Biotechnol. Prog. 1990, 6, 104-1 13
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Conceptual Design of a Cellular Filter To Remove Trace Viral Contaminants in Blood K. Krishna Mohan, I-Fu Tsao,? and H. Y. Wang* Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan 48109
Various process alternatives and designs of using a filter containing cellular adsorbents to remove trace viral contaminants from blood and other protein solutions have been studied. Sterilization charts have been developed that can be used to estimate the filter size required to achieve a desired sterilization criterion. A parametric study was carried out to identify various process parameters that may affect this physical trace removal process. It has been demonstrated that the adsorption rate constant is a critical parameter in the design of an efficient cellular filter for viral contaminant removal. This constant is characteristic of the virus-cell system under consideration and is shown to be particularly sensitive to the cell surface receptor density, adsorbent diameter, and fluid flow rate. Higher log titer reduction in virus concentrations can be achieved with low flow rates and no recycle. Preliminary analyses indicate the feasibility of using a magnetically stabilized fluidized filter (MSFF) reactor design for effective virus removal from these complex solutions.
1. Introduction Viral contaminants in blood and its components present well-recognizedhealth risks as exemplified by AIDS and viral hepatitis. A similar problem exists for therapeutic solutions derived from modern mammalian cell culture technology. The presence of even trace quantities of such contaminants can influence the acceptability of these proteinacious products. Innovative approaches are needed to effect microseparation and inactivation of these biological contaminants. Adsorption processes are not widely used for recovering viruses and their variants from therapeutic protein solutions or blood primarily because of a dearth of suitable and efficient adsorbents. Although nonspecific adsorbents such as activated carbon can be used to remove a fairly broad spectrum of viruses, they are not satisfactory since protein molecules compete with the viruses for binding sites. This results in reduced efficiency of removal and a concomitant loss of valuable proteins. On the other hand, immunoadsorbents using mono- or polyclonal antibodies that demonstrate high binding affinities for specific target viruses may be overly specific and may miss the variants that frequently occur in virus replication. There is a need to develop adsorbents and adsorption processes that possess a delicate balance between adsorption spectrum and specificity for the removal and inactivation of viral contaminants in blood and other protein solutions. A novel approach has been undertaken in our laboratory to use cellular receptors on the plasma membrane of various cells as biospecific ligands to bind and thus remove viral contaminants from protein solutions including blood (1). The cellular adsorbents were prepared by immobilizing cells that carry the complementary receptors for different target viruses onto inert supports followed by stabilization of the immobilized cells with a cross-
* To whom correspondence should be addressed.
' Current address: Ortho Pharmaceutical, Raritan, NJ. 8756-7938/90/3006-0 104$02.50/0
linking reagent to prevent the disintegration of cells and cell membrane. Two different strategies were employed to immobilize the cells. One method involves growing cells on microcarriers and stabilizing them with a crosslinking agent. Figure l a shows a photograph of HFF cells grown on microcarriers. These adsorbents have been used to bind human cytomegalovirus (HCMV) from serum (1). Initial experimental results indicated that cell stabilization with glutaraldehyde did not impede the virus binding function in various model systems including HSV1 (herpes simplex virus type 1)and HCMV (I). The second approach involves using clusters or aggregates of cells around microparticles. A representative photograph of such adsorbents is also shown in Figure lb. This SEM picture shows clusters of chemically stabilized T cells aggregates with magnetic microspheres. The magnetic nature of the microspheres used for clustering the T cells makes the separation of cellular adsorbents from the fluid much easier. Experiments were conducted to ascertain that receptors were responsible for the biospecific binding of viruses. Receptor blocking using WGA-lectin (which specifically binds to glycoproteins responsible for HSV- 1 attachment) suggests that cellular receptors, rather than other membrane components, are by far the major binding mechanism for these adsorbed viruses. The immobilized cellular receptors were found to function even in a complex medium such as serum. A conceptual illustration of the viral filter using these adsorbents is shown in Figure 2. Besides developing an appropriate adsorbent, the design of an efficient and cost-effective filter utilizing these adsorbents presents a formidable engineering challenge owing to the stringent sterilization criteria demanded by the public and the complex nature of the process fluids. Modeling provides a means to understand the physical removal process and to elicit the significance of various process parameters involved. This would be of considerable help to the biomedical scientist and engineer who are interested in designing an efficient filter to meet the steril-
0 1990 American Chemical Society and American Institute of Chemical Engineers
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plug flow type adsorption column is a natural choice because it provides a steeper concentration gradient of the viruses to be removed than CSTR (continuous stirred tank reactor) and batch reactors and hence a higher adsorption rate can be achieved. Consequently, the adsorption column gives the maximum sterilization for a given adsorbent volume among these types of reactors mentioned above. This consideration is extremely important when the concentrations of viral contaminants are low and the sterilization criteria are stringent. 2.1. Mathematical Formulation of a Filter Model. We attempt to address the issue of design and feasibility in this preliminary evaluation. Initially, a macroscopic diffusion model may be sufficient for this purpose. The assumption of continuity may not hold a t extremely low concentrations of adsorbates, and a stochastic modeling approach may be warranted. The macroscopic diffusion model of a typical packed bed reactor is based on a mass balance on a thin slice of bed along the length of the bed. In this thin segment, the rate of accumulation of viruses in the fluid region should be equal to the net rate of transport into the slice less the number of viruses adsorbed by the solid phase. This model can be described mathematically by a set of material balance equations together with the appropriate boundary and initial conditions as follows: conservation of mass
adsorption rate RA = k,ac(C - ce)
adsorption equilibrium q = KC,
(3)
C(0,t) = co
(6)
initial conditions Figure 1. (a) HFF cells o n microcarriers. (1)) Clusters of' '1'lvmphocytes and microspheres.
boundary conditions
MAGNETICALLY VIRAL FILTER /
CELL
MICROCARRIERS
AGGREGATES
-
I . IN Figure 2. Conceptual design of a viral filter using cellular adsorbents.
ization needs. The physical removal can be supplemented with other inactivation procedures such as chemical or irradiation sterilization. The following section outlines various parameters involved in designing a cellular filter.
2. Engineering Design of a Cellular Filter The protein solution can be brought into contact with the cellular adsorbents in various reactor designs. The
ac(L,t)/az = o (7) where C and Co are the concentrations of the adsorbate in the bulk solution and in the influent, respectively. C, is the concentration in the liquid, which is in equilibrium with the adsorbent concentration. Vi is the interstitial velocity, and L is the bed length. The rate a t which the number of viruses are exchanged between a liquid volume and an adsorbent surface in contact with it is shown by eq 2. Due to the extremely low concentrations of adsorbates being considered, it can be safely assumed that the adsorption isotherms are linear. This is shown in eq 3. Equations 4 and 5 simply state that the column is devoid of any viruses before the protein solution is passed through it. Equation 6 states that the inlet concentration of virions is constant. If part of the output from the column is recycled, this concentration would become a time-dependent one. In the whole length of the column, the minimum concentration occurs only a t the end, and eq 7 is a mathematical statement of this fact. 2.2. Estimation of Model Parameters. The diffusivity, viscosity, and density of the fluid were assumed to be constant throughout the bed and were obtained from literature (2). The equilibrium constants K were
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Table I. Binding Constants for Various Biological Systems
biological interaction binding constant (M-') per site ref io5-io8 a antibody-hapten 105- 1012 a antibody-an tigen HIV-T4-lymphocyte 2.5 X lo8 b reovirus-thymoma 9.6 X 10" c 4X-174-E. coli 1.0x 1013 10 A-receptor protein-cell 2.0 x loll 10 FMDV-cell 5.0 X 10l2 10 a Bell G . I.; Delisi, C. P. Cell. Immunol. 1974, 10, 415. Lasky, L. Cell 1987,50, 975. Co, M. S.; Gaulton, G. N.; Fields, B. N.; Greene, M. I. Proc. Natl. Acad. Sci. U.S.A. 1984, 82, 1494.
obtained from literature. Most of the data for equilibrium constants in the literature are obtained by assuming a reversible binding between the virus and the cells. The interaction between the virus and the receptors on the cell surface is known to be very strong. The association constants for virus-cell interactions are of the same order as the antigen-antibody binding constants (Table I). A very common method of estimating equilibrium constants is based on Scatchard plot and analysis, where the ratio of the concentration of bound ligand/virus to the free ligand/virus is plotted against the concentration of the bound ligand/virus. The slope of the resulting straight line is the equilibrium constant or association constant in liters/mole. However, the equilibrium constant given in eq 3 relates the concentration of the virus in the liquid phase and adsorbent in a linear fashion. Consequently, the units of this constant are in cm3/ cm3. It should be noted that the constant given in eq 3 is a product of the equilibrium constants reported in the literature and the total concentration of receptor or binding sites. The equilibrium constants used in the simulation cases were in the range of 101-105 cm3/cm3. This range should be sufficient to describe the equilibrium constants for quite a range of virus-cell systems. In an ideal plug flow reactor, the fluid would travel like a piston with the concentration of the virions along the surface of the piston (plug) being uniform by virtue of complete mixing along the radial direction and no mixing in the axial direction. This can be achieved only at very high flow rates. In a real packed bed reactor, there is mixing in the axial direction and mixing in the radial direction may not be complete. These two deviations from ideality are usually described by two constants called the radial and axial dispersion coefficients. If the ratio of the length of the column to the diameter of the column is not too close to unity, then radial dispersion can be neglected. In our analysis, we have assumed that radial dispersion is not significant, and care has been taken to see that the ratio of the length of the column to the diameter of the column is greater than unity. D, is the axial dispersion coefficient of viruses and can be determined by the empirical correlation given by previous researchers ( 3 ) as a function of Reynolds number (Re) and the viscosity of the fluid if the viruses are assumed to be spherical nonreactive particles. The correlation given by Chung and Wen can be written as
pD,--
Re I.L 0.2 0.11~eO.~~ The adsorption rate constant can be obtained from simple batch experiments. It is characteristic of the virusreceptor system under consideration and is also governed by several other factors including the hydrodynamic conditions employed and receptor density. A good understanding of the underlying phenomena of the whole
+
Direction of Fluid Motion
a 1
Figure 3. Mechanisms of virus transport from the bulk and the interaction with the cell surface.
process of virus adsorption onto cell surface is essential for the prediction of the adsorption rate constant under various processing conditions. Analysis of virus adsorption onto the cellular adsorbents can be accomplished by dividing the process of adsorption into two steps (4): (1) a transport step, in which the virions are transported from the bulk of the solution to the adsorbent surface, and (2) a subsequent attachment or adsorption step, in which the virions make contact with the specific receptor by overcoming any repulsive surface forces that may be important at relative short distance. The primary forces that are relevant to these two steps may be classified into three categories: (a) forces related to the motion of the fluid and the motion of the virions relative to the fluid and the forces causing the Brownian motion of the particles (The hydrodynamic forces and diffusive forces fall under this category. These forces are relevant to the transport step.); (b) external forces such as those due to electric, magnetic, and gravitational fields (These forces influence the transport step as well.); (c) chemical and colloidal forces that result from the interactions of the viruses and the adsorbents as well as the interaction forces due to the particles and molecules and ions in the solution (These include the van der Waals forces, Coulombic forces, and other surface forces. These forces are important for the adsorption step.). The cellular receptor adsorbent has a surface that has a specific number of highly reactive receptor sites. The interaction between the virus and the cellular receptor can be considered to be essentially irreversible because the equilibrium constants for virus-receptor interactions are very high (Table I). This implies that if the virus comes into contact with the specific receptor it would be immobilized immediately. However, the number of receptors per cell are finite. Consequently, the attachment step results from multiple collisions before molecular docking can occur. This depends on the number of receptors per adsorbent or the receptor density. The process of adsorption from the bulk of the solution and onto the adsorbent is illustrated in Figure 3. A section of the surface of adsorbent and the fictitious surface layers surrounding it is shown. The viruses are represented by sphericalparticles, and the receptors are shown as circular disks. The outer layer surrounding the adsorbent is called the hydrodynamic boundary layer, and the transport step involves transporting the viruses across
Biotechnol. Prog., 1990, Vol. 6, No. 2
this layer. The inner layer is very close to the surface, and the adsorption step occurs in this layer. The surface forces play an important role in this layer. To understand how the receptor density can affect the adsorption step, consider the pathways of three virions labeled A, B, and C after they have crossed the boundary layer. Virion A collides with the receptor directly and gets immobilized. Virion C collides with the surface of the adsorbent and, after a couple of unsuccessful collisions with the surface, hits a receptor and gets immobilized. Virion B collides with the surface on a non receptor site and, after a series of unsuccessful collisions, goes back into the hydrodynamic boundary layer. The chances of virions B and C getting immobilized on a receptor obviously depend on the receptor density. If the whole surface of the adsorbent were covered by receptors, then virion B can never go back into the solution. This implies that the virions get immobilized as soon as they enter the inner layer, and the rate of adsorption would depend on how fast the transport step is. This limiting case is termed as the liquid-phase diffusion control. In contrast, if the number of receptors were fewer compared to the number of virions transported across the boundary layer, then most of the virions would follow the pathway of B and the rate of adsorption would be dependent on the surface adsorption step. The phenomenon of mass transfer from the bulk liquid to the inner layer is usually characterized by the film theory, which assumes that all the resistance for mass transfer in a particular phase lies in a thin fictitious film close to the interface. According to this theory, the rate of mass transfer in the liquid phase is given by
RA = kcac(C- Ci) (9) where k , is the mass transfer coefficient, a, is the area of interface per unit volume of solid also known as the specific surface area, C and Ci are the concentrations of the viruses in the bulk of the fluid and in the inner layer, respectively. For the case of dilute systems, it can be shown that the mass-transfer coefficient is the ratio of diffusivity of the particle in the liquid and the thickness of the fictitious film. On the other hand, surface adsorption phenomenon should depend on the concentration of virions in the inner layer. The adsorption step in the inner layer can be described by viewing the interaction between the virus and the receptor as a reversible ligand binding reaction V+L=VL where V denotes a virion, L and VL represent a receptor and a receptor-virion complex, respectively. The assumption that the virion-receptors are monovalent (that is, one virion binds with only one receptor) most likely is an oversimplification. For the case of dilute concentrations of virions, the rate expression using the above kinetics can be written as
RA = kaac(Ci- C,) (10) where Ci is the concentration of virions in the inner layer and C, is the concentration of virions in the liquid phase in equilibrium with the adsorbent concentration. It should be noted that the concentration of the virions in the inner layer is considered to be uniform. The forward rate constant k , is unique to the virus and receptor under consideration and depends on the total concentration of the receptors as well. The reverse rate accounts for the virions that go back into the boundary layer following the path of virion B. The number of virions that follow this
107
path depends on the number of virions that are already bound, thereby depleting the number of available receptor sites. It is assumed that all the surface forces that influence the process of adsorption are characterized by the forward and reverse rate constants adequately. From the equations for mass transfer in the boundary layer and the adsorption in the inner layer, the following equation in terms of overall concentration difference can be derived where k, can be obtained from
The units of k, are in cm/s, and the adsorption rate constant k is obtained by multiplying k, with the specific surface area a,. Assuming that the adsorbents are spherical, a, can be shown to be equal to 6/d,, where d, is the diameter of the adsorbent. This equation can be rearranged as
This equation shows that when the value of k , is much lower than the value of k,, then the overall adsorption rate constant is governed by the forward rate constant in the adsorption step. If the forward rate constant per receptor in the adsorption step is denoted as k,,, then k , can be represented as
where N R is the concentration of the receptors. If the number of receptors on the adsorbent is very high, the k , value would be very high, and the adsorption rate constant is governed by the liquid-phase mass-transfer coefficient. This suggests that the adsorption rate constant depends on the receptor density in a hyperbolic fashion. In the case of adsorption of Coliphage X to its host (5), the adsorption rate was shown to be dependent on the receptor density in a hyperbolic fashion. In another experimental study of binding of (2,4-dinitrophenyl)(aminocaproy1)-L-tyrosine (DCT) to monoclonal anti-DNP IgE (DNP = dinitrophenyl) (6), it was shown that the relationship between receptor density and adsorption rate constant is hyperbolic. The dependence of the adsorption rate constant on the receptor density is also similar to the expressions derived by other researchers (6-9) although the basis for derivation was not the same. In the references cited, k,a, corresponds to the forward rate constant estimated from Smoluchowski’s equation. In the case of batch adsorption experiments, the value of k,a, will be very close to the rate constant estimated from Smoluchowski’s equation if the agitation is not too high. In the case of packed columns, the value of k , is governed by Brownian motion as well as the hydrodynamics. On the basis of the analysis outlined above, it can be deduced that the adsorption rate constant depends on the liquid-phase mass-transfer coefficient and the surface adsorption rate constant. The latter is characteristic of the virus-cell system under consideration. The relative magnitudes of these two coefficients determines the regime of maximum resistance. Thus, the governing resistance is system specific. A comparison of the experimental adsorption rate constants with the rate constants cal-
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Table 11. Comparison of the Maximum Experimental Adsorption Rate Constants with Those Calculated for the Diffusion-Limited Case virus T4 T5
x
T7 P22 $JX-174 polio rhino FMDV mengo EMC
108D,,, cm2/s
1080,,, cm2/s
3.0 4.0 5.0 6.0 7.0 13.7
4.6 6.1 7.2 9.2 11.7' 19.6
17.0d
25.0
10-llkcalcd,o 10-llkmax,b M-l s-l M-1 s-l 0.46 0.61 0.72 0.92 1.17 1.96 9.4
0.2 0.48 1.3 2.0" 1.4 0.72 4.0 8.4 8.7 8.9
HI
ref 14,15 14,16 14, 5 14 17j 18 19, e 21 21 22,23 24 24
a Adsorption rate constant estimated using Smoluchowski's diffusion theory, kcalcdE 47rDa, where D is the diffusivity and a is the radius of the adsorbing particle. For bacteria, a = 1.33 X cm cm. Experimental adsorption for mammalian cells, a = 5.0 X rate constants obtained by assuming pseudo-first-orderreaction between viruses and adsorbents in the presence of excess adsorbents. Logarithms of the titer reductions were plotted with time, and the initial slopes of the curves were determined. The slope is equal to kC,where C is the concentrationof the adsorbent. 'At 41 "C. Foot-and-mouth-diseasevirus (FMDV), encephalomyocarditis virus (EMC),poliovinus, rhinovirus, and mengovirus are all members of the picornavirusfamily and may differ slightly in the diameter of their icosahedral-shapedparticles. Thus, their diffusion coefficients should be very similar, and this value is the average of the five different members of the family.
culated for the diffusion-limited case was done by Incardona (IO). The data compiled by Incardona is reproduced in Table I1 to show that the dominant resistance for adsorption is system specific. It can be seen from the table that in some cases the diffusion-limited rate constant based on Smoluchowski's theory is greater than the experimentally calculated value while, in some other cases, the converse is true. If the experimentally estimated value is lower than the diffusion-limited calculation, it can be inferred that the dominant resistance for adsorption lies in the adsorption layer. This appears to be true for viruses belonging to the picornavirus family. On the contrary, if the experimentally estimated value is greater than the constant estimated by the diffusion-limitedequation, then the dominant resistance lies in the boundary layer. In such a case, hydrodynamics can play a very important role in determining the rate of adsorption. The adsorption rate constant k for the adsorption of HSV-1 on BSC-1 cells were estimated from batch experiments. The adsorption rate constant is a combination of the liquid-phase mass-transfer coefficient and the forward rate constant in the adsorption step. The liquidphase mass-transfer coefficients were estimated with the Frossling's correlation ( I I ) :
Sh = 2.0 + 0.552Re0*5Sc0*5 (12) In shake flask experiments, the liquid-phase masstransfer coefficient is significantly enhanced if the velocity of the liquid with respect to the adsorbent particle is high. If the density difference between the adsorbent and the fluid is not much, then the adsorbents would be traveling with the fluid and the velocity differential would be low. Consequently, the second term in eq 12 would not contribute significantly for the Sherwood number. Taking the limiting value of 2 for the Sherwood number, the liquid-phase mass-transfer coefficient can be estimated from the diffusivity of the virus in the liquid and the diameter of the adsorbent particle. Knowing the value of the adsorption rate constant and the liquid-phase masstransfer coefficient, the value of the forward rate con-
Qr = Recycle Flowrate
Ui
L = Length of bed in the column
Q
=
Total Flowrate
CO (concentration of virions at inlet) Q = Flowrate
Figure 4. Reactor (column) configuration used in simulations.
stant in the adsorption step can be evaluated. This value was estimated and is characteristic of the adsorbents used in the experiments because they have a specific number of receptors. This forward rate constants is termed as the base case, and all the other forward rate constants are determined by increasing the number of receptors in multiples of the number of receptors for the base case. The actual enhancement of receptor density can be achieved through genetic cloning and amplification.
3. Simulation Results Equations 1-7 are known as the dispersed plug flow model with linear equilibrium and linearized rate expression for mass-transfer resistance. This set of equations was solved numerically by use of an implicit finite difference method. The reactor configuration that was used for these simulations is illustrated in Figure 4. A sensitivity analysis was performed to determine the effect of various parameters on the log titer reduction of viruses that can be achieved for a known volume of adsorbent. When the effect of recycle is examined, part of the output is sent back to be mixed with the influent and fed to the filter. This changes the boundary condition in eq 6 to a time-dependent one. The total volume of solution treated in all the following results was 450 mL unless otherwise stated. The diameter of the bed in all the simulations was taken as 2 cm, which is very close on the experimental system. The performance of the adsorption column was ascertained by two methods. The first involved passing a solution containing a constant concentration of virions at the inlet through a column of defined geometry until the exit concentration reached a set maximum. The average concentration of the column effluent and the total volume of solution that can be treated until the set maximum is reached were computed. The maximum outlet concentrations were set at 0.1 and 0.01 of the inlet concentrations. The simulations were done for two different values of equilibrium constants. The plots of these two simulations are shown in Figure 5. In these plots, the log titer is plotted as a function of a modified Damkohler number at various values of P6clet number. The P6clet number represents the ratio of the convective transport to the transport by axial dispersion. The Darnkohler number represents the ratio of the rate of adsorption to the convective transport. For a given virus-cell system, the equilibrium constant is fixed. The strength of interaction between viruses and receptors is determined by the magnitude of the equilibrium constant. Note that as the P6clet number increases, the convective forces dominate over the dispersion forces significantly and the flow becomes essentially plug flow. It can be seen from the figure that the average outlet concentrations were not
109
Biotechnd frog., 1990,Vol. 6, No. 2 1.0
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be sufficient to achieve an 8 log reduction, which is a significant degree of sterilization if liquid-phase diffusion is controlling. However, if the transport is limited by surface adsorption, even a 20-cm-long column will not be sufficient to achieve a single log titer reduction. It can be seen from the plot that the adsorption rate constant has a significant impact on a realistic log titer reduction of the viral contaminants. This is particularly obvious if one notes that by increasing the adsorption rate constant by approximately 1order of magnitude, one can increase the log titer reduction from less than 1 to more than 5 for a column of the same length. This increase in adsorption rate constant corresponds roughly to a 10fold increase in receptor density. We conclude from this analysis that the adsorption rate constant is a very important parameter in designing an efficient filter and that the receptor density used to remove viral contaminants has a very strong influence on the adsorption rate constant. As elaborated in the previous section, the adsorption rate constant depends on two constants characteristic of the liquid-phase mass transport and surface adsorption. The former depends both on the Brownian motion as well as convective transport. In the virus filter, the convective contribution to the liquid-phase mass-transfer coefficient is much higher than that of diffusion alone. To stress this point, the log titer reductions obtained by calculating the liquid-phase mass-transfer coefficient based on diffusion alone and convective forces alone are plot-
Biotechnol. Prog., 1990,Vol. 6 , No. 2
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1.0
1
10-2
Surface Adsomtion
__^_..___.._.._______..___I__________
-..---..-I-..-."-."-.__.
0.02
0.06
0.10
0.14
0.18
dp (cm)
Figure 8. Effect of adsorbent diameter d, on adsorption rate constant.
ted for the case of the liquid-phase mass-transfercontrolling domain in Figure 7. It can be seen from Figure 7 that for the case of convective transport the log titer reduction for a 6-cm filter is about 8 while that for nonconvective transport is less than 1. However, when the same comparison is made when surface adsorption is controlling, the change in log titer reduction is not so significant. This indicates that most of the virus-cell systems exhibit surface-adsorption-controlphenomenon. The fact that convection does not contribute much to the log titer reduction when surface adsorption is controlling implies that the log titer reduction can be improved by decreasing the flow rate, thereby increasing the Damkohler number. Besides the receptor density of the cell, the adsorbent diameter also plays a key role in determining the log titer reduction for a particular volume of adsorbent. The diameter of the adsorbent affects the liquid-phase masstransfer coefficient and the specific surface area. For liquid-phase mass-transfer domain, the mass-transfer coefficient is proportional to the square root of the reciprocal of the diameter. The specific surface area is inversely proportional to the diameter of the particle. Thus, as the diameter of the adsorbent increases, the liquidphase mass-transfer coefficient and the specific surface are reduced. This effect of adsorbent diameter on the adsorption rate constant is illustrated in Figure 8 for two different flow rates. The specific surface area of tne microcarrier adsorbent can be calculated from the diameters of the microcarrier and cells. The specific surface area of the cellular aggregate is higher than the microcarrier. However, not all the receptors in the aggregates are accessible to viruses owing to steric hindrances. This can be modeled with use of another resistance step for mass transfer within the aggregate. In order to estimate the increase in adsorption constant by virtue of the increase in specific area, a rough estimate can be made by comparing the specific surface areas of identical diameter microcarriers and cellular aggregates assuming that only a fraction of the cellular aggregate area is effective. In Figure 8, this fraction is changed between 0.5 and 1. It can be seen that even if only 50% of the cellular aggregate area is available, the adsorption rate constant shows a 4-5fold increase resulting in a significantly higher log titer reduction. This shows that the cellular aggregates are perhaps better adsorbents than microcarriers. From Figure 8, it can be seen that the adsorption rate constant decreases with increasing adsorbent diameter for all cases.
10-6 10-8.
I
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This implies that when liquid-phase mass transfer is limiting, the adsorption rate constant can be improved by reducing the adsorbent diameter. Reducing the adsorbent diameter ensures that liquid-phase mass transfer is minimized. If the adsorption is controlled by surface phenomena, the adsorbent diameter is nut useful in controlling the adsorption rate constant. The effects of two other process parameters, flow rate and recycle rate, on the log titer reduction were determined. Increasing the flow rate increases the liquidphase mass-transfer coefficient, and if the domain of maximum resistance is the liquid phase, this will increase the adsorption rate constant. A t the same time, the residence time of the fluid in the filter is reduced since it is inverselyproportional to the flow rate. Hence, even though the adsorption rate constant is increased by virtue of higher flow rate, the liquid does not spend enough time in the column to transport the viruses to the adsorbents. As a result, higher flow rates are not desirable for log titer reduction of the viral contaminants. This is also true for the case of mass transfer controlled by surface adsorption as well. When the resistances on the surface and in the liquid phase are equally important, the adsorption rate constant is strongly dependent on the flow rate. When the flow rate is increased, the liquid-phase mass-transfer coefficient is increased, which makes the surface adsorption the main resistance. Hence, the flow rate increases, the maximum resistance shifts from a mixed region to the surface adsorption domain. At the same time, the residence time is reduced, which makes the log titer reduction lower. This is also the case of surface adsorption limited mass transfer because the increase of flow rate has no effect on the adsorption rate constant, but the residence time is reduced, which makes the log titer reduction decrease significantly. This is shown graphically in Figure 9 with cellular adsorbents of diameter 200 pm. An alternative way of studying the effect of flow rate is by examining the sterilization chart (Figure 6). An increase in the flow rate increases the value of adsorption rate constant by the square root of the velocity but decreases
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111
Figure 10. Experimentally magnetically stabilized fluidized filter (MSFF) system developed a t the University of Michigan Biochemical Engineering Laboratory.
the Damkohler number since it is inversely proportional to the velocity. However, an increased flow rate results in a smaller dispersion. To achieve high log titer reduction, we require high P6clet and Damkohler numbers. But, since high flow rate increases the P6clet number and decreases the Damkohler number, we need to look for an optimum combination of the two parameters. The recycle was effected by mixing part of the effluent with the influent. This changes the inlet boundary condition 6 to a time-dependent one. Recycle changes the process in two ways. Since the effluent has a much lower concentration that the influent, recycling dilutes the influent, a fact which is not necessarily desirable, because it reduces the available concentration gradient. A t the same time, changes the residence time of the fluid, and the log titer reduction is reduced. The effect of recycle ratio on the log titer reduction was investigated by simulations, and the above results were noted. The simulations were done for two extreme cases of surface adsorption control domain and liquid-phase diffusion-control domain. If a major fraction of the effluent is recycled, the total flow rate in the column increases. Consequently, the liquid-phase mass-transfer coefficient increases. At the same time, the residence time of the liquid decreases and the influent concentration decreases. The relative magnitude of these opposing factors decides the final conversion. In order to make the comparison meaningful, the residence times of the liquid in the columns with and without recycle were made identical. This was achieved by repeatedly passing the whole volume of liquid through the column with recycle. It was noted that recycle has a detrimental effect in both the limiting cases of mass-transfer resistance. This is due to the fact that the influent concentration is reduced. As an alternative for more efficient use of a filter, the effluent can be passed back through the column for a second time after letting the entire volume pass through once. If the filter is not already saturated, improved log titer reduction can be achieved provided that the binding is irreversible. However, the processing time would be doubled.
4. Experimental Design of a Cellular Filter A prototype magnetically stabilized fluidized bed reactor containing a specific type of cellular adsorbent or a mixture of two or more different adsorbents has been constructed and experimentally tested (2) in our laboratory (Figure 10). The cellular adsorbent has minute wagnetic particles entrapped within the immobilization matrices so that the fluidized particles are stabilized under the influence of an inducible magnetic field. When the magnetic field is turned off, the column behaves as a regular fluidized bed reactor. The total bed volume can be adjusted from 5 to 30 mL. The introduction of magnetic particles into the matrices increases the effective density, which results in a wider range of operating velocity above fluidization. Since the magnetic field is used as a stabilizing influence (12), the dispersion is higher than the fixed reactors but much lower compared to the fluidized beds. Consequently, the conversions expected should be lower than those of fixed beds but higher than most fluidized bed operations. The feasibility of the viral filter was evaluated experimentally by passing a solution containing influenza A virus through a filter packed with microcarriers with immobilized and stabilized erythrocytes. The preparation of the filter was described previously ( I ) . As shown in Table 111, the viruses were removed below the detectable range after the second pass. The detection tests for the subsequent passes yielded negative results indicating that the viruses were not released from the beads. The virus adsorption experiments were conducted at 4 "C. 5. Discussion The results from computer modeling and simulations identify the various key parameters in designing an efficient viral filter. Also, a series of sterilization charts that can serve as a useful tool in designing an efficient cellular filter to remove viruses from blood and other protein solutions are presented. It should be noted that the filter is assumed to have a finite capacity, and as more solution is passed through it, the binding capacity decreases until it is completely saturated. However, the capacity
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112
Table 111. Removal of Influenza A Viruses Using Immobilized and Stabilized Erythrocytes.
HAunit control 1st pass 2nd pass 3rd pass 4th pass 5th pass
1
2
4
8
16
32
64
+ +
+ -
+ -
+ -
+ -
+ -
+ -
-
-
-
-
-
-
-
-
128
+
-
-
-
-
-
-
-
-
-
-
Hemagglutinating tests were performed with 2-fold serial dilution. The positive sign means that the viruses are present and are preventing the settlement of erythrocytes, while the negative sign indicates that virus titer is below the detectability of the HA test. However, viruses may not be completely absent from solutions with a negative HA test result.
of the filter is assumed to be infinite (the receptor sites are much more than the viruses), then the time-dependent term in eq 1 would vanish under a pseudo-steadystate approximation. The adsorption rates will also reduce to a function that depends linearly on the virus concentrations in the bulk solution alone. Analytical solutions exist for such a system, and the solutions have been presented graphically elsewhere (13). It should be noted that the log titer reductions preducted by these charts are much higher than those from our chart for identical Damkohler and PBclet numbers. It is prudent to overdesign the cellular filter for the application of removing infectious viral contaminants from complex protein solutions. Actual performance of a viral filter can only be evaluated through experiments. The simulation results indicate that the adsorption rate constant is perhaps the most critical parameter that governs the log titer reduction achievable. This has been shown to be strongly dependent on the receptor density of the adsorbent. The basic premise that the surface masstransfer coefficient is linearly proportional to the number of receptors has to be verified experimentally for the virus-cell systems under consideration. It should be noted that the linear assumption might not hold true if the virus binding is multivalent. It was also assumed that the onset of the eclipse phase in the virus-cell interaction is very slow compared to the surface adsorption and the liquidphase transport. If surface adsorption is indeed the controlling resistance, efforts should be directed at increasing the forward rate constant in the surface adsorption step. Although the forward rate constant has been shown to be dependent on the receptor density, other factors that could strongly affect this are the pH and the ionic strength of the fluid. In his studies on the effect of receptor density on the adsorption of Coliphage X to E. coli, Schwartz ( 5 ) found that the magnesium ion concentration influences the adsorption rate constant. Taking advantage of the fact that the structural gene of the glycoprotein receptor is located in one of the maltose operons, he manipulated the receptor density on the cell surface by adding inducers of maltose operons to the growth medium and by changing the degree of catabolite repression. For any virus-cell system of interest, it is possible to increase the receptor density by the techniques of genetic engineering and cell cloning. However, it has been shown here that by changing the cellular adsorbent diameter and the hydrodynamic condition of the filter, the adsorption rate constant can also be improved if the resistance for adsorption lies in the liquid phase. High flow rates and the recycle generally have a detrimental effect on the log titer reduction. Low flow rates are desirable because adequate time is needed for the
viruses to diffuse and attach to the adsorbents in the filter. The geometry of the packed column should be chosen in such a way that the aspect ratio is at least greater than 3. The use of a packed bed filter to remove viral contaminants is more efficient than the use of a CSTR. However, from an operational viewpoint, the packed bed filter may pose problems such as high pressure drop and clogging. An alternative to be considered is a fluidized bed filter, which eliminates these problems. Nevertheless, the primary disadvantage of the fluidized bed design is that it increases radial dispersion significantly over the fixed bed. Furthermore, the operating range of fluid velocity for the fluidized bed is very narrow because the density difference between the cellular adsorbent and the fluid is not significant. A more promising filter design that combines the advantages of fixed and fluidized beds is the magnetically stabilized fluidized based filter (MSFF). For the use of such a filter, the cellular adsorbents must be magnetically sensitized. It also increases the density of the cellular adsorbent, thereby increasing the range of operating velocity for the fluidizing medium. The parameter that is affected significantly in a magnetically fluidized bed is the fluid dispersion. The dispersion levels in this are more of the order of dispersion in fixed beds. An additional operating parameter, the magnetic field strength, would be of use in controlling the removal process. Additional studies on such a filter are currently underway in our laboratory.
Notation specific surface area, area of interface per unit volume of liquid, cm2/cm3 specific surface area, area of interface per unit volume of adsorbent, cm2/cm3 fluid-phase concentration, virions/cm3 concentration in the bulk of solid phase in terms of liquid-phase concentration, virions/cm3 fluid-phase concentration at solid-liquid interface, virions/cm3 fluid-phase concentration at inlet, virions/cm3 diffusivity of viruses in fluid, cmz/s longitudinal dispersion coefficient, cm2/s diameter of adsorbent, cm volume equilibrium constant, mL/mL adsorption rate constant, s-' liquid-phase mass-transfer coefficient, cm/s surface mass-transfer coefficient, cm/s total mass-transfer coefficient, cm/s length of the column, cm number of virions per unit volume, mL-' number of virions per unit volume at inlet, mL-' concentration of receptors, mL-l V,L/D, PBclet number solid-phase concentration, virions/cm3 flow rate of fluid at the inlet, mL/min flow rate of the recycled fraction, mL/min flow rate through the column (Q,+ Q), mL/min adsorption rate, virions/(cm3/s) Vsd,/u, Reynolds number u/D, Schmidt number k,d,/D, Sherwood number time, s superficial velocity (QJarea of cross section of the column), cm/s Vs/t, interstitial velocity, cm/s volume of solution treated, mL
113
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Z Ly
t
P V
axial position, cm fraction of the total surface area available for virus adsorption voidage fraction fluid density, g/cm3 kinematic viscosity, cm2/s
Acknowledgment We acknowledge the partial financial support of the National Science Foundation.
Literature Cited (1) Tsao, I-Fu, Shipman, Charles, Jr., Wang, Henry Y. Bio/ Technology, 1988,11, 1330-1333. (2) Tsao, I-Fu. Ph.D. Dissertation, Department of Chemical Engineering, University of Michigan, Ann Arbor, MI, 1988. (3) Chung, S. F.; Wen, C. Y. AZChE J. 1968, 14, 857. (4) Rajagopalan, R.; Hirtzel, C. S.Colloidal Phenomena;Noyes: Park Ridge, NJ, 1985; p 126. (5) Schwartz, M. J. Mol. Biol. 1976, 103, 521. (6) Erickson, J.; Goldstein, B.; Holowka, D.; Baird, B. Biophys. J . 1987,52, 657-662. (7) Berg, H. C.; Purcell, E. M. Biophys. J. 1977, 20, 193. (8) DeLisi, C.; Metzger, H. Zmmunol. Commun. 1976, 5, 417. (9) Koch, A. L. Biochim. Biophys. Acta 1960, 39, 311. (10) Incardona, N. L. In Virus Receptors; Lonberg-Holm, K.,
Philipson, L., Eds.; Chapman and Hall: London, 1981; Part 2, p i55. (11) Atkinson, B.; Mavituna, F. Biochemical Engineering and Biotechnology Handbook; Nature Press: New York, 1983; p
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r
ma.
(12) Rosenweig, R. E.; Siegell, J. H.; Lee, W. K.; Mikus, T. AZChE Symp. Ser. 1981, 77 (205), 8-16. (13) . . Aiba, S.: Humphrev, A. E.; Millis, N. F. Biochemical Engineering; Academic-Press: New York, 1973; p 263. (14) Dubin, S. B.; Benedek, G. B.; Bancroft, F. C.; Friedfelder, D. J. Mol. Biol. 1970, 54, 547. (15) Stent, G. S.; Wollman, E. L. Biochem. Biophys. Acta 1952, 8, 260. (16) Lanni, Y. T. Virology 1958,5, 481. (17) Gaertner, M. J.; Reggio, P. H.; Crosby, C. R., 111;Schmidt, R. L.: Mavo. " , J. A. J . Colloid Interface Sci. 1978. 63, 259. (18) Hoffman, B.; Levine, M. J. J. Virol. 1975, 16,' 1547. (19) Bayer, M.; Deblois, R. J . Virol. 1974, 14, 975. (20) Incardona, N. L. J. Theor. Biol. 1983,104, 693-699. (21) Lonberg-Holm, K.; Whiteley, N. M. J. Virol. 1976,19,857. (22) Rueckert, R. R. In Comparative Virology;Maramorosch, K., Kurstah, E., Eds.; Academic Press: New York, 1971, p 255. (23) Thorne, H. V.; Cartwright, S. F. Virology 1961, 15, 245. (24) Miroshina, T.; McClintoch, P. R.; Aulakh, G. S.; Billups, L. C.; Notkins, A. L. Virology 1982, 122, 461. I
Accepted January 29, 1990.
