Use of Magnetic Resonance Imaging to Analyze the Performance of Hollow-Fiber Bioreactors C. DONOGHUE: M. BRIDEAU: P. NEWCOMER: B. PANGRLE: D. DIBIASIO,~.'E. WALSH) AND S . MOOREb aDepartment of Chemical Engineering bDepartinent of Biomedical Engineering WorcesterPolytechnic Institute Worcester,Massachusetts 01609
INTRODUCTION AND OBJECTIVES Multitube hollow-fiber membrane modules are used extensively in animal cell culture, immobilized enzyme reactors, protein purification, and numerous filtration operations in biotechnology. The efficiency of each of these operations is directly related both to the way fluid is distributed to the tubes at the entrance and to the local fluid velocities in the tubes and the shell at each radial and axial position. For mammalian cell reactors, cell growth and metabolism, and hence productivity, are dependent upon the local reactant and product concentrations at all points in the reactor. Local conditions are, in turn, dependent upon the relative contributions and spatial variations in diffusive and convective fluxes. These fluxes result from the complex relationships between flow, pressure drop, membrane structure, membrane permeability, tube and shell geometry, and cell growth. A better understanding of all these factors would result in improved design and analysis of these types of reactors. A major limitation in advancing knowledge of the behavior of hollow-fiber reactors is the inability to obtain direct information on module performance noninvasively. Sampling is difficult to accomplish accurately and fluid flow measurements are limited to inlet/outlet conditions unless probes are inserted. Magnetic Resonance Imaging (MRI) offers the potential of being able to spatially resolve local fluid velocities and cell metabolism noninvasively. It is a technique that, although used for several years in medical diagnoses, has only recently been applied to chemical engineering operations. Flow-sensitive techniques can be used to determine velocities at various radial and axial positions, thus allowing quantitative information on local fluxes. Chemical shift-sensitive techniques can also be spatially applied to determine local biochemical information such as cell growth patterns, pH, ATP concentrations, etc. Because the analysis of hollow-fiber systems with MRI is in its infancy, there is a need to establish proper protocols under controlled and idealized conditions using 'To whom all correspondence should be addressed. 285
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pulse sequences that give valid results. These methods can then be applied with confidence to situations outside of the context from which they were derived. This is especially important because there are few, if any, alternate methods that can be used for independent verification. The main objective of this work was to evaluate the application of a flow-sensitive MRI technique to the analysis of water flow in a cell-free, hollow-fiber unit. The unit was operated with an artificially induced flow field perturbation to test the ability of the method to resolve axial velocities over a range of positive and negative values. A secondary objective was to test the applicability of a diffusion damping method to indirectly resolve cell growth patterns in hollow-fiber units in which mammalian cells had been cultured. The results of these preliminary studies would be used in future work with actual operating reactors. They would also form the basis for MRI methodologies that could be applied in other biochemical operations such as protein filtration.
BACKGROUND Although there have been numerous theoretical studies of flow in porous tube and shell systems (i.e., Apelblat et al.;l Quaile and Levy;2 Terrill;3 Schonberg and et aL5), there have been few experimental studies. Park and Chang6 B e l f ~ r t Salmon ;~ used direct sampling of tubes and photography of a tracer dye in a laboratory-built hollow-fiber unit. Pangrle et aL7used a time-of-flight MRI technique to measure fluid distribution in a commercial hollow-fiber module. These studies demonstrated that feed flow maldistribution results in some tubes acting as “feeders” to other tubes acting as “collectors”. The time-of-flight method was later applied to a ceramic system.s Hammer et aL9 and Heath et a l l o used a phase encoding MRI sequence to experimentally show shell side flow (‘‘leakage’’ or Starling flow) in multifiber (40 fibers) modules. To date, there are no comprehensive studies of fluid flow in commercial hollow-fiber units. Significant progress has been made in assessing cell metabolism in hollow-fiber bioreactors, particularly using NMR. Stewart and Robertson” used 35S-labelingwith autoradiography to measure cell growth. Dale and c ~ - w o r k e d have ~ - ~ successfully ~ applied NMR spectroscopy to study animal cells in small hollow-fiber units, as have Mancuso et a l l 5 who used a 23Na-NMRmethod to obtain cell concentrations. Piret and Cooney16 used freeze-and-section methodology to obtain axial resolution of cell concentrations. They showed that, under unidirectional flow conditions, cell concentration was lowest near the reactor entrance and maximal at the distal end. No reports of noninvasive spatial resolution of cell concentration or metabolism have appeared. In cell reactors, the consequences of feed flow maldistributions, fluid ejection occurring in some tubes and injection in others, and Starling flow are that the unequal distribution of nutrients and the improper clearance of waste products occur. These conditions most likely do not result in optimal cell growth and product formation. Such flow effects would significantly reduce the efficiency, and hence product recovery, of the separation step in filtration operations.
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MATERIALS AND METHODS Hollow-Fiber Module
A Fresenius F-80 unit was used for the flow experiments. It contained 13,000 polysulfone hollow fibers, each with an inner diameter of 200 k m and an outer diameter of 280 km. The shell diameter was 5 cm and the fiber length was 23 cm. These membranes have a molecular weight cutoff of approximately 65,000 daltons. The unit was operated in the closed-shell mode. Water was supplied to the lumen (tube) side of the module with a nonpulsatile pump. Tap water, doped to a concentration of 0.2 g / L with either C u S 0 4 or MnCI2,was used to reduce the NMR T I relaxation time, allowing faster data acquisition. Cell Bioreactor Hollow-fiber reactors in which mammalian cells had been cultured for several weeks were donated by Prosept, Incorporated (Cambridge, Massachusetts). These modules were disconnected from serum feed at Prosept, packed in ice, and transported to the MRI facility. They were then connected to the doped water feed system for imaging. MRI Methodology The MRI experiments were conducted at the Central Massachusetts Magnetic Imaging Center in the Massachusetts Biotechnology Park (Worcester, Massachusetts) using a G E 2.0-T/45-cm CSI-I1 imaging spectrometer, equipped with 20gauss/cm self-shielded gradients, operating at 85.56 MHz for protons. The main bore of the magnet is 45 cm in diameter and about 6 feet in length. Hollow-fiber modules were placed lengthwise in the bore, within an R F coil of 8.25-cm inner diameter. Two types of pulse sequences were used. Velocity Encoding with Flow Compensation This pulse sequence was used to obtain flow images for the cell-free hollow-fiber unit with doped water only (no cells). The technique produces 16 two-dimensional images of a single cross-sectional slice, each representing the fluid flowing within a specific velocity range. The signal intensity or local “brightness” in a given image is proportional to the amount of fluid flowing within the corresponding velocity “window”. Negative and positive velocities can be resolved with this method. The pulse sequence, using a concept described by Moran,” is shown in FIGURE 1. A 90” slice-selective pulse is used to excite the protons that “dephase” primarily because of magnetic field inhomogeneities. At time = TE/2, a 180” slice-selective pulse is applied in order to refocus the effects of magnetic inhomogeneities, producing a “spin echo” at time = TE. The slice-selective gradient and an R F phase “ramp” (not shown) define the location of the slice to be imaged.
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The purpose of flow compensation is to eliminate the dephasing effects that result when imaging nonplug flow (apart from desired position or velocity phaseencoding). If flow compensation techniques are not used, the flow field can cause the signal to “spread out” artifactually across the image in the phase-encode direction. The phase that is accumulated by the spins in the presence of a changing magnetic field gradient in, for example, the z direction, G,(t),is given by (1)
G,:
G, :
G :
RF receiver gate: FIGURE 1. MRI pulse sequence used for velocity encoding with flow compensation.
where y is the gyromagnetic ratio of protons (26.752 x lo7 rad/Ts) and Gz(t)is the known (applied) magnetic field gradient in the z direction during the sequence. For spins moving at a constant velocity v , their position z changes as a function of time: z = 2,
+ vt.
(2) In reference to FIGURE1, there are two conditions that must exist in order to fix the amplitude of the two flow compensation gradients in thez direction following the
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90” pulse. The amplitude of the first slice-select gradient is fixed by the bandwidth of the 90” slice-selective pulse. The first condition is that the total area under the sine waves plus half the area under the slice-select gradient must sum to zero for stationary spins (where the magnitudes of the gradient pulses above the reference line are positive and the magnitudes of those below the reference line are negative). The second condition is, that the “vt” term in the integral of equation 1 must equal zero for moving spins. These conditions provide two equations and two unknowns. The phase-encode gradient was applied in the x direction. The purpose of phase-encoding is to use gradients to impart a phase angle, I$, to the spins that is linearly proportional to their x position (in this case). Therefore, the area under the sine waves is not zero and, consequently, the solution for the integral is also not zero. The phase angle imparted to the spins is, however, the same for stationary and flowing spins. The purpose of the velocity-encoding gradient is to obtain quantitative information about flow velocities from the MR images. The velocity-encoding gradient is applied in the z direction (with simultaneous flow compensation). With these “bipolar” velocity-encoding techniques, the moving spins will accumulate a phase angle, I$, that is linearly proportional to the velocity of the spins in the z direction. A different phase angle, is accumulated at each repetition corresponding to each velocity range because the velocity-encoding gradients are stepped up through 16 values, equal in magnitude, but opposite in sign, around the flow compensation gradients. This is the portion of the sequence that results in the 16 velocity-encoded images (after Fourier transforming over the velocity “dimension”). Finally, the y direction is utilized for the readout gradient. The spin echo resulting from the 90” and 180” pulses is read out at time = TE, which is the echo delay time. Flow compensation techniques are also used in the direction with this gradient to ensure that the echo signal is in phase in the center of the data acquisition window for both stationary and moving spins.
+,
Calibration Phantom
A simplified system was set up in order to confirm that the pulse sequence could quantitatively measure fluid flow in both the positive and negative directions. This was important because flow may occur in both directions within the normal operations of the bioreactor. The schematic of this simplified system is shown in FIGURE2a. The flow “phantom” consisted of a sealed test tube, filled with stationary water, that was wrapped by flexible tubing through which water was pumped to flow down along the tubing in the positive z direction and back up along the tubing in the negative z direction. Laminar flow was established in this tubing at a maximum velocity of 16.7 cm/s. The velocity images produced at a single cross-sectional “slice” from this phantom are shown in FIGURE 2b. These and subsequent images of this type are discussed by reference to the row and position numbers as shown in each figure. The upper left image (row 1, position 1) represents the largest negative velocity range, whereas the lower right image (row 4, position 4) is the highest positive velocity range. The velocity range for each image is 2.5 cm/s. The image in row 3, position 1 is
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water out in
stationary POSl TION:
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FIGURE 2. (a) Calibration phantom used for velocity measurements of the laminar flow in a single tube. The dashed line shows the approximate location of the image taken. (b) Imaging results from the calibration phantom of the laminar flow in the positive and negative directions.
the range of -1.25 cm/s Iv I1.25 cm/s. The stationary water in the sealed tube thus produces the highest intensity in this range. A small signal is evident from the low velocity fluid flowing near the tubing wall in both positive and negative directions. There is no signal returned from stationary water in any other images.
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Proceeding left to right in row 3 illustrates the loss of signal from any negative velocities and shows only concentric rings, decreasing in size as the velocity range imaged increases. The highest velocity range (16.25 to 18.75 cm/s) is shown in position 4 of the fourth row. A small contribution from fluid flow near the centerline velocity is evident (16.7 cm/s). For negative velocities, the image in row 2, position 4 represents the fluid flowing within the range of -3.75 to -1.25 cm/s. No stationary or positive flowing fluid is evident. By proceeding right to left in the second and first rows, the succeeding negative velocity ranges are presented. These are essentially “mirror” images of the positive flows. The image in row 1, position 1 is the “Nyquist” image and would show fluid moving faster than 18.75 cm/s in either the positive or negative direction. As expected, it indicates no fluid flowing in this range. The superposition of the sets of annular rings shown (in either direction) demonstrates the expected parabolic flow profile. Each two-dimensional image shown comprises many individual volume elements (voxels) over which the MRI pulse sequence was applied. For this figure, the resolution (a function of machine parameters and the pulse sequence) provided a voxel with dimensions of 0.78 mm x 0.78 mm x 10 mm. Although the resolution and the total velocity range over which the images were taken may be different, all subsequent figures representing results from velocity-encoded pulse sequences are presented with the same convention as FIGURE 2b.
Diffusion Damping Sequence Instead of selecting certain velocity components, it is also possible to use magnetic field gradients to minimize the NMR signal received from moving protons, especially those moving incoherently.Is As discussed in the last section, a bipolar field gradient imparts a velocity-dependent phase angle to moving spins. For the case of molecular diffusion, which is an incoherent process, a distribution of phases will result, with a concomitant reduction of the summed NMR bulk magnetization signal. Further diffusion sensitization of the received NMR signal may be accomplished by modifying a standard spin-echo imaging sequence to use a gradient pair of the same polarity on both sides of the 180”pulse, as shown in FIGURE 3. For this sequence, the log of the ratio of the acquired NMR signal with and without the diffusion damping gradients, assuming purely molecular diffusion, is given byI9 In(S/So) = -yZG262(A - 6/3)D,
(3)
where y is the gyromagnetic ratio of protons, 6 is the pulse width of each gradient pulse, A is the time interval between the start of each gradient pulse, G is the magnitude of the applied magnetic field gradients (in T/cm), and D is the diffusion constant of the molecules in the medium (D = 2.09 x cm2/sfor water at 21 “C). If the NMR signal is measured for several different values of gradient strength (all else being constant and known), the diffusion constant may be calculated by fitting a straight line to the log of the signals using equation 3. If the diffusion is restricted, for example, by cellular membranes, then the distance through which the average water spin would migrate during the time A - 6/3 is limited; thus, the signal from such
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“compartmentalized” water would not be reduced as much as the signal from truly “free” water. The diffusion damping technique should also have interesting applications for discriminating between intracellular and extracellular protons in a bioreactor. Even if the cells are rather large, such that restricted diffusion inside the cells may not provide sufficient signal discrimination by itself, the diffusion damping of the extracellular water in a bioreactor may be enhanced simply by turning on a pump and increasing the motion components of spins in the “free” water. Strictly speaking, many of the extracellular spins will be moving coherently, for example, under laminar flow conditions inside the tubes; however, because of the wide range of velocities of the water inside the tubes or flowing “around” cell clusters in the shell side of the bioreactor, the vector sum of the local bulk magnetization in such regions will be significantly reduced.
180
90
c
DIFFUSION DAMPING GRADIENTS
p*--I-‘“
FIGURE 3. MRI diffusion damping sequence used in imaging bioreactors with cells.
In the preliminary experiment reported here, we used A = 19.8 ms and 6 = 10 ms, whereas the diffusion gradient strength was increased up to a maximum of 6 x T/cm. The image obtained for each value of diffusion gradient strength was qualitatively compared with the images acquired from the previous gradient strengths to look for changes. The integrated NMR signal from the excited slice was reduced by a factor of -20 (S/So 0.05) at the maximum gradient strength. The signal reduction, S/So, for freely diffusing water at this gradient value would only be about 0.4. The expected rms displacement for water molecules diffusing during the time, A - 6/3, is -8 pm, which is larger than the size of the mammalian cells in the bioreactor. Therefore, we were operating in the restricted diffusion regime for the intracellular component of the NMR signal and the signal would have been reduced even less for this component than for free water. This implies that the flowing extracellular water component must have been responsible for most of the signal loss because the total diffusion damping factor was 0.05.
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RESULTS AND DISCUSSION Flow Images (No Cells) Hollow-fiber cartridges were operated in the closed-shell mode with water feed to the lumen (tube side) only. FIGURE 4 shows a schematic indicating the approximate location of the images obtained under flow conditions. The voxel size (resolution) of the images presented here is 0.94 mm x 0.94 mm x 10 mm. The twodimensional photographs show a cross section of the unit, presenting pixels of 0.94 mm x 0.94 mm. A perturbation was introduced into the flow field of the unit in order to conduct a significant test of the MRI pulse sequence. A hole was drilled in the inlet distributor head along the vertical centerline, approximately halfway between the inlet feed line and the bottom of the unit. An area of tubes was then blocked (in the potted region) by injecting epoxy into the entrance of these tubes. A rubber stopper was used to seal the hole. The approximate location of the region of plugged tubes is shown in FIGURE 4.
Inlet Distributor Head Images taken in the distributor head and fore-potted region (not shown) indicated that epoxy penetrated at least the depth of the potted region and that water was prevented from entering these tubes in the inlet. The presence and flow of water in these plugged tubes can then only come from injection due to positive shell-totube pressure drops or from backflow from the exit of the unit.
Inlet Region The first set of images, shown in FIGURE 5, were acquired from a cross section about 30 cm downstream of the fore-potted region (see FIGURE4). Water was flowing at a total rate of 435 mL/min and the velocity range covered by the 16 images was -10 cm/s to +10 cm/s. The image in position 1 of row 3 has been blocked out because its brightness would have dominated the rest of the photograph. Because that image represents stationary or very slowly moving water, it showed that essentially all of the shell and tubes (including those blocked at the entrance) were filled with water. It is important to note that the images displayed in this and all subsequent flow results are inverted from the actual orientation of the hollow-fiber unit in the imaging magnet. Thus, the bottom edge of each image corresponds to the top of the membrane module. The resolution obtained in these images was not sufficient to be able to distinguish flow in individual tubes. Hence, a pixel intensity represents the composite of shell and tube side flow velocities. Because the tube bundle is nonuniform and the spacing of tubes is not at all regular in these units, it is not possible to know exactly how many tubes are in a given pixel at any position in the image. The approximate number, if placement were ordered, is 22. In FIGURE 5, the first two images in the positive velocity range (row 3, positions 2
F i g u r e5
I .
Figure6
I
Figure7
sections imaged and presented in the figure referenced.
FIGURE 4. Schematic of the Fresenius F-80 hollow-fiber cartridge used for imaging flow.Dashed lines are the approximate locations of the cross
\4
Inlet Distributor
!2
0
z
2 M
gm
8
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and 3) show that there is little maldistribution of fluid and that most fluid is moving (regardless of radial position) at velocities less than 3.75 cm/s. The dark region in the upper portion of each image shows that there is no flow in the tubes that were plugged. The dark ring visible in the image in row 3, position 2 represents a region where flow is absent due to the presence of part of the module casing. There is a small region of flow around this structure and its absence in the second image indicates that the velocity of this material is less than 2.50 cm/s. The brighter region at the bottom of the image in row 3, position 2 shows that there is more fluid flowing at that spot; this is near the shell side outlet port. Inspection of the image in row 2, position 4 indicates that there is also some flow in the negative direction in an area
POSITION: ROW
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FIGURE 5. Image taken from a cross section of a hollow-fiber module just after the inletpotted region.
adjacent to this. The location of this fluid relative to the tube bundle is such that this fluid is most likely in the shell space. Apparently, the presence of the outlet port (even with no flow out of it) along a n otherwise smooth inside wall causes a disruption in the flow with some sort of recirculation pattern. There is little, if any, flow in the module at this axial position beyond these velocity ranges and essentially only noise remains for images with I u I > 3.75 cm/s. If the total feed was equally distributed among all tubes, the maximum centerline velocity in any tube would be 3.56 cm/s. These results are thus consistent with a fairly uniform flow distribution at this axial position.
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-
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FIGURE 6. Image taken from a cross section of a hollow-fiber module near the exit, including the aft-potted region.
Outlet Region
FIGURE 6 presents the results taken from the exit region of the unit including the aft-potted section (see FIGURE4). Conditions are the same as in FIGURE5. Examination of the images in row 3 shows that most of the fluid is moving at velocities in the low range. Position 4 in row 3 indicates fluid flowing at a moderate velocity at the center of the image. This signal persists in row 4 up to a maximum velocity of 7.5 cm/s. This is due to the acceleration of fluid as it leaves the potted region and enters the exit distributor head near the exit tube. The interesting features of this cross section relate to the region of plugged tubes. The images in row 3, positions 2 and 3 indicate that there is fluid flowing in the positive direction near these tubes at low velocities. Most likely, this is either shell side flow or the net effect of positive flow in some of the tubes and the shell. However, examination of row 2, positions 4,3,2, and 1 shows that there is significant flow in the negative direction in this region. The absence of upstream tube side flow results in pressures inside the tubes being low enough to allow fluid in the exit distributor head to flow back into them. This negative z-direction flow exists in these tubes at velocities up to -4.375 cm/s. It would also be expected that this would persist upstream along the length of the tube until all the mass that had entered these tubes had been ejected into the shell space. This could be confirmed by taking flow images at several upstream cross sections until the position was found where negative flow was absent. It could also be confirmed by imaging the exit distributor head and
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by looking for regions of negative flow consistent with the location of the tubes described earlier. Outlet Distributor Head
FIGURE 7 shows the results obtained from a cross section that includes the outlet distributor and part of the outlet tubing. The voxel dimensions are the same as those of previous images, but the total flow rate was 335 mL/min. Rows 3 and 4 (positive velocities) show that most of the fluid is slow-moving, but that near the center of the distributor head there are regions of faster-moving fluid. The dark area at the bottom of the image (top of unit) is a trapped air bubble. As expected, there is a region of fast-moving fluid near and in the outlet tube. All fluid is exiting the unit through a 4-mm-diameter outlet port. An average velocity of 11.8 cm/s would result from this flow and this is beyond the 10-cm/s maximum measurable at these imaging conditions. Thus, a signal persists at the image center throughout the positive velocity ranges. In fact, velocities much greater than 11.8 cm/s would be expected as fluid accelerates from the outlet head into the outlet port. The presence of these velocities is observed by “aliasing” artifacts displayed in the negative velocity images in row 1. As a consequence of the imaging process, a wraparound effect occurs when velocities higher than the measured range exist. These higher velocity images are displayed in the negative velocity image range, starting at the highest negative range (- 10 cm/s). Successively smaller signals are observed from positions 1 to 4 (row l ) , consistent with the expectation that the amount of fluid moving at velocities higher than the
POSITION: ROW
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FIGURE 7. Image taken from the exit distributor head, including the exit tube.
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average decreases as water exits the outlet port. This would, of course, obscure the results of observing real negative velocities in this range, although it does not appear to have occurred in this case. The problem of aliasing can be serious when it is not possible to know in advance what the range of velocities in a given sample might be. Repeating images using different total velocity ranges and at different flows is then necessary to eliminate the effect. It was not necessary in this case due to the absence of high negative velocities. The results shown in the second row confirm the fact that there is an area of relatively slow-moving, but negative flow in the outlet distributor head. Fluid exiting the tubes is circulated back toward the aft-potted region. It is this circulation that results in the flow back into the area of tubes that were plugged at the inlet distributor head. Fluid cannot reenter tubes that have water exiting from them. The dark area in the center of the images in row 2 is a result of the fact that all the fluid in this region is moving in the positive direction, out of the distributor head, and thus produces no signal in the negative range. Radial flow could be possible in the outlet head. The measurement technique used in this experiment was sensitive only to axial flow, so no signal would have been returned from radial flows. The dark areas or rings visible in some of the images in FIGURE7 may be due to radial flow. Significant radial flow was probably not present because the bubble (position 1, row 3) did not move during the acquisition period of 15-20 minutes. Radial flow could be detected by images taken from the sagittal and coronal planes (data not shown) rather than the cross sections displayed. Bioreucforwifh Cells
A hollow-fiber unit in which mammalian cells had been cultured was obtained, as described earlier, from Prosept, Incorporated (Cambridge, Massachusetts). The diffusion damping imaging technique discussed earlier was used to indirectly show the location of regions of cell mass. The advantages of this method are that it is relatively easy to implement (compared to chemical shift imaging), it eliminates tube side flow contributions completely, and it can be used to obtain preliminary data on the extent of radial and axial cell growth patterns. The disadvantages are that cell viability cannot be determined and that regions of no flow where no cell growth also occurred would appear as if cell mass were present. The images obtained from two cross sections of the bioreactor with diffusion damping gradient strengths of 6 gauss/cm are shown in FIGURE 8. These images are not presented like the previous figures. In these pictures, regions of high image intensity represent regions of cell growth (no flow). Dark regions are those corresponding to flowing water. The images are displayed in the same module orientation that was used for culturing the cells and conducting the imaging experiments. FIGURE 8a was taken near the front of the unit. It shows that most cell growth occurred along the bottom third of the unit. A region of little or no growth was present in the center of the module. FIGURE 8b was obtained from a cross section near the outlet of the reactor. Note that the cell growth region extends further into the inner regions of the reactor and only a few regions of poor cell growth are apparent. These results are qualitatively similar to those of Piret and Cooney16 in that more cell growth was observed near the distal end of the reactor. However, in addition to being noninva-
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sive, the MRI technique can also resolve radial cell growth patterns. The cell growth patterns are presumably due to the maldistribution of nutrients and to both tube and shell side flow patterns that are nonuniform. Visual inspection of the unit confirmed the presence of more cell mass along the bottom region of the reactor. It was not possible to conduct further independent evaluations of the cell growth patterns.
FIGURE 8. (a) Image taken from a hollow-fiber module containing cells showing a cross section near the entrance. Bright regions are cell mass. (b) Image taken from the reactor in part a (containing cells) from a cross section near the exit.
SUMMARY
Preliminary experiments were described that demonstrate that MRI is an effective tool for the noninvasive study of hollow-fiber bioreactors. Flow-compensated velocity-encoding pulse sequences were successively applied to analyze the velocity patterns in a module operated without cells, with an artificially induced flow field perturbation. Diffusion damping pulse sequences were also used to spatially resolve regions of cell growth in a bioreactor. These experiments provide the necessary basis from which future flow and spectroscopic studies can be conducted.
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ACKNOWLEDGMENT
We would like to thank C. Sardonini of Prosept, Incorporated. REFERENCES 1. AF-ELBLAT, A., A. KATZIR-KATCHALSKY & A. SILBERBERG. 1974. A mathematical analysis of capillary-tissue fluid exchange. Biorheology 11: 1-49. 2. QUAILE,J. P. & E. K. LEVY.1975. Laminar flow in a porous tube with suction. J. Heat Transfer 97: 6674. R. M. 1982. An exact solution for flow in a porous pipe. Z. Angew. Math. Phys. 3. TERRILL, 3 3 547-557. J. A. & G. BELFORT.1987. Enhanced nutrient transport in hollow-fiber 4. SCHONBERG, perfusion bioreactors: a theoretical analysis. Biotechnol. Prog. 3: 80. 1988. A theoretical investigation of 5. SALMON,P. M., S. B. LIBICKI& C. R. ROBERTSON. convective transport in the hollow-fiber reactor. Chem. Eng. Commun. 6 6 221-247. 6. PARK,K. P. & N. N. CHANG.1986. Flow distribution in the fiber lumen side of a hollow-fiber module. AIChE J. 32: 1937. 7. PANGRLE,B. J., E. G. WALSH,S. MOORE& D. DIBIASIO.1989. Investigation of fluid flow patterns in a hollow-fiber module using magnetic resonance velocity imaging. Biotechnol. Tech. 3: 67-72. 8. PANGRLE,B. J., E. G. WALSH,S. C. MOORE& D. DIBIASIO.1992. Magnetic resonance imaging of laminar flow in porous tube and shell systems. Chem. Eng. Sci. 47: 517-526. 9. HAMMER,B. E., C. A. HEATH,S. D. MIRER& G. BELFORT.1990. Quantitative flow measurements in bioreactors by nuclear magnetic resonance imaging. Bio/Technology 8: 327-330. C. A., G. BELFORT, B. E. HAMMER, S. D. MIRER& J. M. PIMBLEY. 1990. Magnetic 10. HEATH, resonance imaging and modeling of flow in hollow-fiber bioreactors. AIChE J. 3 6 547558. 1988. Product inhibition of immobilized Escherichiu 11. STEWART,P. S. & C. R. ROBERTSON. coli arising from mass transfer limitation. Appl. Environ. Microbiol. 54( 10): 2464-2471. D. D. DRURY & B. E. DALE.1986. Design and application 12. GILLIES,R. J., T. J. CHRESAND, of bioreactors for analyses of mammalian cells by NMR. Rev. Magn. Reson. Med. l(2): 155-179. 13. DRURY,D. D., B. E. DALE& R. J. GILLIES.1988. Nuclear magnetic resonance analysis of an oxygen-limited mammalian cell bioreactor. Biotechnol. Bioeng. 32(8): 966-975. & B. E. DALE. 1989. Analyses of bioreactor performance 14. GILLIES,R. J., N. E. MACKENZIE by nuclear magnetic resonance spectroscopy. Bio/Technology 1: 50-54. A., E. J. FERNANDEZ, H. W. BLANCH & D. S. CLARK.1990. A nuclear magnetic 15. MANCUSO, resonance technique for determining hybridoma cell concentration in hollow-fiber bioreactors. Bio/Technology 8: 1282-1285. 16. PIRET, J. M. & C. L. COONEY.1990. Mammalian cell and protein distributions in ultrafiltration hollow-fiber bioreactors. Biotechnol. Bioeng. 3 6 902-910. 17. MORAN,P. R. 1982. A flow velocity zeugmatographic interface for NMR imaging in humans. Magn. Reson. Imag. I: 197-203. P. C. M. & C. T. W. MOONEN.1990. Complete water suppression for solutions of 18. VANZIJL, large molecules based on diffusional differences between solute and solvent (DRYCLEAN). J. Magn. Reson. 87: 18-25. E. 0. & J. E. TANNER. 1965. Spin diffusion measurements: spin echoes in the 19. STEJ~KAL, presence of a time-dependent field gradient. J. Chem. Phys. 42: 288-292.
INTRODUCTION AND OBJECTIVES Multitube hollow-fiber membrane modules are used extensively in animal cell culture, immobilized enzyme reactors, protein purification, and numerous filtration operations in biotechnology. The efficiency of each of these operations is directly related both to the way fluid is distributed to the tubes at the entrance and to the local fluid velocities in the tubes and the shell at each radial and axial position. For mammalian cell reactors, cell growth and metabolism, and hence productivity, are dependent upon the local reactant and product concentrations at all points in the reactor. Local conditions are, in turn, dependent upon the relative contributions and spatial variations in diffusive and convective fluxes. These fluxes result from the complex relationships between flow, pressure drop, membrane structure, membrane permeability, tube and shell geometry, and cell growth. A better understanding of all these factors would result in improved design and analysis of these types of reactors. A major limitation in advancing knowledge of the behavior of hollow-fiber reactors is the inability to obtain direct information on module performance noninvasively. Sampling is difficult to accomplish accurately and fluid flow measurements are limited to inlet/outlet conditions unless probes are inserted. Magnetic Resonance Imaging (MRI) offers the potential of being able to spatially resolve local fluid velocities and cell metabolism noninvasively. It is a technique that, although used for several years in medical diagnoses, has only recently been applied to chemical engineering operations. Flow-sensitive techniques can be used to determine velocities at various radial and axial positions, thus allowing quantitative information on local fluxes. Chemical shift-sensitive techniques can also be spatially applied to determine local biochemical information such as cell growth patterns, pH, ATP concentrations, etc. Because the analysis of hollow-fiber systems with MRI is in its infancy, there is a need to establish proper protocols under controlled and idealized conditions using 'To whom all correspondence should be addressed. 285
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pulse sequences that give valid results. These methods can then be applied with confidence to situations outside of the context from which they were derived. This is especially important because there are few, if any, alternate methods that can be used for independent verification. The main objective of this work was to evaluate the application of a flow-sensitive MRI technique to the analysis of water flow in a cell-free, hollow-fiber unit. The unit was operated with an artificially induced flow field perturbation to test the ability of the method to resolve axial velocities over a range of positive and negative values. A secondary objective was to test the applicability of a diffusion damping method to indirectly resolve cell growth patterns in hollow-fiber units in which mammalian cells had been cultured. The results of these preliminary studies would be used in future work with actual operating reactors. They would also form the basis for MRI methodologies that could be applied in other biochemical operations such as protein filtration.
BACKGROUND Although there have been numerous theoretical studies of flow in porous tube and shell systems (i.e., Apelblat et al.;l Quaile and Levy;2 Terrill;3 Schonberg and et aL5), there have been few experimental studies. Park and Chang6 B e l f ~ r t Salmon ;~ used direct sampling of tubes and photography of a tracer dye in a laboratory-built hollow-fiber unit. Pangrle et aL7used a time-of-flight MRI technique to measure fluid distribution in a commercial hollow-fiber module. These studies demonstrated that feed flow maldistribution results in some tubes acting as “feeders” to other tubes acting as “collectors”. The time-of-flight method was later applied to a ceramic system.s Hammer et aL9 and Heath et a l l o used a phase encoding MRI sequence to experimentally show shell side flow (‘‘leakage’’ or Starling flow) in multifiber (40 fibers) modules. To date, there are no comprehensive studies of fluid flow in commercial hollow-fiber units. Significant progress has been made in assessing cell metabolism in hollow-fiber bioreactors, particularly using NMR. Stewart and Robertson” used 35S-labelingwith autoradiography to measure cell growth. Dale and c ~ - w o r k e d have ~ - ~ successfully ~ applied NMR spectroscopy to study animal cells in small hollow-fiber units, as have Mancuso et a l l 5 who used a 23Na-NMRmethod to obtain cell concentrations. Piret and Cooney16 used freeze-and-section methodology to obtain axial resolution of cell concentrations. They showed that, under unidirectional flow conditions, cell concentration was lowest near the reactor entrance and maximal at the distal end. No reports of noninvasive spatial resolution of cell concentration or metabolism have appeared. In cell reactors, the consequences of feed flow maldistributions, fluid ejection occurring in some tubes and injection in others, and Starling flow are that the unequal distribution of nutrients and the improper clearance of waste products occur. These conditions most likely do not result in optimal cell growth and product formation. Such flow effects would significantly reduce the efficiency, and hence product recovery, of the separation step in filtration operations.
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MATERIALS AND METHODS Hollow-Fiber Module
A Fresenius F-80 unit was used for the flow experiments. It contained 13,000 polysulfone hollow fibers, each with an inner diameter of 200 k m and an outer diameter of 280 km. The shell diameter was 5 cm and the fiber length was 23 cm. These membranes have a molecular weight cutoff of approximately 65,000 daltons. The unit was operated in the closed-shell mode. Water was supplied to the lumen (tube) side of the module with a nonpulsatile pump. Tap water, doped to a concentration of 0.2 g / L with either C u S 0 4 or MnCI2,was used to reduce the NMR T I relaxation time, allowing faster data acquisition. Cell Bioreactor Hollow-fiber reactors in which mammalian cells had been cultured for several weeks were donated by Prosept, Incorporated (Cambridge, Massachusetts). These modules were disconnected from serum feed at Prosept, packed in ice, and transported to the MRI facility. They were then connected to the doped water feed system for imaging. MRI Methodology The MRI experiments were conducted at the Central Massachusetts Magnetic Imaging Center in the Massachusetts Biotechnology Park (Worcester, Massachusetts) using a G E 2.0-T/45-cm CSI-I1 imaging spectrometer, equipped with 20gauss/cm self-shielded gradients, operating at 85.56 MHz for protons. The main bore of the magnet is 45 cm in diameter and about 6 feet in length. Hollow-fiber modules were placed lengthwise in the bore, within an R F coil of 8.25-cm inner diameter. Two types of pulse sequences were used. Velocity Encoding with Flow Compensation This pulse sequence was used to obtain flow images for the cell-free hollow-fiber unit with doped water only (no cells). The technique produces 16 two-dimensional images of a single cross-sectional slice, each representing the fluid flowing within a specific velocity range. The signal intensity or local “brightness” in a given image is proportional to the amount of fluid flowing within the corresponding velocity “window”. Negative and positive velocities can be resolved with this method. The pulse sequence, using a concept described by Moran,” is shown in FIGURE 1. A 90” slice-selective pulse is used to excite the protons that “dephase” primarily because of magnetic field inhomogeneities. At time = TE/2, a 180” slice-selective pulse is applied in order to refocus the effects of magnetic inhomogeneities, producing a “spin echo” at time = TE. The slice-selective gradient and an R F phase “ramp” (not shown) define the location of the slice to be imaged.
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The purpose of flow compensation is to eliminate the dephasing effects that result when imaging nonplug flow (apart from desired position or velocity phaseencoding). If flow compensation techniques are not used, the flow field can cause the signal to “spread out” artifactually across the image in the phase-encode direction. The phase that is accumulated by the spins in the presence of a changing magnetic field gradient in, for example, the z direction, G,(t),is given by (1)
G,:
G, :
G :
RF receiver gate: FIGURE 1. MRI pulse sequence used for velocity encoding with flow compensation.
where y is the gyromagnetic ratio of protons (26.752 x lo7 rad/Ts) and Gz(t)is the known (applied) magnetic field gradient in the z direction during the sequence. For spins moving at a constant velocity v , their position z changes as a function of time: z = 2,
+ vt.
(2) In reference to FIGURE1, there are two conditions that must exist in order to fix the amplitude of the two flow compensation gradients in thez direction following the
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90” pulse. The amplitude of the first slice-select gradient is fixed by the bandwidth of the 90” slice-selective pulse. The first condition is that the total area under the sine waves plus half the area under the slice-select gradient must sum to zero for stationary spins (where the magnitudes of the gradient pulses above the reference line are positive and the magnitudes of those below the reference line are negative). The second condition is, that the “vt” term in the integral of equation 1 must equal zero for moving spins. These conditions provide two equations and two unknowns. The phase-encode gradient was applied in the x direction. The purpose of phase-encoding is to use gradients to impart a phase angle, I$, to the spins that is linearly proportional to their x position (in this case). Therefore, the area under the sine waves is not zero and, consequently, the solution for the integral is also not zero. The phase angle imparted to the spins is, however, the same for stationary and flowing spins. The purpose of the velocity-encoding gradient is to obtain quantitative information about flow velocities from the MR images. The velocity-encoding gradient is applied in the z direction (with simultaneous flow compensation). With these “bipolar” velocity-encoding techniques, the moving spins will accumulate a phase angle, I$, that is linearly proportional to the velocity of the spins in the z direction. A different phase angle, is accumulated at each repetition corresponding to each velocity range because the velocity-encoding gradients are stepped up through 16 values, equal in magnitude, but opposite in sign, around the flow compensation gradients. This is the portion of the sequence that results in the 16 velocity-encoded images (after Fourier transforming over the velocity “dimension”). Finally, the y direction is utilized for the readout gradient. The spin echo resulting from the 90” and 180” pulses is read out at time = TE, which is the echo delay time. Flow compensation techniques are also used in the direction with this gradient to ensure that the echo signal is in phase in the center of the data acquisition window for both stationary and moving spins.
+,
Calibration Phantom
A simplified system was set up in order to confirm that the pulse sequence could quantitatively measure fluid flow in both the positive and negative directions. This was important because flow may occur in both directions within the normal operations of the bioreactor. The schematic of this simplified system is shown in FIGURE2a. The flow “phantom” consisted of a sealed test tube, filled with stationary water, that was wrapped by flexible tubing through which water was pumped to flow down along the tubing in the positive z direction and back up along the tubing in the negative z direction. Laminar flow was established in this tubing at a maximum velocity of 16.7 cm/s. The velocity images produced at a single cross-sectional “slice” from this phantom are shown in FIGURE 2b. These and subsequent images of this type are discussed by reference to the row and position numbers as shown in each figure. The upper left image (row 1, position 1) represents the largest negative velocity range, whereas the lower right image (row 4, position 4) is the highest positive velocity range. The velocity range for each image is 2.5 cm/s. The image in row 3, position 1 is
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water out in
stationary POSl TION:
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ROW 1
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FIGURE 2. (a) Calibration phantom used for velocity measurements of the laminar flow in a single tube. The dashed line shows the approximate location of the image taken. (b) Imaging results from the calibration phantom of the laminar flow in the positive and negative directions.
the range of -1.25 cm/s Iv I1.25 cm/s. The stationary water in the sealed tube thus produces the highest intensity in this range. A small signal is evident from the low velocity fluid flowing near the tubing wall in both positive and negative directions. There is no signal returned from stationary water in any other images.
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Proceeding left to right in row 3 illustrates the loss of signal from any negative velocities and shows only concentric rings, decreasing in size as the velocity range imaged increases. The highest velocity range (16.25 to 18.75 cm/s) is shown in position 4 of the fourth row. A small contribution from fluid flow near the centerline velocity is evident (16.7 cm/s). For negative velocities, the image in row 2, position 4 represents the fluid flowing within the range of -3.75 to -1.25 cm/s. No stationary or positive flowing fluid is evident. By proceeding right to left in the second and first rows, the succeeding negative velocity ranges are presented. These are essentially “mirror” images of the positive flows. The image in row 1, position 1 is the “Nyquist” image and would show fluid moving faster than 18.75 cm/s in either the positive or negative direction. As expected, it indicates no fluid flowing in this range. The superposition of the sets of annular rings shown (in either direction) demonstrates the expected parabolic flow profile. Each two-dimensional image shown comprises many individual volume elements (voxels) over which the MRI pulse sequence was applied. For this figure, the resolution (a function of machine parameters and the pulse sequence) provided a voxel with dimensions of 0.78 mm x 0.78 mm x 10 mm. Although the resolution and the total velocity range over which the images were taken may be different, all subsequent figures representing results from velocity-encoded pulse sequences are presented with the same convention as FIGURE 2b.
Diffusion Damping Sequence Instead of selecting certain velocity components, it is also possible to use magnetic field gradients to minimize the NMR signal received from moving protons, especially those moving incoherently.Is As discussed in the last section, a bipolar field gradient imparts a velocity-dependent phase angle to moving spins. For the case of molecular diffusion, which is an incoherent process, a distribution of phases will result, with a concomitant reduction of the summed NMR bulk magnetization signal. Further diffusion sensitization of the received NMR signal may be accomplished by modifying a standard spin-echo imaging sequence to use a gradient pair of the same polarity on both sides of the 180”pulse, as shown in FIGURE 3. For this sequence, the log of the ratio of the acquired NMR signal with and without the diffusion damping gradients, assuming purely molecular diffusion, is given byI9 In(S/So) = -yZG262(A - 6/3)D,
(3)
where y is the gyromagnetic ratio of protons, 6 is the pulse width of each gradient pulse, A is the time interval between the start of each gradient pulse, G is the magnitude of the applied magnetic field gradients (in T/cm), and D is the diffusion constant of the molecules in the medium (D = 2.09 x cm2/sfor water at 21 “C). If the NMR signal is measured for several different values of gradient strength (all else being constant and known), the diffusion constant may be calculated by fitting a straight line to the log of the signals using equation 3. If the diffusion is restricted, for example, by cellular membranes, then the distance through which the average water spin would migrate during the time A - 6/3 is limited; thus, the signal from such
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“compartmentalized” water would not be reduced as much as the signal from truly “free” water. The diffusion damping technique should also have interesting applications for discriminating between intracellular and extracellular protons in a bioreactor. Even if the cells are rather large, such that restricted diffusion inside the cells may not provide sufficient signal discrimination by itself, the diffusion damping of the extracellular water in a bioreactor may be enhanced simply by turning on a pump and increasing the motion components of spins in the “free” water. Strictly speaking, many of the extracellular spins will be moving coherently, for example, under laminar flow conditions inside the tubes; however, because of the wide range of velocities of the water inside the tubes or flowing “around” cell clusters in the shell side of the bioreactor, the vector sum of the local bulk magnetization in such regions will be significantly reduced.
180
90
c
DIFFUSION DAMPING GRADIENTS
p*--I-‘“
FIGURE 3. MRI diffusion damping sequence used in imaging bioreactors with cells.
In the preliminary experiment reported here, we used A = 19.8 ms and 6 = 10 ms, whereas the diffusion gradient strength was increased up to a maximum of 6 x T/cm. The image obtained for each value of diffusion gradient strength was qualitatively compared with the images acquired from the previous gradient strengths to look for changes. The integrated NMR signal from the excited slice was reduced by a factor of -20 (S/So 0.05) at the maximum gradient strength. The signal reduction, S/So, for freely diffusing water at this gradient value would only be about 0.4. The expected rms displacement for water molecules diffusing during the time, A - 6/3, is -8 pm, which is larger than the size of the mammalian cells in the bioreactor. Therefore, we were operating in the restricted diffusion regime for the intracellular component of the NMR signal and the signal would have been reduced even less for this component than for free water. This implies that the flowing extracellular water component must have been responsible for most of the signal loss because the total diffusion damping factor was 0.05.
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RESULTS AND DISCUSSION Flow Images (No Cells) Hollow-fiber cartridges were operated in the closed-shell mode with water feed to the lumen (tube side) only. FIGURE 4 shows a schematic indicating the approximate location of the images obtained under flow conditions. The voxel size (resolution) of the images presented here is 0.94 mm x 0.94 mm x 10 mm. The twodimensional photographs show a cross section of the unit, presenting pixels of 0.94 mm x 0.94 mm. A perturbation was introduced into the flow field of the unit in order to conduct a significant test of the MRI pulse sequence. A hole was drilled in the inlet distributor head along the vertical centerline, approximately halfway between the inlet feed line and the bottom of the unit. An area of tubes was then blocked (in the potted region) by injecting epoxy into the entrance of these tubes. A rubber stopper was used to seal the hole. The approximate location of the region of plugged tubes is shown in FIGURE 4.
Inlet Distributor Head Images taken in the distributor head and fore-potted region (not shown) indicated that epoxy penetrated at least the depth of the potted region and that water was prevented from entering these tubes in the inlet. The presence and flow of water in these plugged tubes can then only come from injection due to positive shell-totube pressure drops or from backflow from the exit of the unit.
Inlet Region The first set of images, shown in FIGURE 5, were acquired from a cross section about 30 cm downstream of the fore-potted region (see FIGURE4). Water was flowing at a total rate of 435 mL/min and the velocity range covered by the 16 images was -10 cm/s to +10 cm/s. The image in position 1 of row 3 has been blocked out because its brightness would have dominated the rest of the photograph. Because that image represents stationary or very slowly moving water, it showed that essentially all of the shell and tubes (including those blocked at the entrance) were filled with water. It is important to note that the images displayed in this and all subsequent flow results are inverted from the actual orientation of the hollow-fiber unit in the imaging magnet. Thus, the bottom edge of each image corresponds to the top of the membrane module. The resolution obtained in these images was not sufficient to be able to distinguish flow in individual tubes. Hence, a pixel intensity represents the composite of shell and tube side flow velocities. Because the tube bundle is nonuniform and the spacing of tubes is not at all regular in these units, it is not possible to know exactly how many tubes are in a given pixel at any position in the image. The approximate number, if placement were ordered, is 22. In FIGURE 5, the first two images in the positive velocity range (row 3, positions 2
F i g u r e5
I .
Figure6
I
Figure7
sections imaged and presented in the figure referenced.
FIGURE 4. Schematic of the Fresenius F-80 hollow-fiber cartridge used for imaging flow.Dashed lines are the approximate locations of the cross
\4
Inlet Distributor
!2
0
z
2 M
gm
8
E
*
N
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and 3) show that there is little maldistribution of fluid and that most fluid is moving (regardless of radial position) at velocities less than 3.75 cm/s. The dark region in the upper portion of each image shows that there is no flow in the tubes that were plugged. The dark ring visible in the image in row 3, position 2 represents a region where flow is absent due to the presence of part of the module casing. There is a small region of flow around this structure and its absence in the second image indicates that the velocity of this material is less than 2.50 cm/s. The brighter region at the bottom of the image in row 3, position 2 shows that there is more fluid flowing at that spot; this is near the shell side outlet port. Inspection of the image in row 2, position 4 indicates that there is also some flow in the negative direction in an area
POSITION: ROW
1
2
3
4
1
2
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4
FIGURE 5. Image taken from a cross section of a hollow-fiber module just after the inletpotted region.
adjacent to this. The location of this fluid relative to the tube bundle is such that this fluid is most likely in the shell space. Apparently, the presence of the outlet port (even with no flow out of it) along a n otherwise smooth inside wall causes a disruption in the flow with some sort of recirculation pattern. There is little, if any, flow in the module at this axial position beyond these velocity ranges and essentially only noise remains for images with I u I > 3.75 cm/s. If the total feed was equally distributed among all tubes, the maximum centerline velocity in any tube would be 3.56 cm/s. These results are thus consistent with a fairly uniform flow distribution at this axial position.
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-
1
2
3
4
1
2
3
4
FIGURE 6. Image taken from a cross section of a hollow-fiber module near the exit, including the aft-potted region.
Outlet Region
FIGURE 6 presents the results taken from the exit region of the unit including the aft-potted section (see FIGURE4). Conditions are the same as in FIGURE5. Examination of the images in row 3 shows that most of the fluid is moving at velocities in the low range. Position 4 in row 3 indicates fluid flowing at a moderate velocity at the center of the image. This signal persists in row 4 up to a maximum velocity of 7.5 cm/s. This is due to the acceleration of fluid as it leaves the potted region and enters the exit distributor head near the exit tube. The interesting features of this cross section relate to the region of plugged tubes. The images in row 3, positions 2 and 3 indicate that there is fluid flowing in the positive direction near these tubes at low velocities. Most likely, this is either shell side flow or the net effect of positive flow in some of the tubes and the shell. However, examination of row 2, positions 4,3,2, and 1 shows that there is significant flow in the negative direction in this region. The absence of upstream tube side flow results in pressures inside the tubes being low enough to allow fluid in the exit distributor head to flow back into them. This negative z-direction flow exists in these tubes at velocities up to -4.375 cm/s. It would also be expected that this would persist upstream along the length of the tube until all the mass that had entered these tubes had been ejected into the shell space. This could be confirmed by taking flow images at several upstream cross sections until the position was found where negative flow was absent. It could also be confirmed by imaging the exit distributor head and
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by looking for regions of negative flow consistent with the location of the tubes described earlier. Outlet Distributor Head
FIGURE 7 shows the results obtained from a cross section that includes the outlet distributor and part of the outlet tubing. The voxel dimensions are the same as those of previous images, but the total flow rate was 335 mL/min. Rows 3 and 4 (positive velocities) show that most of the fluid is slow-moving, but that near the center of the distributor head there are regions of faster-moving fluid. The dark area at the bottom of the image (top of unit) is a trapped air bubble. As expected, there is a region of fast-moving fluid near and in the outlet tube. All fluid is exiting the unit through a 4-mm-diameter outlet port. An average velocity of 11.8 cm/s would result from this flow and this is beyond the 10-cm/s maximum measurable at these imaging conditions. Thus, a signal persists at the image center throughout the positive velocity ranges. In fact, velocities much greater than 11.8 cm/s would be expected as fluid accelerates from the outlet head into the outlet port. The presence of these velocities is observed by “aliasing” artifacts displayed in the negative velocity images in row 1. As a consequence of the imaging process, a wraparound effect occurs when velocities higher than the measured range exist. These higher velocity images are displayed in the negative velocity image range, starting at the highest negative range (- 10 cm/s). Successively smaller signals are observed from positions 1 to 4 (row l ) , consistent with the expectation that the amount of fluid moving at velocities higher than the
POSITION: ROW
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1
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FIGURE 7. Image taken from the exit distributor head, including the exit tube.
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average decreases as water exits the outlet port. This would, of course, obscure the results of observing real negative velocities in this range, although it does not appear to have occurred in this case. The problem of aliasing can be serious when it is not possible to know in advance what the range of velocities in a given sample might be. Repeating images using different total velocity ranges and at different flows is then necessary to eliminate the effect. It was not necessary in this case due to the absence of high negative velocities. The results shown in the second row confirm the fact that there is an area of relatively slow-moving, but negative flow in the outlet distributor head. Fluid exiting the tubes is circulated back toward the aft-potted region. It is this circulation that results in the flow back into the area of tubes that were plugged at the inlet distributor head. Fluid cannot reenter tubes that have water exiting from them. The dark area in the center of the images in row 2 is a result of the fact that all the fluid in this region is moving in the positive direction, out of the distributor head, and thus produces no signal in the negative range. Radial flow could be possible in the outlet head. The measurement technique used in this experiment was sensitive only to axial flow, so no signal would have been returned from radial flows. The dark areas or rings visible in some of the images in FIGURE7 may be due to radial flow. Significant radial flow was probably not present because the bubble (position 1, row 3) did not move during the acquisition period of 15-20 minutes. Radial flow could be detected by images taken from the sagittal and coronal planes (data not shown) rather than the cross sections displayed. Bioreucforwifh Cells
A hollow-fiber unit in which mammalian cells had been cultured was obtained, as described earlier, from Prosept, Incorporated (Cambridge, Massachusetts). The diffusion damping imaging technique discussed earlier was used to indirectly show the location of regions of cell mass. The advantages of this method are that it is relatively easy to implement (compared to chemical shift imaging), it eliminates tube side flow contributions completely, and it can be used to obtain preliminary data on the extent of radial and axial cell growth patterns. The disadvantages are that cell viability cannot be determined and that regions of no flow where no cell growth also occurred would appear as if cell mass were present. The images obtained from two cross sections of the bioreactor with diffusion damping gradient strengths of 6 gauss/cm are shown in FIGURE 8. These images are not presented like the previous figures. In these pictures, regions of high image intensity represent regions of cell growth (no flow). Dark regions are those corresponding to flowing water. The images are displayed in the same module orientation that was used for culturing the cells and conducting the imaging experiments. FIGURE 8a was taken near the front of the unit. It shows that most cell growth occurred along the bottom third of the unit. A region of little or no growth was present in the center of the module. FIGURE 8b was obtained from a cross section near the outlet of the reactor. Note that the cell growth region extends further into the inner regions of the reactor and only a few regions of poor cell growth are apparent. These results are qualitatively similar to those of Piret and Cooney16 in that more cell growth was observed near the distal end of the reactor. However, in addition to being noninva-
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sive, the MRI technique can also resolve radial cell growth patterns. The cell growth patterns are presumably due to the maldistribution of nutrients and to both tube and shell side flow patterns that are nonuniform. Visual inspection of the unit confirmed the presence of more cell mass along the bottom region of the reactor. It was not possible to conduct further independent evaluations of the cell growth patterns.
FIGURE 8. (a) Image taken from a hollow-fiber module containing cells showing a cross section near the entrance. Bright regions are cell mass. (b) Image taken from the reactor in part a (containing cells) from a cross section near the exit.
SUMMARY
Preliminary experiments were described that demonstrate that MRI is an effective tool for the noninvasive study of hollow-fiber bioreactors. Flow-compensated velocity-encoding pulse sequences were successively applied to analyze the velocity patterns in a module operated without cells, with an artificially induced flow field perturbation. Diffusion damping pulse sequences were also used to spatially resolve regions of cell growth in a bioreactor. These experiments provide the necessary basis from which future flow and spectroscopic studies can be conducted.
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ANNALS NEW YORK ACADEMY OF SCIENCES
ACKNOWLEDGMENT
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