Use of an Ultrasound Blood-Mimicking Fluid for Doppler Investigations of Turbulence In Vitro

Ultrasound in Med. & Biol., Vol. 34, No. 7, pp. 1163–1173, 2008 © 2008 Published by Elsevier Inc. on behalf of the World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/08/$–see front matter

doi:10.1016/j.ultrasmedbio.2007.12.014

● Original Contribution USE OF AN ULTRASOUND BLOOD-MIMICKING FLUID FOR DOPPLER INVESTIGATIONS OF TURBULENCE IN VITRO MEGHAN L. THORNE,*† TAMIE L. POEPPING,†‡ RICHARD N. RANKIN,§ DAVID A. STEINMAN,¶ and DAVID W. HOLDSWORTH*†§ *Robarts Research Institute, London, ON, Canada; Departments of †Medical Biophysics, ‡Physics and Astronomy, and §Diagnostic Radiology and Nuclear Medicine, University of Western Ontario, London, ON, Canada; and ¶ Biomedical Simulation Laboratory, University of Toronto, Toronto, ON, Canada (Received 26 July 2007; revised 13 December 2007; in final form 19 December 2007)

Abstract—Turbulence is an important factor in the assessment of stenotic disease and a possible causative mechanism for thromboembolism. Previous Doppler studies of turbulence have typically used whole-blood preparations or suspensions of erythrocytes. Recently, a water-glycerol based blood-mimicking fluid (BMF) has been developed for use in Doppler ultrasound studies. This fluid has desirable ultrasound properties but it has not previously been described during in vitro investigations of turbulence intensity. We report on investigations of grid-generated and constrained-jet turbulence in an in vitro test system. The BMF was found to generate significant levels of turbulence during steady flow at physiological flow rates, producing turbulent patterns in the distal region that were consistent with previous studies. Turbulence intensity increased significantly with flow rate (p < 0.005) for both the constrained jet and the constrained grid. Based on our observations, we conclude that a water-glycerol based BMF provides a suitable working fluid during in vitro investigations of turbulence using Doppler ultrasound. (E-mail: [email protected]) © 2008 Published by Elsevier Inc. on behalf of the World Federation for Ultrasound in Medicine & Biology. Key Words: Doppler ultrasound, Blood-mimicking fluid, In vitro modeling, Blood flow velocity, Orifice, Grid, Backscattered power, Turbulence intensity.

INTRODUCTION

sive disease may result in increased flow resistance and, hence, flow reduction, increased residence time, platelet activation, increased wall shear stress and, potentially, increased risk of plaque rupture. It is, therefore, a reasonable hypothesis that the detection of turbulence may provide a more sensitive diagnosis of clinically significant stenosis than the observation of elevated peak systolic velocity levels alone, as is typically done. Although it is difficult to quantify turbulence levels during conventional Doppler ultrasound (DUS) examinations, recent advances in processing algorithms make this approach more feasible. Turbulence may not be well identified by increases in spectral width (Garth et al. 1983) but can be measured in terms of random fluctuations superimposed on a periodic velocity waveform (Hinze 1959). It is this possibility of enhanced diagnosis and treatment planning related to carotid occlusive disease that has resulted in continued interest in the characterization and detection of turbulence (Banks and Bressloff 2007; Casty and Giddens 1984; Felix et al. 1976; Ryval et al. 2004).

Disturbed flow patterns and turbulence distal to vessel stenoses have been implicated as a risk factor for thromboembolic stroke (Sigel 1998) and as a potential indicator of significant stenosis (Ku 1997; May et al. 2001). Disturbed flow is characterized by transient fluctuations in an otherwise laminar flow field, which causes the flow to deviate from streamlined motion. As described by Yellin (1966), a region of disturbed flow may be described as turbulent, but true turbulence is self-preserving, rather than transient. Turbulence, characterized by random fluctuations in pressure and velocity in both space and time, has been reported distal to moderate and severe stenoses (Bascom et al. 1997; Yongchareon and Young 1979). Turbulence associated with carotid occlu-

Address correspondence to: D.W. Holdsworth, Imaging Research Laboratories, Robarts Research Institute, P.O. Box 5015, 100 Perth Drive, London, Ontario, N6A 5K8, Canada. E-mail: david. [email protected] 1163

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Doppler ultrasound was first proposed as a technique to measure turbulence nearly 30 years ago (Sigel et al. 1970). Recent DUS studies have investigated the effect of turbulence on returned Doppler power from red blood cell (RBC) suspensions. Previous in vitro studies in straight-tube models, under steady and pulsatile flow (Bascom et al. 1997; Cloutier et al. 1995; Cloutier and Shung 1993) and uniform flow through a screen grid (Shung et al. 1992, 1984; Wu et al. 1998), found that Doppler power increased in regions of turbulence. This may be a result of the behavior of scattered particles under turbulent flow (Cloutier et al. 1995), where different hemodynamic conditions may alter the interaction between the RBCs resulting in a change in returned backscatter signal (Shung et al. 1992; Wu et al. 1998). However, this does not take into consideration knowledge that the ultrasound backscatter from blood is influenced by a number of factors, including hematocrit, shear rate and the nature of flow (Shung et al. 1992; Wu et al. 1998). Other DUS studies have investigated a promising method of quantifying turbulence by direct measurement of velocity fluctuations, even in the presence of deterministic repetitive variations in vivo (Casty and Giddens 1984) and, recently, this technique has been applied in vitro as well (Cloutier et al. 1996; Poepping et al. 2002). Difficulties in working with real blood or red blood cell suspensions, including complications arising from inconsistencies between batches, the requirement for chemical treatment with anticlotting agents and the tendency for cell lysis, have persuaded researchers to seek out a synthetic alternative. Fortunately, a well-established blood-mimicking fluid (BMF), created by Ramnarine et al. (1998), is available for in vitro DUS experiments. This BMF mimics the high-shear viscosity of blood (which has a direct effect on the hemodynamics of the fluid) and contains nylon scatterers, which simulate red blood cell movement. Although this particular BMF has been used in other DUS studies, it has not been tested under conditions of turbulence. Under such conditions, it is unknown whether there is an effect on the correlation of particle scattering, aggregation of scatterers and cavitations within the fluid itself, all of which may affect the Doppler backscattered signal. We describe an in vitro investigation of a BMF under controlled conditions of constrained round-jet turbulence and constrained two-dimensional (2D) grid-generated turbulence, created using orifices of 2.5-mm and 1.6-mm diameter and a 0.5-mm nylon grid. Doppler velocity spectra, acquired under conditions of steady flow within the turbulent region, are analyzed to determine if this particular BMF returns adequate power under various turbulent conditions, facilitating studies of the shape and extent of turbulent regions distal to an

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obstruction. We hypothesize that the properties of this BMF will be suitable for Doppler ultrasound studies of turbulence in vitro. MATERIALS AND METHODS Blood-Mimicking Fluid A well-established blood-mimicking fluid, described by Ramnarine et al. (1998) for use with Doppler ultrasound, was used for all experiments. This BMF has an attenuation of 0.26 dB/cm at 5MHz, speed of sound of 1547 cm/s, density of 1037 ⫾ 2 kg/m⫺3 and viscosity of 4.1 ⫾ 0.1 mPa/s. Note that this fluid exhibits a volume concentration of scatterers (5 ␮m diameter nylon particles) of 2%, corresponding to approximately 3 ⫻ 108 particles per mL, which is significantly lower than the hematocrit of human blood. We altered the original formulation of the BMF slightly by replacing the surfactant Synperonic (ICI Synperonic N, BDH Laboratory Supplies, Poole, UK) with the household surfactant JET® DRY rinse agent (Reckitt Benckiser Canada Inc., Toronto, ON, Canada). We found that the use of this common surfactant reduced the number of air bubbles that collected at the surface and also limited the initiation of cavitation. A preservative that consists of chloroacetamide and sodium benzoate (CA-24, Biochema Schwaben, Memmingen, Germany) was also added (3 g/L) to increase the shelf-life of the BMF. Both of these adjustments to the formulation do not affect the ultrasound properties of the BMF mentioned above since the additives were introduced in small concentrations by volume and the measured viscosity of the BMF was within experimental error of the value reported by Ramnarine et al. (1998). A fresh batch of BMF was used for this set of experiments and the flow system was operated for at least 1 h before the acquisition of each data set to purge the system of any air bubbles. Flow System The BMF was pumped through a rigid, straight-tube cylinder with an inner diameter of 1.27 cm and an outer diameter of 1.9 cm. The inlet was made of acrylic and was machined to a length of 120 cm, ensuring fully developed flow. The inlet length (L) can be estimated from the Reynolds Number (Re) and the diameter (D) by using the following equation (Langhaar 1942): L ⬇ 0.06ReD

(1)

For a Reynolds number calculated as 380, at a maximum flow rate of 15 mL/s, the inlet length should be greater than 29.0 cm to ensure fully developed laminar flow. Figure 1 illustrates a longitudinal cross-section of the flow model used in this experiment. The acrylic inlet was coupled to an ultrasound-compatible thin-walled

Use of a blood-mimicking fluid ● M. L. THORNE et al.

Fig. 1. Longitudinal cross-section of flow model with insert and two-dimensional (2D) acquisition area. Note that in this figure, the orifice is not drawn to scale. The solid grey box represents the full extent of the Doppler interrogation for 2D mapping. The central dot illustrates one of the central locations where extended acquisitions were performed. The small inset illustrates the matrix spacing that was used to sample the Doppler interrogation region. A 3 ⫻ 3 matrix of acquisition points is illustrated (with 1-mm spacing between each point) but in practice there is a total of 533 sample locations utilized over the entire region.

high-density polyethylene (PE) portion that extended 8 cm downstream, maintaining an inner diameter of 1.27 cm and having an outer diameter of 1.9 cm. Due to the design of the phantom, the one-piece high-density PE portion must be machined from a solid rod, constraining the choice of ultrasound-compatible plastics. We selected PE because it provides low attenuation and an acceptable speed of sound (approximately 1950 m/s). Note that the resulting mismatch in speed of sound between the PE wall and the BMF could provide a limitation for data collection in the horizontal plane, adjacent to the lumen boundary. For this reason, in this study, we have avoided data collection in the regions near walls. At the transition region between the acrylic inlet and the ultrasound-compatible section, there was a demountable unit where modular inserts could be introduced into the laminar flow field to create inherently unsteady or aperiodic turbulent flow, as in the case of flow accelerating through a constriction. This design allowed the operator to switch between flow conditions within the distal segment, creating either fully developed laminar flow (with no insert), constrained jet turbulence (using either 2.5-mm or 1.6-mm orifice insert) or constrained homogeneous isotropic wake turbulence (using a 0.5-mm grid). Figure 2 illustrates the two types of modular inserts: a 2.5-mm orifice insert shown from the transverse view in Fig. 2a and in the lateral side view shown in Fig. 2b; and a 0.5-mm grid, shown from the transverse view in Fig. 2c and an enlarged view of the grid in Fig. 2d. The orifice inserts were fabricated from a polyethylene disk with a diameter of 27 mm and a thickness of 1.53 mm fitting into the demountable sec-

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tion. Drilling a 2.5-mm or 1.6-mm opening in the center of this disk created the orifice itself. These orifice models were selected, as they represent constrained-jet approximations of a range of carotid disease; the 2.5-mm orifice approximates the residual diameter of a moderate stenosis (i.e., 55% as graded by the North American Symptomatic Carotid Endarterectomy Trial (NASCET) and the 1.6-mm orifice approximates the residual diameter a severe stenosis (i.e., 70% NASCET grade), assuming a normal distal internal carotid artery diameter of 5.6 mm (Smith et al. 1996). The nylon grid was characterized by a grid opening, s, of 0.5 mm, thread diameter of 0.3 mm, w, mesh count of 12.6 per cm, an open area of 39% (O-CMN-500, Small Parts Inc., Hollywood, FL, USA) and was cut to fit into the demountable unit. The bloodmimicking fluid previously described was pumped through the flow system using a computer-controlled flow simulator (Holdsworth et al. 1991) (UHDC Flow System, Shelley Medical Imaging Technologies, London, ON, Canada). With this pump, controlled steady flow was produced, with a mean flow rate that was set by the user. For our experiments, we used flow rates ranging from 2.5 to 15 mL/s, with 2.5 mL/s increments.

Fig. 2. Schematic diagram demonstrating the geometry of two of the inserts used to produce turbulence in this study, each shown in two views: (a) 2.5-mm orifice insert with a diameter, d, of 27 mm; (b) profile of orifice insert with a thickness of 1.53 mm; (c) 0.5-mm nylon grid insert with a diameter, d, of 27 mm; (d) close-up of nylon grid insert with a grid diameter, s, of 0.5 mm, thread diameter, w, of 0.3 mm, mesh count of 12.6 per cm and an open area of 39% (Small Parts Inc. O-CMN-500).

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Data Acquisition Ultrasound acquisition was performed with a data acquisition and computer-controlled positioning system previously described by Poepping et al. (2002). A clinical duplex Doppler ultrasound machine (Ultramark 8, Advanced Technology Laboratories - ATL, Bothell, WA, USA) with a 5 MHz annular array transducer was used to acquire demodulated in-phase and quadrature data within a 1.5-mm sample volume length. Doppler parameters were set as follows: a PRF of 25000 Hz producing a Nyquist velocity of 380 cm/s, power set to 100%, gain of 50%, wall filter of 50 Hz, Doppler angle of 60° and a sample-volume depth of 2.1 cm. The ultrasound probe was held in place and positioned by a computer-controlled three-dimensional (3D) stage, which provided step changes in x, y and z directions. The computer-controlled 3D stage was programmed to acquire a 2D raster of points at 1-mm increments in a vertically oriented transverse plane, starting 1.7 cm distal to the modular insert and extending 4 cm downstream (as shown in Fig. 1). To quantify the amount of turbulence at each sample point, we must acquire multiple estimates of velocity; therefore, one second of data was acquired under conditions of steady flow at each of the 533 points that made up the 2D raster. This sampling pattern acquired data that allowed us to derive a spatial distribution map of turbulence intensity distal to both the orifice and grid, at steady flow rates of 5 mL/s, 7.5 mL/s, 10 mL/s, 12.5 mL/s and 15 mL/s. For these flow rates, the Reynolds numbers within the larger jet orifice ranged from 644 (for a flow rate of 5 mL/s) to 1933 (for a flow rate of 15 mL/s), where 2000 is the critical Re for a straight, ideal cylinder. The Reynolds number for the smaller jet orifice ranged from 1006 (for a flow rate of 5 mL/s) to 3020 (for a flow rate of 15 mL/s). Based on the 2D distribution of turbulence distal to each flow condition, a central point was selected where turbulence was seen to be significant. One second of Doppler data was acquired at these central points 3.8 cm distal to the 2.5-mm orifice, 4.3 cm distal to the 1.6-mm orifice and 3.3 cm distal to grid. For the case of the orifice, Doppler data were acquired at steady flow rates of 2.5 mL/s, 5 mL/s, 7.5 mL/s, 10 mL/s, 12.5 mL/s and 15 mL/s and, in the case of the mesh, additional flow rates of 17.5 mL/s and 20 mL/s were investigated to ensure that an appropriate range of turbulence was studied. Doppler acquisition was repeated 10 times at each of these central sample points, allowing the determination of measurement repeatability. Following these acquisitions, we repeated acquisitions at each of the central sample points for selected flow rates of 5, 10 and 15 mL/s under each condition of turbulence (orifice and grid) to evaluate the short- and longer-term reproducibility of the BMF, with a 30 min interval between acquisitions. To investigate the incident flow pro-

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file in the absence of the orifice or mesh insert, we also acquired 1 s of Doppler data, repeated 10 times, within a central location located 3.8 cm distal to the origin for all flow rates. Data Analysis All in-phase and quadrature data were digitized at 44.1 kHz and analyzed using a 1024-point fast Fourier transform (FFT) with a 512-point Hanning window and 512-point overlap between each FFT, producing instantaneous power spectra every 12 ms, with a frequency resolution of 43 Hz. Using the Doppler frequency of the transducer (ft, MHz), the speed of sound through water (c, m/s) and the cosine angle of the transducer to the direction of flow (␪°) the resulting Doppler-shifted frequencies were converted to velocities (v, cm/s), via the Doppler equation: v⫽

fd · c 2 · f t · cos␪

(2)

Mean velocities were extracted from each spectrum, providing a value for each time-point. Turbulence intensity (TI, cm/s) was then calculated as the root-meansquared deviation about the averaged mean velocity (u, cm/s) (Hinze 1959): TI ⫽

冑

兺 (u ⫺ u)2 n

(3)

Note that while we investigate only turbulence intensity in this paper, it is important to distinguish TI from turbulence intensity level, where turbulence intensity level (To) is typically normalized by the mean velocity (eqn 4) (Hinze 1959): To ⫽

TI u

(4)

To characterize the flow field distal to either the orifice or grid insert, TI was calculated for each of the 533 points within the 2D raster. For visual evaluation, the data were presented as a color-encoded map, where TI values were assigned to a particular color. The turbulent core of each color-encoded distribution map was then quantified as the area of turbulence intensity values above a selected threshold. To investigate the precision of TI measurements we analyzed 1-s intervals of data that were acquired 10 times sequentially at a point 3.8 cm distal to the 2.5-mm orifice, 4.3 cm distal to the 1.6-mm orifice and 3.3 cm distal to the grid insert. We calculated mean velocity, power and turbulence intensity for each flow rate. The average power over each 1-s interval was calculated in arbitrary units that represent the integral power over all positive and negative velocities. From

Use of a blood-mimicking fluid ● M. L. THORNE et al.

Fig. 3. Color-encoded turbulence intensity (TI) distribution map created from measurements made between 1.7 cm and 5.7 cm distal to a 2.5-mm orifice insert at five flow rates: (a) 5 mL/s; (b) 7.5 mL/s; (c) 10 mL/s; (d) 12.5 mL/s; and (e) 15 mL/s. The black dot in panel a, located 3.8 cm downstream, indicates the sample-point for repeated centerline acquisitions.

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expected for Doppler ultrasound measurement precision for steady flow (Rickey et al. 1992). Once each insert was placed in the holder, the flow distributions became turbulent, as seen in Figs. 3, 4 and 5. By examining Fig. 3a at a flow rate of 5 mL/s, we can see that a 2.5-mm orifice placed within the laminar flow field created a sufficient step-discontinuity to produce a constrained turbulent jet. Figure 3a also illustrates that turbulence increased conically from the jet, with a maximum turbulence intensity value of around 23 cm/s. As we increased the flow rate to 7.5 mL/s, turbulence continued to increase conically but the spread of the turbulence is larger both in the axial and radial directions and the maximum turbulence intensity value increased to around 35 cm/s. Turbulence continued to spread axially as the flow rate was increased and the turbulence increased in the radial direction until the turbulent region contacted the chamber walls at flow rates between 12.5 and 15 mL/s, as in Fig. 3d and e. The maximum value of turbulence intensity occurred at 15 mL/s, where it reached 218 cm/s. Similar results are seen in Fig. 4, for the case of a 1.6-mm orifice. In Fig. 4c– e, we can see that the turbulent region no longer spreads radially, as the turbulent region has contacted the chamber walls. The maximum

these values linear regressions were performed, determining the relationships between average mean velocity and flow rate, TI and flow rate, and backscattered power and TI. Finally, the longer-term stability was determined by performing a paired t-test on repeated TI measurements over three flow rates of 5, 10 and 15 mL/s, with a 30 min interval between acquisitions. RESULTS Spatial Distributions of Turbulence Turbulence intensity values calculated within a 2D raster of points were plotted as color-encoded distribution maps, as seen in Figs. 3, 4 and 5. The distributions presented are those acquired distal to a 2.5-mm orifice, 1.6-mm orifice and distal to a 0.5-mm grid at five different flow rates: 5, 7.5, 10, 12.5 and 15 mL/s. Table 1 lists the calculated Re for the laminar inlet and orifice conditions investigated in this study. When no modular insert was employed (i.e., fully developed laminar flow), the observed peak centerline velocity at 15 mL/s was 25.5 ⫾ 1.1 cm/s, in good agreement with the theoretical prediction for Poiseuille flow (23.7 cm/s). The observed fluctuation in velocity (4.3% or 1.0 cm/s) is in the range

Fig. 4. Color-encoded turbulence intensity (TI) distribution map created from measurements made between 1.7 cm and 5.7 cm distal to a 1.6-mm orifice insert at five flow rates: (a) 5 mL/s; (b) 7.5 mL/s; (c) 10 mL/s; (d) 12.5 mL/s; and (e) 15 mL/s. The black dot in panel a, located 4.3 cm downstream, indicates the sample-point for repeated centerline acquisitions.

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laminar flow field. The grid created turbulence that is approximately homogeneous and isotropic, with no coherent structures distal to the grid. Figure 5a illustrates that the grid produces a maximum turbulence intensity value of 10 cm/s at a flow rate of 5 mL/s. This value of turbulence is considerably lower than in the previous case of a 2.5-mm constrained-jet orifice at the same flow rate (23 cm/s). As the flow rate was increased to 7.5 mL/s, as seen in Fig. 5b, the maximum turbulence intensity value doubled to 20 cm/s and the homogeneity of the turbulent field expanded to the full radial extent of the chamber. When the flow rate was increased further to 10, 12.5 and 15 mL/s (as seen in Fig. 5c– e) turbulence spread axially. Figure 5b– e all exhibit comparable maximum values of turbulence intensity ranging from 20 cm/s at 7.5 mL/s to 36 cm/s at 15 mL/s.

Fig. 5. Color-encoded turbulence intensity (TI) distribution map created from measurements made between 1.7 cm and 5.7 cm distal to a 0.5-mm nylon grid insert at five flow rates: (a) 5 mL/s; (b) 7.5 mL/s; (c) 10 mL/s; (d) 12.5 mL/s; and (e) 15 mL/s. The black dot in panel a, located 3.2 cm downstream, indicates the sample-point for repeated centerline acquisitions.

value of turbulence intensity occurred at 12.5 mL/s (Fig. 4d), where it reached 104 cm/s. The smaller, 1.6-mm orifice, produced another feature not seen in the larger, 2.5-mm orifice, where as the flow rate was increased the region of turbulence intensity was progressively displaced downstream. Figure 5 illustrates the distribution of the distal flow field when we introduced a 0.5-mm grid within the

Turbulent Core To characterize the color-encoded turbulence maps more thoroughly, the area of the turbulent core was calculated for each distribution map. The area of the core was defined as the region of measured turbulence intensity above a selected threshold of 21 cm/s for the orifice studies and 7 cm/s for the mesh; this threshold corresponds to approximately 20% of the peak turbulence intensity observed in the distal region, for all flow rates tested. Figure 6 illustrates the area of the turbulent core at each flow rate for the 2.5-mm orifice, 1.6-mm orifice and the 0.5-mm grid. The solid regression line and the finely dotted line in Fig. 6, corresponding to the large 2.5-mm orifice and small 1.6-mm orifice, respectively, indicates that as we increased the flow rate through each orifice the area of the turbulent core increased linearly (p ⬍ 0.001; R2 ⫽ 0.99). The results for the 0.5-mm mesh (coarsely dotted line in Fig. 6) indicate that in this case the turbulent core remains relatively constant in area over the range in flow rates from 7.5 mL/s to 15 mL/s, retaining the area of approximately 275 mm2. The tur-

Table 1. Reynolds numbers, measured peak velocities and theoretical peak velocities from the controlled situation with no modular insert for all flow rates, as well as, Reynolds numbers and theoretical peak velocities within the 2.5-mm and 1.6-mm orifice inserts. No insert Flow rate (ml/s) 2.5 5 7.5 10 12.5 15

2.5-mm orifice

1.6-mm orifice

Reinlet

Measured upeak (cm/s) Mean ⫾ SD (n ⫽ 10)

Theoretical upeak (cm/s)

Reorifice

Theoretical upeak (cm/s)

Reorifice

Theoretical upeak (cm/s)

63 127 190 254 317 380

5.1 ⫾ 0.5 9.1 ⫾ 0.6 13.2 ⫾ 0.8 17.3 ⫾ 0.9 21.5 ⫾ 1.0 25.5 ⫾ 1.1

4 8 12 16 20 24

322 644 966 1288 1610 1933

51 102 153 204 255 306

503 1006 1510 2013 2516 3020

124 249 373 497 622 746

Theoretical values of peak velocities within each orifice were calculated assuming plug flow.

Use of a blood-mimicking fluid ● M. L. THORNE et al.

Fig. 6. Relationship between the area of core turbulence (at a threshold of 21 cm/s for the orifices and 6 cm/s for the grid inserts) and flow rate.

bulent core area for the grid at 5 mL/s was significantly lower than at higher flow rates, with an area of 33 mm2. Repeated Centerline Acquisition From the distribution maps plotted in Figs. 3, 4 and 5, and from the analysis of the area of the turbulent core, we selected a central point for each condition along the centerline and performed repeated measurements at each point (10 times). We studied the trend and reproducibility of mean velocity and turbulence intensity versus flow rate (see Fig. 7a and b). Mean velocity data acquired 3.8 cm downstream of the 2.5-mm orifice, 4.3 cm downstream of the 1.6-mm orifice and 3.2 cm downstream of the 0.5-mm grid were plotted in Fig. 7a. Regression analysis was performed (with regression forced to go through zero) and mean velocity was found to be linearly dependent on flow rate (p ⬍ 0.0001) for all conditions. Mean velocity was forced through zero because theoretically when flow rate is zero, the mean velocity is zero. Turbulence intensity versus flow rate was plotted in Fig. 7b. For the 2.5-mm orifice, 1.6-mm orifice and 0.5-mm mesh turbulence intensity increased with flow rate. Regression analysis was performed and demonstrated a strong dependence of TI on flow rate (p ⬍ 0.005) for each condition. The data were not forced through zero because at a flow rate of 0 mL/s, fluctuations may still be measured, not due to turbulence but due to inherent Doppler ultrasound system noise. Note that the turbulence values reported in Fig. 7 are lower than the maximum values observed within the maps shown in Figs. 3, 4 and 5; this is due to the fact that the repeated measurements analyzed in Fig. 7 were acquired at a fixed central location that was not intended to correspond with the location of maximum turbulence. For both conditions of jet- and grid-generated turbulence, the blood-mimicking fluid was tested for shortterm reproducibility (within a few seconds) and longerterm reproducibility (approximately 30 min apart). Re-

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sults for short-term reproducibility of turbulence intensity measurements made distal to an orifice and nylon grid are summarized in Table 2. Results for longerterm reproducibility of turbulence intensity measurements (30 min apart) acquired distal to a 2.5-mm orifice, 1.6-mm orifice and 0.5-mm nylon grid are summarized in Table 3. A paired t-test of the mean values over three flow rates demonstrated that repeated longer-term measurements were not significantly different for the 2.5-mm orifice (p ⫽ 0.55), 1.6-mm orifice (p ⫽ 0.59) and 0.5-mm nylon grid (p ⫽ 0.56). Power Figure 8 shows the relationship between power and turbulence intensity in our models. Note that while power has not been calibrated in absolute units for this investigation, Doppler ultrasound acquisition parameters were held constant for all three studies, allowing relative power to be compared quantitatively between Fig. 8a– c. Figure 8a illustrates Doppler backscattered power versus turbulence intensity, distal to the 2.5-mm orifice. Linear regression analysis reported a slope that was significantly different than zero (p ⬍ 0.05; R2 ⫽ 0.76), indicating that power increases slightly with increasing turbulence intensity. Figure 8b illustrates Doppler backscattered power versus turbulence intensity distal to the 1.6-mm

Fig. 7. Fluid behavior within a turbulent region 3.8 cm distal to a 2.5-mm orifice insert (solid circles), 4.3 cm distal to a 1.6-mm orifice insert (solid triangles) and 3.2 cm distal to a 0.5-mm nylon grid insert (open circles): (a) mean velocity and standard errors with increasing flow rate; and (b) turbulence intensity (TI) and standard errors with increasing flow rate.

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Table 2. Mean and standard error of turbulence intensity values calculated from 10 samples collected sequentially at different flow rates 3.8 cm distal to a 2.5-mm orifice, 4.3 cm distal to a 1.6-mm orifice and 3.3 cm distal to a 0.5mm nylon grid. Turbulence intensity (cm/s) Mean ⫾ SE (n ⫽ 10) Flow rate (ml/s)

2.5-mm orifice

1.6-mm orifice

0.5-mm nylon grid

7.9 ⫾ 0.2 11.0 ⫾ 0.4 17.3 ⫾ 0.5 24.8 ⫾ 0.8 32.5 ⫾ 1.6 40.8 ⫾ 2.1

16.4 ⫾ 0.4 29.5 ⫾ 1.2 43.6 ⫾ 1.6 55.8 ⫾ 1.2 75.9 ⫾ 2.2 84.6 ⫾ 2.9

0.31 ⫾ 0.02 1.07 ⫾ 0.06 3.44 ⫾ 0.23 2.33 ⫾ 0.18 2.91 ⫾ 0.20 4.11 ⫾ 0.19

2.5 5 7.5 10 12.5 15

not significantly different from zero (p ⫽ 0.58), suggesting that changes in backscattered power are not accounted for by changes in mean velocity alone.

orifice. In this case, power remains relatively constant up to a TI value of about 56 cm/s, with an apparent increase in power for high values of TI (i.e., TI ⬎ 75 cm/s). Linear regression analysis for the 1.6-mm orifice reported a slope that was not significantly different than zero (p ⫽ 0.083; R2 ⫽ 0.57). Figure 8c illustrates Doppler backscattered power versus turbulence intensity distal to the 0.5-mm grid. Linear regression analysis reported a slope that was significantly different than zero (p ⬍ 0.005; R2 ⫽ 0.61), indicating that power increases linearly with increasing turbulence intensity. To investigate whether the observed changes in turbulence intensity with respect to power could be partially explained by a correlation between TI and mean velocity, in the absence of turbulence, we performed an additional analysis. One second of data was acquired in a region of undisturbed laminar flow on the centerline of the tube with all inserts removed. This analysis was repeated 10 times for flow rates of 2.5 mL/s, 5 mL/s, 7.5 mL/s, 10 mL/s, 12.5 mL/s and 15 mL/s, resulting in mean velocities between 4 and 24 cm/s. Linear regression analysis between backscattered power and mean velocity under these conditions reported a slope that was

DISCUSSION Our investigation indicates that a previously developed blood-mimicking fluid is suitable for in vitro investigations of turbulent flow conditions, using Doppler ultrasound. The synthetic fluid provided appropriate Doppler power under conditions of both laminar and turbulent flow, facilitating quantitative assessment of mean velocity and velocity fluctuations (i.e., turbulence intensity). The blood-mimicking fluid exhibited excellent reproducibility over periods ranging from a few seconds to hours. Readily available components ensure consistency between experiments and between laboratories, which is not necessarily the case with human or animal blood preparations. The flow conditions under which the fluid was studied are comparable with disturbed or turbulent flow distal to diseased human vessels, such as carotid stenoses. Our orifice models represent a range of moderate to severe carotid disease. The maximum mea-

Table 3. Mean and standard error of turbulence intensity values acquired distal to a 2.5-mm orifice, 1.6-mm orifice, and 0.5 mm nylon mesh calculated from ten samples collected sequentially at three flow rates and at two time-points. Turbulence intensity (cm/s) Mean ⫾ SE (n ⫽ 10) 2.5-mm orifice Flow rate (ml/s) 5 10 15

1.6-mm orifice

0.5-mm nylon grid

Baseline

30 min

Baseline

30 min

Baseline

30 min

11.0 ⫾ 0.4 24.8 ⫾ 0.8 40.8 ⫾ 2.1

11.9 ⫾ 0.3 23.7 ⫾ 0.8 43.2 ⫾ 1.5

29.5 ⫾ 1.2 55.8 ⫾ 1.2 84.6 ⫾ 2.9

29.2 ⫾ 0.7 58.9 ⫾ 1.0 73.8 ⫾ 2.7

1.07 ⫾ 0.06 2.33 ⫾ 0.18 4.11 ⫾ 0.19

0.45 ⫾ 0.01 2.9 ⫾ 0.13 4.0 ⫾ 0.24

A paired t-test of the mean values over all flow rates demonstrate that repeated longer-term measurements were not significantly different. (p ⬎ 0.5).

Use of a blood-mimicking fluid ● M. L. THORNE et al.

Fig. 8. Power (⫾SE) at different levels of turbulence intensity (TI) within a turbulent region (a) 3.8 cm distal to a 2.5-mm orifice insert, (b) 4.3 cm distal to a 1.6-mm orifice insert and (c) 3.2 cm distal to a 0.5-mm nylon grid insert. Solid lines represent the result of linear regression analysis.

sured values of turbulence in these cases (10 to 80 cm/s) were found to be similar to those reported for in vivo studies of human disease conditions such as aortic stenosis, where turbulence values between 10 cm/s (Isaaz et al. 2003) and 40 cm/s (Walburn et al. 1983) have been reported. This investigation of a BMF for in vitro studies of turbulence employed two relatively simple conditions of turbulence that are common in engineering and physics: jet- and grid-generated (Adam and Burstein 1997; Bruneau et al. 1999). In both cases, we investigated constrained turbulence, which occurs when the distal turbulent flow field is confined by a solid boundary. As walleffects are significant for constrained turbulence, there are no straightforward comparisons with analytical models or closed-form solutions, hence investigations are typically performed semiempirically (Liggett 1994; Liu et al. 1997). Flow through a step orifice is understood to

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become turbulent at orifice Re of between 300 and 400 (Evans et al. 1988; Milnor 1982). In this study, orifice Re ranged from 300 to 3000, ensuring the development of constrained jet turbulence in the distal region. In the case of the constrained jet, previous studies have also shown that steady flow through a small diameter orifice creates a high velocity jet and that flow first becomes unstable in the region of shear layer bounding the jet (Batchelor 1967; Mathieu 2000; Yongchareon and Young 1979). This creates a conical pattern of relatively high turbulence distal to the orifice jet, as shown in Figs. 3 and 4. The velocity patterns distal to the smaller orifice (Fig. 4) were slightly different than those observed with the larger orifice. This smaller orifice created a larger stepdiscontinuity in velocity, thus, causing a high velocity, nonturbulent jet that continues farther down the flow field, until the energy dissipates due to viscous forces and the jet breaks up into fluctuating or turbulent flow (Fei et al. 1988; Modi and Akutsu 1990; Yoganathan et al. 1988). Although it is interesting to note that the maximum value of turbulence intensity was higher in the larger orifice, it is not appropriate to make conclusions about the relative turbulence intensity that may occur in different clinical stenosis grades. This could be subject of future study in anthropomorphic models (Poepping et al. 2004). The second type of turbulence studied was gridgenerated turbulence, as illustrated in Fig. 5. The observed turbulence pattern distal to the grid approximated homogeneous isotropic turbulence, which is known to occur distal to a grid (Bradshaw 1971; Bruneau and Kellay 2005; Wu et al. 1998). Similar patterns of lowlevel, uniform turbulence intensity, extending axially distal to a grid, have been observed in in vitro studies of turbulence distal to a vena cava filter (Leask et al. 2001). Our observations that mean velocity and turbulence intensity linearly increases with increasing flow rate are also in agreement with previous studies (Stein and Sabbah 1974). Previous Doppler ultrasound investigations have indicated a relationship between backscattered power and turbulent flow (Bascom et al. 1993; Cloutier et al. 1996; Shung et al. 1984). These experiments, typically carried out using whole blood (Wu et al. 1998) or red blood cell suspensions with normal hematocrit (Bascom et al. 1997; Cloutier and Shung 1993), have reported an increase in returned Doppler power with increasing turbulence. This effect is likely due to a decrease in correlation between red blood cells. Our study, using 5-␮m diameter nylon particles as scatterers, also reports a significant increase in Doppler power with increasing turbulence intensity (Fig. 8a and c). This observation raises the possibility that changes in Doppler backscatter power may be partly related to two-phase flow physics, rather than biochemical interactions between blood cells. It is important to

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note in any case that the blood-mimicking fluid is not expected to accurately mimic all of the properties of real blood (such as shear-related aggregation and the formation of rouleaux). Caution should be used in an in vitro investigation where the intent is to use Doppler power as a direct indication of turbulence. For example, in a previous study, Cloutier et al. (1995) reported no change in Doppler power with increasing turbulence when 20 to 50 ␮m Sephadex particles were used as scatterers in a different blood-mimicking fluid. In the current study, turbulence intensity was calculated directly from fluctuations in mean velocity, which can be quantified accurately provided that there is a suitable level of returned Doppler power under all flow conditions. Further experiments, providing a direct comparison of the BMF to blood flow in vivo, will be required to understand the differences in two-phase flow observed in a BMF (i.e., rigid-nylon particles suspended in a water-based solution) vs. that exhibited by blood in vivo. These experiments will be necessary to translate in vitro findings to the in vivo situation, particularly with respect to studies of Doppler backscattered power in turbulent conditions. Limitations with this study include the fact that relatively simple geometrical models were used to investigate turbulent flow conditions. The step orifice and mesh models used here are only an approximation of the complex conditions found in vivo. Nonetheless, the standardized conditions of constrained-jet and constrainedgrid turbulence facilitate comparison with previous engineering studies, while allowing us to investigate turbulence in a controlled environment. Our study also included only steady flow conditions, rather than physiologically relevant pulsatile flow. However, our results indicate that the same fluid could be used to study turbulence in anthropomorphic ultrasound flow phantoms, which mimic the geometry and flow waveforms found in humans (Poepping et al. 2002). The capability to visualize and quantify turbulence during in vitro studies is important in a wide range of investigations related to diagnosis of vessel disease and the design of medical devices. Turbulence is thought to play a role in platelet activation and thrombus formation; thus it is essential to understand the distribution and level of turbulence in diseased vessels and near implanted therapeutic devices with small orifices or grids. This linkage between turbulence and clot formation has provided the motivation for previous turbulence studies related to stenotic vessel disease (Bascom et al. 1993; 1997; Cloutier et al. 1996; Ghalichi and Deng 2003; Stein and Sabbah 1976; Stroud et al. 2002; Varghese and Frankel 2003), regurgitant jets (Krabill et al. 1989; Liu et al. 1997; Meyer et al. 2001; Sugawara et al. 1991), heart valve design (Bluestein et al. 2000, 2002; Huang et al. 1994; Wang et al. 2001), and blood pump design (Suku-

Volume 34, Number 7, 2008

mar et al. 1996). While many of these investigations have been carried out with laser-Doppler velocimetry or hot-wire anemometry, our results indicate that conventional Doppler ultrasound techniques can also be used effectively to study turbulent flow in a controlled environment, using a standardized blood-mimicking fluid. CONCLUSIONS Our findings indicate that the blood-mimicking fluid tested is compatible with in vitro Doppler ultrasound flow systems for turbulence investigations. We were successful in creating a system that mimics constrained jet turbulence and constrained grid-generated turbulence, and we were able to measure this turbulence reliably under conditions of steady flow. The blood-mimicking fluid exhibited DUS characteristics similar to those previously reported for blood and produced an adequate level of power in the backscattered signal, allowing for calculation of instantaneous velocity spectra and from this, turbulence intensity. Acknowledgments—The authors acknowledge ATL (Advanced Technology Laboratories, Philips, Seattle, WA, USA) for the UM8 ultrasound unit. Financial support has been provided by the Heart and Stroke Foundation of Ontario (grant no. T-5135). Vessel models were fabricated with support from the Canadian Institutes for Health Research (group grant no. GR-14973). Drs. Holdsworth and Steinman are Career Investigators, supported by the Heart and Stroke Foundation of Ontario.

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