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Ultrasonic backscatter from flowing whole blood. I: Dependence on shear rate and hematocrit

Y.W. Yuan and K. K. Shung Bioengineering Program, 233 Engineering Laboratory and Office Building, Pennsylvania State University, University Park, Pennsylvania 1•802

(Received 12 January 1988; accepted for publication 17 March 1988)

Previous results show that ultrasonic backscatter from red blood cells (RBCs) suspended in saline is a function of hematocrit and frequency and that it can be affected by flow disturbance. The experimental data agree well with the theories. In the present article, results on ultrasonic backscatter from flowing whole blood are reported. Studies have been conducted on porcine, bovine, and human blood. Ultrasonic backscatter of flowing whole blood differs from that of RBC suspensions in that it is shear-rate dependent, which means that it is a function of spatial position of the blood in the flow conduit. Moreover, the results indicate that it is also species dependent. This behavior can be readily understood when red cell aggregation is considered.

PACS numbers: 43.80.Cs, 43.80.Jz, 43.35.Bf

INTRODUCTION

Ultrasonic Doppler flow meters make use of the signals backscattered from blood to obtain information as to the

flow speed of blood within blood vessels. For this reason, ultrasonic scattering properties of blood have been exten- sively studied. •-8 The preliminary indication has been that blood scattering is caused mainly by red cells (erythrocytes). In an earlier study 5 on ultrasonic backscatter from human red blood cells suspended in saline, the experimental results showed that the backscatter from such suspensions has fourth-power frequency dependence at hematocrits of 8% and 26%, as predicted by Rayleigh scattering of small particles. 9 In a previous study, 6 we showed that measured ultrasonic backscatter for bovine erythrocyte suspensions under uniform flow is in excellent agreement with recent theoretical models for concentrated small spherical scatterers, which predict a scattering maximum at a hematocrit of 13%. •ø-•2

The aggregation of erythrocytes was also found to increase scattering. 7 However, few attempts have been made to measure ultrasonic scattering properties of whole blood. With the improvement in instrumentation and the introduction of high-frequency scanners, blood flow now may be visualized ultrasonically. •3-•6 A further understanding of the scattering process of ultrasound in whole blood becomes even more crucial.

Ultrasonic scattering properties of whole blood are more complex than those of saline suspensions of erythrocytes. This happens because erythrocyte aggregation does not occur in saline •7 but does occur in stationary whole blood or in whole blood at low shear rates. •s'•9 In this article, we report the results that have been obtained in an effort to determine the dependence of the ultrasonic backscatter from flowing whole blood on the hematocrit and on the shear rate of the blood flow. Along with these results, a discussion of the significance of the results is given. The frequency dependence and the effect of fibrinogen concentration on ultrasonic backscatter from whole blood are now under investiga- tion in our laboratory. These results will be presented in a subsequent article.

I. METHODS AND MATERIALS

Ultrasonic backscatter from whole blood under laminar

flow was measured as a function of hematrocrit and of mean

shear rate of the flow, respectively. The procedures used for blood sample preparation were similar to those used in a previous study. 6 The experimental technique used to measure ultrasonic backscatter was a substitution method pro- posed by Sigelmann and Reid. 2ø Details of the experimental electronic system can also be found in Ref. 6. The ultrasound frequency used was 7.5 MHz.

In this work, we employed a specially designed flow system to obtain a steady and fully developed laminar flow for two reasons: ( 1 ) The flow disturbance that may affect scattering/'rom blood 5'6 could thus be avoided; and (2) th• shear rate would be well defined and easily controlled. This experimental apparatus is shown in Fig. 1. The flow conduit was a long cylindrical Tygon tube with a 2.54-cm inner diameter, a 130-cm length, and a 0.635-cm wall thickness. Ultrasonic backscatter was measured through a circular acoustic window that, with a diameter of 2 cm, was located at 110 cm downstream from the entrance of the conduit.

The entrance of the conduit was directly connected to a reservoir, while the exit was connected to another reservoir through a tube. Since the blood level in the exit reservoir, which could be adjusted by a jiffy-jack, was lower than that in the entrance reservoir, the blood flow was driven from the entrance reservoir to the exit reservoir by gravity. A calibrated roller pump with variable speed then circulated the blood from the exit reservoir back to the entrance reservoir to

maintain the height difference between blood levels in those two reservoirs. The flow rate was proportional to the height difference and to the speed of the roller pump; therefore, it could be read directly from the calibrated roller pump when the flow system was at steady state. Utilizing such a flow arrangement, the pulsation of the flow caused by the roller pump could be completely eliminated allowing a steady flow within the conduit to be obtained.

There was a partition placed in the middle of the entrance reservoir separating it into two compartments (refer to Fig. 1 ). The top edge of the partition was 1 cm below the

52 J. Acoust. Soc. Am. 84 (1), July 1988 0001-4966/88/070052-07500.80 @ 1988 Acoustical Society of America 52

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PARTITION

WATER TANK

i

i

FLOW DIRECTION

ACOUSTIC WINDOW

I.Im

l

--,..,

ROLLER PUMP

• 20cm "-!"

EXIT

RESERVOIR

FIG. 1. Diagram illustrating the experimental arrangement for the ultrasonic backscatter measurements on blood un-

der steady laminar flow.

JIFFY-- JACK

blood level; as a consequence, the blood in the left compartment coming from the roller pump must flow over the partition to the right compartment to which the flow conduit was connected. The main function of this partition was to block the flow disturbance induced by the inlet tube in the left compartment, making the blood flow at the entrance of the conduit more uniform. If air bubbles had been produced by pumping, they would flow over the partition and remain mostly near the top. Since the output of the entrance reservoir was located near the bottom, it is highly unlikely that these air bubbles would be introduced into the flow conduit.

Assuming that the fluid is Newtonian, experiments and theoretical analyses 2• have shown that, for a flow arrangement such as that used in this study, when the flow rate was increased up to 53 ml/s, a fully developed laminar flow could be assumed near the vicinity of the acoustic window.

In a fully developed laminar flow, the velocity profile is parabolic and the shear rate increases continuously from 0 at the center axis to a maximum at the wall. The mean shear

rate D across the conduit is given by D = 8 U/3a, where U and a are the average flow velocity and the radius of the flow conduit, respectively. During ultrasonic measurements, different mean shear rates could thus be obtained by adjusting the flow rates to the appropriate values because the mean shear rate is proportional to the average flow velocity. For a flow rate of 53 ml/s, the mean shear rate of the flow near the vicinity of the acoustic window was 22 s-•.

Since the shear rate increases along with the radius of the conduit as indicated above, it was of interest to study the effect of the spatial position of the blood within the conduit on the ultrasonic backscatter. To do this, we have measured the backscatter from whole blood in different scattering volumes radially across the flow. Figure 2 illustrates the transverse cross section of the acoustic window. The scattering volume was defined by the ultrasound beam and the length of electronic gate. Two scattering volumes evenly across the radius along the ultrasound beam were employed: ( 1 ) scat-

tering volume A, which represents a volume in the central core of the flow conduit, and (2) scattering volume B, a volume in the periphery. A simple calculation reveals that the average shear rate of the peripheral zone is approximately 2.33 times the magnitude of that of the central core.

At a given mean shear rate, the ultrasonic backscattering coefficients for blood in both scattering volumes A and B were measured, respectively. If these two values differed in

TRANSDUCER

I I

I I I

uLTRASOUND BEAM I

ACOUSTIC WINDOW I

I I

I

SCATTERING VOLUME

FIG. 2. Schematic diagram of the transverse cross section of the acoustic window in Fig. 1.

53 J. Acoust. Soc. Am., Vol. 84, No. 1, July 1988 Y.W. Yuan and K. K. Shung: Backscatter from flowing blood 53


magnitude, we would define the average of them as the mean backscattering coefficient at that given mean shear rate because the blood flow profile within the conduit should be radially symmetrical.

In order to clarify the effect of erythrocyte aggregation on scattering further, we investigated it by following two approaches: (1) comparing the experimental results obtained on whole blood to those obtained on saline suspensions of erythrocytes, and (2) using different species of blood with varying RBC aggregation tendencies. Zijlstra and Mook •-•- reported that the tendency for erythrocytes to aggregate is related to the animal species: Bovine blood has a minimal tendency; rabbit blood has a slight tendency; porcine blood and dog blood have a moderate tendency; while horse blood has an excessive tendency. The tendency for normal human whole blood to aggregate is closer to that of porcine or dog whole blood than any of the others mentioned.

Bovine and porcine whole blood were thus used in most of this research for several apparent reasons: ( 1 ) They have different RBC aggregation tendencies; (2) the RBC aggregation tendency of porcine blood resembles that of human blood; and, most importantly, (3) they can be easily obtained in large quantities required by the flow arrangement. An EDTA-saline solution was mixed with the blood to pre- vent clotting. Same measurements on porcine RBC suspensions were also performed.

In addition, using a simple alternative experimental arrangement that needs less blood, we have performed measurements on human whole blood under both stationary and stirred conditions for comparison. The experimental arrangement was similar to that used in the previous study for human RBC suspensions (Fig. 3 of Ref. 6). A rectangular chamber containing as little as 40 ml of blood was placed in a water bath; the blood was stirred by a magnetic bar as neces- sary. The drawbacks of this arrangement are apparent: ( 1 ) Although the stirring bar would reduce RBC aggregation, the shear rate is unknown; and (2) the stirring bar would cause the flow disturbance that may affect the ultrasonic scattering. 5'6 In spite of these problems, results obtained on human whole blood were still valuable because they provide clues as to the effect of RBC aggregation on ultrasonic scattering from human blood.

All the measurements were performed at a temperature of 23 øC _ 1 øC.

II. RESULTS AND DISCUSSION

A. Bovine blood

For bovine whole blood, at given conditions, the measured backscatter from scattering volume A was approximately equal to that from scattering volume B, indicating that the ultrasonic backscatter from bovine whole blood un-

der laminar flow is independent of the position of the blood across the flow. Figure 3 shows the typical measured ultrasonic backscatter from bovine whole blood under laminar

flow as a function of mean shear rate at three hematocrits.

The triangles, squares, and diamonds represent data for hematocrits of 4%, 12%, and 46%, respectively. These results

0 5 10 15 20 25

FIG. 3. Measured ultrasonic backscatter from bovine whole blood under laminar flow as a function of mean shear rate at three hematocrits.

clearly indicate that the backscatter from bovine whole blood under laminar flow is shear-rate independent.

Figure 4 shows the measured backscatter of bovine whole blood as a function of hematocrit. The triangles represent the average from six measurements for bovine whole blood under laminar flow. The squares represent the average for stationary bovine whole blood. The solid line represents the calculated theoretical curve for spherical scatterers whose dimension is much smaller than the wavelength, •ø-•- as given by

Wo( 1 - Wo) 40'bs V= , (1)

(1 + 2Wo) •- V where Wo is the volume concentration of the scatterers, is the backscattering cross section, and Vis the volume of the scatterer. In obtaining the theoretical curve, we have assumed the following values: Bovine RBC compressibility = 35.2 X 10- • cm•/dyn; plasma compressibility - 40.9 X 10- •- cm•/dyn; bovine RBC density = 1.084 g/ cm3; bovine plasma density = 1.029 g/cm3; and volume of bovine RBC = 57/•m 3 (see Refs. 5, 23, and 24).

Previously, we showed 6 that ultrasonic backscatter from RBC suspensions under uniform flow is in good agreement with the theoretical models. The results of bovine

whole blood under laminar flow, as indicated by Fig. 4, agree reasonably well with the theoretical models. It is interesting to note that in Fig. 4 the curve of stationary bovine whole

10 15 20 25 30 35 40 45 50

11e•r•toe•t (•)

FIG. 4. The ultrasonic backscatter from bovine whole blood as a function of

hematocrits. Solid line represents the theoretical curve. The triangles and squares represent data points for laminar flow and stationary blood, respectively. Standard deviation for each data point is included.

54 J. Acoust. Sec. Am., Vol. 84, No. 1, July 1988 Y.W. Yuan and K. K. Shung: Backscatter from flowing blood 54


blood bears a similar shape to that of bovine whole blood under laminar flow except that the scattering maximum shifts from a hematocrit of 13% to approximately 18 %. In addition, the measured backscatter from stationary bovine whole blood was higher than that from bovine whole blood under laminar flow, but the difference between them at a hematocrit of 44% was approximately 2 dB.

The bovine RBC aggregation in whole blood, although its tendency is minimal, might have contributed to the increase in backscatter from stationary bovine whole blood. Also, because of its minimal tendency, the RBCs might disaggregate completely soon after the blood flow was started. Under such circumstances, the bovine erythrocytes could be considered as small scatterers randomly distributed in the flow conduit. Therefore, the backscatter from bovine whole blood under laminar flow would be expected to be shear-rate independent and to conform to the theoretical models [Eq. (1)].

According to Rayleigh scatteringf the scattering is proportional to the volume square of the scatterer if the dimension of the scatterer is small compared to wavelength. Gen- erally speaking, since the RBC aggregation increases the size of the scatterer, the backscatter should increase. ? Moreover, it has been suggested •'s that the aggregative trends of erythrocytes would decrease the correlations among the scatterers, not only causing the scattering to increase further, but also causing the scattering peak to shift from a hematocrit of 13% (with no RBC aggregation) to a higher hematocrit. Since the tendency of RBC aggregation is minimal in bovine blood, perhaps only a small degree of RBC aggregation occurs in the stationary bovine whole blood. This might result in a minor increase in the backscatter and a shift of the scattering peak to a higher hematocrit at 18%.

B. Porcine blood

Before beginning a discussion on the results for porcine whole blood, it should be pointed out that the experimental results for porcine whole blood were not as consistent as those for bovine whole blood. We observed that, at given conditions, the measured backscatter from porcine whole blood varied from sample to sample. This might be due to the variation of fibrinogen concentration among blood sam- ples. 25 Since fibrinogen variation was not easy to be controlled, data presented from Figs. 5-9 represent the results of

• 100 ß

*! 10

i• • &•& He•rgatoc•'it • 47•

\ \

\ \

0 5 10 15 20 25

Mea• Shear Rate

FIG. 6. Measured ultrasonic backscatter from porcine whole blood in two different scattering volumes across the radius of the flow chamber as a function of mean shear rate at a hematocrit of 47%. Triangles and squares represent data points for scattering volume A (central core) and scattering volume B (periphery, refer to Fig. 2).

one typical series of measurements in which the fibrinogen concentration of the porcine whole blood was 210 mg/dl.

In Fig. 5, the mean ultrasonic backscatter from porcine whole blood in log scale is plotted as a function of mean shear rate for five hematocrits. The triangles, squares, diamonds, hexagons, and crosses represent data for hematocrits of 4.5%, 14.5%, 25%, 34%, and 47%, respectively. Unlike bovine whole blood, these results indicate that the ultrasonic backscatter from porcine whole blood strongly depends on shear rate. At each hematocrit, the backscatter for a low mean shear rate of 2 s-• was much higher than that for a high shear rate of 22 s-•, and the difference between them was at least 15 dB. Also note that the curves in Fig. 5 indicate that the backscatter decreases rapidly at low shear rates as shear rate is increased, and it reaches a steady state asymp- totically as the shear rate is increased further.

The flow properties of normal human whole blood are known to be non-Newtonian at low shear rates but would

become Newtonian at high shear rates. •7 This non-Newtoni- an behavior, i.e., the apparent viscosity increases with de- creasing shear rate, has been postulated to be caused by RBC aggregation. Comparing the results shown in Fig. 5 to the apparent viscosity of normal human blood as a function of shear rate, 25'26 one can easily see the similarities between them. This observation seems to suggest that the dependence of ultrasonic backscatter on shear rate is the result of

erythrocyte aggregation.

lOOO

lOO

1

0 5 lO 15 20 •-5

Mea• Shear Re, re (t/e)

FIG. 5. Measured mean ultrasonic backscatter from porcine whole blood under laminar flow as a function of mean shear rate at five hematocrits.

0 5 10 15 •-0

Mea• Shear J•e•te (I/e)

FIG. 7. Same as in Fig. 6, except at a hematocrit of 34%.



100

0 {5 10 15 •0

FIG. 8. Same as in Fig. 6, except at a hematocrit of 25%.

• 100

\ \ • He•r•atoe•t '•N &• 14.5%

\ ß

0 5 tO lB ;•0

FIG. 9. Same as in Fig. 6, except at a hematocrit of 14.5%.

Assuming that no RBC aggregation exists in porcine whole blood and the porcine erythrocytes are the small scatterers, we estimated the theoretical backscatter from porcine erythrocytes suspended in plasma based on Eq. ( 1 ). Doing this, we have assumed the following values: Porcine RBC compressibility = 34.985 X 10-12 cm2/dyn; plasma compressibility = 40.9X 10-12 cm:/dyn; porcine RBC density = 1.078 g/cm3; porcine plasma density = 1.022 g/cm3; and volume of porcine RBC = 68/•m 3 (see Refs. 5, 23, and 24). A comparison between these calculated values and the results in Fig. 5 shows that the measured backscatter at a mean shear rate of 22 s-1 was still much higher than the calculated value for all hematocrits of porcine whole blood used. This observation seems to indicate that the porcine RBC aggregates are still present at a mean shear rate of 22 s-•. Since the data in Fig. 5 suggest that the backscatter would drop to an asymptotic constant, we may postulate that, for a given hematocrit, if the shear rate is further increased beyond a certain value so that the RBC aggregates are completely dispersed, ultrasonic backscatter from porcine whole blood should approach the calculated value given by Eq. (1).

Figure 5 also shows that a clear relation did not exist between the measured backscatter and the hematocrit for

porcine whole blood at mean shear rates of below 22 s-•, especially for hematocrits higher than 15%. In Fig. 5, the four curves representing the backscatter from porcine whole blood for hematocrits of 14.5%, 25%, 34%, and 47% were intertwined. The only consistent result was that, at all mean shear rates used, the measured backscatter for a hematocrit of 4.5% was lower than that for those four higher hematocrits.

This might be attributed to the complex behavior of RBC aggregation and the change in blood flow properties under different conditions. Generally speaking, an increase in hematocrit up to the physiological range tends to favor RBC aggregation; however, at a given shear rate, an increase in hematocrit would tend to cause rouleau deformation and

dispersion. •5 Also, the non-Newtonian property of whole blood, caused by the presence of RBC aggregation at low shear rates, would blunt the blood flow profile. 25'•6 The non- Newtonian property of whole blood depends upon the hematocrits as well. 26 In addition, monitoring the porcine whole

blood under laminar flow by an ultrasonic scanner, we have observed :? that sometimes at high hematocrits there ap- peared a small dark hole at the center of the flow conduit indicating a region of low cell concentration. This certainly could complicate the issue further. The behavior of the hole and the mechanism for the appearance of the hole with lower echogenecity are unknown at present and are worth investi- gating.

Because the shear rate varied radially in the flow conduit, the ultrasonic backscatter of porcine whole blood at different positions of scattering volume within the flow conduit was measured. Figures 6-9 show the results for hematocrits of 47%, 34%, 25%, and 14.5%, respectively. The triangles and squares represent the measured backscatter for scattering volumes A and B (refer to Fig. 2), respectively. These results clearly show that, under laminar flow condition, the ultrasonic backscatter from porcine whole blood in the scattering volume A was higher than that from porcine whole blood in the scattering volume B.

As previously discussed, the ultrasonic backscatter from porcine whole blood was strongly shear-rate dependent, and the RBC aggregation persisted at mean shear rates of up to 22 s-•. Therefore, it should not be a surprise to see that the backscatter from porcine whole blood in the central core (scattering volume A) of the flow conduit was higher than that from porcine whole blood in the periphery (scattering volume B), since the average shear rate of the central core was lower than that of the periphery. As mentioned earlier, the average shear rate of the peripheral zone was 2.33 times the magnitude of that of the central core for Poiseuille flow. At low shear rates with the presence of RBC aggregation, however, the non-Newtonian behavior of whole blood will blunt the velocity profile in the central portion. •'•6 Con- sequently, the difference between the average shear rates of the periphery and the central core would become even more prominent at low shear rates.

Similar experiments were also repeated on saline suspensions of porcine erythrocytes. Ultrasonic backscatter from porcine erythrocyte suspensions under laminar flow was found independent of the position of the scattering volume within the conduit. At given conditions, the experimental •esults from different suspensions, unlike those for porcine whole blood, were all reasonably close. Figure 10 shows



m 100

0 5 10 15 20 25

FIG. 10. Measured ultrasonic backscatter from porcine RBC suspensions under laminar flow as a function of mean shear rate at three hematocrits.

the typical measured backscatter from porcine erythrocyte suspensions under laminar flow as a function of mean shear rate at three hematocrits. The triangles, squares, and diamonds represent data for hematocrits of 4%, 13%, and 46%, respectively. These results clearly indicate that the ultrasonic backscatter from porcine erythrocyte suspensions under laminar flow is shear-rate independent.

Figure 11 shows the backscatter from porcine erythrocyte suspensions under laminar flow as a function ofhemato- crit. The triangles represent the typical experimental results, and the solid line represents the theoretical prediction calculated from Eq. (1). In obtaining the theoretical curve for porcine erythrocyte suspensions, we have assumed following values: Porcine erythrocyte compressibility = 34.985 X 10-22 cm2/dyn; saline compressibility = 44.3 X 10- • cm:/dyn; porcine erythrocyte density = 1.078 g/cm3; saline density = 1.005 g/½m3; and volume of porcine erythrocyte = 68 •tm 3 (see Refs. 5, 23, and 24). The experimental results again are in good agreement with the theoretical models, as were observed for bovine erythrocyte suspensions under uniform flow and for stationary human erythrocyte suspensions. 6

Reviewing the results obtained on porcine blood, one can easily see that, at mean shear rates of below 22 s-2, the porcine whole blood and the saline suspensions of porcine erythrocytes differ significantly in their ultrasonic backscattering properties. This difference may be mainly attributed to RBC aggregation. The erythrocytes do not aggre-

0 5 10 15 20 25 ao 35 40 45 50

FIG. 11. The ultrasonic backscatter from porcine RBC suspensions as a function of hematocrit. Solid line represents theoretical curve. Triangles represent typical experimental results for laminar flow.

gate when suspended in saline, while, as indicated earlier, the porcine RBC aggregates may still exist at a mean shear rate of 22 s-2. Then, an interesting question arises: If the shear rate is further increased so that RBCs are completely disag- gregated, will the ultrasonic scattering properties of porcine whole blood become closer or similar to those of porcine erythrocyte suspensions? The reason that this question is of interest is that results for higher shear rates would be more applicable to blood flow in an arterial system. Presently lim- ited by the experimental difficulties, the mean shear rate could not be raised beyond 22 s-2.

In attempting to answer this question, we may compare the results of bovine whole blood to those of porcine erythrocyte suspensions. Since the tendency of RBC aggregation in bovine whole blood is minimal, the RBC aggregates seem to be disrupted immediately following the flowing of the blood. Thus, at mean shear rates of beyond 2 s-•, the following similarities between the experimental results of bovine whole blood and those of porcine erythrocyte suspensions were observed: (1) The measured backscatter was shear-rate independent; and (2) the measured backscatter as a function of hematocrit agreed with theoretical models. Therefore, it seems reasonable to postulate that the answer to the above question is positive. In fact, the findings that, at each hematocrit, the measured backscatter from porcine whole blood decreased with increasing shear rate and probably would approach an asymptotic constant at high shear rates seem to support this answer as well. However, one presumption of this postulation is that the blood flow has to be laminar at high shear rates. Should turbulent flow occur at high shear rates, it could also affect the ultrasonic backscatter.

C. Human blood

Since the behavior of the ultrasonic backscatter for bo-

vine whole blood is so different from that for porcine whole blood as suggested by the experimental results, another interesting question may arise: What is the behavior of the ultrasonic backscatter for human whole blood like? Unfor-

tunately, because a large quantity of human blood required for the flow system was not possible to obtain, an alternative experimental arrangement that required only 40 ml of blood had to be used. The backscatter from human whole blood

was measured only under stirred and s•tationary conditions. Results for human whole blood collected from two nor-

mal male subjects are shown in Table I. It is important to note here that the spin motion of the magnetic stirrer not only disrupted RBC aggregates but also induced flow disturbance, which might cause the backscatter to increase. De- spite this, the results in Table I indicate that, at 3 and 5 min

TABLE I. Measured ultrasonic backscatter data from human whole blood

at hematocrits of normal range under stationary and stirred conditions. All values are in units of 1/cm/sr.

,, Stationary Hematocrit Stirred 3 min 5 min

44% 6.9X 10E- 5 40.1X 10E- 5 102.1X 10E -- 5 47% 6.6X 10E -- 5 65.9X 10E- 5 103.9X 10E- 5



after the stirring was stopped, the measured backscatter from human whole blood increased by approximately 8 and 11 dB, respectively. In addition, a comparison indicates that the backscatter from stationary human whole blood measured at 5 min following the termination of stirring was approximately 20 dB higher than that from stationary human erythrocyte suspensions at the same hematocrit. 6

These results clearly showed that the ultrasonic backscatter from human whole blood was high if the blood was stationary and dropped significantly when shear forces were applied. This observation suggests that the ultrasonic backscatter from human whole blood behaves more like porcine whole blood than bovine whole blood, validating the observation 22 that the RBC aggregation tendency of porcine whole blood resembles that of normal human whole blood.

Certainly, the details of the ultrasonic scattering properties of human whole blood remain to be determined.

III. CONCLUSION

The main findings of this research are summarized below.

( 1 ) In bovine whole blood, which is known to have minimal RBC aggregation tendency, the ultrasonic backscatter is shear-rate independent and under laminar flow condition its relation to hematocrit agrees reasonably well with theoretical models for small spherical scatterers.

(2) In porcine whole blood, which has a greater RBC aggregation tendency, the ultrasonic backscatter does de- pend upon the shear rate, which leads to the observation that the ultrasonic backscatter is a function of spatial position of the blood in the flow conduit. These results suggest that high shears disaggregate the erythrocytes.

(3) In saline suspensions of porcine erythrocytes that do not exhibit aggregation, the ultrasonic backscatter is shear-rate independent, and its variation with hematocrit agrees well with theoretical models.

(4) In human whole blood whose aggregation properties are known to be similar to those of porcine whole blood, initial results show that the ultrasonic backscatter is shear-

rate dependent but the details remain to be determined.

ACKNOWLEDGMENT

This research has been supported by NIH Grant #HL28452.

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