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Supplementary materials
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Improvement of the accuracy of continuous hematocrit measurement
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under various blood flow conditions
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Myounggon Kim1 and Sung Yang1, 2,*
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500-712, Republic of Korea
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School of Mechatronics, Gwangju Institute of Science and Technology (GIST), Gwangju
Department of Medical System Engineering, GIST, Gwangju 500-712, Republic of Korea
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Information on the corresponding author
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Tel.: +82-62-715-2407
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Fax: +82-62-715-2384
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E-mail address: syang@gist.ac.kr.
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FIG. S1. HCT measurement error for (a) the modified and (b) the original blood models.
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FIG. S2. Relative differences between the measured HCT (HCTmeas) values using the modified and
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the original models.
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TABLE SI. Chi-square (χ2) values obtained from curve-fitting using two models for sample 1.
Opposite electrode
Longitudinal electrode
Shear rate
Original
Modified
Original
Modified
(W/o Cw)
(W/ Cw)
(W/o Cw)
(W/ Cw)
0
2.39 × 10-4
5.82 × 10-5
8.21 × 10-4
3.63 × 10-5
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1.73 × 10-4
5.66 × 10-5
8.04 × 10-4
4.70 × 10-5
87
1.43 × 10-4
5.51 × 10-5
8.23 × 10-4
5.10 × 10-5
208
1.29 × 10-4
5.40 × 10-5
8.44 × 10-4
5.57 × 10-5
347
1.17 × 10-4
4.96 × 10-5
8.35 × 10-4
5.53 × 10-5
521
1.04 × 10-4
4.51 × 10-5
8.24 × 10-4
5.43 × 10-5
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(s )
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Figs. S1a and b show the HCT measurement error (|(HCTref – HCTmeas) / HCTref × 100|)
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values predicted by the modified blood model with Cw and the original model without Cw,
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respectively. It turns out that the measurement of HCT utilizing the modified model has relatively
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high accuracy compared to the original one. Fig. S2 presents the reference HCT (HCTref), HCT
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measured by the modified model (HCTmeas,M), HCT measured by the original model (HCTmeas,O), and
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the relative difference ((HCTmeas,M - HCTmeas,O) / HCTmeas,M × 100) between the two HCT values. The
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maximum difference is approximately 10% . Table SI shows the chi-square (χ2) values obtained from
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the curve-fitting using two models for sample 1. The modified model has shown the smaller chi-
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square values for all cases compared with the ones of the original model. Also the similar results have
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been obtained from all other samples (2 to 6), which are not presented in here. It implies that the
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prediction based on the modified model has better accuracy in the curve-fitting of the impedance data
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obtained under various conditions (shear rates and electrode configurations). Therefore, the modified
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model has been applied for impedance analysis in this experiment.
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FIG. S3. (a) Experimental setup, and variation in (b) measured blood impedance and (c) HEP with
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time. The RBC infused into the device was stable during the experiments. This experimental setup
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solves the problem of RBC sedimentation in the syringe.
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The most important aspect of the experimental setup was the maintenance of the same
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number of RBCs flowing through the device during the experiments. Fig. S3a shows the experimental
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setup in which the blood was contained in a sealed glass bottle placed on a magnetic stirrer. The
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magnetic stirrer was rotated at 300 rpm and used to maintain the blood sample in an isotropic state.
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The blood sample was supplied to the device by the infusion of compressed air and its impedance was
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measured using a commercially available precision impedance analyzer (4294A; Agilent, CA, US).
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The impedance and HEP calculated from the measured impedance were constant during the
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experiments (Figs. S3b and c). The modified infusion method is therefore appropriate for continuous
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HCT measurement and eliminates concern about RBC sedimentation in the sealed glass bottle.
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FIG. S4. (a) Time-lapse images of the RBC flow obtained by image-based velocimetry. (b) Variation
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of the shear rate after stopping the pump, for input flow rate of 2.5 ml/min. The image was captured
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by a high-speed camera with a frame rate of 500 Hz.
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FIG. S5. Explanation of the effective area Aeff. Aeff is the sum of the total cross-sectional areas of all
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the RBCs that intercept the surrounding electric field. In the simplified model, 16 RBCs are located in
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a rectangular channel and the electrodes are on opposite walls and face each other. Here, (d)
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longitudinal, (e) slanted, and (f) vertical represent the cases of minimum, intermediate, and maximum
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effective areas. In the single RBC image, the color and line represent the magnitude of the current
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density and the electric field line, respectively. (a) The Nyquist plot was obtained using the simulation
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model, and the blood modeling parameters Ri and Rp were calculated by a curve-fitting procedure
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using the impedance data. (c) It shows the resistance (Rp and Ri) values for three kinds of orientation
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(longitudinal, slanted, and vertical) and the relative variation of the resistances for slanted and vertical
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orientations compared to the ones for longitudinal orientation. As the orientation changes from
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longitudinal to vertical, Rp increases owing to the hindrance of the current flow. And the relative
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variation of Rp is about 9.6% and 20.1% for the slanted and the vertical orientations, respectively.
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The simplified model was simulated using COMSOL 4.2. The diameter and volume of the
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single RBC were 7.8 μm and 94 μm3, respectively. Further information about the geometry of the
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RBC was obtained from the work of Fung.1 A single-shelled model was used for the RBC and was
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considered to be a dielectric material. Some of its electrical properties are listed in Table SII.2
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TABLE SII. Diagram and parameters for the electrical modeling of the RBC
Electrical modeling
(Single shell)
Item
Conductivity (s/m)
Relative permittivity
Cytoplasm
σcyto = 0.31
εcyto = 59
Membrane
σmem = 1E-6
εmem = 4.44
PBS
σm = 1.6
εm = 80
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FIG. S6. Variation of the impedance of the blood sample (RBC in PBS) with time.
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FIG. S7. Simulation results for the behavior of the impedance during the RBC sedimentation process.
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(a) In the simplified model, 9 RBCs are placed in a rectangular channel and the electrodes are located
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on opposite walls and face each other. This is similar to the previous simulation model (Fig. S4). The
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state of Sedimentation 2 and Sedimentation 3 represent that of the RBCs sedimented from the initial
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state (Sedimentation 1) with respect to the time. (b) The magnitude of the impedance of the simulated
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blood decreases with the sedimentation, which is in agreement with the experimental results (Fig. S5).
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(c) Ri and Rp respectively increase and decrease with the sedimentation.
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To confirm the variation of the blood impedance with the sedimentation, a simplified blood
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model was simulated using the COMSOL 4.2 software. The magnitudes of the impedance of the
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simulated blood (Fig. S7b) and Ri (Fig. S7c) respectively decreased and increased with the
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sedimentation, which is in agreement with the experimental results.
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Non-physiological hemodynamics, including extremely high shear stress, turbulence, and
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prolonged contact between RBCs and foreign surfaces, may induce various kinds of damage to the
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blood, such as the activation of platelets, increasing aggregation, decreasing deformability, and the
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release of free hemoglobin into the plasma.3 The threshold level of hemolysis is shear stress of
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approximately 150 Pa for exposure times on the order of 102 s or over shear rate of 2000 s-1.3, 4 The
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employed experimental conditions, as described in the manuscript, were 417 s-1 (τ = 1.2 Pa) for an
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exposure time of approximately 180 s. Thus, we believe that the damage on RBCs, which may cause
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the change in the rheological properties of blood, will be minimal and shows the independency of the
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aggregation process on the history of shear driven deformation.
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FIG. S8. Nyquist plot for (a) the OE configuration and (b) LE configuration.
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FIG. S9. Explanation on the HEP characteristics for LE configuration. (a) The value of HEP changes
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significantly in the high-shear region. The recessed region is located between the two electrodes of the
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PCB-based device. (b) Blood flow in the recessed region. The line and color represent the stream line
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and magnitude of the velocity, respectively. The cell depletion zone (CDZ) in the recessed region
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increases with increasing shear rate owing to the inertial force of the RBC. This shows that the HEP is
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sensitive to changes in the shear rate.
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References
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1
Y.C. Fung, Biomechanics Mechanical Properties of living tissues, 2nd, Springer (1993).
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S. Park, Y. Zhang, T.H. Wang, and S. Yang, Lab Chip 11, 2893 (2011).
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Hemodynamics, Ch. 5, IOS Press, (2007).
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H. Reul, B. Meyns, Aftif. Organs, 31, 316 (2007).
O.K. Baskurt, M.R. Hardeman, M.W. Rampling, H.J. Meiselman, Handbook of Hemorheology and
I. Bakir, M.F. Hoylaerts, T. Kink, L. Foubert, P. Luyten, S. Van Kerckhoven, V. Leunens, H. Bollen,
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