The material of most blood contacting surfaces was titanium. The capillary tube was made of stainless steel, with an inner diameter of 0.027 inches and a length of 12 inches. A warmed nitrogen purge flow was used above the spinning disk to avoid contact with oxygen. The glass bead test used a 13 × 100 mm test tube (Curtis-Matheson Scientific No. 055–863), with eight glass beads (4 mm in diameter, made of solid flint glass, Thomas Scientific No. 5663L19) and 5 ml of bovine blood. For the stainless steel bead test, the cap was removed from a 7 ml red topped vacutainer tube (Becton Dickinson No. 367819), five 1/8 inch diameter balls (McMaster-CARR No. 96415K71) were inserted, and 3 ml of bovine blood was added to the now recapped tube. The tube was then rocked on a shaker at room temperature (22–23°C). Only the stainless steel bead test was operated at room temperature, as stated in Kameneva’s protocol.8 All other tests were performed at 37°C. All test devices used bovine whole blood, without resuspension in other fluids or filtering. During the actual testing, the blood was kept at 37°C in the water bath used for the Biopump testing. A control sample was taken before each test and repetition.
Initially, it was decided to run each device at a speed that would produce shear stresses in the nominal range of 3,000 dynes/cm2. The “threshold” stress for significant hemolysis has been estimated to be in the range of 1,500–7,000 dynes/cm2;19 the stress of 3,000 dynes/cm2 should produce a significant amount of hemolysis so that our measurement technique does not have to differentiate minor differences in free hemoglobin, without homogenizing the blood, as might happen at very high speeds. However, as discussed in the following sections, practical issues dominated the final speed choices. For the hemoresistometer, because the geometry of the rotating cube is complex, there is no existing equation for the calculation of shear stress in the device. Therefore, we chose from the literature1 a running speed of 3,300 rpm and a time period of 15 minutes. For the spinning disk, when we ran the device at the calculated speed,2 we experienced very severe blood foaming. As a result, we decreased the speed until there was no foaming during a test period of 15 minutes. The final speed we used was 600 rpm. For the concentric cylinder viscometer, a speed of 2,400 rpm was calculated from empirical equations20 and used for the study, with the same test duration of 15 minutes. The syringe pump used a 50 cc syringe to drive blood through the capillary tube at an average velocity of 7.15 m/s, which would produce a shear stress of 3,000 rpm. The test tube shaker (Barnstead/Thermolyne Model M48725) oscillated at its maximum speed, 20 cycles/minute, to perform the bead tests. The shaker is able to operate with 16 test tubes in each test. Table 1 supplies some key characteristics of the test devices.
Test Pump and Running Conditions
The test pump was a Biopump BP80 (Medtronic-Biomedicus, Minneapolis, MN), driven by a CCF built driver, which used a magnet assembly supplied by Biomedicus. The test conditions were 5 L/min flow rate and 100 mm Hg pressure rise. The test duration was 4 hours, based upon the protocol developed at the Cleveland Clinic Foundation.19 The hemolysis test set up is shown in Figure 6. The circulating water bath maintains a 37°C blood temperature. The loop is first primed with 0.9% saline, to remove air, and then a maximum amount of saline drained before infusing 2 units (approximately 1 L) of blood into the circuit, through a 5 micron filter (Pall blood transfusion filter P/N SQ40S, Pall Biomedical Inc., Fajardo, PR). Total fluid volume for calculations includes both actual infused blood and residual saline. The circuit is pumped briefly to mix the fluid, and a control syringe of blood is withdrawn. During a 4 hour test, blood samples are withdrawn every hour from the loop and the control syringe. These samples are immediately centrifuged twice and frozen until assayed.
The measurement of hemoglobin used a method from Sigma, based upon Drabkin’s solution (Sigma No. 525-A),21 which contained potassium cyanide and potassium ferricyanide. When mixed with Drabkin’s solution, the hemoglobin will be oxidized by potassium ferricyanide to methemoglobin, which in turn reacts with potassium cyanide to form cyanmethemoglobin. Because the cyanmethemoglobin has maximum absorption at 540 nm, the hemoglobin concentration could be determined by a spectrophotometer (Beckman Coulter Model DU 640B) at this wavelength.
Initial Test Series
To compare the candidate calibrators, we performed an initial test series with two batches of bovine blood. For each batch of blood, a series of tests were performed on 4 consecutive days. We believed that aging would increase mechanical fragility and increase the range of data. On each test day, three repeat tests were made with each test device while the pump test was running simultaneously. The pump was tested once a day because it used a larger volume of blood and the run took a much longer time.
Second Test Series
In the second test series, a smaller number of candidate devices (based upon the results of the first test series and ease of use) and the pump were compared again, using three more batches of blood and more repeats. The stainless steel bead test, which was not involved in the first test series, was included in the second tests series, after Dr. Marina Kameneva, of the University of Pittsburgh, recommended it to us. The test protocol was supplied by Dr. Kameneva.8
Characterization of Fragility
For the pump, the index of hemolysis (IH) was used to characterize the fragility. The definition of IH (g/100L) is as follows:
where V (L) is the volume of the blood in the loop, Ht is the hematocrit, ΔfHb (g/L) is the increment of free hemoglobin during a time period of t (min), and F (L/min) is the flow rate. This form of equation was first published by Koller and Hawrylenko22 in 1967, and later by Naito23 in 1994, and is now defined as the “normalized index of hemolysis.”
For the test devices, mechanical fragility was characterized by ΔfHb (g/dl), as calculated by the following equation:
where fHbt (g/dl) and fHbc (g/dl) are the free hemoglobin concentration of test sample and control sample, respectively.
In the second test series, the fragility was also characterized by an index of hemolysis for a device, or Device-IH, as shown in Equation 3
where fHbtotal is the total blood hemoglobin concentration.
Principal component analysis24 was used to test our first hypothesis that all test devices and the Biopump measured the same property of blood. It was expected that each device would have a different level of hemolysis, but the trends should be the same if the same characteristic of blood was being measured. Analysis of the eigenvalue decomposition of the Z matrix (obtained from the data set) provides an indication of how much information content each eigenvector carries. Only eigenvalues greater than unity were considered.25 The analysis involves the calculations of eigenvalues and eigenvectors of the Z matrix, as defined by the following equation:
where Z is the data set matrix, x is the eigenvector, and λ is the eigenvalue. Equations 5 and 6 were used to calculate eigenvalues and eigenvectors, respectively.
where “det” stands for determinant, I is a unit matrix, and xi is the eigenvector associated with the ith eigenvalue, λi.
Correlation analysis was used to select the best candidate calibrators after the initial tests had been performed. The correlation coefficient r is the covariance of two data sets divided by the product of their standard deviations.26 Another criterion for the selection was the ease of performance for each test device.
Many equations exist to estimate the sample size, with different assumptions and applicable usages. In this case, the population variance was unknown. The operating characteristic curves provided by Hines and Montgomery27 plot type II error β against a parameter d for various sample sizes n. Curves are provided for both the two sided and one sided alternatives and for α = 0.05 or α = 0.01. For the two sided alternative, the abscissa scale factor d is defined as
where μ and μ0 are the mean of the true population and test samples, respectively. If one wishes to detect a small difference in the mean, one might use a value of d ≤ 1. Once d is selected, a sample size n will be determined from the characteristic curves.
Initial Test Results
Table 2 shows the initial test results obtained with batch 1 and batch 2 blood. As expected, as the blood aged, hemolysis increased. The blood fragility caused by the five test devices follows the same trend. Among the results obtained from the five test devices, the capillary tube has the lowest level of hemolysis, and the concentric cylinder viscometer has the highest level of hemolysis, approximately three orders higher than that of the capillary tube. The levels of hemolysis caused by hemoresistometer, spinning disk, and the glass bead test are of the same order and fall between the level of the concentric cylinder viscometer and the level of the capillary tube.
Testing the first hypothesis.
The first hypothesis of this study is that the relative mechanical fragility of the blood is a property of the blood and does not depend upon the testing devices. To test this hypothesis, a principal component analysis of the data set matrix (including pump data) was performed, using Equations 5 and 6. As shown in Table 3, only one eigenvalue was greater than unity. Other eigenvalues were excluded from consideration because they were less than unity.25 The existence of only one eigenvalue means that each test device and the pump represent the same data population for mechanical fragility of the blood.
Testing for usefulness as a calibrator.
To identify the most practical candidates for calibration devices, correlation analysis was performed. Table 4 shows the correlations between pump and each test device, based upon the initial test results.
Table 4 shows that the hemoresistometer has highest correlation with pump for all three columns (all > 0.800). This device was not very difficult to operate. Therefore, it was chosen as one candidate.
The disk device had good correlation with the pump for batch 1 and batch 2 blood individually, but not with the combination of the two batches. However, also considered was following subjective sequence of ease of performance for all the five test devices (with easiest at first place):
The disk device was most difficult to work with. Thus, the spinning disk was not chosen as a candidate for a practical, routine use calibrator.
Another choice was the capillary tube. This device had good correlation with pump with batch 1 blood and the combination of both batches of blood (both > 0.800), but not with batch 2 blood. Why this would occur is not clear. However, because of its ease of performance, it was chosen as another candidate, and the sample size was increased in the second test series to further determine its correlation with the pump.
Based upon the correlations between each device and pump, and the ease of use, the hemoresistometer and the capillary tube were chosen as candidate calibrators for the RBC mechanical fragility, with respect to the Biopump BP80. Additionally, the stainless steel bead, rather than glass bead test, was evaluated in the second test series, based upon the good experience in Kameneva’s lab.
Determination of sample sizes for the second test series.
From the operating characteristic curves provided by Hines and Montgomery,27 when we chose d = 1, a sample size of n = 10 was obtained for the two sided t-test for a level of significance α = 0.05 and a power of 1 − β = 80%. For the second test series, each candidate device was tested 12 times on each test day, except for the stainless steel bead tests with batch 3 blood because this was the first test with this new test system.
Second Test Results
Table 5 shows the second test results obtained with blood batches 3, 4, and 5. With batch 3 and batch 4 blood, the tests were performed on 4 consecutive days, similarly to the first tests. With batch 5 blood, the tests were performed on 3 nonconsecutive days (days 1, 4, and 7, respectively), instead of on 4 consecutive days because less blood was obtained and a greater range of fragility was desired.
Again, with the blood getting older, the hemolysis caused by the pump increased. The blood fragility caused by the three test devices follows the same trend. Among the results obtained from the three test devices, the capillary tube has the lowest level of hemolysis. The level of hemolysis caused by the hemoresistometer is one order higher than that caused by the capillary tube.
Rechecking the first hypothesis.
Table 6 shows the principal component analysis results performed with the second test results. Only one eigenvalue was greater than unity, which reconfirmed the hypothesis that all devices measured the same mechanical fragility. Because of the larger sample size, this principle component analysis is even more convincing than the first analysis, with respect to the relevance of these tests to pump test results.
Rechecking the pump/calibrator correlations.
Table 7 shows the correlations between pump and each test device. The correlations in the “Overall” column are more interesting in that they were from a bigger data set. The numbers in this column show that the capillary tube has the worst correlation with the pump, and the HR has the best correlation. It is also shown that HR-IH and SS Bead-IH have very close correlation with the pump. Figure 7 plots the correlation between the pump testing and the calibration device testing. As shown, the stainless steel bead test and the hemoresistometer have good fit to the points, but the stainless steel bead test has a non-zero intercept with the axis. Presumably this represents hemolysis caused by an additional crushing action not present in the Biopump or most other blood pumps. This runs counter to the mathematical analysis, which does not reveal a fundamental difference between pump and bead test. Perhaps a more sophisticated test series would reveal a lower level effect.
Reduction of Sample Sizes
Using the mean and standard deviation values for each device as shown in Tables 2 and 5, the sample sizes needed for a statistical significance of 0.05 and a power of 80% were recalculated. The method from Hines and Montgomery27 was still used, and two conditions were considered: | δ | = | μ − μ0 | = 50% of sample mean, and | δ | = | μ − μ0 | = 25% of sample mean. For each of these two conditions, an abscissa scale factor d was calculated, and a sample size was then obtained from reading the characteristic curves. The results in Table 8 show that when | δ | = | μ − μ0 | = 50% of sample mean, the pump test alone needed a sample size of 40 to have a significance of 0.05 and a power of 80%. When the pump test result was normalized by dividing by the results of the stainless steel bead calibration test, a sample size of only 11 was needed (either characterized by ΔfHb or by SS Bead-IH) to have the same significance and same power. The pump tests normalized by the hemoresistometer or capillary tube also reduce the sample size, but not by as much as the stainless steel bead calibrated test.
To reach a final conclusion, each test device (including HR-IH and SS Bead-IH) was ranked from 1–5 (high rank number means good score) with respect to several factors. When two or more ranks were tied, the mean of the ranks that would have been assigned to these ranks was calculated as if they had not been tied, and this mean was assigned to each of the tied ranks. For example, the SS Bead and the SS Bead-IH should be ranked 5 and 4, respectively, if there was no tie, for they were easiest to perform. However, there was a tie because they were equivalent in ease of use, so their ranks were finally assigned as (5 + 4) / 2 = 4.5.
The results in Table 9 show that the stainless steel bead test, when characterized by SS Bead-IH, has the highest total score.
This first series of tests seems to indicate that all five devices are measuring the same mechanical fragility characteristic of blood, despite the different area/volume ratios, shear stress levels, and test durations. The second test series confirms this conclusion for three devices, with a greater sample number for the data. Because they indicate a fragility parameter relevant to at least the Biopump, it may be reasonable to identify one test as a mechanical fragility standard calibration. At this point, the normal range of values for bovine or any other blood cannot be stated. The calibration test must be repeated multiple times to get a statistically significant calibration number. Use of a calibration test number to normalize the pump hemolysis test result dramatically reduces the size of the standard deviation and therefore the number of repeat tests required to obtain a statistically significant value. A standard calibration performed by all laboratories may reduce lab to lab results scatter caused by blood variability. The stainless steel bead test per Kameneva’s protocol may be the most practical test for routine test normalization efforts. Multiple tests are quickly run, using economical equipment readily available to most laboratories. Despite theoretical questions, the normalization effect seems excellent. However, because of the zero offset, and mechanical as well as fluid stress on cells during the bead test, the hemoresistometer test may better simulate pump caused hemolysis and be a preferable configuration for studies of device related hemolysis and the effects of test parameters, blood characteristics, and flow effects upon hemolysis.
1. Indeglia RA, Shea MA, Varco RL, Bernstein EF: Mechanical and biologic considerations in erythrocyte damage. Surgery
62: 47–55, 1967.
2. Lampert RH, Williams MC: Effects of surface materials on shear-induced hemolysis. J Biomed Mater Res
6: 499–532, 1972.
3. Leverett LB, Hellums JD, Alfrey CP, Lynch EC: Red blood cell damage by shear stress. Biophysic J
12: 257–273, 1972.
4. Hellums JD, Brown CH: Blood cell damage by mechanical forces, in Hwang NHC, Normann NA (eds), Cardiovascular Flow Dynamics and Measurements
. Baltimore MD: University Park Press, 1977, pp. 799–823.
5. Nevaril CG, Hellums JD, Alfrey CP, Lynch EC: Physical effects in red blood cell trauma. AICHE J
15: 707–711, 1968.
6. Bacher RD, Williams MC: Hemolysis in capillary flow. J Lab Clin Med
76: 485–496, 1970.
7. Jasper DE, Jain NC: Effects of lipemia upon erythrocyte fragility, sedimentation rate, and plasma refractometer indexes in the dog. Am J Vet Res
26: 332–338, 1965.
8. 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
43: M571–575, 1997.
9. Blackshear PL Jr: Mechanical hemolysis in flowing blood, in Fung YC, Perrone N, Anliker M (eds), Biomechanics, Its Foundations and Objectives
. Englewood Cliffs, NJ: Prentice Hall, 1972, pp. 501–572.
10. Blackshear PL Jr, Dorman FD, Steinbach JH, et al
: Shear wall interaction and hemolysis. Trans Am Soc Artif Intern Organs
12: 113–120, 1966.
11. Bernstein EF, Gleason LR: Factors influencing hemolysis with roller pumps. Surgery
61: 432–442, 1967.
12. Jikuya T, Tsutsui T, Shigeta O, et al
: Species differences in erythrocyte mechanical fragility: Comparison of human, bovine, and ovine cells. ASAIO J
44: M452–455, 1998.
13. Kletschka HD, Rafferty EH, Olsen DA, et al
: Artificial Heart III. Development of efficient atraumatic blood pump. A review of the literature concerning in vitro
testing of blood pumps for hemolysis. Minnesota Med
58: 757–781, 1975.
14. Tanaka S, Yamamoto S, Yamakoshi K, Kamiya A: A compact centrifugal blood pump for extracorporeal circulation: Design and performance. J Biomechanic Eng
109: 272–278, 1987.
15. Jikuya T, Sasaki T, Aizawa T, et al
: Development of an atraumatic small centrifugal pump for second generation cardiopulmonary bypass. Artif Organs
16: 559–606, 1992.
16. Oku T, Harasaki H, Smith W, Nose Y: Hemolysis: A comparative study of four nonpulsatile pumps. Trans Am Soc Artif Organs
34: 500–504, 1988.
17. Jakob H, Kutschera Y, Palzer B, Prellwitz W, Oelert H: In vitro
assessment of centrifugal pumps for ventricular assist. Artif Organs
14: 278–283, 1990.
18. Fok FP, Schubothe H: Studies on various factors influencing mechanical haemolysis of human erythrocytes. Br J Haematol
6: 355–361, 1960.
19. Gu L: Mechanical fragility calibration of red blood cells. Doctoral dissertation. 2002.
20. Bilgen E, Boulos R: Functional dependence of torque coefficient of coaxial cylinders on gap width and Reynolds numbers. Trans ASME J Fluids Eng
95: 122–126, 1973.
21. Drabkin DL, Austin JH: Spectrophotometric studies. II. Preparations from washed blood cells; nitric oxide hemoglobin and sulfhemoglobin. J Biol Chem
112: 51, 1935.
22. Koller T, Hawrylenko A: Contribution to the in vitro
testing of pumps for extracorporeal circulation. J Thorac Cardiovasc Surg
54: 22–29, 1967.
23. Naito K, Mizuguchi K, Nose Y: The need for standardizing the index of hemolysis. Artif Organs
18: 7–10, 1994.
24. Davis BL, Vaughan CL: Phasic behavior of EMG signals during gait: Use of multivariate statistics. J Electromyogr Kinesiol
3: 51–60, 1993.
25. Kaiser HF: A note on Guttman's lower bound for the number of common factors. Br J Math Stat Psychol
14: 1–2, 1961.
26. Triola MF: Elementary Statistics, 5th ed
. Boston: Addison Wesley, 1992.
Copyright © 2005 by the American Society for Artificial Internal Organs
27. Hines WW, Montgomery DC: Probability and Statistics in Engineering and Management Science, 3rd ed
. New York: Wiley, 1990.