column and a flashlight at the other side. As a result of the cylindrical form of the column the air bubbles on the pictures were oval. The diameter of the corresponding spherical air bubble was calculated from db= (dt d2), with d1 being the smallest and d2 the largest diameter of the oval. During the experiments every half hour a sample was taken from the bubble-column. In these samples the number of cells was measured microscopically using a Burker-Turk counting chamber. Cell viability was determined using the exclusion of Trypan Blue (0.4%) in phosphate-buffered saline as indication of viability.

3 Discussion of results The results of the experiments with varying air flows and varying heights H of the cell suspension in the bubblecolumn have been published previously [5, 6]. The results clearly demonstrated that the first-order death-rate constant kd is proportional to the air flow F and to the reciprocal height H. From the latter it can be concluded that the rising of the air bubbles through the cell suspension has a negligible damaging effect. This observation is supported by Emery et al. [3] and Randa et al. [4] for hybridomas, myelomas and baby hamster kidney cells in bubble-sparged reactors. From the above results it can also be concluded that, if Eq. (5) is valid, the hypothetical killing volume X is independent of the air flow F and the height H. The results of the experiments in which only the diameter D of the bubble column was varied, keeping the air flow F, the height H and the sparger the same are summarized in Fig. 1, in which the first-order death-rate constant kd is plotted as a function of the reciprocal square bubble-column diameter. Again, a linear relationship is seen. In other words, Xis independent of D, if (5) applies. Determination of the size effect of the air bubbles appeared to be much more difficult to realize in practice. Even though nozzle diameters varying between 0.1 and

J. Tramper et al.: Design of insect-cell bioreactor

39

Table 1. First-order death-rate constant kd (average and standard deviation) as a function of air-bubble diameter db (range and average)

5

10-s s-1

./

!.c 4 EVl

83

db-range [mm]

db-average [mm]

10 5 · (kd± s ·db) [s-1]

5.00

1.85 2.50 2.83 3.14 3.38 3.70 4.30 4.73 5.18

3.12 ± 1.58 3.51 ± 1.18 3.16 ± 0.83 2.89 ± 0.71 2.54 ± 1.04 3.35 ± 0.84 3.29 ± 0.64 2.87 ± 0.89 3.24 ± 0.87

QJ

+-

~ 2

.i=

Ci

QJ

01

/.

/. 0 0

4

2

8

6

m- 2 10

Reciprocal square diameter

Fig. 1. First-order death-rate constant of insect cells in an aerated suspension as a function of the square bubble-column diameter

This very simple equation can be used to estimate kd for each desired bubble-column, provided that X' is known. X' can easily be obtained from one experiment such as those described above. Growth of insect cells in a continuous culture can be described by first-order kinetics: (8) In order for growth of insect cells to occur in a bubblecolumn, kd should be smaller than kg:

O+---~-~~~-~-~-~

0

2

4

mm 6

Air-bubble diameter db

Fig. 2. First-order death-rate constant of insect cells in a bubble column as a function of air-bubble diameter

2 mm were applied, the range of air-bubble diameters produced varied only between about 1.8 and 5.2 mm (Table I). Five independent series of experiments were performed, as initially contradicting dependencies were obtained. To structure the cloud of data points, the various air-bubble diameters were grouped and averaged as given in Table 1. The table also gives the corresponding average kd with the standard deviation. In Fig. 2, kd is plotted as a function of the air-bubble diameter. From this figure it is concluded, in contrast to the other three parameters, that kd is independent of the air-bubble diameter db. In other words, the hypothetical killing volume X must be proportional to the volume of the air bubbles, which is quite plausible. Introducing a specific hypothetical killing volume X' defined as the hypothetical killing volume X divided by the volume of one air bubble gives:

x X'=--(tndt)'

(6)

(9) For scale-up of insect-cell cultures, in wich oxygen is supplied by sparging air through the suspension, it is important to correlate shear sensitivity and oxygen need of the cells. The oxygen transfer rate OTR (mo! 0 2 · m- 3 • s- 1) can be written as:

(I 0) with kL being the oxygen transfer coefficient (m · s- 1), C5, the concentration of oxygen in the liquid when in equilibrium with air (mo!· m- 3 ), C0 , the actual oxygen concentration in the bulk liquid (mo!· m- 3), OUR' the oxygen uptake rate of cells (mo! 0 2 · ce11- 1 · s- 1), and A the specific surface area of the air-bubbles (m 2 · m- 3 ). The specific surface area A can also be written as:

A=

¢' · n ·di 2 4 n·D ·H I

'

(11)

with ¢' being the number of air-bubbles present in the suspension:

6F H ¢'=-·n 'dt V; '

(12)

where v; (m/s) is the rising velocity of the air bubbles. Substitution of¢' in 11 gives:

and substitution in (4) and (5) gives: (7)

24F

A=-----,-2 n ·db· v; · D •

(13)

40

Bioprocess Engineering 3 (1988)

From (10) the minimal specific surface area obtained:

Amin

is

and the air-bubble diameter db are not easily adjustable design parameters, and the air flow F and the column diameter D both appear in the same way in both equations, thus affect kd and A identically. Eqs. (7), (8), (9), (13) and (14) can be used for the design and scale-up of insect-cell-culture bioreactors, which are aerated by sparging. This will be illustrated below by some numerical examples using data obtained in our laboratory. The minimal doubling time of the insect cells we use in our studies is about 24 h, which means that k 0 = 8 · 10-b s- 1• In order for growth of these insect cells to occur in a bubble column kd should be smaller than this value. Figure 3 shows the results of the calculations for a vessel with H = D (standard fermentor) and H = 10 D (typical for bubble-column), using the equations given in the preceding paragraph. Fig. 4 illustrates the procedure. The value substituted for kL (the oxygen transfer coefficient) is low, but extracted from experimental results. The values for OUR', Ci. Ct, 2 and X' are experimentally determined or derived from previously reported data [5, 6]. We have frequently observed that the oxygen concentration in a surface aerated slowly stirred continuous culture drops to zero, without significant increase in the number of dead cells. The average value of X for the pertinent insect cells, calculated from all our experiments in the bubble-column is 4.5 · 10- 10 m 3, corresponding to a spherical volume with a diameter of about I mm. The corresponding specific

(14) with C~!n being the minimum liquid oxygen concentration (mo!· m- 3) at which cells are able to grow. Inspection of the equations for kd and A (Eqs. (7) and (13)) reveals that especially the height H of the bubblecolumn is the parameter to adjust in order to meet the demands set by Eqs. (9) and (14). The rising velocity v;

0.1+--,---r-~-r-rrrr--.----r-,-.,..,-rrr,-----,-,.----,-r"'rrrrl

0.001

0.01

m3 1

0.1

Volume V

Fig. 3. Double-logarithmic plot of the ratio of the first-order growth and death-rate constant as a function of the bubblecolumn working volume

OUR'= 2.1

* 10- 16 mol 02/(cell.s)

* 10 12 cell/m 3 kt= 1.05 * 10-• mis 3 Co 2 * = 0.27 mol/m Ct = l

co,"j" -

0 •ol/o'

Amin= OUR' .Ctl 1 ?

tion scheme for growth of insect cells

J. Tramper et al.: Design of insect-cell bioreactor

hypothetical killing volume X' for an air bubble with a diameter of 6 mm is 4 · 10- 3 m 3/m 3. As can be expected from inspection of the formulas, growth of the cells can be expected to improve as the volume, or rather the height, of the bubble-column increases. Naturally, the HID ratio cannot be increased unlimited, as at a certain point oxygen depletion in the air bubbles becomes a limiting factor of cell growth.

41

Acknowledgements The authors are indebted to Ms. Magda Usmany, Mr. Peter Koenen and Mr. Ido Wolters for technical assistance. The authors also acknowledge the skillful assistance of Ms. Hetty Geitenbeek in typing the manuscript.

References I. Cherry, R. S.; Papoutsakis, E. T.: Hydrodynamic effects on

4 Conclusions 2.

The mathematical model presented in this paper appeared to be quite useful in determining the effect of various bubble-column parameters on insect cells. So far, the experimental results support our model. If the proposed hypothetical killing volume X indeed exists, it is logical that it is, as has been found, independent of the height and diameter of the bubble-column, and also independent of the number of air bubbles, i.e. the air flow. In contrast, since X is the killing volume associated with each air bubble during its lifetime, it is likely that it is, as observed, dependend on the size or volume of the air bubble. This makes the formula for the first-order death-rate constant kd, one of the design equations, even more simple. Comparison of this formula with that of the specific surface A of the air bubbles reveals that especially the height H, or the slenderness (HID) of the bubble-column, is the parameter to adjust to meet the demands set by the minimum specific surface area needed to supply sufficient oxygen and by the fact that the growth rate of cells should be faster than the death rate in order for growth to occur. The numerical example, based on data from our experiments with insect cells, clearly showed that growth should improve, if slenderness or height of the bubblecolumn increases. This is due to a relatively longer lifetime of the air bubbles and, therefore, to a more efficient utilization of the oxygen in the air bubbles, naturally up to the point where oxygen exhaustion becomes limiting. Work is under way to validate the model by performing experiments on a larger scale and with mammalian cells to investigate the general validity of our model for animal cells.

3.

4.

5.

6. 7.

8.

9.

cells in agitated tissue culture reactors. Bioprocess Eng. 1 (1986) 29-41 Croughan, M. S.; Hamel, J. F.; Wang, D. I. C.: Hydrodynamic effects on animal cells grown in microcarrier cultures. Biotechnol. Bioeng. 29 (1987) 130-141 Emery, A. N.; Lavery, M.; Williams, B.; Handa, A.: Largescale hybridoma culture. In: Webb, C.; Mavituna, F. (Eds.): Plant and animal cell cultures: Process possibilities, pp. 137 - 146. Chichester: Ellis Horwood 1987. Handa, A.; Emery, A. N.; Spier, R. E.: On the evaluation of gas-liquid interfacial effects on hybridoma viability in bubble column bioreactors. Presented at 7th ESACT meeting, Baden, Austria. To be published in Develop. Biol. Stand. Tramper, J.; Joustra, D.; Vlak, J. M.: Bioreactor design for growth of shear-sensitive insect cells. In: Webb, C.; Mavituna, F. (Eds.): Plant and animal cell cultures: Process possibilities, pp. 125-136. Chichester: Ellis Horwood 1987 Tramper, J.; Williams, J. B.; Joustra, D.; Vlak, J. M.: Shear sensitivity of insect cells in suspension. Enzyme Microb. Technol. 8 (1986) 33-36 Tramper, J.; Vlak, J. M.: Some engineering and economic aspects of continuous cultivation of insect cells for the production of baculoviruses. Ann. N. Y. Acad. Sci. 469 (1986) 279-288 Vaughn, J. L.; Goodwin, R. H.; Tompkins, G. J.; The establishment of two cell lines from the insect Spodoptera frugiperda (Lepidoptera: Noctuidae). In Vitro 13 (1977) 231-217 Hink, W. F.: Established insect cell line from the cabbage looper, Trichoplusia ni. Nature 226 (1970) 466-467

Received April 27, 1987 J. Tramper, D. Smit, J. Straatman Agricultural University, Department of Food Science, Food and Bionengineering Group, De Dreijen 12, NL-6703 BC Wageningen, The Netherlands J.M. Vlak, Department of Virology