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A rotating torus phantom for assessing color Doppler accuracy
Ultrasound in Med. & Biol., Vol. 25, No. 8, pp. 1251–1264, 1999 Copyright © 1999 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/99/$–see front matter
PII S0301-5629(99)00084-8
● Original Contribution A ROTATING TORUS PHANTOM FOR ASSESSING COLOR DOPPLER ACCURACY SANDY F. C. STEWART Hydrodynamics and Acoustics Branch, Center for Devices and Radiological Health, Food and Drug Administration, Rockville, MD 20850 USA (Received 23 February 1999; in final form, 10 June 1999)
Abstract—A rotating torus phantom was designed to assess the accuracy of color Doppler ultrasound. A thin rubber tube was filled with blood analog fluid and joined at the ends to form a torus, then mounted on a disk submerged in water and rotated at constant speeds by a motor. Flow visualization experiments and finite element analyses demonstrated that the fluid accelerates quickly to the speed of the torus and spins as a solid body. The actual fluid velocity was found to be dependent only on the motor speed and location of the sample volume. The phantom was used to assess the accuracy of Doppler-derived velocities during two-dimensional (2-D) color imaging using a commercial ultrasound system. The Doppler-derived velocities averaged 0.81 ⴞ 0.11 of the imposed velocity, with the variations significantly dependent on velocity, pulse-repetition frequency and wall filter frequency (p < 0.001). The torus phantom was found to have certain advantages over currently available Doppler accuracy phantoms: 1. It has a high maximum velocity; 2. it has low velocity gradients, simplifying the calibration of 2-D color Doppler; and 3. it uses a real moving fluid that gives a realistic backscatter signal. © 1999 World Federation for Ultrasound in Medicine & Biology. Key Words: Color Doppler accuracy, Doppler ultrasound phantom, Color Doppler ultrasound.
String phantoms are accurate and useful for calibrating pulsed Doppler systems (Walker et al. 1982; Phillips et al. 1990), but are not particularly suitable for two-dimensional (2-D) color imaging (Rickey et al. 1992). The moving string forms a narrow color image, from which velocity is difficult to measure. To provide a larger target for assessing color Doppler, a phantom was developed that uses a moving belt of flexible foam (Rickey et al. 1992). A rotating rubber disk has also been used to assess Doppler accuracy (McDicken et al. 1983; Fleming et al. 1994; Schwarz et al. 1995). Some of these devices use materials that may not produce a realistic backscatter signal. Phantoms based on parabolic flow in a tube (McDicken 1986) or between parallel plates (Boote and Zagzebski 1988) use actual flowing fluids. However, the assessment of color Doppler is complicated by the strong dependence on position of the fluid velocity in such phantoms, so that the color pixel intensity is also heavily dependent on position. Entrance effects may cause errors: if the entrance section is not long enough for the flow to develop fully, the velocity field will not have the assumed parabolic flow (Fung 1996; Law et al. 1989). The maximum velocity is also limited, because high flow
INTRODUCTION Doppler ultrasound is a widely accepted technique for the clinical assessment of cardiovascular blood flow due to its relatively low cost per examination, noninvasive character, high level of safety and demonstrated effectiveness. Doppler has made significant strides in replacing older, more invasive (and less safe) methodologies, such as dye angiography for assessing valvular regurgitation. However, it has yet to be displaced by newer technologies such as magnetic resonance (MR) flow imaging. Despite the wide use of Doppler ultrasound in all its modalities, one subject that has received less attention than it deserves is that of accuracy. Calibration, standards and accuracy assessment all lag behind the technology itself. This may be due, in part, to the lack of a generally accepted standard for assessing Doppler accuracy. Numerous methods have been described for assessing the accuracy of Doppler ultrasound (US) systems.
Address correspondence to: Sandy F. C. Stewart, Ph.D., Hydrodynamics and Acoustics Branch, Food and Drug Administration, 9200 Corporate Blvd. (HFZ-132), Rockville, MD 20850 USA. E-mail: [email protected] 1251
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rates may be associated with turbulent flow, which will invalidate the assumed velocity profile. The maximum velocity may be less than 100 cm/s, less than the range available on most commercial US systems, and less than velocities commonly found in stenotic vessels or regurgitant heart valves (which can reach 5– 6 m/s). To their advantage, tube phantoms provide a more physiologically appropriate model of flow in the vasculature, and can be used to assess methods to calculate volume flow (Picot et al. 1995; Forsberg et al. 1995; Holland et al. 1996), to derive the velocity profile (Hein and O’Brien 1992), or to characterize three-dimensional (3-D) color Doppler systems (Guo et al. 1995). This study was designed to characterize a new phantom for assessing color Doppler accuracy that overcomes many of the problems of previous methods. The phantom consists of a submerged rotating torus, filled with blood analog fluid (Stewart 1995). Numerical studies and flow visualization experiments were employed to confirm the assumed solid-body flow of the fluid within the torus. Detailed reproducibility tests were performed to determine effects of day-to– day variabilities. The torus phantom was then used to assess the effects of certain instrument settings on color Doppler-derived velocities from a commercial ultrasound system. METHODS Phantom description The torus phantom was made from a thin rubber bicycle inner tube, measuring 0.064 cm in thickness and 3.0 cm in diameter. The tube was filled with a bloodmimicking fluid (described below) and joined end-to– end by clamping both ends onto a short hollow plastic cylinder. The rubber torus was then mounted on the rim of a disk 52 cm in diameter and glued in place with silicone adhesive (Fig. 1). The distance between the center of the disk and the center of the tube was 27.5 cm; thus, the torus had a minor radius equal to 1.5 cm and a major radius equal to 27.5 cm. The disk and torus were submerged in a bath of degassed water with the axis oriented vertically. The disk rotation was driven by a gear motor (Model 32D5BEPM5F, Bodine Electric Company, Chicago, IL) mounted vertically above the disk. The motor speed was monitored by an optical encoder (Accucoder Model 220C, Encoder Products Co., Sandpoint, ID) coupled to the main shaft by a drive belt, and electronically controlled by a digital velocity feedback system (Model DLC300, Minarik Electric, Glendale, CA). It was hypothesized that the fluid within the torus spins as a solid body at the same angular velocity as the torus, after some finite acceleration time during which secondary flows dominate. This hypothesis was con-
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Fig. 1. Schematic of torus phantom for assessing Doppler accuracy.
firmed in flow visualization and numerical experiments described below. Thus, the circumferential velocity of the torus fluid was assumed to be equal to the torus angular velocity times the radial position of the sample volume. This was the standard against which the Doppler-derived velocity was compared. The blood-mimicking fluid used (R.G. Shelley Ltd., North York, Ontario, Canada) was 50% water and 50% machine cutting fluid (Syn-Cut HD, Acra Tech, Ontario, Canada), with acoustic and viscous properties closely matching those of blood (Rickey et al. 1995). Ultrasound reflection was provided by suspended 10-m diameter nylon copolymer particles (Orgasol 3501 EXD, ELF Atochem, Ontario, Canada). One potential problem with the torus phantom is settling (or floating) of the echogenic particles over time when the phantom is not in use. These would be inconvenient to resuspend in the closed tube. It was speculated, however, that transient secondary flows at the commencement of rotation helped to redistribute the particles. This hypothesis was confirmed during the flow visualization experiments. Doppler ultrasound system An ATL Ultramark 9 HDI ultrasound system (Advanced Technology Laboratories, Bothell, WA) outfitted with a Model L10-5 linear array transducer (Doppler frequency ⫽ 6.0 MHz, aperture ⫽ 38 mm) was used for all laboratory experiments. The transducer was mounted via a specially designed clamp in a three-axis positioning system (Velmex, Inc., Bloomfield, NY). The transducer’s active face was suspended 1.0 cm above the torus and parallel to the torus tube axis, with the US beam focused on the center of the torus fluid. The Doppler angle was fixed at 70°, representative of the clinical case with a vessel parallel to the skin. The degassed water
Color Doppler accuracy phantom ● S. F. C. STEWART
bath in which the torus was immersed provided a path for the US beam between the transducer and the torus. Radial calibration Two 1.0-cm ⫻ 0.5-cm rectangles of US-absorbing rubber (Corsaro et al. 1982) were glued 0.1 cm apart on the disk upper surface, with the gap 22.1 cm from the torus major axis (Fig. 1). The transducer was first positioned to maximize the specular reflection (as seen in the 2-D display) of the disk between the two rubber rectangles. This indicated that the midplane of the ultrasound beam was 22.1 cm from the torus major axis. The transducer was then translated radially outward a distance r using the positioning system, until the sample volume was centered within the torus tube, determined by noting a maximum in brightness of the specular reflection of the bottom surface of the tube. The radial position of the sample volume RSV was then calculated by RSV ⫽ r ⫹ 22.1 cm. This procedure allowed accurate radial positioning of the ultrasound beam without having to make assumptions about the position of the beam with respect to the transducer housing. The actual velocity of the fluid insonated by the transducer Vf was then calculated by multiplying RSV by the torus angular velocity , or Vf ⫽ RSV 䡠 . The color Doppler-derived velocity Vcd was then compared to Vf. Experimental studies Reproducibility of the torus calibration system was assessed by comparing the measured torus fluid velocity and the color Doppler-derived velocity over five experiments, using a torus speed of 40 RPM. Before each experiment, the transducer was removed from and then replaced into its mounting clamp and the 3-D positioning system was readjusted for an optimal image. In addition, the US system was powered down, reset, and the instrumentation settings returned to a fixed set of values, which were optimized for a subjectively noise- and dropoutfree signal (see Table 1). Next, the effects on reproducibility of deliberate variations in transducer positioning, power setting, color gain and width of the color Doppler subset of the 2-D image were assessed. Finally, the effects on color Doppler accuracy of systematic variations in the pulse-repetition frequency (PRF) and wall filter frequency (WFF) were investigated in detail. Six different torus rotational speeds (10, 20, 40, 60, 80 and 100 RPM) were used, corresponding to six fluid velocities (Vf ⫽ 28.8, 57.6, 115.2, 172.8, 230.4 and 288.0 cm/s, respectively). The PRF was varied between 1.0 kHz and 10 kHz, corresponding to maximum velocities as labeled on the instrument between 12 and 170 cm/s (with the baseline velocity set to zero). Due to the Doppler angle (approximately 70°), the actual velocity Vf ⫽ 28.8 cm/s was
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Table 1. ATL Ultramark 9 HDI nominal instrument settings used in color Doppler reproducibility tests Instrument parameter
Setting used
Pulse-repetition frequency Wall filter HDI/high frequency Variance Output power Color gain Color sensitivity Color persistence Dynamic filtering Color box width
4.5 kHz 800 Hz on/on off ISPTA.3† ⫽ 20 mW/cm2, MI‡ ⫽ 0.5 94% Maximum ⫽ 16 Minimum ⫽ 0 Off 1.2 cm
†Spatial peak temporal average intensity, derated. ‡Mechanical index.
measured at approximately 9 cm/s, which could be measured without aliasing at a maximum velocity of 12 cm/s. The lowest PRF was chosen so that aliasing was avoided, and the highest PRF was chosen when the color was not quite invisible to the eye. At each PRF, the WFF was varied between 50 and 800 Hz; however, not all WFF settings were available at all PRFs. All other instrument settings were fixed as in the reproducibility tests (Table 1). The output power was characterized by the ISPTA.3 (spatial peak temporal average intensity, mW/cm2, derated by 0.3 dB/cm-MHz; AIUM/NEMA 1998a) and MI (mechanical index; AIUM/NEMA 1998b). The ISPTA.3 and MI were set initially to 20 mW/cm2 and 0.5 at the lowest WFF and PRF; however, the values tended to increase somewhat as the PRF and WFF were increased. In all cases, velocities from n ⫽ 10 images were recorded for each instrument setting and experimental setup. Image processing and data analysis Images from the ultrasound system’s RGB video output were captured using a Flashpoint 128 video frame grabber (Integral Technologies, Indianapolis, IN) mounted in a personal computer running Windows 95. Images captured with a resolution of 640 ⫻ 480 pixels and color depth of 24 bits (i.e., 8 bits per color red, green, and blue) were saved onto hard disk in Windows BMP image file format. A custom color/velocity map on the ultrasound system was used to encode velocities in the red image plane, using a strictly linear velocity-to– color translation scheme. Red byte values varied from zero to 255, with zero corresponding to zero velocity and 255 corresponding to the maximum velocity. Green was added to make the color maps more visible to the eye, with pixel values of zero and 197 corresponding to one half the maximum velocity and the maximum velocity, respectively. The green pixel values were ignored when calibrating or measuring velocities during image analysis.
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ities using the computer mouse, the velocities at each pixel within the parallelogram were calculated, and the mean velocity over all the pixels was recorded. Statistical analyses were performed using Minitab for Windows Release 12 (Minitab, Inc., State College, PA), running on a personal computer.
Fig. 2. Definition of Doppler angles. Top: side view of torus (seen from center). is the conventional Doppler angle between the US beam and fluid velocity in the plane of the beam. Bottom: top view of torus (note: minor radius is exaggerated for clarity). is the Doppler angle due to curvature of the torus (outside plane of beam), which varies with position (but is considered to be negligible).
A correction for the Doppler angle between the tube axis and the axis of the transducer beam was performed during image analysis to find the fluid velocity parallel to the rim of the torus (Fig. 2, top). Vcd was also dependent on the variable angle between the plane of the ultrasound beam and the torus itself, due to the mild curve of the major radius (Fig. 2, bottom; Gill 1985). Errors due to this angle were calculated to be less than 0.1% for a 2.0-cm error in the placement of the transducer, however, and were, therefore, ignored. Image files stored on disk were analyzed by a program written in Borland Pascal for Windows, version 7.0 (Borland International, Scotts Valley, CA). After an image was read into this program, distances and velocities were calibrated first. The linear array transducer emitted the US beam along parallel lines (Fig. 3); therefore, the Doppler angle was assumed to be constant over the entire color image. The angle was measured graphically on the screen, and the color-encoded velocities were adjusted by dividing by cos . A graphic parallelogram was then drawn around the color-encoded veloc-
Flow visualization studies Flow visualization studies were performed in a transparent version of the torus to verify that the fluid within the torus rotates as a solid body, following a brief spin-up period during which transient secondary flows dominate. The transparent torus was made of 2.54 cm i.d. Tygon tubing filled with an approximately 65%/35% water/glycerine solution in which 300 – 860-m ion exchange resin particles (Amberlite IRA-95, Sigma Chemical Co., St. Louis, MO) were suspended. The mixture was formulated to make the resin particles as neutrally buoyant as possible. The torus was mounted on the disk, but was not suspended in the water tank. A Pulnix TM 9701 video camera was mounted vertically over the torus to record the motion of the particles, at 30 full frames/s. The torus was illuminated by two frosted floodlights. No attempt was made to single out a single cross-sectional plane (e.g., as with a laser sheet). Video images of the torus (after spin-up) were downloaded to a computer. Two images exactly 1 revolution apart were analyzed, for rotational speeds of 20, 40, 60 and 90 RPM. The two images were colored red and green, respectively, in a commercial image analysis program (Corel Photo-Paint, Corel Corporation, Ottawa, Ontario, Canada) and superimposed to detect relative motion of the particles with respect to each other or to the torus wall, which would indicate nonsolid body motion. Finite element simulations Finite element simulations of a fluid-filled rotating torus were also performed to test the hypothesis that the fluid within the torus moves as a solid body. The simulations also provided detailed information on the accelerating and transient flows occurring during spin-up. The simulations were performed using the FIDAP finite element program (version 7.6, Fluent, Inc., Evanston, IL) running on an IBM 350 RISC workstation. The nonlinear Navier–Stokes equations of fluid flow were descretized for an axisymmetric, laminar, transient model of a torus, with a major radius equal to 28 cm and minor radius equal to 1.5 cm. The model used a 2-D mesh modeling a cross-section of the rubber tube (Fig. 4), consisting of 2232 4-node, 2-D quadrilateral elements. The outer boundary was represented by 156 2-node, 1-D edge elements. The complete model included a total of 2388 elements and 2311 nodes. Only 1 vertical half of the tube cross-section was modeled, to
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of velocities in the direction were allowed, so that the entire torus could be represented by one cross-section of the tube in the r-z plane. The torus and the fluid within were set initially at rest. Axial velocities uz at the plane of symmetry of the torus were fixed at zero throughout the simulation. Angular velocities corresponding to 25, 50 or 75 RPM were imposed on the torus wall, ramped up from 0 over a period of 1 s to simulate acceleration of the torus. The imposed circumferential velocity u varied linearly with the radial coordinate r from the inner wall to the outer wall (Table 2). The simulation was solved over successive time steps, using a trapezoidal (second order) integration scheme. The initial time step was set to 5 ⫻ 10⫺3 s, but was allowed to vary according to the convergence requirements of the program, with the maximum time step limited to 0.33 s. The time step tended to increase with time as the secondary flows disappeared and the remaining u velocities approached steady state. The resulting velocity maps vs. time were analyzed to determine how rapidly the fluid accelerated to the speed of the torus, and how rapidly the transient secondary flows disappeared. RESULTS
Fig. 4. Mesh used in finite element analyses to simulate torus cross-section.
exploit the symmetry. Effects of gravity and buoyancy were neglected. All three velocity components, ur, uz, and u, were simulated (where r, z, and represent the radial, axial, and circumferential directions of the torus, Fig. 1), but were functions only of r and z. No variations
Flow visualization studies Despite care in preparation, the water/glycerine solution did not exactly match the density of the ion exchange resin particles. Some of the particles were not perfectly neutrally buoyant and were observed to settle to the bottom of the tube overnight when the torus motor was turned off. When the motor was turned on again, however, the particles were observed to mix immediately due to the transient secondary flows identified in the finite element simulations (see below). Turning the motor off also produced transient secondary flows that caused mixing. Turning the motor on and off several times served to resuspend the particles, which then remained in suspension more than long enough for the experiments to be run. The two superimposed images 1 revolution apart for each of the four speeds are shown in Fig. 5. In each case, the pattern of particles was unchanged; no relative mo-
Table 2. Conditions used in finite element simulations Velocity (cm/s) vs r (z ⫽ 0) Torus speed (RPM) 25 50 75
Angular velocity, (s⫺1)
r ⫽ 26.5 cm (inner wall)
r ⫽ 27.9 cm
r ⫽ 28.0 cm (tube center)
r ⫽ 28.1 cm
r ⫽ 29.5 cm (outer wall)
2.62 5.24 7.85
69.4 138.8 208.1
73.0 146.1 219.1
73.3 146.6 219.9
73.6 147.1 220.7
77.2 154.5 231.7
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tion of the particles with respect to each other or to the walls was observed. There was a ⬃0.2-cm shift between the two images, however, indicating that either 1. the torus motor speed was not perfectly accurate, or 2. the video frame rate was not exactly 30 frames/s, or 3. both. If the video camera frame rate was considered to be accurate, then the additional 0.2-cm displacement indicated that the torus rotational speed was actually 20.02 RPM, rather than the motor controller’s set value of 20.0 RPM. The error was calculated to be about 0.1%. It was concluded that, after spin-up, the velocity field consisted of a uniform circumferential motion. Finite element simulations Results of the numerical simulations also showed that fluid in the torus rotated as a solid body after a brief acceleration period. When the simulated torus was set in motion, the fluid circumferential velocity u in the center of the tube (the central node in Fig. 4) approached that of the torus within approximately 15 s at all torus speeds simulated (Fig. 6). Fluid near the tube wall was found to accelerate even faster. At a torus rotational speed of 50 RPM, the circumferential velocity profiles along a central cross-section of the tube, parallel to the torus major radius, rapidly approached a straight line (Fig. 7, left panel). The velocities varied between 138.8 cm/s at the inner wall and 154.5 cm/s at the outer wall, or by ⫾ 5.4%. Along a cross-section parallel to the torus axis (i.e., at a constant radius), the circumferential velocity profiles rapidly approached a steady state value of 146.6 cm/s, which was constant across the tube (Fig. 7, right panel). In the simulation, the torus acceleration caused appreciable secondary flows in the plane of the tube crosssection. Flows in the axial and radial directions are shown as a function of time in Fig. 8. These represent a double helical flow mirrored about the torus plane of symmetry that disappeared completely within 20 s of startup. Acceleration of fluid in torus A pulsed Doppler recording of the torus phantom starting up is shown in Fig. 9, where the torus final speed was 40 RPM. The narrow spikes represented reflections from the plastic coupler joining the two ends of the rubber tube. These appeared every 1.5 s, which is consistent with a torus speed of 40 RPM. About 6 s were required for the fluid to reach its final velocity, less than half the time needed in the finite element simulations. Reproducibility tests When the transducer was removed and replaced in the clamp, the x-y–z positioning system reset, and the US system turned off and on with the instrument parameters
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returned to fixed values, good reproducibility was observed (Fig. 10a). Analysis of variance did show significant differences, but only between the fourth observation and the others; all other pairs of observations were not significant. Vvf varied between 100.7 and 102.1 cm/s, or approximately ⫾ 0.7%. Vcd was observed to be considerably lower than the imposed fluid velocity Vf of 115.2 cm/s, however. A statistically significant effect of the output power was observed (p ⬍ 0.001, Fig. 10b), but mainly because of the relative drop-off at low power (ISPTA.3 ⬍ 12 mW/cm2). Better reproducibility could be achieved by keeping the power as constant as possible, at a value ⬎ 12 mW/cm2. Subsequent studies used a power equivalent to an ISPTA.3 ⫽ 20 mW/cm2 (although the instrument automatically modified this value somewhat as the WFF and PRF were adjusted). Color gain, when varied between 80% and 100%, did not show a statistically significant effect on the Doppler accuracy (p ⫽ 0.881, Fig. 10c). Color gain was kept at 94% for all other testing. The color box width also did not have a statistically significant effect (p ⫽ 0.859, Fig. 10d). This was fortunate, because this parameter had to be adjusted by eye while manipulating the instrument’s trackball. The box width was kept as close as possible to 1.2-cm wide for all other testing. Varying the radial position of the transducer had a statistically significant effect (p ⬍ 0.001, Fig. 10e). This was expected because the true velocity of the fluid within the torus, Vf, is linearly dependent on the radius. Linear regression provided an estimate of this relationship: V f ⫽ 3.487 s ⫺1 䡠 R sv ⫹ 3.983 cm兾s.
(1)
The theoretical relationship is: V f ⫽ R sv 䡠 .
(2)
where ⫽ (40 RPM/60s 䡠 min⫺1) 䡠 2.0 䡠 ⫽ 4.189 s⫺1. Thus, the fitted slope (3.487 s⫺1) was approximately 20% lower than the theoretical one (4.189 s⫺1). This corresponds well to the fact that, overall, Vcd was observed to be lower than Vf (see below). The fitted offset, 3.983 cm/s, may be due to experimental errors in measuring minor differences in radius. Varying the lateral position of the transducer (tangential to the torus), XSV, also had a significant effect (p ⫽ 0.002, Fig. 10f), but the fitted dependence on XSV (Vf ⫽ 0.649 s⫺1 䡠 XSV ⫹ 101.3 cm/s) was substantially less than the dependence on radius. Color Doppler accuracy assessment Sample color Doppler images for a torus RPM of 20 (Vf ⫽ 57.6 cm/s) as a function of PRF and WFF are
Color Doppler accuracy phantom ● S. F. C. STEWART
Fig. 3. Color Doppler image from linear transducer. Color Doppler velocities are confined to within parallelogram. Torus speed ⫽ 40 RPM; fluid velocity ⫽ 115.2 cm/s; PRF ⫽ 4.5 kHz; WFF ⫽ 600 Hz. Top edge of torus tube (1) is parallel to the face of the transducer (2) and color Doppler box (3). ⫽ Doppler angle ⫽ 70°.
Fig. 5. Results from flow visualization studies: (a) 20 RPM; (b) 40 RPM; (c) 60 RPM; and (d) 90 RPM. Two video images of a transparent torus tube as seen from above are superimposed. The first image was converted to red and the second image, taken 1 complete revolution later, was converted to green.
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Fig. 6. Results of finite element studies. Circumferential velocity of fluid (u) at center of torus tube.
shown in Fig. 11. Qualitative differences were plainly visible, especially at PRFs from 1.8 to 3.0 kHz, where the images for WFF ⫽ 100 Hz had a distinct mottled appearance lacking at higher WFFs. Overall, the color intensity was observed to decrease with increasing WFF.
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The overall decrease in color intensity with increasing PRF was expected, because the maximum velocity range increased with increasing PRF. The color Doppler-derived velocities as a function of RPM, PRF and WFF are compared in Fig. 12. Significant errors in Doppler accuracy were observed. With few exceptions, Vcd underestimated Vf, by an average 19% ⫾ 11%. In 3 cases, Vcd overestimated Vf, at 10 RPM, PRFs ⫽ 4.0, 4.5 and 5.0 kHz, and WFF ⫽ 800 Hz. Most of the observed differences between Vf and Vcd were greater than 3 standard deviations and, so, were statistically significant. At each RPM, a slight overall decrease in Vcd was observed with increasing PRF. The variation with WFF was more complex. At low PRF, Vcd decreased with increasing WFF and, at high PRF, Vcd increased with increasing WFF. At constant WFF, Vcd first increased with increasing PRF, formed a maximum at an intermediate PRF, and then decreased with increasing PRF. A 3-way analysis of variance was performed using a general linear model approach. Because the US system limited the PRFs and WFFs that could be used at any particular RPM, the full data set was disconnected; therefore, only the main effects could be analyzed. In this case, Vcd was found to be dependent significantly on RPM, PRF and WFF at the p ⬍ 0.001 level of significance. To provide a balanced set of data for analysis of the
Fig. 7. Velocity profiles from finite element study at 50 RPM. Left: velocities along tube centerline parallel to radius of torus. Right: velocities along tube centerline parallel to axis of torus.
Color Doppler accuracy phantom ● S. F. C. STEWART
Fig. 8. Axial velocities (left semicircle) and radial velocities (right semicircle) within cross-sectional plane of torus tube at times: (a) 0.50 s; (b) 0.76 s; (c) 1.03 s; (d) 1.24 s; (e) 1.49 s; (f) 2.02 s; (g) 3.00 s; (h) 5.06 s; (i) 20.1 s.
Fig. 9. Pulsed Doppler spectrum of accelerating flow in torus.
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Fig. 10. Reproducibility test results: (a) transducer removed and replaced in clamp, positioning system reset, ultrasound system reset. Subsequent studies tested dependence on (b) output power; (c) color gain; (d) color Doppler box width; (e) radial position of sample volume; and (f) lateral position of sample volume.
interactions among the independent variables, a second ANOVA was performed using a small, connected subset of the data. In this case, the data analyzed included only the velocities Vcd at 10, 20 and 40 RPM, with the PRF varied from 3.5 to 5.0 kHz and WFF varied from 200 to 600 Hz. For this subset of data, Vcd was again observed to be dependent significantly on RPM, PRF, and WFF (p ⬍ 0.001). In addition, all of the interaction terms were significant at p ⬍ 0.001: RPM ⫻ PRF, PRF ⫻ WFF, WFF ⫻ RPM and RPM ⫻ PRF ⫻ WFF. This supports
the conclusion that the complex behavior observed was due to strong interactions among the independent variables, not just random error. Error analysis The flow visualization experiments and numerical simulations showed that, after the brief spin-up period, the fluid within the torus tube moved at the same velocity as the torus. Therefore, the velocity of the-
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Fig. 11. Color Doppler images at torus RPM ⫽ 20 (fluid velocity ⫽ 57.6 cm/s) showing variations with pulse-repetition frequency (PRF) and wall filter frequency (WFF).
fluid within the torus depended only on the motor speed, given by a digital readout, and the sample volume radius, RSV, determined by calibrating the beam via the x-y–z positioning system as described above. The flow visualization experiments suggested that the motor speed accuracy was within approximately ⫾ 0.02 RPM. The reproducibility experiments
suggested that the accuracy of RSV was within approximately ⫾ 0.2 cm. At 100 RPM (near the maximum speed), the torus had a circumferential velocity at the center of the tube of 288.0 cm/s. Given the assumed errors in motor speed and RSV, at 100 RPM, the overall accuracy of the fluid velocity was calculated to be within approximately ⫾ 2.4 cm/s, or ⫾ 0.83%. At 10
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Fig. 12. Variations in color Doppler accuracy with pulse-repetition frequency and wall filter settings, at 6 velocity magnitudes: (a) fluid velocity ⫽ 28.8 cm/s; (b) fluid velocity ⫽ 57.6 cm/s; (c) fluid velocity ⫽ 115.2 cm/s; (d) fluid velocity ⫽ 172.8 cm/s; (e) fluid velocity ⫽ 230.4 cm/s; and (f) fluid velocity ⫽ 288.0 cm/s.
RPM, with a fluid velocity Vf of 28.8, the accuracy was calculated to be within ⫾ 0.5 cm/s, or ⫾ 1.7%. Errors in calculated velocity related to the measured Doppler angle were potentially more severe. The Doppler angle was measured from the color Doppler box during image analysis (Fig. 3). Overall, the measured Doppler angle averaged 70.41° ⫾ 0.14° (mean ⫾ standard deviation, n ⫽ 226). This was very close to the value of 70° given in the US system manufacturer’s literature.1 The L10-5 linear array transducer was positioned as used clinically, with the transducer face parallel to flow direction, as in Fig. 3. However, the observed angle was produced by the instrument’s image-forming software, and did not account for errors, if any, in the actual beam angle. The cosine function is nonlinear, so that the magnitude of errors in the Doppler angle correction varies with the angle. At a Doppler angle of 70°, an uncertainty of ⫾ 1° (⫾ 1.5%) leads to an uncertainty in the velocity of approximately ⫾ 5% (Picot et al. 1995), 3–5 times the error due to radial positioning and motor speed. Without measuring the actual beam angle with respect to the 1
Ultramark 9 Ultrasound System Reference Manual, p. 4A-7.
transducer face (and torus velocity), however, it is impossible to assess how much, if any, of the approximately 19% error seen in the accuracy assessments can be attributed to errors in the Doppler angle. DISCUSSION The torus phantom was shown in this study to be an accurate and reliable device for assessing color Doppler accuracy. The device has many desirable characteristics. Unlike string and belt phantoms, the torus uses a real fluid to calibrate the transducer, thus providing a more realistic ultrasound backscatter signal. In this study, the torus was filled with a commercially available blood analog fluid optimized for US studies, but anticoagulated animal or human blood could easily be substituted. Experiments using contrast agents could also be performed (Fan et al. 1993). Unlike flow phantoms based on parabolic flow in a cylindrical tube, the fluid in the torus phantom moves as a solid body, and has a very low velocity gradient. This is especially useful for color Doppler, which images a 2-D area that is much bigger in size than the small sample volume used in pulsed Doppler. Thus, color Doppler can be unambiguously cali-
Color Doppler accuracy phantom ● S. F. C. STEWART
brated over a large area of fluid that is flowing at almost the same velocity. The torus phantom also has a high maximum velocity (approaching 300 cm/s), a maximum that could be increased further with either a faster motor or larger diameter torus. Some disadvantages were observed, however; the device was rather large and unwieldy, and it was inconvenient to fill the torus and eliminate air bubbles. At high speeds, the rotating torus possessed considerable energy, so it had to be used with care. The flow visualization experiments and finite element simulations supported the hypothesis that the fluid in the torus achieves total solid body motion after a brief acceleration phase. Rotational motion was rapidly convected from the torus wall to the fluid by viscous forces. Thus, the motion of the fluid could be accurately and correctly inferred from the motion of the torus itself. The numerical work suggested that the acceleration phase lasted up to 15 s but, in the pulsed Doppler test, the actual torus fluid took less than half that time to accelerate. It was speculated that this was due to the plastic coupler used to fasten the ends of the rubber tube together. The coupler inside diameter was about half that of the rubber tube, and may have provided an extra viscous force to accelerate the fluid. This narrowing was not modeled in the simulations. The flow visualizations and numerical simulations also demonstrated that there was considerable mixing due to transient secondary flows during spin-up (and spin-down, for that matter). The circumferential velocity of fluid was initially higher near the walls than in the middle of the torus. The momentum of this rapidly moving fluid tended to force fluid near the wall from the inner radius to the outer radius of the torus. The fluid in the tube center was, thus, displaced and made to flow back in from the outer radius to the inner radius of the torus. This set up a counter-rotating, double-helical flow. This is analogous (but opposite in nature) to flow in a curved tube (such as the ascending aorta), where higher velocity fluid in the middle of the tube tends to be thrown to the outer wall of the bend, forcing fluid near the walls to flow back toward the center of the bend in a doublehelical pattern (Pedley 1980). The existence of the transient secondary flows turned out to be a useful feature. The particles in the blood analog fluid used in the US experiments tended to float if the fluid was left undisturbed overnight, and the particles used in the flow visualization experiments tended to settle. Turning the motor on and off a few times (at one of the higher speeds) served to mix the particles thoroughly. Thus, the protocol for assessing Doppler accuracy should include cycling the motor at the start of an experiment.
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It was concluded that the torus phantom could provide reliable reference velocities up to 300 cm/s within an error of ⫾ 1.7%. Errors in the Doppler-derived velocity In this study, the Doppler-derived velocities averaged about 19% low. One possible source of error is the Doppler angle; at 70°, an error of only 4° (6%) could completely account for the 19% error seen (Picot et al. 1995). Thus, the overall error most likely was not due to flaws in the US system per se but, rather, due to the nonlinear nature of Doppler angle-related errors. Refraction between the water bath and blood-mimicking fluid may also have contributed to the error seen. Using Snell’s law and the speed of sound in the water bath (1485 m/s) vs. that in the blood-mimicking fluid (1540 m/s), an incident beam angle in the water bath of 20° to the normal (corresponding to a Doppler angle of 70°) would be refracted to an angle of 20.77° in the blood-mimicking fluid within the tube (corresponding to a Doppler angle of 69.23°). At 70°, an error in the Doppler angle of 0.77° can cause the Doppler-derived velocity to be approximately 3.8% low (Picot et al. 1995). This latter effect may contribute to the observed error, but it is insufficient to account for all of it. Some of the of the overall 19% underestimation of the true velocity may have been due to dropouts (dark pixels mixed in with brightly colored pixels) at low WFF settings (e.g., WFF ⫽ 100 Hz, PRF ⫽ 3.0 kHZ, Fig. 11). No attempt was made to eliminate these pixels, so that they were averaged in with the colored pixels. However, dropouts cannot account for all the variation in Dopplerderived velocity with WFF and PRF, because most images did not have significant dropout (Fig. 11). The increase in Doppler-derived velocities with increased filter setting at high PRFs may be due to the wall filter removing some of the lower frequencies. However, the decrease in Doppler-derived velocities with increased filter setting at low PRFs is not explained by this mechanism. SUMMARY This study should not be taken as a critique of one manufacturer’s instrument. Color Doppler remains a widely accepted and extremely useful tool for assessing blood flow in a safe, noninvasive and effective manner. Color Doppler has been shown to work well for the many clinical uses to which it has been applied, and new applications continue to be developed. The quality of patient care has clearly increased as a direct result of the technology. Despite wide acceptance, color Doppler imaging remains largely qualitative. Analyzing the approximate color brightness and the layout with respect to adjacent
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solid tissues takes precedence over quantifying the precise spatial dependence of velocities. Often, clinical analysis consists of asking simple questions or making comparisons. When assessing heart valve function one might ask, Is aliasing present during forward flow when the valve is open, suggesting stenosis? Are regurgitant jets visible when the valve is closed? Color Doppler gives an excellent overall view of the flow field, and can easily provide answers to these kinds of qualitative questions. If quantitative analysis is needed, the instrument can be switched to pulsed or continuous-wave Doppler mode. This provides a spectrum of the velocities vs. time, but forfeits the 2-D imaging capability. In contrast, quantitative analysis of the color-encoded velocity field is chiefly the subject of research (e.g., in measuring volumetric flows in regurgitant heart valves) (Grimes et al. 1994; Stewart 1998). Overall, the L10-5 transducer examined in this study was not as accurate as one might wish in color Doppler mode. In preliminary experiments similar to the ones shown in Fig. 12, the machine’s P3-2 phased array transducer was found to be more accurate, with an overall ratio of the Doppler-derived to actual velocity of 0.90 ⫾ 0.08 (range 0.56 to 1.16). This may be due, in part, to the lower Doppler angle used (approximately 45°). Therefore, the most important finding of this study is not the limitation of one transducer, but the significant effect of instrument settings on accuracy, a characteristic that may not be limited to one transducer or machine. Clinicians should be aware of the possibility of these variations, particularly when comparing repeated exams, and should consider investigating the color Doppler accuracy of the machines and transducers they use. The torus phantom described herein is a tool that can be used to assess color Doppler accuracy of current machines, and assist with the design of more accurate ones. It can accurately characterize color Doppler ultrasound at high flow velocities and low velocity gradients, using blood-mimicking fluids with a realistic backscatter signal. The area of interrogation is large, which is beneficial for color Doppler and allows easy calibration. With these characteristics, the torus phantom provides a number of advantages over previously described Doppler accuracy phantoms. Acknowledgements—This paper is dedicated to the memory of Ronald F. Carey, Ph.D., whose enthusiasm, encouragement and expertise were fundamental to the success of this work. The expert machining assistance of James Duff and Bruce Fleharty in building the phantom and making many excellent suggestions is gratefully acknowledged. The assistance of Gerald R. Harris, Ph.D. with the optical motor controller is also appreciated, as is the assistance of Ronald A. Robinson with the flow visualization experiments. The mention of commercial products, their source, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the U. S. Department of Health and Human Services.
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REFERENCES AIUM/NEMA. Acoustic output measurement standard for diagnostic ultrasound measurement. Laurel, MD: AIUM/NEMA, 1998a. AIUM/NEMA. Standard for real-time display of thermal and mechanical acoustic output indices on diagnostic ultrasound equipment, revision 1. Laurel, MD: AIUM/NEMA, 1998b. Boote EJ, Zagzebski JA. Performance tests of Doppler ultrasound equipment with a tissue and blood-mimicking phantom. J Ultrasound Med 1988;7:137–147. Corsaro RD, Klunder JD, Jarzynski J. Filled rubber materials system: application to echo absorption in water filled tanks. J Acoust Soc Am 1980;68:655– 664. Fan P, Czuwala PJ, Nanda NC, Rosenthal SM, Yoganathan A. Comparison of various agents in contrast enhancement of color Doppler flow images: an in vitro study. Ultrasound Med Biol 1993;19:45–57. Fleming AD, McDicken WN, Sutherland GR, Hoskins PR. Assessment of colour Doppler tissue imaging using test-phantoms. Ultrasound Med Biol 1994;20:937–951. Forsberg F, Liu JB, Russell KM, Guthrie SL, Goldberg BB. Volume flow estimation using time domain correlation and ultrasonic flowmetry. Ultrasound Med Biol 1995;21:1037–1045. Fung YC. Biomechanics: Circulation. (2nd ed.) New York: Springer, 1996:182–189. Gill RW. Measurement of blood flow by ultrasound: accuracy and sources of error. Ultrasound Med Biol 1985;11:625– 641. Grimes RY, Burleson A, Levine RA, Yoganathan AP. Quantification of cardiac jets: theory and limitations. Echocardiography 1994;11: 267–280. Guo Z, Moreau M, Rickey DW, Picot PA, Fenster A. Quantitative investigation of in vitro flow using three-dimensional colour Doppler ultrasound. Ultrasound Med Biol 1995;21:807– 816. Hein IA, O’Brien WD. A flexible blood flow phantom capable of independently producing constant and pulsatile flow with a predictable spatial flow profile for ultrasound flow measurement validations. IEEE Trans Biomed Eng 1992;39:1111–1122. Holland CK, Clancy MJ, Taylor KJW, Alderman JL, Purushothaman K, McCauley TR. Volumetric flow estimation in vivo and in vitro using pulsed-Doppler ultrasound. Ultrasound Med Biol 1996;22: 591– 603. Law YF, Johnston KW, Routh HF, Cobbold RSC. On the design and evaluation of a steady flow model for Doppler ultrasound studies. Ultrasound Med Biol 1989;15:505–516. McDicken WN. A versatile test-object for the calibration of ultrasonic Doppler flow instruments. Ultrasound Med Biol 1986;12:245–249. McDicken WN, Morrison DC, Smith DSA. A moving tissue-equivalent phantom for ultrasound real-time scanning and Doppler techniques. Ultrasound Med Biol 1983;9:L455–L459. Pedley TJ. The fluid mechanics of large blood vessels. London: Cambridge University Press, 1980. Phillips DJ, Hossack J, Beach KW, Strandness DE Jr. Testing ultrasonic pulsed Doppler instruments with a physiologic string phantom. J Ultrasound Med 1990;9:429 – 436. Picot PA, Fruitman M, Rankin RN, Fenster A. Rapid volume flow rate estimation using transverse colour Doppler imaging. Ultrasound Med Biol 1995;21:1199 –1209. Rickey DW, Rankin R, Fenster A. A velocity evaluation phantom for colour and pulsed Doppler instruments. Ultrasound Med Biol 1992; 18:479 – 494. Rickey DW, Picot PA, Christopher DA, Fenster A. A wall-less vessel phantom for Doppler ultrasound studies. Ultrasound Med Biol 1995;21:1163–1176. Schwarz KQ, Bezante GP, Chen X. When can Doppler be used in place of integrated backscatter as a measure of scattered ultrasound intensity? Ultrasound Med Biol 1995;21:231–242. Stewart SFC. A new phantom for assessing Doppler accuracy. (Abstr.) J Am Soc Echocardiog 1995;8:407. Stewart SFC. Aliasing-tolerant color Doppler quantification of regurgitant jets. Ultrasound Med Biol 1998;24:881– 898. Walker AR, Phillips DJ, Powers JE. Evaluating Doppler devices using a moving string test target. J Clin Ultrasound 1982;10:25–30.
PII S0301-5629(99)00084-8
● Original Contribution A ROTATING TORUS PHANTOM FOR ASSESSING COLOR DOPPLER ACCURACY SANDY F. C. STEWART Hydrodynamics and Acoustics Branch, Center for Devices and Radiological Health, Food and Drug Administration, Rockville, MD 20850 USA (Received 23 February 1999; in final form, 10 June 1999)
Abstract—A rotating torus phantom was designed to assess the accuracy of color Doppler ultrasound. A thin rubber tube was filled with blood analog fluid and joined at the ends to form a torus, then mounted on a disk submerged in water and rotated at constant speeds by a motor. Flow visualization experiments and finite element analyses demonstrated that the fluid accelerates quickly to the speed of the torus and spins as a solid body. The actual fluid velocity was found to be dependent only on the motor speed and location of the sample volume. The phantom was used to assess the accuracy of Doppler-derived velocities during two-dimensional (2-D) color imaging using a commercial ultrasound system. The Doppler-derived velocities averaged 0.81 ⴞ 0.11 of the imposed velocity, with the variations significantly dependent on velocity, pulse-repetition frequency and wall filter frequency (p < 0.001). The torus phantom was found to have certain advantages over currently available Doppler accuracy phantoms: 1. It has a high maximum velocity; 2. it has low velocity gradients, simplifying the calibration of 2-D color Doppler; and 3. it uses a real moving fluid that gives a realistic backscatter signal. © 1999 World Federation for Ultrasound in Medicine & Biology. Key Words: Color Doppler accuracy, Doppler ultrasound phantom, Color Doppler ultrasound.
String phantoms are accurate and useful for calibrating pulsed Doppler systems (Walker et al. 1982; Phillips et al. 1990), but are not particularly suitable for two-dimensional (2-D) color imaging (Rickey et al. 1992). The moving string forms a narrow color image, from which velocity is difficult to measure. To provide a larger target for assessing color Doppler, a phantom was developed that uses a moving belt of flexible foam (Rickey et al. 1992). A rotating rubber disk has also been used to assess Doppler accuracy (McDicken et al. 1983; Fleming et al. 1994; Schwarz et al. 1995). Some of these devices use materials that may not produce a realistic backscatter signal. Phantoms based on parabolic flow in a tube (McDicken 1986) or between parallel plates (Boote and Zagzebski 1988) use actual flowing fluids. However, the assessment of color Doppler is complicated by the strong dependence on position of the fluid velocity in such phantoms, so that the color pixel intensity is also heavily dependent on position. Entrance effects may cause errors: if the entrance section is not long enough for the flow to develop fully, the velocity field will not have the assumed parabolic flow (Fung 1996; Law et al. 1989). The maximum velocity is also limited, because high flow
INTRODUCTION Doppler ultrasound is a widely accepted technique for the clinical assessment of cardiovascular blood flow due to its relatively low cost per examination, noninvasive character, high level of safety and demonstrated effectiveness. Doppler has made significant strides in replacing older, more invasive (and less safe) methodologies, such as dye angiography for assessing valvular regurgitation. However, it has yet to be displaced by newer technologies such as magnetic resonance (MR) flow imaging. Despite the wide use of Doppler ultrasound in all its modalities, one subject that has received less attention than it deserves is that of accuracy. Calibration, standards and accuracy assessment all lag behind the technology itself. This may be due, in part, to the lack of a generally accepted standard for assessing Doppler accuracy. Numerous methods have been described for assessing the accuracy of Doppler ultrasound (US) systems.
Address correspondence to: Sandy F. C. Stewart, Ph.D., Hydrodynamics and Acoustics Branch, Food and Drug Administration, 9200 Corporate Blvd. (HFZ-132), Rockville, MD 20850 USA. E-mail: [email protected] 1251
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rates may be associated with turbulent flow, which will invalidate the assumed velocity profile. The maximum velocity may be less than 100 cm/s, less than the range available on most commercial US systems, and less than velocities commonly found in stenotic vessels or regurgitant heart valves (which can reach 5– 6 m/s). To their advantage, tube phantoms provide a more physiologically appropriate model of flow in the vasculature, and can be used to assess methods to calculate volume flow (Picot et al. 1995; Forsberg et al. 1995; Holland et al. 1996), to derive the velocity profile (Hein and O’Brien 1992), or to characterize three-dimensional (3-D) color Doppler systems (Guo et al. 1995). This study was designed to characterize a new phantom for assessing color Doppler accuracy that overcomes many of the problems of previous methods. The phantom consists of a submerged rotating torus, filled with blood analog fluid (Stewart 1995). Numerical studies and flow visualization experiments were employed to confirm the assumed solid-body flow of the fluid within the torus. Detailed reproducibility tests were performed to determine effects of day-to– day variabilities. The torus phantom was then used to assess the effects of certain instrument settings on color Doppler-derived velocities from a commercial ultrasound system. METHODS Phantom description The torus phantom was made from a thin rubber bicycle inner tube, measuring 0.064 cm in thickness and 3.0 cm in diameter. The tube was filled with a bloodmimicking fluid (described below) and joined end-to– end by clamping both ends onto a short hollow plastic cylinder. The rubber torus was then mounted on the rim of a disk 52 cm in diameter and glued in place with silicone adhesive (Fig. 1). The distance between the center of the disk and the center of the tube was 27.5 cm; thus, the torus had a minor radius equal to 1.5 cm and a major radius equal to 27.5 cm. The disk and torus were submerged in a bath of degassed water with the axis oriented vertically. The disk rotation was driven by a gear motor (Model 32D5BEPM5F, Bodine Electric Company, Chicago, IL) mounted vertically above the disk. The motor speed was monitored by an optical encoder (Accucoder Model 220C, Encoder Products Co., Sandpoint, ID) coupled to the main shaft by a drive belt, and electronically controlled by a digital velocity feedback system (Model DLC300, Minarik Electric, Glendale, CA). It was hypothesized that the fluid within the torus spins as a solid body at the same angular velocity as the torus, after some finite acceleration time during which secondary flows dominate. This hypothesis was con-
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Fig. 1. Schematic of torus phantom for assessing Doppler accuracy.
firmed in flow visualization and numerical experiments described below. Thus, the circumferential velocity of the torus fluid was assumed to be equal to the torus angular velocity times the radial position of the sample volume. This was the standard against which the Doppler-derived velocity was compared. The blood-mimicking fluid used (R.G. Shelley Ltd., North York, Ontario, Canada) was 50% water and 50% machine cutting fluid (Syn-Cut HD, Acra Tech, Ontario, Canada), with acoustic and viscous properties closely matching those of blood (Rickey et al. 1995). Ultrasound reflection was provided by suspended 10-m diameter nylon copolymer particles (Orgasol 3501 EXD, ELF Atochem, Ontario, Canada). One potential problem with the torus phantom is settling (or floating) of the echogenic particles over time when the phantom is not in use. These would be inconvenient to resuspend in the closed tube. It was speculated, however, that transient secondary flows at the commencement of rotation helped to redistribute the particles. This hypothesis was confirmed during the flow visualization experiments. Doppler ultrasound system An ATL Ultramark 9 HDI ultrasound system (Advanced Technology Laboratories, Bothell, WA) outfitted with a Model L10-5 linear array transducer (Doppler frequency ⫽ 6.0 MHz, aperture ⫽ 38 mm) was used for all laboratory experiments. The transducer was mounted via a specially designed clamp in a three-axis positioning system (Velmex, Inc., Bloomfield, NY). The transducer’s active face was suspended 1.0 cm above the torus and parallel to the torus tube axis, with the US beam focused on the center of the torus fluid. The Doppler angle was fixed at 70°, representative of the clinical case with a vessel parallel to the skin. The degassed water
Color Doppler accuracy phantom ● S. F. C. STEWART
bath in which the torus was immersed provided a path for the US beam between the transducer and the torus. Radial calibration Two 1.0-cm ⫻ 0.5-cm rectangles of US-absorbing rubber (Corsaro et al. 1982) were glued 0.1 cm apart on the disk upper surface, with the gap 22.1 cm from the torus major axis (Fig. 1). The transducer was first positioned to maximize the specular reflection (as seen in the 2-D display) of the disk between the two rubber rectangles. This indicated that the midplane of the ultrasound beam was 22.1 cm from the torus major axis. The transducer was then translated radially outward a distance r using the positioning system, until the sample volume was centered within the torus tube, determined by noting a maximum in brightness of the specular reflection of the bottom surface of the tube. The radial position of the sample volume RSV was then calculated by RSV ⫽ r ⫹ 22.1 cm. This procedure allowed accurate radial positioning of the ultrasound beam without having to make assumptions about the position of the beam with respect to the transducer housing. The actual velocity of the fluid insonated by the transducer Vf was then calculated by multiplying RSV by the torus angular velocity , or Vf ⫽ RSV 䡠 . The color Doppler-derived velocity Vcd was then compared to Vf. Experimental studies Reproducibility of the torus calibration system was assessed by comparing the measured torus fluid velocity and the color Doppler-derived velocity over five experiments, using a torus speed of 40 RPM. Before each experiment, the transducer was removed from and then replaced into its mounting clamp and the 3-D positioning system was readjusted for an optimal image. In addition, the US system was powered down, reset, and the instrumentation settings returned to a fixed set of values, which were optimized for a subjectively noise- and dropoutfree signal (see Table 1). Next, the effects on reproducibility of deliberate variations in transducer positioning, power setting, color gain and width of the color Doppler subset of the 2-D image were assessed. Finally, the effects on color Doppler accuracy of systematic variations in the pulse-repetition frequency (PRF) and wall filter frequency (WFF) were investigated in detail. Six different torus rotational speeds (10, 20, 40, 60, 80 and 100 RPM) were used, corresponding to six fluid velocities (Vf ⫽ 28.8, 57.6, 115.2, 172.8, 230.4 and 288.0 cm/s, respectively). The PRF was varied between 1.0 kHz and 10 kHz, corresponding to maximum velocities as labeled on the instrument between 12 and 170 cm/s (with the baseline velocity set to zero). Due to the Doppler angle (approximately 70°), the actual velocity Vf ⫽ 28.8 cm/s was
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Table 1. ATL Ultramark 9 HDI nominal instrument settings used in color Doppler reproducibility tests Instrument parameter
Setting used
Pulse-repetition frequency Wall filter HDI/high frequency Variance Output power Color gain Color sensitivity Color persistence Dynamic filtering Color box width
4.5 kHz 800 Hz on/on off ISPTA.3† ⫽ 20 mW/cm2, MI‡ ⫽ 0.5 94% Maximum ⫽ 16 Minimum ⫽ 0 Off 1.2 cm
†Spatial peak temporal average intensity, derated. ‡Mechanical index.
measured at approximately 9 cm/s, which could be measured without aliasing at a maximum velocity of 12 cm/s. The lowest PRF was chosen so that aliasing was avoided, and the highest PRF was chosen when the color was not quite invisible to the eye. At each PRF, the WFF was varied between 50 and 800 Hz; however, not all WFF settings were available at all PRFs. All other instrument settings were fixed as in the reproducibility tests (Table 1). The output power was characterized by the ISPTA.3 (spatial peak temporal average intensity, mW/cm2, derated by 0.3 dB/cm-MHz; AIUM/NEMA 1998a) and MI (mechanical index; AIUM/NEMA 1998b). The ISPTA.3 and MI were set initially to 20 mW/cm2 and 0.5 at the lowest WFF and PRF; however, the values tended to increase somewhat as the PRF and WFF were increased. In all cases, velocities from n ⫽ 10 images were recorded for each instrument setting and experimental setup. Image processing and data analysis Images from the ultrasound system’s RGB video output were captured using a Flashpoint 128 video frame grabber (Integral Technologies, Indianapolis, IN) mounted in a personal computer running Windows 95. Images captured with a resolution of 640 ⫻ 480 pixels and color depth of 24 bits (i.e., 8 bits per color red, green, and blue) were saved onto hard disk in Windows BMP image file format. A custom color/velocity map on the ultrasound system was used to encode velocities in the red image plane, using a strictly linear velocity-to– color translation scheme. Red byte values varied from zero to 255, with zero corresponding to zero velocity and 255 corresponding to the maximum velocity. Green was added to make the color maps more visible to the eye, with pixel values of zero and 197 corresponding to one half the maximum velocity and the maximum velocity, respectively. The green pixel values were ignored when calibrating or measuring velocities during image analysis.
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ities using the computer mouse, the velocities at each pixel within the parallelogram were calculated, and the mean velocity over all the pixels was recorded. Statistical analyses were performed using Minitab for Windows Release 12 (Minitab, Inc., State College, PA), running on a personal computer.
Fig. 2. Definition of Doppler angles. Top: side view of torus (seen from center). is the conventional Doppler angle between the US beam and fluid velocity in the plane of the beam. Bottom: top view of torus (note: minor radius is exaggerated for clarity). is the Doppler angle due to curvature of the torus (outside plane of beam), which varies with position (but is considered to be negligible).
A correction for the Doppler angle between the tube axis and the axis of the transducer beam was performed during image analysis to find the fluid velocity parallel to the rim of the torus (Fig. 2, top). Vcd was also dependent on the variable angle between the plane of the ultrasound beam and the torus itself, due to the mild curve of the major radius (Fig. 2, bottom; Gill 1985). Errors due to this angle were calculated to be less than 0.1% for a 2.0-cm error in the placement of the transducer, however, and were, therefore, ignored. Image files stored on disk were analyzed by a program written in Borland Pascal for Windows, version 7.0 (Borland International, Scotts Valley, CA). After an image was read into this program, distances and velocities were calibrated first. The linear array transducer emitted the US beam along parallel lines (Fig. 3); therefore, the Doppler angle was assumed to be constant over the entire color image. The angle was measured graphically on the screen, and the color-encoded velocities were adjusted by dividing by cos . A graphic parallelogram was then drawn around the color-encoded veloc-
Flow visualization studies Flow visualization studies were performed in a transparent version of the torus to verify that the fluid within the torus rotates as a solid body, following a brief spin-up period during which transient secondary flows dominate. The transparent torus was made of 2.54 cm i.d. Tygon tubing filled with an approximately 65%/35% water/glycerine solution in which 300 – 860-m ion exchange resin particles (Amberlite IRA-95, Sigma Chemical Co., St. Louis, MO) were suspended. The mixture was formulated to make the resin particles as neutrally buoyant as possible. The torus was mounted on the disk, but was not suspended in the water tank. A Pulnix TM 9701 video camera was mounted vertically over the torus to record the motion of the particles, at 30 full frames/s. The torus was illuminated by two frosted floodlights. No attempt was made to single out a single cross-sectional plane (e.g., as with a laser sheet). Video images of the torus (after spin-up) were downloaded to a computer. Two images exactly 1 revolution apart were analyzed, for rotational speeds of 20, 40, 60 and 90 RPM. The two images were colored red and green, respectively, in a commercial image analysis program (Corel Photo-Paint, Corel Corporation, Ottawa, Ontario, Canada) and superimposed to detect relative motion of the particles with respect to each other or to the torus wall, which would indicate nonsolid body motion. Finite element simulations Finite element simulations of a fluid-filled rotating torus were also performed to test the hypothesis that the fluid within the torus moves as a solid body. The simulations also provided detailed information on the accelerating and transient flows occurring during spin-up. The simulations were performed using the FIDAP finite element program (version 7.6, Fluent, Inc., Evanston, IL) running on an IBM 350 RISC workstation. The nonlinear Navier–Stokes equations of fluid flow were descretized for an axisymmetric, laminar, transient model of a torus, with a major radius equal to 28 cm and minor radius equal to 1.5 cm. The model used a 2-D mesh modeling a cross-section of the rubber tube (Fig. 4), consisting of 2232 4-node, 2-D quadrilateral elements. The outer boundary was represented by 156 2-node, 1-D edge elements. The complete model included a total of 2388 elements and 2311 nodes. Only 1 vertical half of the tube cross-section was modeled, to
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of velocities in the direction were allowed, so that the entire torus could be represented by one cross-section of the tube in the r-z plane. The torus and the fluid within were set initially at rest. Axial velocities uz at the plane of symmetry of the torus were fixed at zero throughout the simulation. Angular velocities corresponding to 25, 50 or 75 RPM were imposed on the torus wall, ramped up from 0 over a period of 1 s to simulate acceleration of the torus. The imposed circumferential velocity u varied linearly with the radial coordinate r from the inner wall to the outer wall (Table 2). The simulation was solved over successive time steps, using a trapezoidal (second order) integration scheme. The initial time step was set to 5 ⫻ 10⫺3 s, but was allowed to vary according to the convergence requirements of the program, with the maximum time step limited to 0.33 s. The time step tended to increase with time as the secondary flows disappeared and the remaining u velocities approached steady state. The resulting velocity maps vs. time were analyzed to determine how rapidly the fluid accelerated to the speed of the torus, and how rapidly the transient secondary flows disappeared. RESULTS
Fig. 4. Mesh used in finite element analyses to simulate torus cross-section.
exploit the symmetry. Effects of gravity and buoyancy were neglected. All three velocity components, ur, uz, and u, were simulated (where r, z, and represent the radial, axial, and circumferential directions of the torus, Fig. 1), but were functions only of r and z. No variations
Flow visualization studies Despite care in preparation, the water/glycerine solution did not exactly match the density of the ion exchange resin particles. Some of the particles were not perfectly neutrally buoyant and were observed to settle to the bottom of the tube overnight when the torus motor was turned off. When the motor was turned on again, however, the particles were observed to mix immediately due to the transient secondary flows identified in the finite element simulations (see below). Turning the motor off also produced transient secondary flows that caused mixing. Turning the motor on and off several times served to resuspend the particles, which then remained in suspension more than long enough for the experiments to be run. The two superimposed images 1 revolution apart for each of the four speeds are shown in Fig. 5. In each case, the pattern of particles was unchanged; no relative mo-
Table 2. Conditions used in finite element simulations Velocity (cm/s) vs r (z ⫽ 0) Torus speed (RPM) 25 50 75
Angular velocity, (s⫺1)
r ⫽ 26.5 cm (inner wall)
r ⫽ 27.9 cm
r ⫽ 28.0 cm (tube center)
r ⫽ 28.1 cm
r ⫽ 29.5 cm (outer wall)
2.62 5.24 7.85
69.4 138.8 208.1
73.0 146.1 219.1
73.3 146.6 219.9
73.6 147.1 220.7
77.2 154.5 231.7
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tion of the particles with respect to each other or to the walls was observed. There was a ⬃0.2-cm shift between the two images, however, indicating that either 1. the torus motor speed was not perfectly accurate, or 2. the video frame rate was not exactly 30 frames/s, or 3. both. If the video camera frame rate was considered to be accurate, then the additional 0.2-cm displacement indicated that the torus rotational speed was actually 20.02 RPM, rather than the motor controller’s set value of 20.0 RPM. The error was calculated to be about 0.1%. It was concluded that, after spin-up, the velocity field consisted of a uniform circumferential motion. Finite element simulations Results of the numerical simulations also showed that fluid in the torus rotated as a solid body after a brief acceleration period. When the simulated torus was set in motion, the fluid circumferential velocity u in the center of the tube (the central node in Fig. 4) approached that of the torus within approximately 15 s at all torus speeds simulated (Fig. 6). Fluid near the tube wall was found to accelerate even faster. At a torus rotational speed of 50 RPM, the circumferential velocity profiles along a central cross-section of the tube, parallel to the torus major radius, rapidly approached a straight line (Fig. 7, left panel). The velocities varied between 138.8 cm/s at the inner wall and 154.5 cm/s at the outer wall, or by ⫾ 5.4%. Along a cross-section parallel to the torus axis (i.e., at a constant radius), the circumferential velocity profiles rapidly approached a steady state value of 146.6 cm/s, which was constant across the tube (Fig. 7, right panel). In the simulation, the torus acceleration caused appreciable secondary flows in the plane of the tube crosssection. Flows in the axial and radial directions are shown as a function of time in Fig. 8. These represent a double helical flow mirrored about the torus plane of symmetry that disappeared completely within 20 s of startup. Acceleration of fluid in torus A pulsed Doppler recording of the torus phantom starting up is shown in Fig. 9, where the torus final speed was 40 RPM. The narrow spikes represented reflections from the plastic coupler joining the two ends of the rubber tube. These appeared every 1.5 s, which is consistent with a torus speed of 40 RPM. About 6 s were required for the fluid to reach its final velocity, less than half the time needed in the finite element simulations. Reproducibility tests When the transducer was removed and replaced in the clamp, the x-y–z positioning system reset, and the US system turned off and on with the instrument parameters
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returned to fixed values, good reproducibility was observed (Fig. 10a). Analysis of variance did show significant differences, but only between the fourth observation and the others; all other pairs of observations were not significant. Vvf varied between 100.7 and 102.1 cm/s, or approximately ⫾ 0.7%. Vcd was observed to be considerably lower than the imposed fluid velocity Vf of 115.2 cm/s, however. A statistically significant effect of the output power was observed (p ⬍ 0.001, Fig. 10b), but mainly because of the relative drop-off at low power (ISPTA.3 ⬍ 12 mW/cm2). Better reproducibility could be achieved by keeping the power as constant as possible, at a value ⬎ 12 mW/cm2. Subsequent studies used a power equivalent to an ISPTA.3 ⫽ 20 mW/cm2 (although the instrument automatically modified this value somewhat as the WFF and PRF were adjusted). Color gain, when varied between 80% and 100%, did not show a statistically significant effect on the Doppler accuracy (p ⫽ 0.881, Fig. 10c). Color gain was kept at 94% for all other testing. The color box width also did not have a statistically significant effect (p ⫽ 0.859, Fig. 10d). This was fortunate, because this parameter had to be adjusted by eye while manipulating the instrument’s trackball. The box width was kept as close as possible to 1.2-cm wide for all other testing. Varying the radial position of the transducer had a statistically significant effect (p ⬍ 0.001, Fig. 10e). This was expected because the true velocity of the fluid within the torus, Vf, is linearly dependent on the radius. Linear regression provided an estimate of this relationship: V f ⫽ 3.487 s ⫺1 䡠 R sv ⫹ 3.983 cm兾s.
(1)
The theoretical relationship is: V f ⫽ R sv 䡠 .
(2)
where ⫽ (40 RPM/60s 䡠 min⫺1) 䡠 2.0 䡠 ⫽ 4.189 s⫺1. Thus, the fitted slope (3.487 s⫺1) was approximately 20% lower than the theoretical one (4.189 s⫺1). This corresponds well to the fact that, overall, Vcd was observed to be lower than Vf (see below). The fitted offset, 3.983 cm/s, may be due to experimental errors in measuring minor differences in radius. Varying the lateral position of the transducer (tangential to the torus), XSV, also had a significant effect (p ⫽ 0.002, Fig. 10f), but the fitted dependence on XSV (Vf ⫽ 0.649 s⫺1 䡠 XSV ⫹ 101.3 cm/s) was substantially less than the dependence on radius. Color Doppler accuracy assessment Sample color Doppler images for a torus RPM of 20 (Vf ⫽ 57.6 cm/s) as a function of PRF and WFF are
Color Doppler accuracy phantom ● S. F. C. STEWART
Fig. 3. Color Doppler image from linear transducer. Color Doppler velocities are confined to within parallelogram. Torus speed ⫽ 40 RPM; fluid velocity ⫽ 115.2 cm/s; PRF ⫽ 4.5 kHz; WFF ⫽ 600 Hz. Top edge of torus tube (1) is parallel to the face of the transducer (2) and color Doppler box (3). ⫽ Doppler angle ⫽ 70°.
Fig. 5. Results from flow visualization studies: (a) 20 RPM; (b) 40 RPM; (c) 60 RPM; and (d) 90 RPM. Two video images of a transparent torus tube as seen from above are superimposed. The first image was converted to red and the second image, taken 1 complete revolution later, was converted to green.
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Fig. 6. Results of finite element studies. Circumferential velocity of fluid (u) at center of torus tube.
shown in Fig. 11. Qualitative differences were plainly visible, especially at PRFs from 1.8 to 3.0 kHz, where the images for WFF ⫽ 100 Hz had a distinct mottled appearance lacking at higher WFFs. Overall, the color intensity was observed to decrease with increasing WFF.
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The overall decrease in color intensity with increasing PRF was expected, because the maximum velocity range increased with increasing PRF. The color Doppler-derived velocities as a function of RPM, PRF and WFF are compared in Fig. 12. Significant errors in Doppler accuracy were observed. With few exceptions, Vcd underestimated Vf, by an average 19% ⫾ 11%. In 3 cases, Vcd overestimated Vf, at 10 RPM, PRFs ⫽ 4.0, 4.5 and 5.0 kHz, and WFF ⫽ 800 Hz. Most of the observed differences between Vf and Vcd were greater than 3 standard deviations and, so, were statistically significant. At each RPM, a slight overall decrease in Vcd was observed with increasing PRF. The variation with WFF was more complex. At low PRF, Vcd decreased with increasing WFF and, at high PRF, Vcd increased with increasing WFF. At constant WFF, Vcd first increased with increasing PRF, formed a maximum at an intermediate PRF, and then decreased with increasing PRF. A 3-way analysis of variance was performed using a general linear model approach. Because the US system limited the PRFs and WFFs that could be used at any particular RPM, the full data set was disconnected; therefore, only the main effects could be analyzed. In this case, Vcd was found to be dependent significantly on RPM, PRF and WFF at the p ⬍ 0.001 level of significance. To provide a balanced set of data for analysis of the
Fig. 7. Velocity profiles from finite element study at 50 RPM. Left: velocities along tube centerline parallel to radius of torus. Right: velocities along tube centerline parallel to axis of torus.
Color Doppler accuracy phantom ● S. F. C. STEWART
Fig. 8. Axial velocities (left semicircle) and radial velocities (right semicircle) within cross-sectional plane of torus tube at times: (a) 0.50 s; (b) 0.76 s; (c) 1.03 s; (d) 1.24 s; (e) 1.49 s; (f) 2.02 s; (g) 3.00 s; (h) 5.06 s; (i) 20.1 s.
Fig. 9. Pulsed Doppler spectrum of accelerating flow in torus.
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Fig. 10. Reproducibility test results: (a) transducer removed and replaced in clamp, positioning system reset, ultrasound system reset. Subsequent studies tested dependence on (b) output power; (c) color gain; (d) color Doppler box width; (e) radial position of sample volume; and (f) lateral position of sample volume.
interactions among the independent variables, a second ANOVA was performed using a small, connected subset of the data. In this case, the data analyzed included only the velocities Vcd at 10, 20 and 40 RPM, with the PRF varied from 3.5 to 5.0 kHz and WFF varied from 200 to 600 Hz. For this subset of data, Vcd was again observed to be dependent significantly on RPM, PRF, and WFF (p ⬍ 0.001). In addition, all of the interaction terms were significant at p ⬍ 0.001: RPM ⫻ PRF, PRF ⫻ WFF, WFF ⫻ RPM and RPM ⫻ PRF ⫻ WFF. This supports
the conclusion that the complex behavior observed was due to strong interactions among the independent variables, not just random error. Error analysis The flow visualization experiments and numerical simulations showed that, after the brief spin-up period, the fluid within the torus tube moved at the same velocity as the torus. Therefore, the velocity of the-
Color Doppler accuracy phantom ● S. F. C. STEWART
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Fig. 11. Color Doppler images at torus RPM ⫽ 20 (fluid velocity ⫽ 57.6 cm/s) showing variations with pulse-repetition frequency (PRF) and wall filter frequency (WFF).
fluid within the torus depended only on the motor speed, given by a digital readout, and the sample volume radius, RSV, determined by calibrating the beam via the x-y–z positioning system as described above. The flow visualization experiments suggested that the motor speed accuracy was within approximately ⫾ 0.02 RPM. The reproducibility experiments
suggested that the accuracy of RSV was within approximately ⫾ 0.2 cm. At 100 RPM (near the maximum speed), the torus had a circumferential velocity at the center of the tube of 288.0 cm/s. Given the assumed errors in motor speed and RSV, at 100 RPM, the overall accuracy of the fluid velocity was calculated to be within approximately ⫾ 2.4 cm/s, or ⫾ 0.83%. At 10
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Fig. 12. Variations in color Doppler accuracy with pulse-repetition frequency and wall filter settings, at 6 velocity magnitudes: (a) fluid velocity ⫽ 28.8 cm/s; (b) fluid velocity ⫽ 57.6 cm/s; (c) fluid velocity ⫽ 115.2 cm/s; (d) fluid velocity ⫽ 172.8 cm/s; (e) fluid velocity ⫽ 230.4 cm/s; and (f) fluid velocity ⫽ 288.0 cm/s.
RPM, with a fluid velocity Vf of 28.8, the accuracy was calculated to be within ⫾ 0.5 cm/s, or ⫾ 1.7%. Errors in calculated velocity related to the measured Doppler angle were potentially more severe. The Doppler angle was measured from the color Doppler box during image analysis (Fig. 3). Overall, the measured Doppler angle averaged 70.41° ⫾ 0.14° (mean ⫾ standard deviation, n ⫽ 226). This was very close to the value of 70° given in the US system manufacturer’s literature.1 The L10-5 linear array transducer was positioned as used clinically, with the transducer face parallel to flow direction, as in Fig. 3. However, the observed angle was produced by the instrument’s image-forming software, and did not account for errors, if any, in the actual beam angle. The cosine function is nonlinear, so that the magnitude of errors in the Doppler angle correction varies with the angle. At a Doppler angle of 70°, an uncertainty of ⫾ 1° (⫾ 1.5%) leads to an uncertainty in the velocity of approximately ⫾ 5% (Picot et al. 1995), 3–5 times the error due to radial positioning and motor speed. Without measuring the actual beam angle with respect to the 1
Ultramark 9 Ultrasound System Reference Manual, p. 4A-7.
transducer face (and torus velocity), however, it is impossible to assess how much, if any, of the approximately 19% error seen in the accuracy assessments can be attributed to errors in the Doppler angle. DISCUSSION The torus phantom was shown in this study to be an accurate and reliable device for assessing color Doppler accuracy. The device has many desirable characteristics. Unlike string and belt phantoms, the torus uses a real fluid to calibrate the transducer, thus providing a more realistic ultrasound backscatter signal. In this study, the torus was filled with a commercially available blood analog fluid optimized for US studies, but anticoagulated animal or human blood could easily be substituted. Experiments using contrast agents could also be performed (Fan et al. 1993). Unlike flow phantoms based on parabolic flow in a cylindrical tube, the fluid in the torus phantom moves as a solid body, and has a very low velocity gradient. This is especially useful for color Doppler, which images a 2-D area that is much bigger in size than the small sample volume used in pulsed Doppler. Thus, color Doppler can be unambiguously cali-
Color Doppler accuracy phantom ● S. F. C. STEWART
brated over a large area of fluid that is flowing at almost the same velocity. The torus phantom also has a high maximum velocity (approaching 300 cm/s), a maximum that could be increased further with either a faster motor or larger diameter torus. Some disadvantages were observed, however; the device was rather large and unwieldy, and it was inconvenient to fill the torus and eliminate air bubbles. At high speeds, the rotating torus possessed considerable energy, so it had to be used with care. The flow visualization experiments and finite element simulations supported the hypothesis that the fluid in the torus achieves total solid body motion after a brief acceleration phase. Rotational motion was rapidly convected from the torus wall to the fluid by viscous forces. Thus, the motion of the fluid could be accurately and correctly inferred from the motion of the torus itself. The numerical work suggested that the acceleration phase lasted up to 15 s but, in the pulsed Doppler test, the actual torus fluid took less than half that time to accelerate. It was speculated that this was due to the plastic coupler used to fasten the ends of the rubber tube together. The coupler inside diameter was about half that of the rubber tube, and may have provided an extra viscous force to accelerate the fluid. This narrowing was not modeled in the simulations. The flow visualizations and numerical simulations also demonstrated that there was considerable mixing due to transient secondary flows during spin-up (and spin-down, for that matter). The circumferential velocity of fluid was initially higher near the walls than in the middle of the torus. The momentum of this rapidly moving fluid tended to force fluid near the wall from the inner radius to the outer radius of the torus. The fluid in the tube center was, thus, displaced and made to flow back in from the outer radius to the inner radius of the torus. This set up a counter-rotating, double-helical flow. This is analogous (but opposite in nature) to flow in a curved tube (such as the ascending aorta), where higher velocity fluid in the middle of the tube tends to be thrown to the outer wall of the bend, forcing fluid near the walls to flow back toward the center of the bend in a doublehelical pattern (Pedley 1980). The existence of the transient secondary flows turned out to be a useful feature. The particles in the blood analog fluid used in the US experiments tended to float if the fluid was left undisturbed overnight, and the particles used in the flow visualization experiments tended to settle. Turning the motor on and off a few times (at one of the higher speeds) served to mix the particles thoroughly. Thus, the protocol for assessing Doppler accuracy should include cycling the motor at the start of an experiment.
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It was concluded that the torus phantom could provide reliable reference velocities up to 300 cm/s within an error of ⫾ 1.7%. Errors in the Doppler-derived velocity In this study, the Doppler-derived velocities averaged about 19% low. One possible source of error is the Doppler angle; at 70°, an error of only 4° (6%) could completely account for the 19% error seen (Picot et al. 1995). Thus, the overall error most likely was not due to flaws in the US system per se but, rather, due to the nonlinear nature of Doppler angle-related errors. Refraction between the water bath and blood-mimicking fluid may also have contributed to the error seen. Using Snell’s law and the speed of sound in the water bath (1485 m/s) vs. that in the blood-mimicking fluid (1540 m/s), an incident beam angle in the water bath of 20° to the normal (corresponding to a Doppler angle of 70°) would be refracted to an angle of 20.77° in the blood-mimicking fluid within the tube (corresponding to a Doppler angle of 69.23°). At 70°, an error in the Doppler angle of 0.77° can cause the Doppler-derived velocity to be approximately 3.8% low (Picot et al. 1995). This latter effect may contribute to the observed error, but it is insufficient to account for all of it. Some of the of the overall 19% underestimation of the true velocity may have been due to dropouts (dark pixels mixed in with brightly colored pixels) at low WFF settings (e.g., WFF ⫽ 100 Hz, PRF ⫽ 3.0 kHZ, Fig. 11). No attempt was made to eliminate these pixels, so that they were averaged in with the colored pixels. However, dropouts cannot account for all the variation in Dopplerderived velocity with WFF and PRF, because most images did not have significant dropout (Fig. 11). The increase in Doppler-derived velocities with increased filter setting at high PRFs may be due to the wall filter removing some of the lower frequencies. However, the decrease in Doppler-derived velocities with increased filter setting at low PRFs is not explained by this mechanism. SUMMARY This study should not be taken as a critique of one manufacturer’s instrument. Color Doppler remains a widely accepted and extremely useful tool for assessing blood flow in a safe, noninvasive and effective manner. Color Doppler has been shown to work well for the many clinical uses to which it has been applied, and new applications continue to be developed. The quality of patient care has clearly increased as a direct result of the technology. Despite wide acceptance, color Doppler imaging remains largely qualitative. Analyzing the approximate color brightness and the layout with respect to adjacent
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solid tissues takes precedence over quantifying the precise spatial dependence of velocities. Often, clinical analysis consists of asking simple questions or making comparisons. When assessing heart valve function one might ask, Is aliasing present during forward flow when the valve is open, suggesting stenosis? Are regurgitant jets visible when the valve is closed? Color Doppler gives an excellent overall view of the flow field, and can easily provide answers to these kinds of qualitative questions. If quantitative analysis is needed, the instrument can be switched to pulsed or continuous-wave Doppler mode. This provides a spectrum of the velocities vs. time, but forfeits the 2-D imaging capability. In contrast, quantitative analysis of the color-encoded velocity field is chiefly the subject of research (e.g., in measuring volumetric flows in regurgitant heart valves) (Grimes et al. 1994; Stewart 1998). Overall, the L10-5 transducer examined in this study was not as accurate as one might wish in color Doppler mode. In preliminary experiments similar to the ones shown in Fig. 12, the machine’s P3-2 phased array transducer was found to be more accurate, with an overall ratio of the Doppler-derived to actual velocity of 0.90 ⫾ 0.08 (range 0.56 to 1.16). This may be due, in part, to the lower Doppler angle used (approximately 45°). Therefore, the most important finding of this study is not the limitation of one transducer, but the significant effect of instrument settings on accuracy, a characteristic that may not be limited to one transducer or machine. Clinicians should be aware of the possibility of these variations, particularly when comparing repeated exams, and should consider investigating the color Doppler accuracy of the machines and transducers they use. The torus phantom described herein is a tool that can be used to assess color Doppler accuracy of current machines, and assist with the design of more accurate ones. It can accurately characterize color Doppler ultrasound at high flow velocities and low velocity gradients, using blood-mimicking fluids with a realistic backscatter signal. The area of interrogation is large, which is beneficial for color Doppler and allows easy calibration. With these characteristics, the torus phantom provides a number of advantages over previously described Doppler accuracy phantoms. Acknowledgements—This paper is dedicated to the memory of Ronald F. Carey, Ph.D., whose enthusiasm, encouragement and expertise were fundamental to the success of this work. The expert machining assistance of James Duff and Bruce Fleharty in building the phantom and making many excellent suggestions is gratefully acknowledged. The assistance of Gerald R. Harris, Ph.D. with the optical motor controller is also appreciated, as is the assistance of Ronald A. Robinson with the flow visualization experiments. The mention of commercial products, their source, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the U. S. Department of Health and Human Services.
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REFERENCES AIUM/NEMA. Acoustic output measurement standard for diagnostic ultrasound measurement. Laurel, MD: AIUM/NEMA, 1998a. AIUM/NEMA. Standard for real-time display of thermal and mechanical acoustic output indices on diagnostic ultrasound equipment, revision 1. Laurel, MD: AIUM/NEMA, 1998b. Boote EJ, Zagzebski JA. Performance tests of Doppler ultrasound equipment with a tissue and blood-mimicking phantom. J Ultrasound Med 1988;7:137–147. Corsaro RD, Klunder JD, Jarzynski J. Filled rubber materials system: application to echo absorption in water filled tanks. J Acoust Soc Am 1980;68:655– 664. Fan P, Czuwala PJ, Nanda NC, Rosenthal SM, Yoganathan A. Comparison of various agents in contrast enhancement of color Doppler flow images: an in vitro study. Ultrasound Med Biol 1993;19:45–57. Fleming AD, McDicken WN, Sutherland GR, Hoskins PR. Assessment of colour Doppler tissue imaging using test-phantoms. Ultrasound Med Biol 1994;20:937–951. Forsberg F, Liu JB, Russell KM, Guthrie SL, Goldberg BB. Volume flow estimation using time domain correlation and ultrasonic flowmetry. Ultrasound Med Biol 1995;21:1037–1045. Fung YC. Biomechanics: Circulation. (2nd ed.) New York: Springer, 1996:182–189. Gill RW. Measurement of blood flow by ultrasound: accuracy and sources of error. Ultrasound Med Biol 1985;11:625– 641. Grimes RY, Burleson A, Levine RA, Yoganathan AP. Quantification of cardiac jets: theory and limitations. Echocardiography 1994;11: 267–280. Guo Z, Moreau M, Rickey DW, Picot PA, Fenster A. Quantitative investigation of in vitro flow using three-dimensional colour Doppler ultrasound. Ultrasound Med Biol 1995;21:807– 816. Hein IA, O’Brien WD. A flexible blood flow phantom capable of independently producing constant and pulsatile flow with a predictable spatial flow profile for ultrasound flow measurement validations. IEEE Trans Biomed Eng 1992;39:1111–1122. Holland CK, Clancy MJ, Taylor KJW, Alderman JL, Purushothaman K, McCauley TR. Volumetric flow estimation in vivo and in vitro using pulsed-Doppler ultrasound. Ultrasound Med Biol 1996;22: 591– 603. Law YF, Johnston KW, Routh HF, Cobbold RSC. On the design and evaluation of a steady flow model for Doppler ultrasound studies. Ultrasound Med Biol 1989;15:505–516. McDicken WN. A versatile test-object for the calibration of ultrasonic Doppler flow instruments. Ultrasound Med Biol 1986;12:245–249. McDicken WN, Morrison DC, Smith DSA. A moving tissue-equivalent phantom for ultrasound real-time scanning and Doppler techniques. Ultrasound Med Biol 1983;9:L455–L459. Pedley TJ. The fluid mechanics of large blood vessels. London: Cambridge University Press, 1980. Phillips DJ, Hossack J, Beach KW, Strandness DE Jr. Testing ultrasonic pulsed Doppler instruments with a physiologic string phantom. J Ultrasound Med 1990;9:429 – 436. Picot PA, Fruitman M, Rankin RN, Fenster A. Rapid volume flow rate estimation using transverse colour Doppler imaging. Ultrasound Med Biol 1995;21:1199 –1209. Rickey DW, Rankin R, Fenster A. A velocity evaluation phantom for colour and pulsed Doppler instruments. Ultrasound Med Biol 1992; 18:479 – 494. Rickey DW, Picot PA, Christopher DA, Fenster A. A wall-less vessel phantom for Doppler ultrasound studies. Ultrasound Med Biol 1995;21:1163–1176. Schwarz KQ, Bezante GP, Chen X. When can Doppler be used in place of integrated backscatter as a measure of scattered ultrasound intensity? Ultrasound Med Biol 1995;21:231–242. Stewart SFC. A new phantom for assessing Doppler accuracy. (Abstr.) J Am Soc Echocardiog 1995;8:407. Stewart SFC. Aliasing-tolerant color Doppler quantification of regurgitant jets. Ultrasound Med Biol 1998;24:881– 898. Walker AR, Phillips DJ, Powers JE. Evaluating Doppler devices using a moving string test target. J Clin Ultrasound 1982;10:25–30.