Biotechnol. Prog. 1995, 7 7, 14-20
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ARTICLES Isolation of Human Blood Cells, Platelets, and Plasma Proteins by Centrifugal SPLITT Fractionation C. Bor Fuht and J. Calvin Giddings* Field-Flow Fractionation Research Center, Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
Centrifugal SPLI'M' fractionation, a technique designed for the continuous highresolution separation of colloids and low-density particles, is applied here to fresh human blood, producing six purified fractions consisting of proteins and lipoproteins, platelets, red blood cells, lymphocytes, monocytes, and neutrophils. Production of the six fractions requires five steps, each yielding two fractions. These five steps are carried out in sequence using a single apparatus, with conditions varying from step to step in accordance with theoretical guidelines in order to achieve the desired cut points. In the first step, a stream of diluted blood is separated into one fraction consisting of platelets and plasma and another containing blood cells. The throughput of diluted blood is 162 mL/h and that of whole blood is about 2 mL/h or -lolo cellsh; guidelines are given for significantly increasing throughput. The purity of the blood cell fractions ranged from 92 to 98%, and the viability fell in the range 97-99%.
SPLIT" fractionation (SF)involves a relatively new family of separation techniques that can be used for the discrete or continuous separation of macromoleculesand particles (Giddings, 1985,1988; Springston et al., 1987). Separation is achieved in a SPLITT cell, a thin (submillimeter) flow cell or channel of rectangular cross section, as shown in Figure 1. ("SPLITT cell" is derived from "split-flow thin cell".) Splitters are generally aligned at both ends of the flow cell such that they divide the incoming and outgoing flow streams into adjacent thin laminae. The two incoming laminae, one containing particles to be separated and one consisting only of a carrier liquid, are forced into contact with one another as flow carries the constituent liquids beyond the edge of the inlet splitter. A transverse field or gradient applied to the flow cell initiates transport of components across the surface (the inlet splitting plane or ISP) where the two laminae join, leading to differential mass transfer from the feed lamina into the carrier lamina. A splitter is also located at the outlet end of the SPLIT" channels. The outlet splitter divides the outgoing ribbon of fluid into two laminae (substreams) in which the components to be separated are relatively enriched or depleted, depending upon their rate of transport across the thin dimension of the cell while in transit. The degree of enrichment or depletion of any given component at the outlet depends not only upon the rate of transport of that component but also on the position of the outlet splitting plane (OSP),which is the surface dividing the film of liquid in the flow cell into the two laminae that exit on different sides of the outlet splitter. Details of the SF process have been provided
* Corresponding author.
Present address: Department of Biomedical Engineering, The Cleveland Clinic Foundation, 9500 Euclid Avenue, Cleveland, OH t
44195-5254.
in the cited literature and other publications (Giddings, 1985, 1988,1992; Springston et al., 1987). For practical utilization, the SF process has a number of important advantages. First the separation process is rapid (-1 min) because the separative transport path is only -lo2 ,um in length-somewhat shorter than the thickness of the channel. Second, the SF process can be run continuously, and thus the quantity of material fractionated can be increased in proportion to the operating time. Third, throughput is proportional to field strength and to the area of the flow cell and thus can be readily augmented. Fourth, the resolution is relatively high because there is generally no convective flow along the path of separation; the flow direction is perpendicular to the separative path. Fifth, the separation process is flexible because the degree of transport is governed by the generally adjustable field strength and by the positions of the ISP and OSP, which are controlled by the ratios of the flow rates entering the inlet and outlet substreams, respectively. These advantages make SF promising for the separation of many biological materials requiring purified components in amounts ranging from milligrams to several kilograms (Giddings, 1988). Quantities in this range are often needed for biological and biomedical research, as well as for biotechnology applications. The preparative separation of cells and other blood components is particularly important. Consequently, work on cell separation techniques has become increasingly active (Kompala and Todd, 1991; Pretlow and Pretlow, 1982). SF appears to have some unique capabilities in this area. The specific characteristics of SF separation will, however, depend upon the type of field applied. The transverse field applied across the SPLITT flow cell can be one of several types, depending upon the properties of the particulate material requiring separation (Giddings, 1985, 1988). Sedimentation fields (both
8756-7938/95/3011-0014$09.OO/0 8 1995 American Chemical Society and American institute of Chemical Engineers
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Biotechnol. Prog., 1995, Vol. 11, No. 1 product stream
a
FIELD
product stream
b Figure 1. Generic structure of the flow cell or channel for SPLITT fractionation. The (adjustable) positions of the inlet splitting plane (ISP) and the outlet splitting plane (OSP) are shown. The channel thickness w is exaggerated for clarity of illustration.
gravitational and centrifugal) have been used most frequently (Springston et al., 1987; Gao et al., 1991),but electrical fields (Levin et al., 1989) and concentration gradients (Williamset al., 1992; Levin and Tawil, 1993) have also been employed. The earth‘s gravitational field is the simplest to use and has been employed most often, but this method has a smaller throughput than centrifugal SF and it is not effective with submicrometer-sized particles or with larger particles whose densities are close to that of the suspending liquid (Fuh et al., 1994). While most biological cells are, in principle, subject to effective separation by gravitational SF, the sedimentation coefficient of red blood cells (RBCs) is not sufficient for gravitational transport to readily outstrip the diffusive transport of plasma proteins across a SPLITT flow cell (Levin and Giddings, 1991). In order to extend the breadth of applicability of gravitational SF and to augment throughput the development of a centrifugal SF system has recently been reported (Fuh et al., 1994).The centrifugal SF technique is used in this study. In centrifugal SF, the SPLITT channel is no longer planar, as shown in Figure 1,but is curved around the rotating axis of a special centrifbge system. The circular configuration of the centrifugal SPLITT channel is illustrated in Figure 2. Also illustrated are two different modes of separative operation, as will be described here. Two principal operating modes of SF can be distinguished: the equilibrium mode and the transport mode (Giddings, 1985, 1988). In the equilibrium mode (Figure 2B), different components are driven to different equilibrium positions (frequently adjacent to opposite channel walls) by the applied field. The position of the OSP is then adjusted (by altering the ratio of outlet flow rates) to optimize the separation. The two selectively enriched laminae are then collected as separate substreams (a and b) from the two sides of the outlet splitter. Thus, particles of different densities subjected to a sedimentation field can be rapidly divided into two fractions, one with particle densities higher and one with densities lower than that of the carrier liquid. In the transport mode (Figure 2A), components must be introduced as a thin lamina consisting of liquid flowing above the ISP. All components are driven in the same direction, specifically toward the OSP, but only components with higher transport rates (beyond a predetermined cutoff value) succeed in crossing the OSP. The outlet splitter then divides the channel flow stream a t the position of the OSP, generating two fractions having
different transport rates. When sedimentationfields are used, the separation is based on differences in sedimentation coefficients. Each separation process in SF produces two welldefined fractions, which emerge from opposite sides of the outlet splitter. In order to achieve multicomponent separations, several processing steps are needed. Multistage separations can, in principle, be executed by linking different flow cells together (Giddings, 1985). However, for laboratory studies such as the present one, it is simplest to use a single SPLITT channel for which, in successive stages of the operation, the conditions (field strength and flow rates) are adjusted to provide the necessary cutoff values for each of the constituent single stage separation processes (Gao et al., 1991). The purpose of this study is to determine the feasibility of fractionating blood into its major components by centrifugal SF. To this end, a single centrifugal SF system has been used with conditions altered to suit the needs of different separation steps. The efficacy of the individual fractionation steps is examined, with no effort made at this stage to augment throughput. We note that many other centrifugal techniques have been used to separate blood components (Rickwood, 1984; Lindahl, 1986; Pretlow and Pretlow, 1979; Miller and Phillips, 1969; Cambier and Biemond, 1980; Guyton, 1991). In principle, Centrifugal SF should provide greater flexibility than other techniques, with the capability of fractionating small quantities in a few minutes or larger quantities in extended runs at higher rotation rates. Further scaleup should be achievable by increasing the area bL of the SPLITT channel. In addition, the hydrodynamics of centrifugal SF is consistent with unusually high resolution (Giddings, 1992). An initial effort to implement these capabilities for the separation of blood components is examined here. Theory
The theory of SF is relatively straightforward because of the laminar flow, the uniform channel geometry, and the simple (parabolic) flow profile characteristic of the thin rectangular cross section (Giddings, 1988, 1992; Springston et al., 1987; Williams et al., 1992). Here we provide only a brief account of the theory of transport mode operation. More complete treatments are found in the cited literature. Underlying most transport operations is the so-called “blue” equation. This provides an expression for the
Biofechnol. Prog., 1995, Vol. 11, No. 1
16
A.
B.
Outlet b
Inlet b’
Outlet b
Figure 2. Edge view of centrifugal SPLITT channel operating in (A) transport mode and (B) equilibrium mode. The thickness of the channel is exaggerated to illustrate the two mechanisms of separation.
volumeric flow rate, AV, of the lamina that is traversed by a particle whose velocity (induced by the field) perpendicu1.a.r to the flow direction is U. The relationship between AV and U is given by (Giddings 1988, 1992; Springston et al., 1987)
AV= bLU
(1)
The relative magnitudes of AV and the volumetric flow rate V(t) of the transport lamina (confined between the ISP and OSP) are crucial in defining the ability of a given particle class to reach the OSP and thus exit from outlet b. The value of V(t) can be obtained as the difference in the volumetric flow rate V(a) exiting outlet a and the flow rate V(a’) entering inlet a’:
V(t) = V(a>- V(a’>
(2)
When AV falls short of V(t), the particle will be incapable of crossing the OSP or thus of reaching outlet b. In that case, the retrieval factor, F b (the fraction of particles recovered from outlet b), is 0. At the other extreme, when AV exceeds the volumetric flow rate V(a),the particle is certain to exit outlet b, and thus F b = 1. Between these extremes, the following equation applies:
Fb=
bLU
- V(t)
V(a‘)
for V(t) < bLU 5 V(a> (3)
On the basis of these relationships, we conclude that particles with velocities between UO= V(t)/bL and U1 = V(a)/bL will divide between outlets a and b according to eq 3, whereas all particles with U < Uo will exit outlet a and all particles with U > Ul will exit outlet b. The unresolved range between Uo and U1 can be narrowed (e.g., resolution increased) by decreasing V(a’). However, as a tradeoff, throughput is reduced in proportion to the reduction in V(a’). When sedimentation is responsible for the driving force, U is given by (4)
where s is the sedimentation coefficient, q is the fluid viscosity, d is the effective particle diameter, and A@is the difference in density between the particle and the carrier liquid. The field strength, G, measured as acceleration, equals 1gravity for gravitational SF and o2r0 (where cr) is the angular rotation rate and ro is the
distance between the channel and the axis of rotation) for centrifhgal SF. Since separation is achieved by virtue of differences in U,it is possible to separate cells or other bodies according to differences in their sedimentation coeficients or, correspondingly, in their densities and sizes. Smaller species such as plasma proteins are transported more rapidly by diffusion than by sedimentation under the conditions employed here. The theory of diffusive transport in SPLITT channels has been developed elsewhere (Williams et al., 1992). The advantage of centrifugal SF over a gravitational SF is due to the fact that AV is proprotional to G, which can be increased to high levels by centrifugation. For .a given retrieval factor F b , all flow rates are scaled to AV, including the flow rate of the feed stream V(a’), which governs throughput. In addition to the advantage of enhanced throughput, centrifugationis capable of driving cells and platelets across the transport lamina ahead of the diffusion wave of plasma proteins, thus making possible the clean separation of proteins from cells and platelets.
Materials and Methods The centrifugal SPLITT fractionation system used in this work is the same as that described previously (Fuh et al., 1994). The length L (between splitting edges), breadth b, and thickness w of the SPLITT channel are 26.7, 2.0, and 0.0381 cm, respectively. The calculated void volume (or working volume) of the flow cell is 2.03 mL. The area of the inlet splitter is 6.0 cm2. For the experimental conditions utilized, the blood components to be separated entered the flow cell uniformly distrib: uted over the cross section of the incoming feed lamina (Fuh et al., 1994). Kapton polyimide tape (CHR Industries, New Haven, CT) was used to make the walls of the flow channel relatively inert. The feed stream, consistingof either blood or a fraction of blood diluted in a buffer, was pumped into inlet a’ by a Minipuls 2 peristaltic pump (Gilson, Middleton, WI). The carrier stream was supplied by Kontron LC pump 410 (Kontron Electrolab, London, U.K.). In order to monitor the outlet streams, two variable wavelength U V detectors with flowthrough cells were used at the two outlets. Outlet a was monitored by a Model SPD-6A detector from Shimadzu (Kyoto, Japan), whereas the substream from outlet b was fed to a Model 750 detector from Applied Biosystems (Ramsey, NJ). The system was maintained at room temperature (23 f 0.3 “C) during operation.
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17
Figure 3. Diagram of separation steps used to fractionate human blood into six components.
The carrier solution used for all transport mode separations was a 0.01 M phosphate buffer with pH 7.2, osmolarity = 290 mmol/kg, and density = 1.008 g/mL. For the fractionation carried out in the equilibrium mode, the density of the carrier was adjusted to 1.075 g/mL by adding Ficoll to this buffer. The pH and osmolarity were monitored with a digital pH meter (Extech, Boston, MA) and osmometer (Wescor, Logan, UT), respectively. The sodium citrate, potassium hydroxide, sodium phosphate monobasic, and dextrose used here were obtained from Mallinckrodt, Inc. (Paris, KY), the Ficoll was from Pharmacia (Piscataway,NJ), the Wright stain was from Sigma Chemical Co. (St. Louis, MO), and the human thrombin was from Calbiochem (La Jolla, CA). The freshly drawn human blood samples (diluted with 10% (v/v) acid citrate dextrose) were obtained from the blood bank at the University of Utah Medical Center. Microscopic examination of the fractionated blood products (along with cell and platelet counting) was carried out using an Olympus Model CH microscope (Tokyo, Japan). The platelet and blood cell fractions were treated with Wright stain before counting. A viability test of platelets was carried out by visual observation of aggregation aRer adding the thrombin solution to the reconcentrated platelets.
Results and Discussion Human blood is a complex mixture of many components, including proteins, lipoproteins, platelets, and a variety of blood cells. Red blood cells (RBCs) constitute the majority of all blood cells, outnumbering all others by a ratio of 600/1 or greater (Guyton, 1991). The remaining blood cells are divided into several major classes and numerous subclasses, extending across a broad range of densities and sizes. Separation is complicated by variations (polydispersity) in the size and density of individual cell types. Thus, conditions must be chosen carefully to maximize separability. The overall scheme utilized here for the separation of human blood into components by centrifugal SPLIT" fractionation is illustrated in Figure 3. By carrying out fractionation steps under different conditions,we are able to obtain six major blood components: platelets, plasma
proteins, and four major cellular components consisting of erythrocytes (RBCs), lymphocytes, monocytes, and neutrophils. The purity and viability of the blood cell populations are reported in Table 1. Five separation steps (identified by number in Figure 3) were used for the separation, as reported here. Step 1: Separation of Platelets and Plasma from Blood Cells. This separation step was carried out at 390 rpm (25 gravities) using the flow rates V(a') = 2.7, V(b') = 7.3, V(a) = 5.0, and V(b) = 5.0 mUmin. An initial approximation to the spin rate was chosen on the basis of the theory presented earlier. In order to recover all cells from outlet b?it is necessary that bLU L V(a) where, as noted earlier, V(a) = 5 mumin. Since this condition must apply to all cells, including the smallest lymphocytes, we calculated the G values from eq 4 necessary to fulfill this condition for d = 5 pm and A@ = 0.05 g/mL; this calculation gave us 23 gravities. An experiment was performed under these conditions. However, microscopic observation of the fraction (reconcentrated)eluting from outlet a showed that a few lymphocytes were still present as contaminants to the platelets and plasma proteins. A very slight increase in G, to 25 gravities or 390 rpm, was sufficient to eliminate virtually all lymphocytes from outlet a. At the same time, almost all of the platelets emerged from outlet a, with only a few appearing at outlet b. The retrieval factor Faof the plasma proteins (the fraction collected at outlet a) was calculated to be very close to unity under these conditions. This experiment was carried out with the original blood diluted to 1.2% (v/v) in the phosphate buffer. Under these conditions, the throughput of blood is 2 mL/h or -lolo cellsh. No attempt was made to increase throughput, although theory provides simple guidelines for further gains in this area (Giddings, 1992). Higher throughput would result from a simultaneous increase in G and in all flow rates. More highly concentrated blood samples would also increase throughput. Higher concentrations could probably be used, but this might require the introduction of additives to inlet b' in order to increase the carrier density and eliminate the possibility of convective effects. A study of convective effects is presented later.
Biofechnol. Prog., 1995, Vol. 11, No. 1
18 Table 1. purity and Viability of Fractionated Cells Produced by Centrifugal SPLITT Fractionation’ purity (%) viability (%) lymphocytes 96 & 2 97 f 1 monocytes 94 f 2 98 f 1 neutrophils 92 f 2 98 i 1 erythrocytes 98 f 1 99 f 1 Purity was based on cell counting, and viability was based on dye exclusion experiments. A minimum of 100 cells was counted for all experiments. The uncertainties shown for these values are standard deviations based on three replicate counting sequences.
1BSApeak
outlet 8
Outlecb
a
The separative operation described here was run continuously for 3 h. Detectors (described in the Materials and Methods section)were put on-line with the outlet substreams and they showed a constant response over that period. The two fractions were collected in separate flasks. The liquid collected from outlet b was blood red, indicating the capture of RBCs as predicted. The liquid collected from outlet a was light yellow with no hint of red coloration. The high resolution of this and subsequent separations was confirmed by microscopy (see Table 1). Step 2: Separation of Platelets from Proteins. For this separation step, the spin rate was 660 rpm (71.7 gravities) and the flow rates were $Tat) = 1.5, V(b’) = 3.0,$‘(a) = 2.0, and V(b) = 2.5 mUmin. (We have also found these conditions to be suitable, as expected, for removing proteins from whole blood.) The feed material for this run was the solution of platelets and plasma proteins (along with lipoproteins) collected from outlet a in the experiment described previously. As before, the theoretical equations given earlier provided an initial estimate of the necessary spin rate. For the complete recovery of platelets from outlet b, it was necessary that bLU 2 2.0 n-Umin. Using conservative values of d = 2 pm and he = 0.044 g/mL, eq 6 shows that the necessary G value is 65 gravities (629 rpm). A brief experiment was performed using this spin rate. However, the effluent from outlet a still contained a few platelets, as determined by microscopy. Finally, the spin rate was increased to 660 rpm, producing 71.7 gravities, in order to achieve the virtually complete removal of platelets from outlet substream a. At the same time, diffusion calculations showed that the plasma proteins were unable to diffise across the outlet splitting plane and thus were predicted to be fully collected at outlet a. While no quantitative assays were performed to ensure the absence of plasma proteins from outlet substream b, some indirect experiments were carried out that lend support to the rather complete retrieval of plasma components from the a outlet under the conditions specified earlier. At the same time, blood cells are shown to be almost completely retrieved from outlet b under the same conditions. (The complete retrieval of platelets was confirmed by microscopy, as noted earlier.) These experiments utilized a freshly prepared 1mg/mL solution of bovine serum albumin (BSA) and the blood cells collected from outlet b in step 1. BSA was chosen because albumin not only is the most abundant blood protein but it also diffises more rapidly (and thus is more likely to escape from substream a) than the larger globulins and lipoproteins. The experiment consisted of injecting short pulses (-50 pL) of BSA and/or blood cells into the substream of pure carrier solution entering inlet a’. Detectors placed at the outlets monitored relative retrievals from outlets a and b. Some typical results are shown in Figure 4. In the first run, 50 p L of the BSA solution was injected into inlet substream a’. As shown by Figure 4A, the injected pulse of BSA is found to
I r e b 1
v1
CJ 0
[
blood cell peak
Outleta
1
2
}
blood l5.cells injected
c.
\
3 4 5 TIME (min)
6
7
Figure 4. Detector signals generated at outlets a and b by the injection of narrow pulses of (A) BSA, (B) blood cells, and ( C ) a mixture of BSA and blood cells.
emerge entirely as a sharp peak from outlet a; the detector at outlet b is seen to maintain a steady baseline throughout. On the other hand, injected blood cells emerge entirely from outlet b, as shown by the broad peak generated by the detector at outlet b. When a mixture of BSA and blood cells is injected (Figure 4C), the earlier peak profiles for individual injections of BSA and blood cells are reproduced almost exactly, showing that neither component interferes with the retrieval of the other. Step 3: Separation of Low- and High-Density Bbod C d e . The blood cells isolated from outlet b in step 1 were next subjected to an equilibrium mode SPLITT step to separate low-density cells from those of higher density. For this purpose, Ficoll was added to inlet substream a’ in amounts sufficient to bring the density of the solution to 1.075 glmL; the pH and osmolarity were kept at the previous levels. Inlet substream b’ was cut off since this flow is not neceesary in equilibrium mode operation. This run was carried out at 1000 rpm (164.5 gravities), with the flow rates of V(a’) = 2.0, V(b’) = 0, V(a) = 1.0, and V(b) = 1.0 mumin. Lymphocytes and monocytes were collected at outlet a because their densities were lower than that of the carrier. Erythrocytes and neutrophils, denser than the carrier, were collected at outlet b. The retrieval of purified fractions of the desired subpopulations of cells was again verified by microscopy. Step 4: Separation of Lymphocytes from Monocytes. The lymphocytes and monocytes recovered from outlet a in step 3 were again subjected to transport mode fractionation. Relatively pure populations of the more rapidly sedimenting monocytes were recovered from outlet b; the slower sedimenting lymphocytes were collected from outlet a. (The Ficoll was removed by centrifugation and redilution prior to this step.) The experimental conditions, determined in much the same manner as that described earlier, were 180 rpm (5.3 gravities) with flow rates V(a’) = 2.0, V(b’) = 4.0, V(a) = 4.0, and V(b) = 2.0 mumin. Step 5: Separationof Erythrocytesfrom Neutrophils. A final step in this SPLITT fradianation sequence was another transport mode process for the separation of erythrocytes from neutrophils. Once again, the Ficoll was removed. Erythrocytes, with the lowest sedimentation coefficient,were collected at outlet a and neutrophils were collected at outlet b. The spin rate was 120 v m (2.4 gravities), and the flow rates were V(a’) = 2.0, V(b’) = 4.0, V(a) = 4.0, and V(b) = 2.0 mumin.
Biotechnol. Prog., 1995, Vol. 11, No. 1
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I .o
0.8 (Ap‘ = 0.002ghL)
0.6 Fo 0.4
0.2 0
G (gravities) Figure 5. Plot of retrieval factor Fa for BSA versus centrifugal acceleration G with different amounts of sucrose added to feedstream a’. The density increment caused by the sucrose addition, A@, is also shown.
Convective Disturbances. Most centrifugation techniques must operate with a positive density gradient (density increasing with radial coordinate) in order to stabilize against convective currents acting in the field direction (Rickwood, 1984). These anticonvective gradients are inconvenient and time-consuming to set up. In centrifugal and other forms of SF, the thinness of the channel has its own anticonvective effect. Thus, we have been able to operate both gravitational SF and centrifugal SF (as in the present studies) with a slight negative density gradient: the feed stream lamina, positioned above the ISP and consisting of a dilute suspension of particles in the carrier liquid, is denser than the pure carrier lamina flowing beneath the ISP. Clearly, if the inverted gradient becomes too great because the concentration of particulate matter is too high, transport mode separations will be rendered ineffective by convection. This matter was examined in a previous study in which increasing concentrations of sucrose were introduced into inlet a’ of an SF system subject only to gravitational forces, thus eventually inducing convection across the thin channel dimension (Williams et al., 1992). A similar study for centrifugal SF was carried out as part of this work. In the present experiments the flow rates were V(a’) = 2.8, V(b’) = 7.2, V(a) = 5.0, and V(b) = 5.0 mumin. Carrier solutions were prepared containing different amounts of sucrose ranging from 0.2% to 12%(w/v). The density of the carrier was thereby increased by A@, with values of A@ ranging from 0.0008 to 0.048 g/mL with the sucrose additions. The sucrose-densified carriers were then introduced continuously into inlet a‘ at different spin rates. A small pulse (50pL) of BSA (0.5 mg/mL BSA added to the sucrose solutions) was then introduced into inlet a’ in order to trace any mixing between substreams a’ and the pure carrier stream b’. In the absence of convection, and assuming ideal splitter geometries, the BSA would be recovered entirely from outlet a: Fa = 1.00. Departures from this ideal were examined by placing detectors at the two outlet streams; the measured pulse areas are then proportional to the retrieval factors of BSA from the two respective substreams. The results are shown in Figure 5. This figure shows that Fa, which ideally should be unity, gradually decreases in value as centrifugal acceleration increases and as increasing levels of sucrose are added to the feed stream. For example, a t 200 gravities, Fa drops to 0.9 for 0.2% added sucrose, corresponding to a density difference between substreams of 0.0008 g/mL. When 0.5%sucrose is added, giving a density difference of 0.002
g/mL, Fadrops to 0.8. The two cited density differences, 0.0008 and 0.002 g/mL, would be found for diluted whole blood at concentrations of 2.5% and 6.3% (v/v), respectively. These preliminary results suggest that rather diluted blood (
