where Ue is the jet exit velocity, de is the jet exit diameter (3 mm), and ν is the kinematic viscosity of the fluid. The fixture has dimensions of 51 × 51 × 254 mm and is made from acrylic and stainless steel. The jet entrance, where phosphate buffered saline (PBS) enters the fixture, has a diameter of 3 mm. A beveled 17G needle is used for the infusion of washed bovine RBCs into the fixture. An aspirator with a 1 mm diameter opening is used to collect samples at a nondimensional downstream distance of x/de = 6.5 and y/re = 1.2, where re is the jet exit radius (1.5 mm). Two syringe pumps were used to maintain constant flow rates for blood infusion (Harvard Apparatus, Holliston, MA) and sample collection (New Era Pump Systems, Inc., Farmingdale, NY). The original design by Sallam and Hwang7 was modified for these experiments by the addition of a support beam for the aspirator, which was necessary to eliminate vibration and movement at high Re. In addition, a hydrophone was added on the top surface of the chamber in order to monitor the presence of cavitation in the jet.
Blood Sample Preparation
Whole bovine blood was collected by LAMPIRE Biological Laboratories in CPDA-1 collection bags (LAMPIRE Biological Laboratories, Inc., Pipersville, PA), and delivered overnight in a freezer-packet cold box. An additional 1.5 ml of heparin (10,000 United States Pharmacopeia units/ml) and 1 ml of tobramycin (40 mg/ml) were added to each unit of blood to ensure no clotting during testing. Washed RBCs were obtained by centrifuging the whole blood at 1,000g for 10 minutes and replacing the plasma with PBS. Washed bovine RBCs were resuspended in PBS to achieve a hematocrit (HCT) of 50%. All blood samples were used within 2 days after the date of harvest.
At each given Re, washed RBCs resuspended in PBS were injected into the free jet of PBS through a beveled 17G needle at a flow rate of 54 ml/min. Once blood began to enter the chamber, 10 ml of waste was drawn over 10 seconds, followed by 20 ml of sample drawn over 3.5 seconds.
Lysed Sample Collection
Samples were collected through an aspirator located at x/de = 6.5 and y/re = 1.2 at a rate of 60 ml/min. The sampling location of x/de = 6.5 and y/re = 1.2, which is believed to be a peak hemolytic location, was selected based on the study of Sallam and Hwang.7 A hydrophone and high speed video detected cavitation at Re = 80,000; however, the pressure was raised to 2.37 atm and the cavitation signal disappeared. Either a stainless steel Dayton gear pump (W. W. Grainger, Inc., Lake Forest, IL) or a plastic centrifugal pump (MD-70RZ(T); Iwaki America, Holliston, MA) was used to circulate PBS through the flow loop connecting a 40 L tank with the fixture.
Measure of Hemolysis
The free and total hemoglobin analysis was performed using spectrophotometric technique by Harboe.22 For free hemoglobin measure, the 2 ml tubes were centrifuged for 10 minutes at 1,000g. For each experiment, four 300 μL samples were placed in a 96 well plate for analysis. Initial samples were further diluted by adding an equal amount of PBS to the samples. For total hemoglobin determination, 0.5 ml of sample was added to 2 ml of deionized water. The mixture then sat for at least 10 minutes followed by centrifugation at 1,500g for 30 minutes to separate out cell membranes. After centrifugation, 100 μl of sample was added to 15 ml PBS. Free hemoglobin and total hemoglobin were measured using a spectrophotometer (BioTek Instruments, Inc., Winooski, VT) and characterized using the equation by Harboe22 shown in Equation 2 as follows:
where A380, A415, and A450 are the light absorbance at wavelengths of 380, 415, and 450 nm, respectively.22 To measure HCT on each sample of 50 μL, an automated hematology analyzer (Sysmex KX-21N; Sysmex America, Inc., Lincolnshire, IL) employing a dynamic focusing direct current (DC) detection method was used to measure HCT. Finally, hemolysis was quantified using a percent hemolysis parameter, Hp, shown in Equation 3 as follows:
where h (mg/dl) is free hemoglobin in suspending medium, HCT (%) is hematocrit, and Hb (mg/dl) is the total concentration of hemoglobin when all RBCs in the sample have been lysed.23
All values reported in the table and plotted in the figures are expressed as mean ± standard deviation. Statistical significance was assessed using the Student’s t-test. Significance level was set as p < 0.05.
Laser Doppler Velocimetry
We manufactured an acrylic model of the SA for use in laser Doppler velocimetry (LDV) experiments to determine the Reynolds normal and shear stresses. Because it is known that the measure of a nondimensionalized RSS is constant over Re (i.e., RSS for the jet is linearly dependent on Re), LDV data for the Reynolds stresses were collected only at Re = 20,000.7,10 Specifics of the LDV system can be found in Taylor et al.24
A fluid composed of 37% H2O/63% sodium iodide (NaI) by weight was used to match the refractive index of acrylic (n = 1.49). The fluid had a kinematic viscosity (ν) of 1.45 centistokes (cSt) at 25°C and a density of 1,891 kg/m3. A heat exchanger was used in the flow loop to ensure the fluid remained at 25°C for the duration of the experiment, and a centrifugal pump (Cole-Parmer, Vernon Hills, IL) was used to produce a steady flow rate of 4.1 L/min. This yielded an average nozzle exit velocity (Ue) of 9.67 m/s and a nozzle Re of 20,000.
Despite examining the hemolysis only at x/de = 6.5 and y/re = 1.2, we mapped the entire flow field in our LDV experiment for a rigorous comparison to the study by Sallam and Hwang.7 As illustrated in Figure 2, coincident axial and radial velocities were collected at seven downstream locations, i.e., x/de = 1, 2, 3, 4.5, 5.5, 6.5, and 8.5. Coincidence was established using a 100% gate scale setting. At each downstream location, velocity data were collected at 14 radial locations, starting at the center of the jet and moving radially, i.e., y/re from 0 to 1.73 in increments of 0.2 mm (i.e., y = 0–2.6 mm). The probe volume was an ellipsoid with major and minor axes of 275 and 35 µm, respectively, with the minor axes in the axial and radial directions. Ten thousand 2D velocity measurements were made at each spatial location.
The LDV data were filtered following the procedure of Baldwin et al.13 with an in-house MATLAB code, using an elliptical filter of four standard deviations to remove outliers from the data set. A value of four standard deviations was chosen as this value removed approximately 1% of the data set.
Reynolds Shear Stress
A custom MATLAB code with 2D LDV data was used to calculate RSS and principal RSS at x/de = 6.5 and y/re = 1.2. Note that the RSSs are not invariant to coordinate rotation, thus, it is important to calculate the principal RSS, which is potentially greater than those calculated in the coordinate system used for this experiment. The velocity fluctuations u′ and v′ are defined as the deviations of instantaneous velocities u and v, respectively, from their average values as shown in Equations 4 and 5 as follows:
The RSS and principal RSS shown in Equations 6 and 7, respectively, were normalized by Ue2, and fluid density, ρ, which is the same procedure that Sallam and Hwang7 used,
is RSS and
are Reynolds normal stresses, calculated using Equations 8–10 as follows.
Hemolysis Results for Sallam Apparatus
Hemolysis results are shown in Table 3. The Hp calculated with the results shown in Table 3 over Re is also shown in Figure 3. Based on the data presented in Figure 3, hemolysis in the SA was not obvious at Re of up to 50,000; however, the inception of hemolysis appeared at Re = 60,000 (p = 0.004) and increased exponentially with Re in our experimental conditions.
Reynolds Shear Stress from Laser Doppler Velocimetry
The entire map of normalized principal RSS (i.e., RSSmax) and RSS at x/de from 1 to 8.5 and y/re from 0 to 1.73 for Re = 20,000 is shown in Figure 4. From the LDV, the maximum normalized value of principal RSS and RSS at x/de = 6.5 and y/re = 1.2 were found as 96 and 75, respectively, and these can be converted into 4,270 and 3,336 dyne/cm2 with a given density of 1,000 kg/m3 and jet exit velocity of 6.67 m/s at Re = 20,000 used in our hemolysis testing. Although understanding the principal RSS (or RSSmax) being greater than RSS by 30%, we used the normalized RSS value of 75 to calculate the RSS values for the rest of the Re conditions shown in Table 2. The RSS over Re is shown in Figure 5.
Based on the results shown in Figure 3 and Figure 5, it should be reasonable to conclude that the inception of hemolysis occurs at RSS equal to or greater than 30,000 dyne/cm2. The inception of hemolysis and RSS can be represented as shown in Figure 6. In our study, hemolysis was not apparent at RSS less than 30,000 dyne/cm2; however, once the RSS passed 30,000 dyne/cm2, hemolysis increased in a nonlinear fashion with increasing RSS.
We recreated the turbulence jet apparatus by Sallam and Hwang7 to investigate the hemolytic RSS values. In our study, a RSS of 30,000 dyne/cm2 was found to be hemolytic, which is an order of magnitude greater than the threshold value of 4,000 dyne/cm2 reported by Sallam and Hwang.7
Other groups have tried to resolve the discrepancy on the hemolytic RSS values. Grigioni et al.9 applied 3D stress analysis to the original 1D LDA measurements by Sallam and Hwang7 and found that the principal RSS causing the inception of hemolysis should be “at least” 6,000 dyne/cm2. Lu et al.10 reinvestigated the study by Sallam and Hwang7 by using 2D LDA under similar conditions and found, based on the principal RSS, that the hemolytic threshold should actually be “greater than” 8,000 dyne/cm2. Note that no blood testing was involved in the studies of Grigioni et al.9 and Lu et al.,10 and they never provided a definitive number for “threshold” RSS values.
Yen et al.3 suggested a hemolytic RSS threshold of 5,170 dyne/cm2 from their in vitro study with the porcine blood. However, the spatial resolution of 190 µm with 1,000 frames of the PIV may not be sufficient to capture the smaller turbulent eddies in the flow fields that might have played an important role in causing hemolysis. Liu et al.25 concluded that the smallest turbulent length scale—which offers a more reliable estimate of the effects of turbulence on blood cell damage—was three times the size of a RBC (i.e., approximately 30 µm) and five times the size of platelets. It is known that when the Reynolds number is sufficiently high, the Kolmogorov (smallest) scale eddies can be roughly the size of the RBC and blood damage is possible.26 For this study, we characterized the fluctuating flow fields by using a LDV system with an ellipsoidal probe volume with major and minor axes of 275 and 35 µm, respectively. Having a radial resolution of 35 µm is considered to be much more accurate in capturing small eddies, if not the smallest, affecting blood cell damages. Ten thousand 2D velocity measurements were made at each spatial location, yielding a higher accuracy in measuring RSS values.
It is interesting to note from the study of Lu et al.10 that they found the normalized maximum RSS and principal normalized RSS of 75 and 93, respectively, at x/de = 6 and y/re = 1.2 that are similar to what we found at x/de = 6.5 and y/re = 1.2 in our study (Figure 4). They found no significant effects on the flow field characteristics including the principal RSS from their three different Reynolds numbers. This confirms that our RSS values derived by using the normalized RSS of 75 (or RSSmax of 96) at Re = 20,000 for other Re conditions should be acceptable.
Note that washed RBCs resuspended in PBS were injected into the free jet of PBS. According to Kameneva et al.27 and Sümpelmann et al,28 the fragility of RBCs increases approximately by 3–4 times when RBCs are suspended in saline as opposed to plasma, thus, the critical value of RSS found in the current study may increase by the same factor if it were suspended in plasma. Nevertheless, an order of magnitude underestimation of the critical RSS suggested by Sallam and Hwang7 is still noticeable from this comparative study.
Remarks on Reynolds Stress
In fact, Reynolds stress (often used interchangeably with turbulence stress) is not a physical stress3 and only results from the use of the Re-averaged Navier-Stokes (RANS) equation.11,29 Under certain conditions, there is a correlation between hemolysis and RSS but that correlation does not imply causation. Taskin et al.30 demonstrated that hemolysis index measurements and predictions over different flow rate conditions with different sets of power law constants showed up to two order of magnitude differences in a custom hemolyzer and up to three order of magnitude differences in the CentriMag pump (Thoratec Corp., Pleasanton, CA). Along with Ozturk et al.,31 there is strong evidence that the Kolmogorov scale eddies and the attendant dissipation are a better measure of the effects of turbulence on hemolysis and should be included in any advanced model of hemolysis.3,32,33 We are currently testing our recently developed physics-based hemolysis model by employing the energy dissipation.
Study Limitations and Future Study
Note that the current study used bovine RBCs, and Sallam and Hwang7 used human RBCs. Jikuya et al.34 found that the mechanical fragility of bovine and ovine RBCs was 0.5 and 1.8 times as large as human RBCs, respectively. Thus, the RSS threshold that the current study found may be lesser with human RBCs at given conditions, but it is not an order of magnitude difference. We used the centrifugation that Sallam and Hwang7 used for a fair comparison; however, the centrifugation used in Ziegler et al.,35 for example, may affect the RSS threshold found in the current study. Note that this study used only one peak location (i.e., x/de = 6.5, y/re = 1.2) for assessing hemolysis because of turbulence. A second point somewhere else within the turbulent jet is warranted for further validation of the study.
This study investigated the threshold of 4,000 dyne/cm2 for hemolytic RSS suggested by Sallam and Hwang7 by characterizing the flow fields under a wide range of Reynolds numbers. In our study, a RSS of 30,000 dyne/cm2 was found to be hemolytic, which is an order of magnitude greater than the RSS threshold of 4,000 dyne/cm2 reported by Sallam and Hwang.7 The RSS threshold found in our study is consistent with the values reported by Blackshear et al.4 and Forstrom5 of 30,000 and 50,000 dyne/cm2, respectively. Because the estimation of the critical value of mechanical destruction on RBC damage in terms of both shear stress and exposure time is central, understanding the definite hemolytic RSS value should be an important step in the study of hemolysis. Our experimental results are significant because they have resolved a long-standing discrepancy regarding the critical values of RSS for hemolysis and may provide a foundation for a more accurate hemolysis model.
This study was supported by the National Institutes of Health (R56HL060276).
1. Baldwin JT, Deutsch S, Geselowitz DB, Tarbell JM. LDA measurements of mean velocity and Reynolds stress fields within an artificial heart ventricle. J Biomech Eng 1994.116: 190–200.
2. Antiga L, Steinman DA. Rethinking turbulence in blood. Biorheology 2009.46: 77–81.
3. Yen JH, Chen SF, Chern MK, Lu PC. The effect of turbulent viscous shear stress on red blood cell hemolysis
. J Artif Organs 2014.17: 178–185.
4. Blackshear PL Jr, Dorman FD, Steinbach JH, Maybach EJ, Singh A, Collingham RE. Shear, wall interaction and hemolysis
. Trans Am Soc Artif Intern Organs 1966.12: 113–120.
5. Forstrom RJ. A New Measure of Erythrocyte Membrane Strength—The Jet Fragility Test. 1969.Minneapolis, University of Minnesota,
6. Sutera SP, Mehrjardi MH. Deformation and fragmentation of human red blood cells in turbulent shear flow. Biophys J 1975.15: 1–10.
7. Sallam AM, Hwang NH. Human red blood cell hemolysis
in a turbulent shear flow: Contribution of Reynolds shear stresses. Biorheology 1984.21: 783–797.
8. Tamagawa M, Akamatsu T, Saitoh K. Prediction of hemolysis
in turbulent shear orifice flow. Artif Organs 1996.20: 553–559.
9. Grigioni M, Daniele C, D’Avenio G, Barbaro V. A discussion on the threshold limit for hemolysis
related to Reynolds shear stress
. J Biomech 1999.32: 1107–1112.
10. Lu PC, Lai HC, Liu JS. A reevaluation and discussion on the threshold limit for hemolysis
in a turbulent shear flow. J Biomech 2001.34: 1361–1364.
11. Schlichting H, Gersten K. Boundary-Layer Theory, 2000.8th rev. and enl. ed. Berlin, New York, Springer,
12. Matsuzawa T, Ikarashi Y. Haemolysis of various mammalian erythrocytes in sodium chloride, glucose and phosphate-buffer solutions. Lab Anim 1979.13: 329–331.
13. Baldwin JT, Deutsch S, Petrie HL, Tarbell JM. Determination of principal Reynolds stresses in pulsatile flows after elliptical filtering of discrete velocity measurements. J Biomech Eng 1993.115(4A): 396–403.
14. Untaroiu A, Wood HG, Allaire PE, et al. Computational design and experimental testing of a novel axial flow LVAD. ASAIO J 2005.51: 702–710.
15. Deutsch S, Tarbell JM, Manning KB, Rosenberg G, Fontaine AA. Experimental fluid mechanics of pulsatile artificial blood pumps. Annu Rev Fluid Mech 2006.38: 65–86.
16. Yang N, Deutsch S, Paterson EG, Manning KB. Comparative study of continuous and pulsatile left ventricular assist devices on hemodynamics of a pediatric end-to-side anastomotic graft. Cardiovasc Eng Technol 2010.1: 88–103.
17. Kameneva MV, Burgreen GW, Kono K, Repko B, Antaki JF, Umezu M. Effects of turbulent stresses upon mechanical hemolysis
: Experimental and computational analysis. ASAIO J 2004.50: 418–423.
18. Zhang P, Yeo JH, Qian P, Hwang NH. Shear stress investigation across mechanical heart valve. ASAIO J 2007.53: 530–536.
19. Sallam AM. An Investigation of the Effect of Reynolds Shear Stress
on Red Blood Cell Hemolysis
. 1982.Houston, TX, University of Houston,
20. Kirklin JK, Naftel DC, Pagani FD, et al. Seventh INTERMACS annual report: 15,000 patients and counting. J Heart Lung Transplant 2015.34: 1495–504.
21. Arwatz G, Smits AJ. A viscoelastic model of shear-induced hemolysis
in laminar flow. Biorheology 2013.50: 45–55.
22. Harboe M. A method for determination of hemoglobin in plasma by near-ultraviolet spectrophotometry. Scand J Clin Lab Invest 1959.11: 66–70.
23. Sowemimo-Coker SO. Red blood cell hemolysis
during processing. Transfus Med Rev 2002.16: 46–60.
24. Taylor JO, Good BC, Paterno AV, et al. Analysis of transitional and turbulent flow through the FDA benchmark nozzle model using laser Doppler velocimetry
. Cardiovasc Eng Technol 2016.7: 191–209.
25. Liu JS, Lu PC, Chu SH. Turbulence characteristics downstream of bileaflet aortic valve prostheses. J Biomech Eng 2000.122: 118–124.
26. Dooley PN, Quinlan NJ. Effect of eddy length scale on mechanical loading of blood cells in turbulent flow. Ann Biomed Eng 2009.37: 2449–2458.
27. Kameneva MV, Antaki JF, Yeleswarapu KK, Watach MJ, Griffith BP, Borovetz HS. Plasma protective effect on red blood cells exposed to mechanical stress. ASAIO J 1997.43: M571–M575.
28. Sümpelmann R, Schürholz T, Marx G, Zander R. Protective effects of plasma replacement fluids on erythrocytes exposed to mechanical stress. Anaesthesia 2000.55: 976–979.
29. Tennekes H, Lumley JL. A First Course in Turbulence. 1972.Cambridge, MA, MIT Press,
30. Taskin ME, Fraser KH, Zhang T, Wu C, Griffith BP, Wu ZJ. Evaluation of Eulerian and Lagrangian models for hemolysis
estimation. ASAIO J 2012.58: 363–372.
31. Ozturk M, O’Rear EA, Papavassiliou DV. Hemolysis
related to turbulent eddy size distributions using comparisons of experiments to computations. Artif Organs 2015.39: E227–E239.
32. Jones SA. A relationship between Reynolds stresses and viscous dissipation: Implications to red cell damage. Annals Biomed Eng 1995.23: 21–28.
33. Morshed KN, Bark D Jr, Forleo M, Dasi LP. Theory to predict shear stress on cells in turbulent blood flow. PLoS One 2014.9: e105357.
34. Jikuya T, Tsutsui T, Shigeta O, Sankai Y, Mitsui T. Species differences in erythrocyte mechanical fragility: Comparison of human, bovine, and ovine cells. ASAIO J 1998.44: M452–M455.
35. Ziegler LA, Olia SE, Kameneva MV. Red blood cell mechanical fragility test for clinical research applications. Artif Organs 2016. Dec 7. doi: 10.1111/aor.12826. Epub ahead of print.
Keywords:Copyright © 2018 by the American Society for Artificial Internal Organs
hemolysis; Reynolds shear stress; turbulence jet; laser Doppler velocimetry; Kolmogorov scale