Biological Fluid Separation in Microfluidic Channels Using Flow Rate ...

Proceedings of IMECE05’ Proceedings of IMECE2005 2005 ASME International Mechanical Engineering Congress 2005 ASME International Mechanical Engineering Congress and Exposition Orlando, November 5-11,USA 2005 November 5-11,Florida, 2005, Orlando, Florida

IMECE2005-80501

IMECE2005-80501 BIOLOGICAL FLUID SEPARATION IN MICROFLUIDIC CHANNELS USING FLOW RATE CONTROL Sung Yang Department of Bioengineering The Pennsylvania State University 205 Hallowell, University Park, PA, 16803 Akif Ündar Departments of Pediatrics, Surgery, and Bioengineering, Pennsylvania State University, College of Medicine, Penn State Children’s Hospital, 500 University Drive, Hershey, PA 17033 ABSTRACT A microfluidic device for continuous, real time blood plasma separation is introduced. This device is composed of a blood inlet, a purified plasma outlet, and a concentrated blood cell outlet. It is designed to separate blood plasma from an initial blood sample of up to 45 % hematocrit (Hct). The microfluidic device is designed and analyzed using an analogous electrical circuit, analytical and numerical studies. The numerical study results show that 27 % and 25 % of plasma volume can be separated from a total inlet blood volume of 45 % and 39 % hematocrit, respectively. The functionality of this device was demonstrated using defibrinated sheep blood (Hct=36 %). During 2 hrs. of continuous blood infusion through the device, all the blood cells traveled through the device toward the concentrated blood outlet while only the plasma flowed towards the plasma outlet without any clogging or lysis of cells. The experimentally measured plasma skimming volume was about 33 % for a 36 % inlet hematocrit. Due to the device’s simple structure and control mechanism, this microdevice is expected to be used for highly efficient continuous, real time cell-free blood plasma separation device. NOMENCLATURE Hct: Blood Hematocrit ∆P : Pressure drop R: Flow resistance Q: Flow rate ν: Flow rate ratio L: Length of a channel a: Half width of a channel b: Half depth of a channel µ: Dynamic viscosity

Jeffery D. Zahn Department of Bioengineering The Pennsylvania State University 224 Hallowell, University Park, PA, 16803 η: α: B in subscript: P in subscript:

Plasma skimming volume % Level of significance Blood Plasma

INTRODUCTION Most biological cell analyses require either the removal of cells from a biological fluid, such as the removal of blood cells from whole blood to leave purified plasma, or cell concentration for downstream analyses. In typical laboratories, centrifugation is used to separate plasma, or collect cells from an initial biological sample for clinical analysis. Even though, the centrifugation allows a more purified sample volume (either cells or blood plasma), it is a batch process not suitable for applications where continuous real-time sampling or small sample volumes are required. For instance, several studies have clearly shown that cardiac surgery induces systemic inflammatory responses, particularly when cardiopulmonary bypass (CPB) is used [1-10]. These systemic responses are attributed to several factors, including exposure of blood to nonphysiologic surfaces of the heart-lung circuit, ischemiareperfusion of the involved tissues, surgical trauma and hypothermia [1, 10, 11]. Currently, there is no effective method to prevent this systemic inflammatory response syndrome in patients undergoing CPB. The ability to clinically intervene in inflammation, or even study the inflammatory response to CPB, is limited by the lack of timely measurements of inflammatory responses. Thus, there is a need for a system, which can separate blood plasma from whole blood and measure the concentration of the clinically relevant proteins in real time while the surgery is proceeding. There are currently research activities related for on-chip biological cell or fluid separations based on a variety of working principles (e.g. Brownian Ratchet, Dielectrophoresis,

1

Copyright © 2005 by ASME

Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 08/25/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use

deterministic lateral displacement, field flow fractionation, etc.) [12-16]. In this study, a microfluidic device for continuous, real time blood plasma separation, which may be integrated with a downstream plasma analysis device, is proposed. The device is made from polydimethysiloxane (PDMS), which is considered to be a hemocompatible material. Even though no truly hemocompatible biomaterial has yet been found, PDMS is assumed to be a suitable biomaterial because it causes minimal endotoxin contamination, leukocyte, and complement activations [17, 18]. The principle of the plasma separation device is based on the bifurcation law [19, 20], also called the Zweifach-Fung effect. The bifurcation law describes that, in the microcirculation, when erythrocytes (Red Blood Cells) flow through a bifurcating region of a capillary blood vessel; they have a tendency to travel into the daughter vessel which has the faster flow rate leaving very few cells flowing into the slower flow rate channel. The critical flow rate ratio between the daughter branches for this cell separation is on the order of 2.5:1 when the cell-to-vessel diameter ratio is of the order of 1. The reason for this apportioning is that cells are drawn into the

Figure 1. Schematic diagrams of a microfluidic blood plasma separation device (a) An overview of a device. This device is designed to have a whole blood inlet, a purified plasma outlet, and a concentrated blood cell outlet. Each channel has a 5 mmlong. (b) A zoom-in view of the blood plasma separation region. The main blood channel width is 15 µm and all plasma channels have 9.6 µm-wide. The channel depth for the entire device is fixed as 10 µm-deep. The bifurcation positions are indexed from 1 to 5.

higher flow rate vessel because they are subjected to a higher pressure gradient. In addition, the asymmetric distribution of shear forces on the surface of particle produces a torque on the cell pulling it towards the faster flow rate vessel. In a previous report [21], particle separation based on the bifurcation law was successfully demonstrated using a simple bifurcation channel by controlling flow rate ratio between two daughter microchannels. The flow rate ratios of two daughter channels were controlled by changing the flow resistance through changing the geometry of the downstream channels. It was found that, for the 16 µm-diameter fluorescent particles, the particle recovery or separation efficiencies are 87.2%, 95.7%, and 100% for 2.5:1, 4:1, 6:1, and 8:1 flow rate ratios, respectively. Also, for the 8~10 µm-diameter human C8161 melanoma cells, the cell recovery or separation efficiencies are 88.7%, 98.9%, and 100% for 2.5:1, 4:1, 6:1, and 8:1 flow rate ratios, respectively in a 35 x 35 µm2 channel. For this study, a blood plasma separation device is designed to have a whole blood inlet, a purified plasma outlet, and a concentrated blood cell outlet as shown in figure 1. Each channel is designed to be a 5 mm-long. The main blood channel is designed to be 15 µm-wide and all plasma skimming channels are designed to be 9.6 µm-wide. The channel depth for the entire device is 10 µm. This device is designed to separate plasma from whole blood with up to 45 % hematocrit of the inlet blood with a 14:1 flow rate ratio between main channel and plasma channel to form a critical separation stream-line, which occurs 1 µm from the main channel wall for a 15 µm-wide channel. In order to increase the total plasma volume which may be skimmed from whole blood, a total 5 parallel plasma channels are placed within the device. To obtain a consistent flow rate ratio (14:1) at each bifurcating points, the flow resistance ratios between main (blood) and each branch (plasma) channels were used as a control parameter in the design because the flow rate is inversely proportional to the flow resistance of channel. EXPERIMENTAL SETUP The microfluidic device has been fabricated in Polydimethylsiloxane (PDMS) using the conventional soft lithography process [22, 23]. After preparing the device, it is mounted on an inverted microscope for visualization and the defibrinated sheep blood (Hemostat Labs, Inc., CA, USA) is infused through the device using syringe pump (KDS210, KD Scientific Inc., MA, U.S.A.). In all experiments, defibrinated sheep (Hct = 36 %) blood was used as a test fluid. After purchasing the blood, it was stored at 4 oC and was used within 3 weeks of harvest. All experiments were conducted for 2 hours at an inlet flow rate of 10 µl/h. The blood flow within the microchannels is imaged using two different types of CCD cameras. The first is a conventional NTSC CCD camera, which has a 640x480 pixel resolution and a frame rate of a 30 frames/sec. The other is a high resolution (1376 x 1040 pixels) CCD Camera (Cooke SensiCam QE, MI, U.S.A.) at a 10 frames/sec and variable shutter. For these experiments the shutter is allowed to remain open for 100 µsec/frame. After obtaining images, they are analyzed using an image processor program to obtain the hematocrit change between upstream and downstream of the separation region.

2



RESULTS AND DISCUSSION In order to successfully design a blood plasma separation device, a series of design techniques were used to determine the optimal channel geometries. The optimal channel geometries were determined using an analogous electrical circuit analysis, verified using computational simulation (CFD) and demonstrated experimentally. I. An electrical circuit analysis In order to design a complex fluid circuit, it is essential to have an efficient way to determine the required channel geometry, which meets the design criteria. Since the fluid network contains many channels in parallel and series, the pressure-flow relationship at each network node is inherently coupled and cannot be described analytically, each portion of the network is therefore described by an analogous electrical circuit to obtain optimal resistance ratio between each main and plasma channels. In a manner analogous to an electrical current, fluidic flow rate ( Q ) can be defined by (eq. 1) ∆P = Q ⋅ R Where R is the fluid flow resistance and ∆P is a pressure drop. Thus, the flow rate ratio at each bifurcation can be determined by controlling flow resistance ratio between main channel and plasma channel at each bifurcation. In order to determine the flow resistance of each channel, an analogous electrical circuit is analyzed where the flow rate is modulated by the current and the flow resistance is modulated by an electrical resistance. It is assumed that capacitance (compliance) of the system is negligible because channel dimensions and pressures within the channels are small. In order to have flexibility in the design of the blood plasma separation device, it is essential to obtain a generalized expression for the relationship between flow rate ratio and resistance ratio. Figure 2 shows a generalized equivalent fluidic circuit for arbitrary number of bifurcations. The critical stream line position from wall is assumed to be 1 µm. If the flow rate

ratio is assumed to be ν and the main channel width is assumed to be c µm, then, the resistance relationship between the main and plasma channels at each node should satisfy the criteria that

R P ,i = ν ⋅ c = ν ⋅ (ν + 1) R B ,i

(eq. 2)

Where, RB,i and RP,i are resistances of main and plasma channels at ith node, where i=2,3,4,…,n, RB,1=RB,i⋅(ν+1) and RP,1=RP,i. Based on eq. 2, it was found that the resistance of the plasma channels should be 210 times larger than that of the individual segments of the main channel in order to maintain 14:1 flow rate ratio between them except for channel RB,1. RB,1 requires a resistance 15 times larger than that of the main channel. These resistance values were verified by simulating the analogous electrical circuit, using PSpice (Cadence Design, NY, USA) as shown in figure 3.

Figure 3. An analogous electrical circuit simulation result. When the resistances of plasma channels have a 210 times larger than those of individual segments of the main channel and when RB,1 has a 15 times larger resistance, a 14:1 current ratio (flow rate ratio) is obtained at each bifurcation.

Figure 2. A generalized equivalent fluidic circuit for arbitrary number of bifurcations. It is assumed that there is no capacitance (compliance) term in a circuit. A whole blood inlet can be considered as a current source. Both plasma and concentrated blood cell outlets can be considered as grounds.

II. An analytical fluidic circuit analysis Once the optimal flow resistance ratios are obtained from the electrical circuit analysis, an analytical study was conducted to determine optimal fluid channel dimensions which meet the flow resistance ratio requirements. Eq. 3 describes an analytical solution of flow within a rectangular duct [24] nπb ⎞ ⎛ tanh( )⎟ 4ba 3 ⎛ dP ⎞⎜ 192a ∞ 2 a ⎜ ⎟ (eq. 3) − − Q= 1 ⎜ ⎟ ∑ π 5b n =1,3,5,... n5 3µ ⎝ dx ⎠⎜ ⎟ ⎜ ⎟ ⎝ ⎠ Where µ is a fluid viscosity, ∆P is a pressure drop across a channel length L, a is a half width of a channel, and b is a half

3



depth of a channel. By combining eq. 1 and eq. 3, the flow resistance relationship is, −1

nπb ⎞ ⎛ tanh( )⎟ 3µL ⎜ 192a ∞ (eq. 4) 2a ⎟ ⎜ R= − 1 ∑ π 5b n =1,3,5,... n5 4ba 3 ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ Also, by combining eq. 2 and 4, the generalized relationship between flow rate ratio and device dimensions can be obtained as nπbB ,i ⎞ ⎛

⎜ tanh( )⎟ 2a B ,i ⎟ ⎜ 192a B ,i ∞ µ P ,i LP ,i a B ,i ⎜1 − 5 ∑ ⎟ n5 π bB ,i n=1,3,5,... ⎜⎜ ⎟⎟ (eq. 5) ⎝ ⎠ ν (ν + 1) = nπbP ,i ⎞ ⎛ ⎜ tanh( )⎟ 192a P ,i ∞ 2a P ,i ⎟ 3⎜ µ B ,i LB ,i a P ,i ⎜1 − 5 ∑ ⎟ π bP ,i n=1,3,5,... n5 ⎜⎜ ⎟⎟ ⎝ ⎠ Where B and P in subscript of each parameters denote main and plasma channels. Figure 4 represents the analytically obtained flow resistance ratio vs. the plasma channel (a) and the concentrated blood cell channel (b) widths based on eq. 5 when the main channel width and length are fixed as 15 µm-wide and 20 µmlong, respectively. As shown in Fig. 4a, the plasma channels must be 9.6 µm wide in order to obtain a resistance 210 times larger in the plasma channel than that of the main channel. Also, a 154 µm-wide concentrated blood cell channel is required to obtain a 15 times larger resistance as shown in Fig. 4b. 3

III. A numerical fluidic circuit analysis After determining the optimal channel geometries based on the analogous electrical circuit, the performance of the microfluidic device was verified using computational fluid dynamic (CFD) simulation. For this numerical study, CFDACE+ (CFD Research Corp., AL, USA) was used. In all simulations, the blood is assumed as a homogeneous nonNewtonian fluid which follows the Walburn-Schneck blood model [25] and the Hct was assumed as a constant throughout the main channel region. At the first stage of the numerical study, the flow rate ratio at each bifurcation was calculated and compared with the one obtained from the electrical circuit analysis. As shown in figure 5, even though the CFD simulations slightly overestimate the flow rate ratio, (due to the shear thinning properties of the nonNewtonian flow model) than the electrical circuit analysis, they accurately predict the correct flow rate ratio for both 45 and 39 % hematocrit. Thus, this result reflects that the design technique, which combines the electrical circuit analysis and the analytical techniques, is very useful tool for microfluidic circuit design. Also, the flow rate ratio decreases as hematocrit increases from 39 % to 45 % because the increase in hematocrit in the system produces the increase in viscosity and hence flow resistance in the main channel while maintaining the same flow resistance in the plasma channel. Thus, the flow rate ratio decreases as hematocrit increases. As a measure of the performance of the designed device, the plasma skimming volume %, which can be collected from

Figure 4. Analytical study results; The flow resistance ratio between the plasma channel and the main channel with respect to the plasma channel, when the main channel width and the lengths of each segment are fixed as 15 µm-wide and 20 µmlong, respectively. (a) A 9.6 µm-wide plasma channel is required to get a 210 times larger resistance in the plasma channel than that in the main channel. (b) A 154 µm-wide concentrated blood cell channel is required to meet 14:1 flow rate ratio.

Figure 5. A comparison between CFD and the electrical circuit analyses results in terms of flow rate ratio at each bifurcation.

4



the plasma outlets, was calculated and compared with the one obtained from the electrical circuit analysis. The plasma skimming volume % in terms of hematocrit change can be also defined as ⎛ H ⎞ (eq. 6) η = 100 ⋅ ⎜⎜1 − i ⎟⎟ [%] ⎝ Hf ⎠ Where η is the plasma skimming volume %, Hi, Hf are an initial and a final hematocrit, respectively. As described in figure 6, the electrical circuit analysis overestimates plasma skimming compared with the CFD analysis because it underestimates flow rate ratio, again due to the shear thinning properties of the blood simulated in the CFD model. The plasma skimming volume percent decreases at each bifurcation region as blood travels through the device since

(which are discoid cells with a ~7-8 µm diameter, ~2 µm thick) which have a centroid at least 3 µm from the wall are not expected to flow into the plasma channels. The blood plasma separation experiment was conducted at a 10 µl/hr input flow rate using a commercially available defibrinated sheep blood with a 36% initial hematocrit. As shown in figure 7 (b), and image obtained using the standard NTSC CCD camera shows streak lines which are seen as blood cells flow through the device. These streaklines are seen in the main channel with no streaklines observed in the plasma channel. This image demonstrates the blood cells flowing only towards the concentrated blood cell outlet without any cells traveling into the purified plasma bifurcation. In order to

Figure 6. A comparison between CFD and electrical circuit analyses results in terms of plasma skimming volume [%] at each bifurcation positions. total amount of blood which remains in the main channel decreases after passing a bifurcation as the blood travels through the device. The volume percent also decreases as blood hematocrit decreases because blood viscosity is proportional to hematocrit, so a decrease in hematocrit produces a higher flow rate ratio. By adding the plasma skimming volume percent of each bifurcation it is expected that 27 and 25 vol. % of the total blood volume may be extracted with the infusion of 45 and 39 % hematocrit blood at the inlet, respectively. IV. Experimental study of the blood plasma separation As a first stage of the experiment, 0.85 µm-diameter fluorescent particles were infused through the whole blood inlet at 10 µl/hr to investigate flow pattern at the bifurcation regions. It was assumed that 0.85 µm-diameter fluorescent particles are small enough that they follow flow streamlines and do not experience preferential separation like the blood cells. As shown in figure 7(a), 0.85 µm-diameter fluorescent particles flowed into both the concentrated blood cell outlet and the plasma outlet because they follow flow streamlines. From these studies the critical streamline for preferential separation can be visualized at the flow stagnation point. A particle whose centroid is beyond this critical streamline should flow into the plasma channels. However, since the critical streamline is designed to occur 1 µm from the channel wall blood cells

Figure 7. (a) A fluorescent photograph (40X magnification, 1376 x 1040 pixels) of the separation region after infusing 0.85 µm-diameter fluorescent particles at a flow rate of 10 µl/h. Due to the high particle velocity, the particles appear as streak lines at 10 frames/sec. (b) A photograph (20X magnification, 640x480 pixels) of the blood plasma separation region after infusing defibrinated sheep blood (36 % Hct) through the whole blood inlet at a flow rate of 10 µl/h. (c) Another snap shot of same region taken using a higher resolution (40X magnification, 1376 x 1040 pixels) CCD camera with shorter shutter open time (100 µsec).

5



observe individual blood cells’ motion, another image was taken using the higher resolution (1376 x 1040 pixels) CCD camera with a shorter shutter speed (100 µsec) at 40X magnification. In figure 7 (b), the individual blood cells are more clearly observed. Again, no cells are observed in the plasma outlet. Also, severe deformation of red blood cells was not observed throughout the experiment. During a total of 2 hrs. of continuous infusion of blood, only a few blood cells flowed into the purified plasma outlet. Therefore, only plasma is skimmed into the purified plasma outlet. In addition, no clogging or hemolysis of cells was observed. These results experimentally demonstrate that the continuous, real time blood plasma separation could be accomplished by simply controlling the flow rate ratio at each bifurcation. As a final stage of this study, the plasma skimming volume % was experimentally determined by measuring hematocrit change between upstream and downstream of the separation region. In order to determine hematocrit from the images taken a hemocytometer image processing program (Figure 8), was prepared based on LabVIEW 7.0 (National Instruments Corporation, TX, USA). The hemocytometer was designed to find particles within a given region of interest (Fig. 8a) (ROI) and to count the number of particles (Fig. 8b, 8c). Using a RBC volume of 96 µm3 [26] the hematocrit within a known ROI volume is determined. Based on this procedure, the hematocrit at upstream and downstream positions was measured. In order to maintain same sampling condition, the same ROI areas are used at both positions. Figure 9 shows a significant change in the hematocrit distribution between the upstream and downstream of the separation region. The mean hematocrit at upstream (Hi) and downstream (Hf) of the separation region are 26.5 %, 39.7 % respectively. More detailed statistical information is described in table 1. Table 1. Statistical summary of Hct distribution Sample N Mean Hct SD SE Upstream 203 26.55369 3.52215 0.24721 Downstream 203 39.71626 5.53068 0.38818 N: # of images analyzed, SD: Standard Deviation, SE: Standard Error

In order to evaluate the statistical significance of the change in hematocrit between the upstream and downstream regions a, two sample t-test was applied with a level of significance (α=0.001) and the obtained P value was 3.83 × 1099 . Thus, the hematocrit distributions upstream and downstream of the bifurcation region are significantly different. It should be noted that the measured hematocrit in the upstream position is much lower that the infused hematocrit (26.5 versus 36). This is assumed to be due to Fahraeus effect [27] in which cells entering a small channel from a large reservoir will migrate towards areas of low shear creating a cell free layer close to the wall. This leads to a decrease in hematocrit within the small channel relative to the bulk hematocrit. Since the inlet hematocrit is 36 % and the upstream hematocrit is 26.5 %, there is about 9.5% hematocrit difference between the inlet and the upstream of the separation region because of the Fahraeus effect. However, this effect may also help increase the efficiency of the device as the cells migrate away from the wall and thus away from the critical streamline. Based on eq. 6, the plasma skimming volume % is about 33 %. It is surmised that the experimentally determined value is

Figure 8. A sequence of image processing used determination of plasma skimming volume % (a) representative original image used in image processing After finishing image processing (c) A overlay image of and (b).

in A (b) (a)

Figure 9. Histograms of Hct distributions at upstream and downstream of the separation region.

6



higher than predicted by the analytical analyses (27 %, 25% for 45 %, 39% hematocrit) because the plasma skimming volume % is also proportional to hematocrit, while the hematocrit were assumed to be constant in the computational simulations. In other words, as hematocrit increases throughout the device due to the skimming off plasma from the main channel, the fluid resistance in the main channel increases because the fluid viscosity also increases. Thus, the flow rate ratio between main and plasma channels decreases. Thus the plasma skimming volume also increases as hematocrit increases. CONCLUSIONS A microfluidic device for continuous, real time blood plasma separation is successfully designed and demonstrated. By combining various design techniques including an analogous electrical circuit, analytical, and numerical studies, a microfluidic device, which meet the design criteria (14:1 flow rate ratio at each bifurcation), is successfully designed and estimated. The theoretical study estimates that 27 % and 25 % of plasma can be collected from the total inlet blood volume for 45 % and 39 % hematocrit, respectively. The device’s functionality was clearly demonstrated using defibrinated sheep blood (Hct=36 %). The experimentally measured plasma skimming volume % was about 33 % for the 36 % inlet hematocrit and it is higher than simulated values. Due to the device’s simple structure and simple control mechanism, this microdevice is expected to be used for highly efficient continuous, real-time sample preparation for cell-free plasma preparation which may be analyzed in real-time on a downstream analysis system for continuous patient monitoring. ACKNOWLEDGMENTS This project is funded, in part, under a grant with the Pennsylvania Department of Health using Tobacco Settlement Funds. The Department specifically disclaims responsibility for any analyses, interpretations or conclusions. REFERENCES [1] G. Asimakopoulos (1999). "Mechanisms of the systemic inflammatory response. Perfusion." 14: 269-77. [2] I. Birdi, M. Caputo, M. Underwood, A. Bryan and G. Angelini (1999). "The effects of cardiopulmonary bypass temperature on inflammatory response following cardiopulmonary bypass." Eur. J. Cardiothorac. Surg. 16: 54045. [3] E. Fosse, T. Mollnes and B. Ingvalden (1987). "Complement activation during major operations with or without cardiopulmonary bypass." J. Thorac. Cardiovasc. Surg. 93: 860-66. [4] J. Kirklin and B. Barratt-Boyes (1993). Cardiac Surgery. New York. [5] J. Kirklin, D. Chenoweth and D. Naftel (1986). "Effects of protamine administration after CPB on complement, blood elements, and the hemodynamic state." Ann. Thorac. Surg. 41: 193-99. [6] J. Kirklin, S. Westaby, E. Blacstone, J. C. Kirklin, DE and A. Pacifico (1983). "Complement and the damaging effects of cardiopulmonary bypass." J. Thorac. Cardiovasc. Surg. 86: 845-57. [7] F. Moore, Jr, K. Warner and S. Assousa (1988). "The effects of complement activation during cardiopulmonary

bypass: attenuation by hypothermia, heparin, and hemodilution." Ann Surg. 208: 95-103. [8] G. Schlag, H. Redl and S. Hallstrom (1991). "The cell in shock: The origin of multiple organ failure." Resuscitation 21: 137. [9] J. B. Steinberg, D. P. Kapelanski and J. D. Olson (1993). "Cytokine and complement levels in patients undergoing cardiopulmonary bypass." J. Thorac. Cardiovasc. Surg. 106: 1008-16. [10] S. Westaby (1987). "Organ dysfunction after cardiopulmonary bypass: a systemic inflammatory reaction initiated by the extracorporeal circuit." Intensive Care Med. 13: 89-95. [11] J. R. Utley (1990). "Pathophysiology of cardiopulmonary bypass: current issues." J. Card. Surg. 5: 177-89. [12] R. D. Astumian (1997). "Thermodynamics and kinetics of a Brownian Motor." Science 276: 917-22. [13] P. Gascoyne, C. Mahidol, M. Ruchirawat, J. Satayavivad, P. Watcharasit and F. F. Becker (2002). "Microsample preparation by dielectrophoresis: isolation of malaria." Lab Chip 2(2): 70-75. [14] L. Huang, E. Cox, R. Austin and J. Sturm (2004). "Continuous particle separation through deterministic lateral displacement." Science 304(5673): 987-00. [15] J. Voldman, M. L. Gray, M. Toner and M. A. Schmidit (2002). "A microfabrication-based dynamic array cytometer." Anal. Chem. 74(16): 3984-90. [16] J. Yang, Y. Huang, X. B. Wang, F. F. Beker and P. R. C. Gascoyne (2000). "Differntial analysis of human leukocytes by dielectrophoretic field-flow-fractionation." Biophysical Journal 78(5): 2680-89. [17] M.-C. Bélanger, Y. Marois, R. Raynald, M. Yahye, W. Eric, Z. Ze, K. Martin W., Y. Mingjing, H. Charles and G. Robert (2000). "Selection of a polyurethane membrane for the manufacture of ventricles for a totally implantable artificial heart: Blood compatibility and biocompatibility studies." Artificial Organs 24(11): 879-88. [18] M. B. Gorbet, E. L. Yeo and M. V. Sefton (1999). "Flow cytometric study of in vitro neutrophil activation by biomaterials." Journal of Biomedical Materials Research 44(3): 289 - 97. [19] Y. C. Fung (1973). "Stochastic Flow in Capillary Blood Vessels." Microvasc. Res. 5: 34-48. [20] R. T. Yen and Y. C. Fung (1978). "Effects of Velocity Distribution on Red Cell Distribution in Capillary Blood Vessel." Am. J. Physiol. 235(2): H251-H57. [21] S. Yang and J. D. Zahn (2004). Particle Separation in Microfluidic Channels using Flow Rate Control. Proceedings of ASME Conference, International Mechanical Engineering Conference Exp Fluids Engineering: IMECE 2004- 60862. [22] D. Duffy, J. McDonald, O. Schueller and G. Whitesides (1998). "Rapid Prototyping of Microfluidic Systems in Poly(dimethylsiloxane)." Anal. Chem. 70(23): 4974-84. [23] Y. Xia and G. M. Whitesides (1998). "Soft Lithography." Annu. Rev. Mater. Sci. 28: 153-84. [24] L. Rosenhead (1963). Laminar Boundary Layer. New York, Dover Publications, inc. [25] F. J. Walburn and D. J. Schneck (1976). "A constitutive equation for whole human blood." Biorheology 13(3): 201-10. [26] Y. C. Fung (1993). Biomechanics: Mechanical Properties of Living Tissues, Springer. [27] J. H. Barbee and G. R. Cokelet (1971). "The Fahraeus effect." Microvasc. Res. 3: 6-16.

7

