Computational Fluid Dynamics Characterization of a Bioreactor Mixing ...

Chemical Product and Process Modeling Volume 6, Issue 1

2011

Article 21

Computational Fluid Dynamics Characterization of a Bioreactor Mixing Device for the Animal Cell Culture Valérie Gisèle Gelbgras, Université Libre de Bruxelles Christophe E. Wylock, Université Libre de Bruxelles Jean-Christophe Drugmand, Artelis S.A. Benoît Haut, Université Libre de Bruxelles

Recommended Citation: Gelbgras, Valérie Gisèle; Wylock, Christophe E.; Drugmand, Jean-Christophe; and Haut, Benoît (2011) "Computational Fluid Dynamics Characterization of a Bioreactor Mixing Device for the Animal Cell Culture," Chemical Product and Process Modeling: Vol. 6: Iss. 1, Article 21. DOI: 10.2202/1934-2659.1588 Available at: http://www.bepress.com/cppm/vol6/iss1/21 ©2011 Berkeley Electronic Press. All rights reserved.

Computational Fluid Dynamics Characterization of a Bioreactor Mixing Device for the Animal Cell Culture Valérie Gisèle Gelbgras, Christophe E. Wylock, Jean-Christophe Drugmand, and Benoît Haut

Abstract During a cell culture in a bioreactor, the cells are exposed to the shear stresses mainly generated in the culture medium by the mixing device. Beyond a critical shear stress, this exposition induces cell damages. Therefore, the limitation of the shear stress is an important criterion for the design of bioreactors. An accurate modeling of the flow and the induced shear stresses in the medium is a tool to achieve an effective design of a bioreactor. In this work, a new design of a mixing device is considered. The aims of this work are to develop a methodology to study the flow and the induced shear stresses in the device, to study and to model the relation between the flow, the induced shear stresses and the cell viability, to use the developed model as an optimization tool, and to study the design of the bioreactor mixing device and its scale-up. In a first step, the flow and the induced shear stresses in the device are simulated by Computational Fluid Dynamics. In a second step, the model of the influence of the flow and the induced shear stresses on the cell viability is established by a comparison between the computed flow and the induced shear stresses and experimental measurements of cellular viabilities for different impeller rotation speeds. Finally, the influence of another design of the mixing device on the cell viability is studied. KEYWORDS: flow and shear stress acting on the cells, cell viability, computational fluid dynamics Author Notes: This work was supported by a grant of the FRIA (Fonds pour la formation à la Recherche dans l'Industrie et dans l'Agriculture).

Gelbgras et al.: CFD Characterization of Bioreactor Mixing Device for Cell Culture

1.

Introduction

More and more complex biopharmaceuticals are produced by animal cell cultures in a bioreactor (Blüml 2007; Decker et al. 2007). In a bioreactor, the cells are exposed to the shear stresses generated in the medium by the mixing device (Varley et al. 1999). The exposition to the shear stresses can have several significant impacts on the cells, such as a decreasing cell growth, the cell death … (Ludwing et al. 1992; Camacho et al. 2007; Barbouche 2008). The cell sensitivity to the shear stresses depends on their mechanical properties. The viscous-elastic properties of the cell membrane enable to tolerate high shear stresses during a short time exposure (Prokop 1991; Mazzag 2002). The cell tolerance to the shear stresses depends on several parameters such as the level of the shear stresses, the time of the exposure to the stresses, the physiological state of the cells ... (Zhang et al. 1993; Shiragami et al. 1994; Wu 1999). The cell sensitivity to these shear stresses has to be considered for the bioreactor operation (Elias et al. 1995; Nienow 2006). However, the difficulties to evaluate the shear stresses in a mixing medium system and the complexity of their impact on the cells are a problem to design bioreactors specially for the large scale (Henzler 2000; Ibrahim et al. 2004). Some devices exist to characterize the cell sensitivity to the shear stress. Nevertheless, the flow, the shear stress level, the exposure time of the cells to the shear stresses in these devices are much different than in the bioreactor. The influence of the shear stress on the cells has to be studied in the operating conditions of the cell culture in the bioreactor. Nowadays, the bioreactor design for the animal cells cultures is usually realized by two methods. The first method is based on experimental tests. In a bioreactor prototype, the cell viability is measured for different operating conditions. Often, several prototypes are required before obtaining the final version of the bioreactor. This method is time consuming and cost expensive. The second method is based on the estimation of the maximal shear stress generated in the medium. The operating conditions are defined to remain the maximal shear stress in the medium below the limited shear stress tolerated by the cells (Maranga et al. 2004). This method does not take into account the exposition time of the cell to the flow and the induced shear stresses. Therefore, a more effective design procedure could be based on a better representation of the flow and the induced shear stresses. The first objective of this work is to characterize the flow and the induced shear stresses in a mixing device patented by the biotechnological company Artelis S.A.. The studied mixing device is a centrifugal pump used in a single-use bioreactor for the animal cells (Patent deposit 2006; Artelis SA 2007; Patent deposit 2007; Patent deposit 2007). This characterization is based on the Computational Fluid Dynamics (CFD). CFD is a well developed tool to study the Published by Berkeley Electronic Press, 2011

1

Chemical Product and Process Modeling, Vol. 6 [2011], Iss. 1, Art. 21

flow in complex geometries. Using this technique to study the impact of the flow and the induced shear stresses on the cells is mentioned by several authors as being a promising approach (Barbouche et al. 2007; Hutmacher et al. 2008; Singh et al. 2009). The second objective is to correlate the flow and the induced shear stresses with experimental followings of the time evolution of the viable cell concentration. From this correlation, a relation between the kinetic of the cell death rate and the CFD computed flow and the induced shear stresses is developed. The third objective is to use this correlation to characterize another pump. The influence of the flow generated by this second pump on the kinetic of the cell death is compared to this influence on the kinetic of the cell death rate by the first pump. This paper is organized as follows. The materials and methods used in this work are presented in section 2. The results are discussed in section 3. Finally, the section 4 summarizes and concludes the results.

2.

Material and methods

2.1.

Studied pumps

The studied mixing pump, called iCELLis-A, is a centrifugal pump (Figure 1). This pump is immersed in the tank of a bioreactor. This pump is made of three pieces. The first piece, the impeller, is placed in the center of the second piece, the base. The impeller diameter equals 6.5cm. The impeller rotation speed, written 𝑁, is between 200 and 1000rpm. The diameter of the base equals 23cm. The third piece, the distributor, lies on the base (Figure 2). The diameter of the distributor equals 17cm. Two cross sections of the distributor are presented in Figure 3 and Figure 4. The culture medium enters the pump by the lateral orifices of the distributor (1 in Figure 2 and Figure 3). The medium flows to the center of this piece and is delivered in the base (2 in Figure 2 and Figure 3). Then, the medium is set in a rotational motion by the magnetic driven impeller and flows through the blades of the base (3 in Figure 2). Finally, the medium is ejected of the pump at the outlets in the top of the distributor (4 in Figure 2, Figure 3 and Figure 4). As mentioned in the introduction, another pump is also studied. The influence of the flow on the kinetic of the cell death rate is investigated. This second pump, called iCELLis-B, is geometrically similar to the iCELLis-A. Its volume is 1.5 times larger than the iCELLis-A volume.

http://www.bepress.com/cppm/vol6/iss1/21 DOI: 10.2202/1934-2659.1588

2


Figure 1 – Global view of the iCELLis-A.

Figure 2 – Exploded view of the iCELLis-A with the base, the impeller and the distributor. The arrows indicate the direction of the flow.

Figure 3 – Cross section of the distributor of iCELLis-A with a view of the inlet pipes. The arrows indicate the direction of the flow.

Figure 4 – Cross section of the distributor of iCELLis-A with a view of the outlet pipes. The arrows indicate the direction of the flow.

2.2. Scale of turbulence affecting the animal cell and definition of the induced shear stress acting on the cells A turbulent flow is characterized by a large spectrum of eddies length scales. The cells are affected by the eddies with a length scale close to the cell diameter (𝐷c in m) (Cherry 1993; Chisti 2000; Dooley et al. 2009). The diameter of the mammalian cells is between 10-5 and 1.5 10-5m (Migita et al. 2010). Therefore, as it can be observed later in the simulation of the flow in the pump, the eddy scale affecting the cells is between the Kolmogorov micro-scale (𝜂𝐾 in m, Eq. (1) where 𝜌L is the density of the culture medium in kg/m³, 𝜂𝐿 is the dynamic viscosity of the medium in Pa s and 𝜖 is the turbulent kinetic energy dissipation rate in m²/s³) and a scale in the inertial range (𝑙 in m) (Pope 2000; Ranade 2002). 𝜂L3 𝜂𝐾 = 3 𝜌𝐿 𝜖 Published by Berkeley Electronic Press, 2011

1/4

(1)

3


The shear stress (𝜏 in Pa) is the product of the dynamic viscosity of the medium and the velocity gradient of the flow (Eq. (2) where 𝑣 is the velocity in m/s, and 𝑥 is the position in m). In this work, the turbulence is assumed isotropic at the scale of the cells. The expression of the velocity gradient depends on the considered scale of the isotropic turbulence. At the Kolmogorov micro-scale, the velocity gradient is given by Eq. (3). In the inertial range, the velocity gradient is given by Eq. (4) (Batchelor et al. 2002). Therefore, the shear stress acting on the cells considered in this work is given by Eq. (5) and depends on the cell diameter. The cell diameter is assumed to equal 10-5m. 𝜏 = 𝜂L

𝜕𝑣 𝜕𝑥

𝜕𝑣 𝜖𝜌L = 𝜕𝑥 𝜂L 𝜕𝑣 𝜖 ≅ 1.4 2 𝜕𝑥 𝑙 𝜖𝜌L 𝜂L 𝜏=

2.3.

1.4𝜂L

1/2

𝜖 𝐷c2

1/3

(2)

1/2

(3) 1/3

(4)

if 𝐷c = 𝜂K if 𝐷c > 𝜂K

(5)

Simulation of the flow in the studied pumps

The appropriate configuration of the simulations is identified by comparison of the results for different equation models, geometry mesh refinements and numerical resolution methods. These results are reported in a previous work (Gelbgras 2011). In the following subsections, this identified configuration is described. 2.3.1. Models The CFD simulations are realized with Gambit 2.4 and Fluent 6.3. The simulations are realized with the unsteady sliding mesh (SM) model. Because of the large Reynolds numbers of the pump (between 105 and 106, Eq. (6) where 𝑅 in m is the radius of the impeller and 𝑣∗ in m/s is the medium velocity magnitude at the end of impeller), the flow in the pump is turbulent. The Reynolds Averaged Navier Stokes (RANS) equations are solved. The standard 𝑘 − 𝜖 models are selected (𝑘 is the turbulent kinetic energy in m²/s²). These models are suited for a large range of industrial turbulent flows (Versteeg et al. 1995).


4


Re =

𝜌𝐿 𝑣∗ 2𝑅 𝜂L

(6)

2.3.2. Mesh of the studied pumps with Gambit 2.4 The first step of the systematic procedure of the CFD simulations is the mesh of the studied devices with Gambit 2.4. Firstly, the geometry is imported from an AutoCAD file. The pump is placed in a closed box representing the tank of the bioreactor and the medium to mix. Therefore, the only boundary condition to specify will be the impeller rotation speed. Secondly, for the implementation of the simulation SM model, two zones are defined in the tank. A first zone, called the rotor, is a zone of the medium encircling the impeller in the base of the pump (Figure 5). The second zone, called the stator, is the rest of the medium (in the pump and in the tank). The interface between the two zones has to be a revolution surface (© Fluent Inc. 2006).

Figure 5 – View of the rotor zone; zone of the medium encircling the impeller.

Thirdly, the geometry is meshed. Considering the complexity of the geometry, a mesh with tetrahedral volumes is generated with a T-grid scheme. The selection of the tetrahedron size is led by the mesh quality and the number of tetrahedron. Considering the solution accuracy and the time of the solution convergence, the tetrahedron size equals 4mm. 2.3.3. Numerical resolution of the transport equations with Fluent 6.3 The second step of the systematic procedure of the CFD simulations is the numerical resolution of the RANS, 𝑘 − 𝜖 and continuity equations with Fluent 6.3. Firstly, the solver settings and the flow models are selected. Because the studied flow is incompressible, the pressure-based solver is selected (with an implicit formulation). For the coupling of the pressure and velocity equations, the Published by Berkeley Electronic Press, 2011

5


selected algorithm is the SIMPLE. The culture medium is assimilated to water (density: 𝜌L = 998.2kg/m³, dynamic viscosity: 𝜂L = 1.003 10-3Pa s). The second order upwind discretization scheme is used for the momentum and 𝑘 − 𝜖 conservation equations. The convergence criteria are fixed to 10-3. The formulation of the time discretization scheme is implicit and the time step size corresponds to an impeller rotation of 1 degree. Secondly, the independence of the solution towards the initial conditions and the mesh is assessed by the monitoring of the distribution of the shear stress acting on the cells, written 𝑝v (𝜏i , 𝜏j ). 𝑝v (𝜏i , 𝜏j ) is the fraction of the volume with a shear stresses acting on the cells 𝜏 (defined in section 2.2) between 𝜏i and 𝜏j . To control the independence of the solution towards the initial condition, 𝑝v (𝜏i , 𝜏j ) is monitored during five impeller revolutions. For the studied geometries and considering the distribution of 𝑝v (𝜏i , 𝜏j ), the steady state seems to be reached after the first impeller revolution. To control the independence of the solution towards the mesh, 𝑝v (𝜏i , 𝜏j ) is monitored. When a solution independent of the initial conditions is reached for the initial mesh, 𝑝v (𝜏i , 𝜏j ) is evaluated. Then, the mesh is refined. The tetrahedrons selected for the refining have a velocity gradient between 10% of the maximal velocity gradient in the whole pump and 100% of this maximal velocity gradient. The iterations are performed until a new steady state is reached, and 𝑝v (𝜏i , 𝜏j ) is evaluated once again. This procedure is repeated for several refinements. For the studied geometries and considering the distribution of 𝑝v (𝜏i , 𝜏j ), the solution is independent on the mesh after the second refinement. 2.3.3.1.

Definition of the time averaged shear stress acting on the cells

To take into account the exposure time of the cell to the shear stress, the time averaged shear stress acting on the cells is defined by Eq. (7) (where 𝜏k is the shear stress acting on the cells in the tetrahedron k of the mesh in Pa, 𝑡k is the residence time of the cells in a tetrahedron k in s, and n is the number of the tetrahedrons in the mesh). 𝜏time,av =

n k=1 𝜏k 𝑡k n k=1 𝑡k

(7)

The residence of the cells in the tetrahedron k is defined as the ratio of the volume of the tetrahedron k (𝑉k in m³) and the product of the vector of the flow cross section (𝑆k in m²) and the velocity vector of the flow (𝑣k in m/s). 𝑉𝑘 , 𝑆k and 𝑣k are directly evaluated with Fluent. http://www.bepress.com/cppm/vol6/iss1/21 DOI: 10.2202/1934-2659.1588

6


2.4.

Global characteristics of the pumps

To characterize a pump, its outflow rate and its pressure head have to be estimated to insure the required conditions for the process. The theoretical outflow rate (𝑄th in m³/s) and the theoretical pressure head (𝐻th in m) of a pump are given by Eq. (8) and Eq. (9) (where 𝐶 is the capacity of the pump in m³/(s rpm) and 𝑔 is the gravitational acceleration in m/s²). With these parameters, the theoretical similitude group (𝑁s,th) can be evaluated Eq. (10)). 𝑄th = 𝐶. 𝑁 𝑁𝑅 𝐻th = 𝑔

(8) 2

(9)

1/2

𝑁s,th

𝑁𝑄th = 𝑔𝐻th 3/4

(10)

The real similitude group (𝑁s,r) is estimated with the real outflow rate (𝑄r in m³/s) and the real pressure head (𝐻r in m) (Eq. (11)). The efficiency factor of the pump (𝜂s ) is defined as the ratio of 𝑁s,r and 𝑁s,th (Eq. (12)). If the energy losses by friction are identical between two geometrically similar pumps, their efficiency factors are also identical. However, the change of the impeller rotation speed or the pump scale implies a modification of the magnitude of these losses. To take into account this phenomenon, a correction equation can be applied. Some correction equations are available in the literature (Poulain 1997). In this work, the used correction equation is the Pfleiderer correlation (Eq. (13)) depending on the Reynolds numbers of the flow (Re, Eq. (6)) and the impeller radii. The subscripts A and B reference the iCELLis-A and iCELLis-B, respectively. 1/2

𝑁𝑄r 𝑁s,r = 𝑔𝐻r 3/4 𝜂s =

(11)

𝑁s,r 𝑁s,th

1 − 𝜂s,A ReB = 1 − 𝜂s,B ReA

0.1

(12)

𝑅B 𝑅A

0.05

(13)

𝑄r,B and 𝐻r,B can be obtained from CFD simulations. The characteristics of the iCELLis-B are determined without experimental measurements on iCELLisB. The following procedure can be used. Firstly, the theoretical outflow rate and Published by Berkeley Electronic Press, 2011

7


pressure head of the two studied pumps are evaluated with Eq. (8) and (9). Secondly, the real outflow rates of these two pumps are estimated with Fluent simulations. Thirdly, the real pressure head of the iCELLis-A is experimentally estimated. The theoretical similitude group, the real similitude group and the efficiency factor of the iCELLis-A are then evaluated with Eq. (10), (11) and (12). With the efficiency factor of the iCELLis-A, the efficiency factor of the iCELLisB is estimated using Eq. (13) and this gives the real similitude group of the iCELLis-B (Eq. (12)). Finally, the real pressure head of the iCELLis-B is estimated using Eq. (11). This procedure to determine the real pressure head of the iCELLis-B is summarized in Figure 6.

Figure 6 – Overview of the procedure to determine the real pressure head of the iCELLis-B.

2.4.1. Experimental measurement of the outflow rates and of the pressure heads To measure the outflow rates and the pressure heads of the pumps, a graduated cylinder is placed on the distributor of the pumps. The outflow rates are determined by measurements of the axial velocity of the flow along this cylinder before the medium reaches the pressure head. The pressure heads are measured when the medium reaches a static level.

2.5. Time evolution of the viable cell concentration and of the total cell concentration A balance for the viable cells in the medium, of which the concentration is written 𝑋 (number of cells by unit of the medium volume in cell/m3MED ) leads to Eq. (15). The time evolution of 𝑋 is assumed to be first order with respect to 𝑋. 𝜇 is the specific growth rate of the cells (in s-1) and 𝑘D 𝜏time,av is the kinetic parameter of http://www.bepress.com/cppm/vol6/iss1/21 DOI: 10.2202/1934-2659.1588

8


the cell death rate (in s-1). 𝑘D 𝜏time,av is assumed to depend only on the time averaged shear stress acting on the cells. A balance for the cell (viable and dead), of which the concentration is written 𝑋TOT (in cell/m3MED ), leads to Eq. (16). During the time interval between two measurements of 𝑋 and 𝑋TOT, 𝜇 is assumed to be constant. Therefore, the integration of Eq. (15) and (16) from 𝑡1 , 𝑋1 , 𝑋TOT,1 to 𝑡2 , 𝑋2 , 𝑋TOT,2 leads to Eq. (17) and (18). To estimate 𝜇 and 𝑘D τtime,av , some cell cultures are realized. Their operating conditions are described in section 2.5.1. During these cultures, the time evolutions of 𝑋 and 𝑋TOT are followed. For given values of 𝜇 and 𝑘D τtime,av , the time evolution of 𝑋 and 𝑋TOT during the experimental time interval are computed with Eq. (17) and (18) and compared to the experimental data. 𝜇 and 𝑘D τtime,av are adjusted to minimize the sum of the quadratic differences between the computed and the experimentally determined cell concentrations (for two successive measurements). 𝑑𝑋 = 𝜇 − 𝑘D τtime,av 𝑑𝑡

𝑋

𝑑𝑋TOT = 𝜇𝑋 𝑑𝑡 𝑋2 = 𝑋1 + 𝑒 𝑋TOT,2 = 𝑋TOT,1 +

𝜇 −𝑘 D 𝜏 time,av

(15)

(16)

𝑡 2 −𝑡 1

𝜇 𝑋 − 𝑋1 𝜇 − 𝑘𝐷 (𝜏time,av) 2

(17)

(18)

2.5.1. Experimental cell cultures The iCELLis-A is placed in a tank with an effective medium volume of 5 10−3 m3MED . Cultures of Chinese Hamster Ovary (CHO) cells in suspension are realized for different impeller rotation speeds (200, 400, 600 and 1000rpm). The culture medium is the POWER CHO 1 medium, specially adapted for the culture of CHO cells in suspension (LonzaBio 2010). The conditions of the culture as the pH, the temperature, the species concentrations ... are regulated during the process. The species concentration ranges are given in Table 1. During the cultures, the viable cell concentration and the total cell concentration are measured. These measurements are done by counting cells under microscope with the Trypan Blue Dye Exclusion method (Freshney 2005). The measurements are realized during the phase of the cell growth (the first four days of the culture). Published by Berkeley Electronic Press, 2011

9

Chemical Product and Process Modeling, Vol. 6 [2011], Iss. 1, Art. 21 Table 1 – The ranges of the species concentrations kept during the culture.

Species concentration ranges mol m3MED 2 ≤ 𝐶s ≤ 22.5 0.05 ≤ 𝐶s ≤ 0.1 0 ≤ 𝐶s ≤ 2 0 ≤ 𝐶s ≤ 20

Species Glucose Oxygen Ammonia Lactate

3.

Results and discussion

3.1.

Global characteristic of the pumps

3.1.1. Theoretical characteristics of the pumps

210

1400

60

600

180

1200

50

500

150

1000

40

400

120

800

30

300

90

600

20

200

60

400

10

100

30

200

0

Qth (L/min)

700

0 200

400

600

0

800 1000

0 200 400 600 800 1000

N (rpm) Figure 7 – Theoretical outflow rate and pressure head of the iCELLis-A as a function of the impeller rotation speed.

Hth (cm)

70

Hth (cm)

Qth (L/min)

The theoretical outflow rate and pressure head of the iCELLis-A and iCELLis-B are presented in Figure 7 and Figure 8, respectively. The theoretical similitude group of both pumps (𝑁s,th,A = 𝑁s,th,B) equals 0.154.

N (rpm) Figure 8 – Theoretical outflow rate and pressure head of the iCELLis-B as a function of the impeller rotation speed.

3.1.2. Real characteristics of the iCELLis-A The CFD computed outflow rates of the iCELLis-A are in good agreement with the experimental outflow rates (Figure 9). This agreement is a first level of simulation validation. The real outflow rate is a linear function of the impeller http://www.bepress.com/cppm/vol6/iss1/21 DOI: 10.2202/1934-2659.1588

10


rotation speed as the theoretical outflow rate (Eq. (8)). In Figure 10, the experimental measurement of pressure head is presented as a function of the impeller rotation speed. As the theoretical pressure head (Eq. (9)), the real pressure head is proportional to the square of the impeller rotation speed. The real outflow rate and pressure head of the iCELLis-A enable to estimate the real similitude group of the iCELLis-A. 𝑁s,r,A equals 0.514. This value is in the range (0.1;0.750) mentioned by Perry et al. (1999) for this kind of pump. The efficiency factor of the iCELLis-A equals 3.338. 16 14

Qr (L/min)

12 10

CFD

8 6

Exp.

4

Linear (CFD)

2 0 500

600

700

800

N (rpm)

900

1000

Figure 9 – CFD computed and experimental outflow rates of the iCELLis-A as a function of the impeller rotation speed. The determination coefficient of the linear trend line of the CFD computed outflow rate equals 1.00. The relative error equals 10% of the experimentally determined outflow rate.

50

hr (cm)

40 30 Exp. Trend line

20 10 0 200

400

600

N (rpm)

800

1000

Figure 10 – Experimental pressure head of the iCELLis-A as a function of the impeller rotation speed. The real pressure head is proportional to the square of the impeller rotation speed. The determination coefficient of the trend line of the experimentally determined pressure head equals 1.00. The relative error is too small to observe the error bars in the figure.

Published by Berkeley Electronic Press, 2011

11


3.1.3. Real characteristics of the iCELLis-B The efficiency factor of the iCELLis-B is obtained by the application of the correction equation of Pfleiderer (Eq. (13)) and equals 0.334. With the efficiency factor and the theoretical similitude group of the iCELLis-B, the real similitude group is evaluated and equals 0.460. The CFD computed outflow rates of the iCELLis-B are in good agreement with the experimental outflow rates (Figure 11). The CFD computed outflow rate is always larger than the experimentally determined outflow rate. It is assumed to be due to the operating setting of the pump. Indeed, for instance, the duration to reach an impeller rotation speed equal to 700rpm is measured and equals 8s. Such a duration has a significant influence on the experimentally determination of the outflow rate because the duration of the medium elevation in the graduated cylinder is not much larger than this duration. With the real similitude group and the real outflow rate of the iCELLis-B, its real pressure head can be calculated (Eq. (11)). In Figure 12, the calculated real pressure head of the iCELLis-B is compared to the experimental measurement of this pressure head. A good agreement is observed and enables to validate the method to evaluate the real pressure head of a second pump from the global characteristic of a reference pump and without experimental measurement on the second pump. The evaluation of the pressure head without taking into account the correction of the real similitude group (Eq. (13)) is also presented in Figure 12. It can be observed that the application of the correction equation enables to obtain a more accurate evaluation of the real pressure head. Furthermore, the real pressure head is much smaller than the theoretical pressure head (comparison of Figure 8 and Figure 12). Therefore, a theoretical approach is not sufficient to evaluate the global characteristic of the pump.

3.2. Time averaged shear stress acting on the cells and its relation with the time evolution of the viable cell concentration 3.2.1. Time averaged shear stress acting on the cells From the simulation of the flow in the iCELLis-A, the time averaged shear stress acting on the cells is computed. The time averaged shear stress acting on the cells is a linear function of the impeller rotation speed (Figure 13). With the equation of the linear trend line, the time averaged shear stress acting on the cells can be interpolated to other impeller rotation speeds.


12


25

Qr (L/min)

20 15 CFD Exp.

10

Linear (CFD) 5 0 500

600

700 800 N (rpm)

900

1000

Figure 11 – CFD computed and experimental outflow rates of the iCELLis-B as a function of the impeller rotation speed. The determination coefficient of the linear trend line of the CFD computed outflow rates equals 0.99. The relative error equals 10% of the experimentally determined outflow rate.

70 60

Hr (cm)

50 Exp.

40 30

Mod. (With correction equation)

20

Mod. (Without correction equation)

10 0 300

400

500

600

700

800

900 1000

N (rpm) Figure 12 – Experimental, computed (with application of the correction equation), and computed (without application of the correction equation) pressure heads of the iCELLis-B as functions of the impeller rotation speed.


13


0,3

time,av (Pa)

0,25 0,2 0,15

CFD Linear (CFD)

0,1 0,05 0 500

600

700

800

900

1000

N (rpm) Figure 13 – The computed time averaged shear stress acting on the cells as a function of the impeller rotation speed. The determination coefficient of the linear trend line of the computed time average shear stress acting on the cells equals 0.99. iCELLis-A.

3.2.2. Identification of the specific growth rate of the cells and the kinetic parameter of the cell death rate

3,5

1,4

3

1,2

2,5

1

2

0,8

1,5

0,6

1

0,4

0,5

0,2

0

µ (day-1)

X (1012cell/m³MED)

To identify 𝜇 and 𝑘D 𝜏time,av , some cell cultures are realized with several impeller rotation speeds. The time evolutions of 𝑋 and 𝜇 are presented in Figure 14. 𝜇 changes during the culture. A lag phase can be observed, followed by an exponential growth phase, and followed by a growth deceleration phase.

X µ

0 0

1

2

t (day)

3

4

Figure 14 – Time evolution of 𝑿 and 𝝁. Cell cultures with an impeller rotation speed equal to 600rpm. iCELLis-A.


14


The experimental and computed time evolutions of the total cell concentration for different impeller rotation speeds of the iCELLis-A are presented in Figure 15 to Figure 18. An excellent comparison between the experimental and the computed time evolution can be observed. The identified values of 𝑘D 𝜏time,av used to compute the time evolution of the total cell concentration in Figure 15 to Figure 18 are presented in Table 2. 5

4

XTOT (1012cell/m³MED)


5

3 2 Mod.

1

Exp.

4 3 2

Exp.

0

0 0

1

2

3

4

0

t (day)

1

2

3

4

t (day)

Figure 15 – Experimental and computed time evolutions of the total cell concentration; the impeller rotation speed equals 200rpm. iCELLisA.

Figure 16 – Experimental and computed time evolutions of the total cell concentration; the impeller rotation speed equals 400rpm. iCELLisA.

5

5

4

4



Mod.

1

3 2 Mod.

1

3 2 Mod.

1

Exp.

Exp. 0

0 0

1

2

3

4

t (day) Figure 17 – Experimental and computed time evolutions of the total cell concentration; the impeller rotation speed equals 600rpm. iCELLisA.


0

1

2

t (day)

3

4

Figure 18 – Experimental and computed time evolutions of the total cell concentration; the impeller rotation speed equals 1000rpm. iCELLis-A.

15

Chemical Product and Process Modeling, Vol. 6 [2011], Iss. 1, Art. 21 Table 2 – Identified values of the kinetic parameter of the cell death rate for different impeller rotation speeds. iCELLis-A.

𝑘D (𝜏time,av) (day−1 ) 0.05 0.06 0.08 0.10

N (rpm) 200 400 600 1000

3.2.3. Relation between the time averaged shear stress acting on the cells and the time evolution of the viable cell concentration The identified values of 𝑘D (𝜏time,av) are plotted as a function of the time averaged shear stress acting on the cells (Figure 19). To characterize the relation between 𝑘D (𝜏time,av) and 𝜏time,av, the equation of the linear trend line is determined. This equation enables to evaluate 𝑘D (𝜏time,av) for other impeller rotation speeds. This equation is also used in this work as reference to evaluate 𝑘D (𝜏time,av) from 𝜏time,av for another scale and another design of the pump. 0,11 0,10

kD (day -1)

0,09 0,08 Identified values

0,07

Linear (Identified Values)

0,06 0,05 0,04 0,05

0,1

0,15

0,2

0,25

0,3

time,av (Pa) Figure 19 – The identified values of the kinetic parameter of the cell death rate as a function of the time averaged shear stress acting on the cells. The determination coefficient of the linear trend line of the identified values of 𝒌D (𝝉time,av) equals 0.98. iCELLis-A.

3.2.4. Change of scale and design The simulations of the flow in the iCELLis-B enable to evaluate the time averaged shear stress acting on the cells (Figure 20). With the time averaged shear


16


stress and the result presented in Figure 19, it is possible to evaluate the value of 𝑘D (𝜏time,av) with the characteristic equation of the regression curve in Figure 20. 1,6

time,av (Pa)

1,4 1,2 1

CFD

0,8

Linear (CFD)

0,6 0,4 500

600

700

800

900

1000

N (rpm) Figure 20 – The computed time averaged shear stress acting on the cells as a function of the impeller rotation speed. The determination coefficient of the linear trend line of the computed time averaged shear stress acting on the cells equals 0.98. iCELLis-B.

4.

Conclusions

During a cell culture in a bioreactor, the cells are exposed to the shear stresses generated in the culture medium by the mixing device. This exposition can induce cell damages. Therefore, the shear stresses are an important parameter to take into account for the design of bioreactors. An accurate modeling of the flow and the induced shear stresses in the medium and their influence on the cell viability is a tool to achieve an efficient design of a bioreactor. In this work, a new design of mixing device is considered. The studied device, called iCELLis-A, is a centrifugal pump developed by the biotechnological company, Artelis S.A.. Another pump, geometrically similar to the iCELLis-A, is also studied. This second pump is called iCELLis-B. The objectives of this work are to propose a method, based on CFD, to evaluate the flow and the induced shear stresses in the centrifugal pump. The flow and the induced shear stresses are correlated to experimental measurements of the time evolution of the viable cell concentration. On the basis of this correlation, a model is developed to establish the kinetic of the cell death as a function of the CFD computed flow and induced shear stresses. The eddies affecting the animal cell have a size close to the cell size. Therefore, the considered shear stress is defined as a function of the cell size (Eq. (5)). To take into account the time exposition of the cell to the shear stress, a time averaged shear stress acting on the cells is defined. The global characteristics of the iCELLis-A are studied. The real outflow rate is evaluated from the CFD simulation. This result is experimentally validated Published by Berkeley Electronic Press, 2011

17


on a prototype of the pump. On this prototype, the real pressure head is measured. The outflow rate and the pressure head enable to evaluate the real similitude group. The relation between these three global characteristics are used as model to estimate the real pressure head and the real similitude group of the iCELLis-B only from the computed outflow rate of this pump (Figure 6). The calculated real pressure head of the iCELLis-B is successfully compared with experimental data obtained on a prototype of the pump. The time averaged shear stress acting on the cells of the iCELLis-A, evaluated from CFD, is a linear function of the impeller rotation speed. To study the influence of the time averaged shear stress on the cell viability, some cell cultures are realized with different impeller rotation speeds. During these cultures, the time evolutions of the viable cell concentration and of the total cell concentration are followed. A model of these time evolutions is defined. In this model, two kinetic parameters characterize the cell growth rate and the cell death rate. With the experimental evolutions of the viable cell concentration and the total cell concentration, both kinetic parameters are evaluated. An excellent comparison is reached between the experimentally determined and the computed cell concentration. The kinetic parameter of the cell death rate is a linear function of the time averaged shear stress acting on the cells (Figure 19). This function can be used to evaluate the kinetic parameter of the cell death rate from the time averaged shear stress acting on the cells for other pumps. The time averaged shear stress acting on the cells in the iCELLis-B is evaluated from the CFD simulations. Then, the kinetic parameter of the cell death rate is estimated. For a given value of the real outflow rate, the cell death rate is larger in the iCELLis-B than in the iCELLis-A. With the characterized relation between 𝜏time,av and 𝑘D and the knowledge of 𝜇, the time evolution of the viable cells in a pump can be evaluated only from numerical simulation, thus without realizing expensive cell cultures. In a future work, some cell cultures will be realized in a bioreactor mixed by the iCELLis-B pump. The experimentally determined time evolutions of the viable and the dead cell concentration will be compared to the modeling determined time evolutions of the viable and dead cells in order to complete the validation of the presented work. Other indicators of the cell damage will be also followed, for instance the lactate deshydrogenase concentration.

Notations CFD CHO Exp. iCELLis-A

Computational Fluid Dynamics Chinese Hamster Ovary Experiment Name of the first studied pump


18


iCELLis-B MED Mod. MRF RANS Reg. RNG rpm SM

Name of the second studied pump Medium Model Moving Reference Frame Reynolds Averaged Navier Stokes Regression Reynolds Renormalization Group Revolution Per Minute Sliding mesh

𝐶 𝐶s 𝐷c 𝑒k

Capacity of the pump Species concentration in the medium Cell diameter Length of the edges of the regular tetrahedron equivalent to the tetrahedron k Gravitational acceleration 𝑔 Real pressure head 𝐻r Theoretical pressure head 𝐻th Turbulent kinetic energy 𝑘 𝑘D (𝜏time,av) Kinetic parameter of the cell death rate Inertial scale 𝑙 Impeller rotation speed 𝑁 Number of the tetrahedron in the mesh n 𝑁s,r Real similitude group 𝑁s,th Theoretical similitude group 𝑝v (𝜏i , 𝜏j ) Fraction of the medium volume with a shear stress acting on the cells between 𝜏i and 𝜏j Quality of the mesh based on the equi-angle skew 𝑄EAS Real outflow rate 𝑄r Theoretical outflow rate 𝑄th Radius of the impeller 𝑅 Reynolds number Re Vector of the flow cross section in the tetrahedron k of the 𝑆k mesh Time 𝑡 Residence time of the cell in the tetrahedron k 𝑡k Velocity 𝑣 Velocity of the medium at the end of the impeller 𝑣∗ Velocity vector in the tetrahedron k of the mesh 𝑣k Volume of the tetrahedron k 𝑉𝑘


m3 /(s rpm) mol/m3MED m m m/s 2 m m m2 /s2 s −1 m rpm

m3 /s m3 /s m m2 s s m/s m/s m/s m3

19


𝑥 𝑋 𝑋TOT

Position Viable cell concentration Total cell concentration

𝜖 𝜂K 𝜂𝐿 𝜂s 𝜃e 𝜃max 𝜃min 𝜇 𝜌L 𝜏 𝜏i 𝜏j 𝜏k 𝜏time,av

Turbulent kinetic energy dissipation rate Kolmogorov micro-scale Dynamic viscosity of the medium Efficiency factor Central angle of a regular tetrahedron Largest central angle of a tetrahedron Smallest central angle of a tetrahedron Specific growth rate of the cells Density of the medium Shear stress Value of the shear stress Value of the shear stress Shear stress in the tetrahedron k of the mesh Time averaged shear stress acting on the cells

m cell/m3MED cell/m3MED m2 /s3 m Pa s ° ° ° s −1 kg/m3 Pa Pa Pa Pa Pa

References © Fluent Inc. (2006). Fluent user's guide, http://www.fluentusers.com/, 18/08/2010. Artelis SA (2007). Method of cell Culture and device for implementing it. Patent. WO 070/039600 . Barbouche, N. (2008). Réponse biologique de cellules animales à des contraintes hydrodynamiques: simulation numérique, expérimentation et modélisation en bioréacteurs de laboratoire. Laboratoire des Sciences du Génie Chimique. Nancy, Institut National Polytechnique de Lorraine. Ph.D.Thesis . Barbouche, N., E. Olmos, et al. (2007). Coupling between cell kinetics and CFD to establish a physio-hydrodynamic correlation in various stirred culture systems. European Society for Animal Cell Technology 19th. Dresden, Proceedings. Batchelor, G. K., H. K. Moffatt, et al. (2002). Perspectives in Fluid Dynamics: A Collective Introduction to Current Research. Cambridge, Cambrigde University Press. Blüml, G. (2007). Microcarrier cell culture technology. Animal Cell Biotechnology: Methods and Protocols. R. Pörtner. Berlin, Humana Press. 24: 149-178. http://www.bepress.com/cppm/vol6/iss1/21 DOI: 10.2202/1934-2659.1588

20


Camacho, F. G., J. J. G. Rodriguez, et al. (2007). "Determination of shear stress thresholds in toxic dinoflagellates cultured in shaken flask, implcation in bioprocess engineering." Process Biochem 42: 1506-1515. Cherry, R. S. (1993). "Animal cells in turbulent fluids: details of the physical stimulus and the biological response." Biotechnol Adv 11: 279-299. Chisti, Y. (2000). "Animal-cell in sparged bioreactors." Trends Biotechnol 18 (10): 420-432. Decker, E. L. and R. Reski (2007). "Moss bioreactors producing improved biopharmaceuticals." Curr Opin Biotech 18: 393-398. Dooley, P. N. and N. J. Quinlan (2009). "Effect of eddy length scale on mechanical loading of blood cells in turbulent flow." Ann Biomed Eng 37: 2449-2458. Elias, C. B., R. B. Desai, et al. (1995). "Turbulent shear stress - effect on mammalian cell culture and measurement using laser doppler anemometer " Chemical Engineering Science 50(15): 2431-2440. Freshney, R. I. (2005). Culture of animal cells, a manual of basic technique. New Jersey, Willey. Gelbgras, V. (2011). Développement d'un modèle à compartiments d'un bioréacteur lit-fixe utilisé en culture de cellules animales, en vue d'étudier le design et la montée en échelle. Transfers, Interfaces and Processes, Université Libre de Bruxelles. Ph.D. Thesis . Henzler, H.-J. (2000). "Particle stress in bioreactor." Adv Biochem Biot 67: 3582. Hutmacher, D. W. and S. Harmeet (2008). "Computational fluid dynamics for improved bioreactor design and 3D culture." Trends in Biotechnology 26 (4): 166-172. Ibrahim, S. and A. W. Nienow (2004). "Suspension of microcarriers for cell culture with axial flow impellers." Chem Eng Res Des 82(A9): 1082-1088. LonzaBio (2010). Power CHO Chemically defined serum-free CHO medium (Product data sheet, Form No. 12-770Q), http://www.lonzabio.com, 07/05/2010. Ludwing, A., J. Tomeczkowski, et al. (1992). "Influence of shear stress on adherent mammalian cells during division." Biotechnol Lett 14 (10): 881884. Maranga, L., A. Cunha, et al. (2004). "Scale-up of virus-like particles production: effects of sparging, agitation and bioreactor scale on cell growth, infection kinetics and productivity." J Biotechnol 107: 55-64. Mazzag, B. C. (2002). Mathematical models in biology. Department of Mathematics, University of California. Ph.D.Thesis . Migita, S., K. Funakoshi, et al. (2010). "Cell cycle and size sorting of mammalian cells using a microfluidic device." Anal Method.


21


Nienow, A. W. (2006). "Reactor engineering in large scale animal cell culture." Cytotechnology 50: 9-33. Patent deposit (2006). Device for mobilising a liquid substance/Liquid substance circulation device. Patent. PCT/EP2006/066980 . Patent deposit (2007). Flexible Mixing bag, mixing device and mixing system. Patent. PCT/EP2007/053595 . Patent deposit (2007). Mixing system including a flexible bag, specific flexible bag and hardware therefore. Patent. PCT/EP2007/053998 . Perry, R. H. and D. W. Green (1999). Perry's chemical engineers'handbook. New York, Mc Graw-Hill. Pope, S. B. (2000). Turbulent flows, Cambrigde University Press. Poulain, J. (1997). "Pompes rotodynamiques, Projet d'une pompe." Techniques de l'ingénieur B4 304. Prokop, A. (1991). Animal cell bioreactor, implication of cell biology in animal cell biotechnology. Boston, Butterworth - Heinemann. Ranade, V. V. (2002). Computational flow modeling for chemical reactor engineering. London, Academic Press. Shiragami, N. and H. Unno (1994). "Effect of shear stress on activity of cellular enzyme in animal cell." Bioprocess Eng 10: 43-45. Singh, H. and D. W. Hutmacher (2009). Bioreactor studies and computational fluid dynamics, Springer Berlin / Heidelberg. Varley, J. and J. Birch (1999). "Reactor design for large scale suspension animal cell culture." Cytotechnology 29: 177-205. Versteeg, H. K. and W. Malalasekera (1995). An introduction to computational fluid dynamics, the finite volume method. Glasgow, Pearson Prentice Hall. Wu, S. C. (1999). "Influence of hydrodynamic shear stress on microcarrierattached cell growth: cell line dependency and surfactant protection." Bioprocess Enginnering 21: 201-206. Zhang, Z., M. Al-Rubeai, et al. (1993). "Comparaison of the fragilities of several animal cell lines." Biotechnology Techniques 7(3): 177-182.


22

Computational Fluid Dynamics Characterization of a Bioreactor Mixing ...

Computational Fluid Dynamics Characterization of a Bioreactor Mixing ...

Suggest Documents

Computational Fluid Dynamics - The Colorful Fluid Mixing Gallery

Mixing Analysis in a Stirred Tank Using Computational Fluid Dynamics

Computational Fluid Dynamics Characterization of a Rotating Cylinder ...

Computational fluid dynamics (CFD)

Computational Fluid Dynamics

Computational fluid dynamics

Applied Computational Fluid Dynamics

Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD)

COMPUTATIONAL FLUID DYNAMICS SIMULATION OF

COMPUTATIONAL FLUID DYNAMICS SIMULATION OF ...

VALIDATION OF A COMPUTATIONAL FLUID DYNAMICS ... - CiteSeerX

A computational fluid dynamics investigation of

Computational Fluid Dynamics Simulation of the dynamics of a tilting ...

Computational Fluid Dynamics 2010

Computational Fluid Dynamics (CFD) - MDPI

Computational Fluid Dynamics for Engineers

Computational fluid dynamics (CFD)

Computational Fluid Dynamics Modeling and

A Computational Fluid Dynamics Approach for

Computational Thermo-Fluid Dynamics

Computational Fluid Dynamics for Engineers

COMPUTATIONAL FLUID DYNAMICS - International Building ...

Computational Fluid Dynamics 189 KB