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Quantitative investigation of in vitro flow using three-dimensional colour Doppler ultrasound
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in Med.
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& Biol.. Vol. 2 I. No. 6. pp. X07- 816, iYYS Copyright ~6: 1995 Elsevirr Science Ltd Printed in the USA. All rights reserved 0301-Sh2WY5 ‘FY.SO + .(X)
Original Contribution QUANTITATIVE INVESTIGATION OF IN VZi?‘Z?O FLOW USING THREE-DIMENSIONAL COLOUR DOPPLER ULTRASOUND ZHENYU
Guo, MICHEL
MOREAU, DANIEL W. RICKEY, PAUL A. PICOT and AARON FENSTER The John P. Robarts Research Institute, London, Ontario, Canada; and
Imaging Research Laboratories, Department of Medical Biophysics, (Received
University
15 August
of Western Ontario,
1994; in final
form 28
November
London,
Ontario, Canada
1994)
Abstract-A quantitative in vitro flow study was performed by using a three-dimensionalcolour Doppler imaging system. This system was based on a clinical ultrasound instrument with its transducer mounted on a motor-driven translation stage. A vascular and tissue-mimicking phantom containing two wall-less vessels,one normai and another stenotic, was used to quantify the measurementaccuracy of the flow velocity and the flow field. Steady state flows, having Reynolds numbers ranging between 460 and 1300, were generated by a computer-controlled positive displacementpump. Effects of the parameter settingsof the ultrasound instrument on resultsof the estimation of flow field were alsostudied. Experimental results show that our three-dimensional colour Doppler system’s velocity accuracy was better than 7% of the Nyquist velocity and its spatial accuracy was better than 0.5 mm. The systemshowed a good correlation (r = 0.999) between the estimated and the true mean flow velocity, and a good correlation (r = 0.998) between the estimated maximum and the true mean flow velocity. This study is our first step toward validating the measurementof the three-dimensional velocity and wall shear stressdistributions by using three-dimensionalcolour Doppler ultrasound. Key Words: 3D colour Doppler ultrasound, Quantitative flow measurement,Vascular phantom, Wall shear
stress,Flow visualization, Velocity accuracy.
INTRODUCTION
ing the risk for atherosclerosis (Car0 1977). To clarify the conflict and obtain a complete understanding of atherosclerosis, it is important to study and monitor the three-dimensional (3D) local blood flow velocity and wall shear stress distributions over the whole vessel of interest. Colour Doppler ultrasound has been used extensively as a noninvasive tool for the diagnosis of cardiovascular disease (Assmann and Roelandt 1987: Valdes-Cruz et al. 1986; Zierler et al. 1987). Although most clinical applications of colour Doppler ultrasound involve qualitative flow visualisation, it does have the potential to image the velocity flow field in a quantitative manner (Kitabatake et al. 1990; Rickey et al. 1992; Tamura et al. 1991). But, the conventional colour Doppler technique provides only 2D flow and anatomical information. It cannot be used directly to monitor the 3D local flow velocity and wall shear stress distributions. Recently, 3D colour Doppler systems have been developed to acquire a complete volume surrounding a vessel (Mills and Fuchs 1990; Picot et al. 1993) to provide a cohesive image of the complicated
Atherosclerosis, the primary cause of cardiovascular diseases, is characterized by the development of plaques on the vessel wall (Ross 1993). These plaques narrow the vessel and can restrict or completely obstruct the blood flow. The mechanisms responsible for atherosclerosis are still not well understood; however, it has been suggested that the local hemodynamic and mechanical factors play important roles in the disease initiation and development (Grottum et al. 1983; Ku et al. 1985). The shear stress on the vessel wall produced by the flowing blood has received the most attention and is believed to be closely related to the initiation of atherosclerosis (Car0 et al. 1977; Perktold et al. 1994). At first it was proposed that increased shear stress might be the initiating factor in atherosclerosis (Fry 1969). More recent observations, however, suggest that low shear stress could be a factor increasAddress correspondence to: Dr. Zhenyu Guo, Imaging Research Laboratories, The John P. Robarts Research Institute, 100 Perth Drive, P.O. Box 501.5, London. Ontario N6A 5K8, Canada.
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vascular anatomy and flow. By acquiring a 3D colour Doppler image of a vessel, the local flow velocity field and wall shear stress could be estimated. The 3D image could also be rotated and sliced to reveal a view of any arbitrary plane to help physicians diagnose the early stage of disease and follow-up the disease. Some studies (Mills and Fuchs 1990; Ohbuchi and Fuchs 1990) used an operator-manipulated 2D imager to build up 3D images. This technique is labour-intensive and requires more patient cooperation. Current studies employed a computer-controlled probe positioner to translate mechanically the transducer to acquire the 3D image (Miyagi et al. 1993; Picot et al. 1991, 1993; Pretorius et al. 1992). This approach is fast and efficient in sampling a volume of interest. Because of the finite size of the sample volume, the major problem involved in the estimation of wall shear stress using colour Doppler ultrasound is the determination of the velocity gradient near the wall. Practical methods of wall shear stress estimation are based on extrapolation of the velocity profile which fits the measured velocity points in vessels (Duncan et al. 1990; Ku et al. 1985; Lou et al. 1993). Accurate measurements of velocity and position data are thus our first concerns. As the first step for 3D velocity and wall shear stress measurement, in this study, we validated the measurement of one component of the velocity vector field in a circular symmetric vessel with constant flow. The purpose of the present study was thus to determine the accuracy and precision of the velocity and flow field measurement by using our 3D colour Doppler ultrasound system (Picot et al. 1993). In this article, we first describe the experimental system and our vascular and tissue-mimicking phantom, address the appropriate use of the colour Doppler system, and describe the method for measuring the flow velocity. We then describe the results of our study and show how the 3D velocity profile can be obtained using our system. From the velocity profile, the wall shear stress can be estimated. MATERIALS 30 colour Doppler
AND METHODS system description
Figure 1 is a block diagram of our experimental system. A detailed technical description of the 3D colour Doppler system can be found in Picot et al. ( 1993 ) . For this study, we used an ATL Ultramark 9 HDI colour Doppler ultrasound system with a 3%mm aperture and a ~-MHZ high resolution linear array transducer. For B-mode imaging, the transducer operates at 5 MHz, while in the colour Doppler mode the transducer works at 4 MHz. The linear array transducer was mounted on a motor-driven translation assembly with
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Computer-controled pump
Fig. 1. Block diagram of the 3D colour Doppler imaging system. A 80386-based PC digitizes the colour and greyscalevideo signalsfrom Ultramark9 HDI ultrasound system. The transducer is moved by a motor-driven stage. Blood mimicking flow is generated by a computer-controlled pump. A Macintosh Quadra 650 is used to perform volume reconstruction and analysis.
the translation axis at a known angle to the imaging plane. A set of planar images, transverse to the vessel, was acquired while translating the probe along the vessel at a fixed Doppler angle. The combination set of contiguous 2D image slices constitutes a volume image. A PC 80386-based microcomputer containing two image acquisition boards was used to digitize the colour and grey-scale video signals from Ultramark 9 HDI. Since the Ultramark 9 HDI encodes velocities in 32 discrete bins, the red-green-blue colour video signal was digitised with a precision of 5 bits per colour, while the monochrome video signal was digitised with a precision of 8 bits. After the images were acquired, they were transmitted, via an ethernet link, to a Quadra 650 Macintosh computer for image preprocessing and volume reconstruction. Every colour pixel in the colour images was converted to the corresponding velocity value by means of a precalibrated look-up table created based on the colour map of the Ultramark 9 HDI (&key et al. 1992). The colour and grey-scale images were then combined into a single volume to produce a 3D velocity-plus-anatomy image. Finally, this volume was sheared to compensate for the Doppler angle used for the recovery of the correct geometry. The resulting volume might be viewed or further processed with a volume visualisation program by displaying velocity voxels in colour and tissue voxels in grey-scale (examples shown in Fig. 4 and 6).
In vitro
Vascular phantom and blood-mimicking
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In the present study, the test phantom was composed of a Plexiglas box containing a tissue mimic and two wall-less vessels. This box was covered by a OSmm thick urethane layer, which has an ultrasound impedance similar to tissue, and low attenuation, making it a good acoustic window and preventing the tissue mimic from drying. The tissue mimic is described by Rickey et al. ( 1995) and was based on a water and agar (high strength A-6924, Sigma Chemical) gel. Glycerol (8%) was added to increase the acoustic velocity to that of tissue, and 3% 50-pm cellulose scattering particles (S-5504 Sigmacell, Sigma Chemical) were added to provide an acoustic attenuation to be 3.5 dB/cm at 4 MHz. The “normal” wall-less vessel was formed by pouring the tissue mimic around a metal rod with a diameter of 7.96 mm and then removing the rod after the tissue mimic has set. The stenotic wall-less vessel was formed by removing two rods with the same diameter of 7.96 mm from both ends. One end of each rod was tapered to a cosine shape with a maximal reduction of the cross-section area to be 70%. The two tapered ends were joined at the stenosis so that, after removal, a vessel was formed with a 70% stenosis at the midsection. The blood-mimicking fluid was a solution of machinists cutting fluid ( Acra Tech Syn-Cut HD, Mississauga, Ontario) and distilled water. The ratio of cutting fluid to water was 60% to 40%. Pulverised nylon 612 particles (ELF Atochem Orgasol 3501 EXD), which have a mean diameter of 10 pm, were added to provide the scattering sites. By using a capillary viscometer (Canon 30), the viscosity of the blood mimic was measured and found to be 0.0206 cm’/s. The acoustic velocity of the blood mimic was 1560 m/s (Rickey et al. 1995). This working fluid was pumped through our wall-less vessels by using a computercontrolled positive displacement pump (UHDC flow system, Quest Image Inc., London, Ontario). The pump produces very accurate steady flow and various pulsatile waveforms including reverse flow (Holdsworth et al. 1991). Plexiglas tubes were used to provide straight inlet and outlet for the wall-less vessel. The inside diameter of the Plexiglas tubes was machined to be the same as that of the wall-less vessel. The entrance length of tubes was equivalently 50 tube inside diameters, so that fluid entrance effects would be negligible for laminar steady state flow (Evans et al. 1989). Colour Doppler
system setting
Colour Doppler imaging provides information on the spatial distribution of the flow field. Although the colour area should correspond to the flow field, a num-
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ber of studies, advocating the use of colour Doppler to quantify cardiovascular disease, have shown some technical limitations of colour Doppler imaging (Baumgartner et al. 1991; Mitchell 1990). By using the size and shape of the colour area to quantify valvular regurgitation and vessel stenosis, it has been found that these estimates are highly dependent on numerous operator-dependent as well as instrument-dependent variables. For the purpose of quantitative flow analysis in our present study, the dependence of colour areas on the colour Doppler instrument parameters have been studied. Since the geometry of our vascular phantom is well defined, it provided a reference to determine an optimal setting of instrument parameters for our specific purpose. In the ultrasound instrument, gains are controlled separately for B-mode and colour Doppler. Because colour is typically suppressed over bright echoes, use of a slightly high B-mode gain may decrease the presence of colour noise over the tissue. However, an excessively high B-mode gain may suppress colour within the flow field. An additional important parameter is the colour vs. echo write priority (CEWP) which selects a threshold at which the echo data will overwrite the colour data. Above this threshold, echoes are considered to be strong enough to reject colour and only grey-scale is displayed. In the present study, we selected the highest B-mode and colour gains without overestimating the true flow field and lowest colour reject without causing colour noise. The ultrasound power was also chosen according to the true flow field to yield the best apparent colour flow image with the transmitting focal point set near the centre of the wallless vessel. The persistence level of the system, which determines the number of video frames to be averaged in a weighted manner, can be set between 0 and 7 with a setting of 0 corresponding to no averaging. We used the highest persistence level to obtain good estimates of blood velocity distributions and improve the appearance of colour Bow image. This could be done in our present study because the constant flow was used and the temporal resolution is thus meaningless. For the situation of pulsatile flow, this parameter may have to be reduced to gain a higher frame rate. To demonstrate the dependence of the estimated flow field on the instrument parameters, the transverse flow area of the normal vessel was measured by planimetry after changing one parameter each time from its optimal value and compared to the area measured with the optimal setting: ( 1) colour gain increased in five steps of 4% each; (2) B-mode gain decreased by 30%; (3) colour vs. echo write priority threshold increased by 50%; (4) doubling the ultrasound power;
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and (5) turning off the average (persistence = 0 1. Each measurement was repeated 30 times. Since the HDI only quantifies the flow velocity into 32 levels, the PRF was set to let the Nyquist velocity be just above the maximum velocity for each flow rate tested. This increased the velocity resolution and ensured that no aliasing occurred in the measurement. Additional velocity resolution was achieved in the normal vessel by shifting the colour baseline, since there was no reverse flow in this vessel. Accuracy of velocity and jaw field measurements With our optimal parameter setting, 3D colour Doppler imaging was performed using a Doppler angle of 72”. Steady laminar flows were generated by the computer-controlled pump at flow rates between 6 (Re = 460) and 16 mL/s (Re = 1300) with an increment of 2 mL/s. Parabolic flow was assumed in the normal vessel for all the flow rates tested, since it is impossible for turbulent flow to persist in such a straight smooth tube with these low Reynolds numbers. For each flow rate, 200 contiguous grey-scale and colour 2D image slices, 0.2 mm apart, were acquired for each vessel with every image slice having the dimensions of 160 X 204 pixels. Velocity-plus-anatomy volumes were then reconstructed into 160 X 204 X 200 pixel volumes by combining the anatomy and velocity data and shearing to correct for the Doppler angle. Working in zoomed mode of the colour Doppler system, the resulting voxel dimensions in the X, y and z directions were found to be 0.081 mm X 0.059 mm X 0.2 mm. Therefore, the reconstructed volumes had a dimension of 13 mm x 12 mm x 40 mm. The setting of the colour Doppler system was kept constant except that the PRF was reset for each flow rate as described above. For velocity analysis, the velocity data were corrected for Doppler angle and resealed to obtain the true velocity according to the PRF setting. Since the theoretical velocity distribution of the normal vessel was assumed to be laminar parabolic flow, this vessel was used to quantify the velocity accuracy of the 3D colour Doppler system. Since the flow was constant and the vessel was uniform, for each flow rate, the 200 slices of velocity data of the velocity-plus-anatomy volume were averaged to obtain an estimate of the averaged 3D velocity distribution of one component of the 3D velocity vector field. The 3D standard deviation (SD) distribution was also calculated to quantify the precision of the velocity measurement. The averaged velocity distribution was fitted to a parabolic surface and the root-mean-square (F&IS) error of the fit was calculated to quantify the goodness-of-fit. We then computed the residual error between the averaged ve-
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locity distribution and a theoretical parabolic distribution created with the corresponding flow rate and the vessel diameter of 7.96 mm. The residual error was used to quantify the overall velocity accuracy. Under the parabolic flow condition, the maximum velocity should be exactly twice the mean velocity. In this study, the mean and maximum velocities from every image slice were also computed. One mean velocity, one maximum velocity and their SDS were then calculated from the 200 mean and 200 maximum velocities obtained from each flow rate. These velocity data were plotted as functions of the true mean velocity and regression analysis was performed to quantify the accuracy of mean and maximum velocity measurements. In the 3D colour Doppler image, colour corresponds to the flow field and greyscale to the tissue mimic. To quantify the accuracy of the flow field measurement, the flow area of each slice was estimated by counting the number of colour pixels. For the normal vessel, the mean flow area was computed by averaging the flow areas of 200 slices for every flow rate. For the stenotic vessel, eight locations, as indicated in Fig. 11, were selectedand their areascomputed by counting colour pixels. The mean area at each location was calculated by averaging six areasassociatedwith six flow rates. The B-mode areas of these eight locations were also measured manually as references.
RESULTS Effect of machine parameters on jaw area Using a vessel with the diameter of 7.96 mm, the transverse flow area should be 49.76 mm’. With the
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Fig. 2. The flow area as a function of colwr gain, which increasedin five stepsfrom its optimal value. The true flow areashouldbe 49.76 inn?.
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Fig. 3. Estimatedflow area after changingone instrument parameterat a time from the optimal (OP) setting(mean t standarddeviation). BG = B-mode gain; CEWP = colour vs. echowrite priority; UP = ultrasoundpower; P = persistence.
colour Doppler ultrasound, a flow area of 51.6 + 1.14 mm2 was obtained by using our optimal setting (3.6% larger than the true area). Keeping other parameters at their optimal setting, Fig. 2 shows how the flow area changes with the increase of the colour gain setting in five steps from the optimal value. It can be seen that significant overestimation was obtained with the increase of the colour gain. Figure 3 shows the flow area with variation of some other parameters. When the Bmode gain (BG) was decreased by 30%, the flow area increased to 56.2 2 1.76 mm’. Increasing the colour vs. echo write priority (CEWP) threshold by 50% increased the flow area to 6 1 t- 2.13 mm*. Doubling the ultrasound power (UP) resulted in an area of 61.5 t 2.16 mm’. A flow area of 46.55 + 2.04 mm* resulted by turning off the average (persistence [P] = 0). A paired t test showed that flow areas before and after changing the parameters are significantly different (p < 0.001). The results indicate the importance of choosing the parameter when quantitative analysis is required. 30 colour Doppler imaging
Using a colour map of red-toward/blue-away with yellow and aqua shades at the extreme ends of the colour bar, Fig. 4 shows a colour Doppler volume of the normal vessel with a flow rate of 8 n&/s (Re = 640). Fig. 4a shows a longitudinal cut in a plane near the vessel axis, and Fig. 4b a transverse cut. The expected parabolic flow behaviour can be seen with
Fig. 4. 3D colour Doppler imageof the normal vesselconsistingof 200 contiguoustransverseslices.The diameterof the vesselwas7.96 mm and the flow rate was 8 mL/s (Re = 640). (a) A longitudinal cut plane near the vesselaxis with flow from right to left. (b) A transverse cut plane of the samevolume.
the maximum velocity at the vessel centre and the minimum velocity close to the wail. The 3D image can be interactively rotated and cut in any arbitrary plane in real time to reveal a view in that plane, including views impossib!e to obtain using conventional techniques. Figure 5 shows the B-mode 3D image of the stenotic vessel, which provides the anatomical information of the tissue and vessel complex. Fig. 5a is a longitudinal cut and Fig. 5b-d are the transverse cuts. Figure 6 shows the colour Doppler volume image of the stenotic vessel with a flow rate of 10 mL/s (Re = 740). The four cuts correspond to those of Fig. 5. The same colour map used in Fig. 4 was used to generate this figure but the colour baseline had been changed. A high velocity flow can be seen at the stenosis and disturbed flow seen after the stenosis. Colour is confined approximately in the flow field. Accuracy of velocity and flow field measurement
Figure 7 shows the averaged 3D velocity distribution of one component of the 3D velocity vector field
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Fig. 5. B-mode 3D image of the stenotic vessel which provides only the anatomical information. ( a ) A longitudinal cut of the vessel; and (b)-(d) three transverse cuts distal, at as well as proximal to the stenosis.
Fig. 6. The colour Doppler 3D image of the stenotic vessel (flow rate = 10 mL/s). A complex flow pattern is shown in the zone after the stenosis; (a) - (d) correspond to the cut planes shown in Fig. 5.
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Fig. 7. The averaged 3D velocity distribution calculated from 200 slices of the volume shown in Fig. 4.
using the data of Fig. 4, which should have a maximum velocity of 32 cm/s for the flow rate of 8 mL/s. The PRF had been set to make the Nyquist velocity equal to 42 cm/s in this case. The parabolic surface fit resulted in a distribution with a maximum velocity of 31.06 cm/s (i.e., 0.94 cm/s lower than the expected velocity) and a diameter of 8.4 mm (i.e., 0.44 mm bigger than that of the actual vessel). The RMS error of the fit is 1.04 cm/s, or 2.5% of the Nyquist velocity. For all the flow rates tested, the RMS errors of the fits ranged between 2.35% and 3.25% of the Nyquist velocity. The velocity distributions for the condition of this study are thus in reasonable agreement with the parabolic distribution. Figure 8a shows the distribution of the standard deviations (SD) of Fig. 7 based on 200 transverse images. Values of the SD range between 0.2 cm/s to 7.9 cm/s (0.5% to 19% of the Nyquist velocity). For all the flow rates tested, the SD values ranged between 0.3% and 19% of the Nyquist velocity. These values agree well with those measured by Rickey et al. ( 1992)
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with a belt phantom. The residual errors between Fig. 7 and the theoretical parabolic distribution, created with the same flow rate, are shown in Fig. 8b. The residual errors over the whole cross-section were found to be less than 2.6 cm/s (6% of the Nyquist velocity). For all the flow rates tested, the residual errors were found to range between 5.3% and 7% of the Nyquist velocity. It can thus be concluded that, under the conditions described in this article, the velocity accuracy of our 3D colour Doppler system is better than 7% of the Nyquist velocity. Figure 9a shows the measured mean velocity from all flow experiments as a function of the true mean velocity in the normal vessel. There is an excellent agreement between these two velocities with a good correlation of r = 0.999. The accuracy was defined by the difference between the slope of the linear fit and the expected slope (= 1) and is equal to 0.9%. The maximum velocity as a function of the true mean velocity is plotted in Fig. 9b. An excellent agreement is also obtained with the correlation of r = 0.998. The linear regression results in a slope of 2.012, which is 1.2% larger than the expected value. The flow areas in the normal vessel are shown in Fig. 10 as a function of the Reynolds number. The true vessel area is also shown in this figure as the dotted line. It is clearly seen that the flow field is overestimated in all flow rates with the maximum difference of 6 mm2, which corresponds with the 0.48-mm overestimate in the vessel diameter. For the stenotic vessel, the transverse flow areas estimated at the eight locations by colour Doppler are plotted in Fig. 11 as a function of B-mode areas. The maximum diameter difference is found to be 0.5 mm at the neck of stenosis. Figures 10 and 11 also indicate that higher velocities result in more overestimation of
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Fig. 8. (a) The distribution of the standard deviation of the velocity in Fig. 7, which indicates the precision of the velocity measurements. (b) The residual errors between the velocity distribution of Fig. 7 and a theoretical parabolic distribution calculated by using the flow rate of 8 mL/s and the true vessel diameter of 7.96 mm. These errors indicate the accuracy of velocity measurement.
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Fig. 9. (a) Plot illustrating the correlation between measured and true mean velocities of the flow in the normal vessel (mean 2 standard deviation). Error bars of the first two points are the size of the points. The accuracy of mean velocity measurement is given by the difference between the slope of the linear fit and the expected slope and is equal to 0.9%. (b) Plot showing the correlation between measured maximum velocity and the true mean velocity. For parabolic flow, the maximum velocity should be twice the mean velocity. The accuracy is defined as in (a) and is equal to 1.2%.
the flow field. Taking the worst situation, the spatial accuracy of our 3D colour Doppler system is still better than 0.5 mm. DISCUSSION
AND
CONCLUSION
techniques. Since blood flow is a 3D time-varying process, conventional 2D colour Doppler techniques present only a small fraction of the information necessary to characterise the whole process. Experimental work on the analysis of blood flow in 3D showed the poten-
With the advance of colour Doppler imaging, interest has grown in the development of methods for quantifying the severity of cardiovascular disease and for extracting useful information using colour Doppler
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Fig. 10. Measured flow area in the normal vessel as a function of Reynolds number. Large flow rates resulted in more overestimations. A maximum area of 55.8 mm2 indicates a 0.48~mm overestimation of vessel diameter.
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Fig. 11. The flow areas measured using colour data versus those measured using B-mode images at eight locations of the stenotic vessel. The eight locations are equally distributed from L, to L8 as indicated over a distance of 5 mm. The yerror bars are due to measurements at different flow rates, and the x-error bars represent the variation in the area estimation obtained from 30 measurements of the B-mode areas. The maximum area difference corresponds to a 0.5mmdiameter overestimation.
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tial for acquiring additional clinical relevant information from 3D display of blood flow (Rindt et al. 1990). The advantage of using 3D colour Doppler is clear: it can localise a functional abnormality relative to the underlying anatomy. Some important information not previously available, such as the local velocity distribution and the high or low wall shear stress zone, may be measured by using 3D colour Doppler ultrasound. As a step toward the validation of the technique for determining the 3D velocity and 3D shear stress distributions, we validated the use of 3D colour Doppler ultrasound for estimating 3D velocity distributions of one component of the velocity vector field and quantified the accuracy of the velocity measurements using a simplified vascular and tissue mimicking phantom with constant flow. The results of this study show that our 3D colour Doppler system can be used to estimate the velocity with an accuracy better than 7% of the Nyquist velocity. These results can be further improved by directly acquiring the digital velocity data presented within the ultrasound machine instead of extracting from the video signal of the machine. In the present study, the spatial accuracy has been found to be better than 0.5 mm. As mentioned in the Introduction, the wall shear stress will be estimated by extrapolating the velocity profile which fits the measured velocity points. The accuracy and precision of the wall shear stress estimated using this approach are not straightforward but are dependent on the spatial resolution of the velocity estimates. Thus, with our present system having the accuracy measured in this study, the wall shear stress distribution can be expectedly estimated with acceptable accuracy in those medium to large vessels. The relative low spatial accuracy of colour Doppler system results in the encoding of the colour beyond the true flow field. This results in overestimates of the flow area as shown in Figs. 10 and 11. This problem could arise from the effects of the finite sample size (Tamura et al. 1991) . Even when the centre of the sample volume lies outside the flow field, a portion of the sample volume may lie within the vessel, depending on the sample volume dimensions. Improving the spatial accuracy by decreasing the dimension of the sample volume reduces Doppler sensitivity and the accuracy with which the velocity can be measured. This may partly explain why the colour Doppler imaging causes overestimation of the size of cardiac jets (Klewer et al. 1989). It has been noticed that the jet area depicted by colour imaging is likely to be more dependent on instrument parameters than on vascular anatomy or physiologic characteristics (Mitchell 1990 ) . The finite sample size could also be the reason
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why there are relatively large and constant values along the wall on the SD distribution as shown in Fig. 8a. As pointed out previously, the blood flow in the cardiovascular system is a 3D time-varying process. The study described in this article only defines one component of the velocity vector. This information provides insights into the overall flow pattern and has significant clinical value, but it is only the first step in full flow field analysis. The full flow field can be obtained by imaging from more than one direction to reconstruct actual 3D three-component velocity vectors. Recently, various strategies for calculating 2D velocity vectors from noise-corrupted colour Doppler images obtained at multiple angles have been investigated by Maniatis et al. ( 1994). With the progress of our work, it is expected that the 3D blood velocity distribution as well as 3D wall shear stress distribution will be generated by 3D colour Doppler ultrasound to provide a functional description of the human artery. Acknowledgements-The authors are grateful for the financial support of the Medical Research Council of Canada. The first author gratefully acknowledge a postdoctoral fellowship of PCAR (Fonds pour la Formation de Chercheurs et L’ Aide a la Recherche of Quebec) and the second author gratefully acknowledge a FCAR doctoral fellowship. The fourth author is supported from a traineeship of the Heart and Stroke Foundation of Canada. We are grateful to ATL for providing us with an Ultramark 9 HDI colour Doppler system for these experiments. We thank Lori Gardi and Shane Dunne for their technical support and Shidong Tong and Richard Frayne for their helpful discussions during this project.
REFERENCES Assmann, P. E.; Roelandt, J. R. T. C. Two-dimensional and Doppler echocardiography in acute myocardial infarction and its complications. Ultrasound Med. Biol. 13507-517; 1987. Baumgartner, H.; Schima, H.; Kuhn, P. Importance of technical variables for quantitative measurements by colour Doppler Imaging. Am. J. Cardiol. 67:314-315; 1991. Care. C. G. Mechanical factors in atherosclerosis. In: Hwang, N. H. C.; Normann. N. A.. eds. Cardiovascular flow dynamics and measurements. Baltimore: University Park Press; 1977: 473. Duncan, D. D.; Bargeron, C. B.; Borchardt. S. E.; Deters, 0. J.; Gearhart, S. A.; Mark, F. F.; Friedman, M. H. The effect of compliance on wall shear in casts of a human aortic bifurcation. J. Biomech. Eng. 112:183-188; 1990. Evans, D. S.; McDicken, W. N.; Skidmore, R.; Woodcock, J. P. Doppler ultrasound: Physics, instrumentation, and clinical application. Chichester: John Wiley & Sons; 1989: 9. Fry, D. L. Certain histological and chemical responses of the vascular interface to acutely induced mechanical stress in the aorta of the dog. Circ. Res. 24:93; 1969. Grottum, P.; Svindland, A.; Walloe, L. Localization of atherosclerotic lesions in the bifurcation of the left main coronary artery. Atherosclerosis 4755-62; 1983. Holdsworth, D. W.; Rickey, D. W.; Drangova, M.; Miller, D. I. M.; Fenster, A. Computer-controlled positive displacement pump for physiological Row simulation. Med. Biol. Eng. Comput. 29:565570; 1991. Kitabatake, A.; Tanouchi, J.; Yoshida, Y.; Masuyama. T.; Uematsu, M.: Kamada. T. Quantitative colour flow imaging to measure the two-dimensional distribution of blood flow velocity and the flow rate. Japanese Circ. J. 54:304-308: 1990. Klewer. S. E.; Lloyd. T. R.; Goldberg. S. J. In vivo relation between
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cineangiographic jet width and jet width imaged by colour-coded Doppler. Am. J. Cardiol. 64:13991401; 1989. Ku. D. N.; Giddens, D. P.; Zarins, C. K.; Glagov. S. Pulsatile flow and atherosclerosis in the human carotid bifurcation: Positive correlation between plaque location and low and oscillating shear stress. Atherosclerosis 5:293-302; 1985. Lou. Z.; Yang, W.; Stein, P. D. Errors in the estimation of arterial wall shear rates that result from curve fitting of velocity profiles. J. Biomech. 26:383-390; 1993. Maniatis, T. A.: Cobbold, R. S. C.; Johnston, K. W. Two-dimensional velocity reconstruction strategies for colour flow Doppler ultrasound images. Ultrasound Med. Biol. 20:137145; 1994. Mills, P. H.; Fuchs, H. 3D ultrasound display optical tracking. In: Proceedings of the I st Conference on Visualization in Biomedical Computing. Los Alamitos, CA: IEEE Computer Society Press; 1990:490-497. Mitchell. D. G. Colour Doppler imaging: Principles. limitations, and artifacts. Radiology 177: I- 10; 1990. Miyagi, Y.; Masaoka, H.; Akamatsu, N.; Sekiba, K. Development of a three-dimensional colour Doppler system. Med. Prog. Technol. 18:201-208; 1993. Ohbuchi. R.; Fuchs, H. Incremental 3D ultrasound imaging from a 2D scanner. In: Proceedings of the 1st Conference on Visualization in Biomedical Computing. Los Alamitos, CA: IEEE Computer Society Press; 1990:360-367. Perktold, K.; Thumer, E.; Kenner. T. Flow and stress characteristics in rigid walled and compliant carotid artery bifurcation models. Med. Biol. Eng. Comput. 32:19-26; 1994. Picot, P. A.; Rickey, D. W.; Mitchell, R.; Rankin, R. N.; Fenster, A. Three-dimensional colour Doppler imaging of the carotid artery. In: Image capture, formatting, and display. SPIE proceed-
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ings, Vol. 1444. Bellingham, WA: SPIE-The International Society for Optical Engineering: 1991:206-213 Picot. P. A.; Rickey. D. W.; Mitchell. R.: Rankin. R. N.: Fenstei. A. Three-dimensional colour Doppler imaging. Ultrasound Med Biol. l9:95-104; 1993. Pretorius, D. H.; Nelson. T. R.; Jaffe, J. S. Three-dimensional sono graphic analysis based on color flow Doppler and gray scale image data: A preliminary report, J. Ultrasound Med. 11:X-232; 1992. Rickey, D. W.; Rankin, R.; Fenster, A. A velocity evaluation phantom for colour and pulsed Doppler instruments. Ultrasound Med. Biol. 18:479-494; 1992. Rickey, D. W.; Picot, P. A.; Fenster. A. A wall-less vessel phantom for Doppler ultrasound studies. Ultrasound Med. Biol. [in press]. Rindt, C. C.; Steenhoven, A. A.; Janssen, J. D.; Reneman, R. S.; Segal. A. A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation. I. Biomech. 23:461-473; 1990. Ross, R. The pathogenesis of atherosclerosis: A perspective for the 1990’s. Nature 362801-809; 1993. Tamura, T.; Cobbold, R. S. C.; Johnston, K. W. Quantitative study of steady flow using colour Doppler ultrasound. Ultrasound Med. Biol. 17:595-605; 1991. Valdes-Cruz, L.; Tamura, T.; Dalton, N.; Elias, W. Color flow Doppler shunt areas as indicators of arterial septal defect shunting: Studies in an open chest animal model and initial clinical results. Circulation 74: 1 I - 145; 1986. Zierler, R. E.; Phillips, D. J.; Beach, K. W.; Primozich, J. F.; Strandness, D. E., Jr. Noninvasive assessment of normal carotid bifurcation hemodynamics with color flow ultrasound imaging. Ultrasound Med. Biol. 13:471-476: 1987.
in Med.
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& Biol.. Vol. 2 I. No. 6. pp. X07- 816, iYYS Copyright ~6: 1995 Elsevirr Science Ltd Printed in the USA. All rights reserved 0301-Sh2WY5 ‘FY.SO + .(X)
Original Contribution QUANTITATIVE INVESTIGATION OF IN VZi?‘Z?O FLOW USING THREE-DIMENSIONAL COLOUR DOPPLER ULTRASOUND ZHENYU
Guo, MICHEL
MOREAU, DANIEL W. RICKEY, PAUL A. PICOT and AARON FENSTER The John P. Robarts Research Institute, London, Ontario, Canada; and
Imaging Research Laboratories, Department of Medical Biophysics, (Received
University
15 August
of Western Ontario,
1994; in final
form 28
November
London,
Ontario, Canada
1994)
Abstract-A quantitative in vitro flow study was performed by using a three-dimensionalcolour Doppler imaging system. This system was based on a clinical ultrasound instrument with its transducer mounted on a motor-driven translation stage. A vascular and tissue-mimicking phantom containing two wall-less vessels,one normai and another stenotic, was used to quantify the measurementaccuracy of the flow velocity and the flow field. Steady state flows, having Reynolds numbers ranging between 460 and 1300, were generated by a computer-controlled positive displacementpump. Effects of the parameter settingsof the ultrasound instrument on resultsof the estimation of flow field were alsostudied. Experimental results show that our three-dimensional colour Doppler system’s velocity accuracy was better than 7% of the Nyquist velocity and its spatial accuracy was better than 0.5 mm. The systemshowed a good correlation (r = 0.999) between the estimated and the true mean flow velocity, and a good correlation (r = 0.998) between the estimated maximum and the true mean flow velocity. This study is our first step toward validating the measurementof the three-dimensional velocity and wall shear stressdistributions by using three-dimensionalcolour Doppler ultrasound. Key Words: 3D colour Doppler ultrasound, Quantitative flow measurement,Vascular phantom, Wall shear
stress,Flow visualization, Velocity accuracy.
INTRODUCTION
ing the risk for atherosclerosis (Car0 1977). To clarify the conflict and obtain a complete understanding of atherosclerosis, it is important to study and monitor the three-dimensional (3D) local blood flow velocity and wall shear stress distributions over the whole vessel of interest. Colour Doppler ultrasound has been used extensively as a noninvasive tool for the diagnosis of cardiovascular disease (Assmann and Roelandt 1987: Valdes-Cruz et al. 1986; Zierler et al. 1987). Although most clinical applications of colour Doppler ultrasound involve qualitative flow visualisation, it does have the potential to image the velocity flow field in a quantitative manner (Kitabatake et al. 1990; Rickey et al. 1992; Tamura et al. 1991). But, the conventional colour Doppler technique provides only 2D flow and anatomical information. It cannot be used directly to monitor the 3D local flow velocity and wall shear stress distributions. Recently, 3D colour Doppler systems have been developed to acquire a complete volume surrounding a vessel (Mills and Fuchs 1990; Picot et al. 1993) to provide a cohesive image of the complicated
Atherosclerosis, the primary cause of cardiovascular diseases, is characterized by the development of plaques on the vessel wall (Ross 1993). These plaques narrow the vessel and can restrict or completely obstruct the blood flow. The mechanisms responsible for atherosclerosis are still not well understood; however, it has been suggested that the local hemodynamic and mechanical factors play important roles in the disease initiation and development (Grottum et al. 1983; Ku et al. 1985). The shear stress on the vessel wall produced by the flowing blood has received the most attention and is believed to be closely related to the initiation of atherosclerosis (Car0 et al. 1977; Perktold et al. 1994). At first it was proposed that increased shear stress might be the initiating factor in atherosclerosis (Fry 1969). More recent observations, however, suggest that low shear stress could be a factor increasAddress correspondence to: Dr. Zhenyu Guo, Imaging Research Laboratories, The John P. Robarts Research Institute, 100 Perth Drive, P.O. Box 501.5, London. Ontario N6A 5K8, Canada.
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vascular anatomy and flow. By acquiring a 3D colour Doppler image of a vessel, the local flow velocity field and wall shear stress could be estimated. The 3D image could also be rotated and sliced to reveal a view of any arbitrary plane to help physicians diagnose the early stage of disease and follow-up the disease. Some studies (Mills and Fuchs 1990; Ohbuchi and Fuchs 1990) used an operator-manipulated 2D imager to build up 3D images. This technique is labour-intensive and requires more patient cooperation. Current studies employed a computer-controlled probe positioner to translate mechanically the transducer to acquire the 3D image (Miyagi et al. 1993; Picot et al. 1991, 1993; Pretorius et al. 1992). This approach is fast and efficient in sampling a volume of interest. Because of the finite size of the sample volume, the major problem involved in the estimation of wall shear stress using colour Doppler ultrasound is the determination of the velocity gradient near the wall. Practical methods of wall shear stress estimation are based on extrapolation of the velocity profile which fits the measured velocity points in vessels (Duncan et al. 1990; Ku et al. 1985; Lou et al. 1993). Accurate measurements of velocity and position data are thus our first concerns. As the first step for 3D velocity and wall shear stress measurement, in this study, we validated the measurement of one component of the velocity vector field in a circular symmetric vessel with constant flow. The purpose of the present study was thus to determine the accuracy and precision of the velocity and flow field measurement by using our 3D colour Doppler ultrasound system (Picot et al. 1993). In this article, we first describe the experimental system and our vascular and tissue-mimicking phantom, address the appropriate use of the colour Doppler system, and describe the method for measuring the flow velocity. We then describe the results of our study and show how the 3D velocity profile can be obtained using our system. From the velocity profile, the wall shear stress can be estimated. MATERIALS 30 colour Doppler
AND METHODS system description
Figure 1 is a block diagram of our experimental system. A detailed technical description of the 3D colour Doppler system can be found in Picot et al. ( 1993 ) . For this study, we used an ATL Ultramark 9 HDI colour Doppler ultrasound system with a 3%mm aperture and a ~-MHZ high resolution linear array transducer. For B-mode imaging, the transducer operates at 5 MHz, while in the colour Doppler mode the transducer works at 4 MHz. The linear array transducer was mounted on a motor-driven translation assembly with
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Computer-controled pump
Fig. 1. Block diagram of the 3D colour Doppler imaging system. A 80386-based PC digitizes the colour and greyscalevideo signalsfrom Ultramark9 HDI ultrasound system. The transducer is moved by a motor-driven stage. Blood mimicking flow is generated by a computer-controlled pump. A Macintosh Quadra 650 is used to perform volume reconstruction and analysis.
the translation axis at a known angle to the imaging plane. A set of planar images, transverse to the vessel, was acquired while translating the probe along the vessel at a fixed Doppler angle. The combination set of contiguous 2D image slices constitutes a volume image. A PC 80386-based microcomputer containing two image acquisition boards was used to digitize the colour and grey-scale video signals from Ultramark 9 HDI. Since the Ultramark 9 HDI encodes velocities in 32 discrete bins, the red-green-blue colour video signal was digitised with a precision of 5 bits per colour, while the monochrome video signal was digitised with a precision of 8 bits. After the images were acquired, they were transmitted, via an ethernet link, to a Quadra 650 Macintosh computer for image preprocessing and volume reconstruction. Every colour pixel in the colour images was converted to the corresponding velocity value by means of a precalibrated look-up table created based on the colour map of the Ultramark 9 HDI (&key et al. 1992). The colour and grey-scale images were then combined into a single volume to produce a 3D velocity-plus-anatomy image. Finally, this volume was sheared to compensate for the Doppler angle used for the recovery of the correct geometry. The resulting volume might be viewed or further processed with a volume visualisation program by displaying velocity voxels in colour and tissue voxels in grey-scale (examples shown in Fig. 4 and 6).
In vitro
Vascular phantom and blood-mimicking
flow with
3D colour
jhid
In the present study, the test phantom was composed of a Plexiglas box containing a tissue mimic and two wall-less vessels. This box was covered by a OSmm thick urethane layer, which has an ultrasound impedance similar to tissue, and low attenuation, making it a good acoustic window and preventing the tissue mimic from drying. The tissue mimic is described by Rickey et al. ( 1995) and was based on a water and agar (high strength A-6924, Sigma Chemical) gel. Glycerol (8%) was added to increase the acoustic velocity to that of tissue, and 3% 50-pm cellulose scattering particles (S-5504 Sigmacell, Sigma Chemical) were added to provide an acoustic attenuation to be 3.5 dB/cm at 4 MHz. The “normal” wall-less vessel was formed by pouring the tissue mimic around a metal rod with a diameter of 7.96 mm and then removing the rod after the tissue mimic has set. The stenotic wall-less vessel was formed by removing two rods with the same diameter of 7.96 mm from both ends. One end of each rod was tapered to a cosine shape with a maximal reduction of the cross-section area to be 70%. The two tapered ends were joined at the stenosis so that, after removal, a vessel was formed with a 70% stenosis at the midsection. The blood-mimicking fluid was a solution of machinists cutting fluid ( Acra Tech Syn-Cut HD, Mississauga, Ontario) and distilled water. The ratio of cutting fluid to water was 60% to 40%. Pulverised nylon 612 particles (ELF Atochem Orgasol 3501 EXD), which have a mean diameter of 10 pm, were added to provide the scattering sites. By using a capillary viscometer (Canon 30), the viscosity of the blood mimic was measured and found to be 0.0206 cm’/s. The acoustic velocity of the blood mimic was 1560 m/s (Rickey et al. 1995). This working fluid was pumped through our wall-less vessels by using a computercontrolled positive displacement pump (UHDC flow system, Quest Image Inc., London, Ontario). The pump produces very accurate steady flow and various pulsatile waveforms including reverse flow (Holdsworth et al. 1991). Plexiglas tubes were used to provide straight inlet and outlet for the wall-less vessel. The inside diameter of the Plexiglas tubes was machined to be the same as that of the wall-less vessel. The entrance length of tubes was equivalently 50 tube inside diameters, so that fluid entrance effects would be negligible for laminar steady state flow (Evans et al. 1989). Colour Doppler
system setting
Colour Doppler imaging provides information on the spatial distribution of the flow field. Although the colour area should correspond to the flow field, a num-
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ber of studies, advocating the use of colour Doppler to quantify cardiovascular disease, have shown some technical limitations of colour Doppler imaging (Baumgartner et al. 1991; Mitchell 1990). By using the size and shape of the colour area to quantify valvular regurgitation and vessel stenosis, it has been found that these estimates are highly dependent on numerous operator-dependent as well as instrument-dependent variables. For the purpose of quantitative flow analysis in our present study, the dependence of colour areas on the colour Doppler instrument parameters have been studied. Since the geometry of our vascular phantom is well defined, it provided a reference to determine an optimal setting of instrument parameters for our specific purpose. In the ultrasound instrument, gains are controlled separately for B-mode and colour Doppler. Because colour is typically suppressed over bright echoes, use of a slightly high B-mode gain may decrease the presence of colour noise over the tissue. However, an excessively high B-mode gain may suppress colour within the flow field. An additional important parameter is the colour vs. echo write priority (CEWP) which selects a threshold at which the echo data will overwrite the colour data. Above this threshold, echoes are considered to be strong enough to reject colour and only grey-scale is displayed. In the present study, we selected the highest B-mode and colour gains without overestimating the true flow field and lowest colour reject without causing colour noise. The ultrasound power was also chosen according to the true flow field to yield the best apparent colour flow image with the transmitting focal point set near the centre of the wallless vessel. The persistence level of the system, which determines the number of video frames to be averaged in a weighted manner, can be set between 0 and 7 with a setting of 0 corresponding to no averaging. We used the highest persistence level to obtain good estimates of blood velocity distributions and improve the appearance of colour Bow image. This could be done in our present study because the constant flow was used and the temporal resolution is thus meaningless. For the situation of pulsatile flow, this parameter may have to be reduced to gain a higher frame rate. To demonstrate the dependence of the estimated flow field on the instrument parameters, the transverse flow area of the normal vessel was measured by planimetry after changing one parameter each time from its optimal value and compared to the area measured with the optimal setting: ( 1) colour gain increased in five steps of 4% each; (2) B-mode gain decreased by 30%; (3) colour vs. echo write priority threshold increased by 50%; (4) doubling the ultrasound power;
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and (5) turning off the average (persistence = 0 1. Each measurement was repeated 30 times. Since the HDI only quantifies the flow velocity into 32 levels, the PRF was set to let the Nyquist velocity be just above the maximum velocity for each flow rate tested. This increased the velocity resolution and ensured that no aliasing occurred in the measurement. Additional velocity resolution was achieved in the normal vessel by shifting the colour baseline, since there was no reverse flow in this vessel. Accuracy of velocity and jaw field measurements With our optimal parameter setting, 3D colour Doppler imaging was performed using a Doppler angle of 72”. Steady laminar flows were generated by the computer-controlled pump at flow rates between 6 (Re = 460) and 16 mL/s (Re = 1300) with an increment of 2 mL/s. Parabolic flow was assumed in the normal vessel for all the flow rates tested, since it is impossible for turbulent flow to persist in such a straight smooth tube with these low Reynolds numbers. For each flow rate, 200 contiguous grey-scale and colour 2D image slices, 0.2 mm apart, were acquired for each vessel with every image slice having the dimensions of 160 X 204 pixels. Velocity-plus-anatomy volumes were then reconstructed into 160 X 204 X 200 pixel volumes by combining the anatomy and velocity data and shearing to correct for the Doppler angle. Working in zoomed mode of the colour Doppler system, the resulting voxel dimensions in the X, y and z directions were found to be 0.081 mm X 0.059 mm X 0.2 mm. Therefore, the reconstructed volumes had a dimension of 13 mm x 12 mm x 40 mm. The setting of the colour Doppler system was kept constant except that the PRF was reset for each flow rate as described above. For velocity analysis, the velocity data were corrected for Doppler angle and resealed to obtain the true velocity according to the PRF setting. Since the theoretical velocity distribution of the normal vessel was assumed to be laminar parabolic flow, this vessel was used to quantify the velocity accuracy of the 3D colour Doppler system. Since the flow was constant and the vessel was uniform, for each flow rate, the 200 slices of velocity data of the velocity-plus-anatomy volume were averaged to obtain an estimate of the averaged 3D velocity distribution of one component of the 3D velocity vector field. The 3D standard deviation (SD) distribution was also calculated to quantify the precision of the velocity measurement. The averaged velocity distribution was fitted to a parabolic surface and the root-mean-square (F&IS) error of the fit was calculated to quantify the goodness-of-fit. We then computed the residual error between the averaged ve-
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locity distribution and a theoretical parabolic distribution created with the corresponding flow rate and the vessel diameter of 7.96 mm. The residual error was used to quantify the overall velocity accuracy. Under the parabolic flow condition, the maximum velocity should be exactly twice the mean velocity. In this study, the mean and maximum velocities from every image slice were also computed. One mean velocity, one maximum velocity and their SDS were then calculated from the 200 mean and 200 maximum velocities obtained from each flow rate. These velocity data were plotted as functions of the true mean velocity and regression analysis was performed to quantify the accuracy of mean and maximum velocity measurements. In the 3D colour Doppler image, colour corresponds to the flow field and greyscale to the tissue mimic. To quantify the accuracy of the flow field measurement, the flow area of each slice was estimated by counting the number of colour pixels. For the normal vessel, the mean flow area was computed by averaging the flow areas of 200 slices for every flow rate. For the stenotic vessel, eight locations, as indicated in Fig. 11, were selectedand their areascomputed by counting colour pixels. The mean area at each location was calculated by averaging six areasassociatedwith six flow rates. The B-mode areas of these eight locations were also measured manually as references.
RESULTS Effect of machine parameters on jaw area Using a vessel with the diameter of 7.96 mm, the transverse flow area should be 49.76 mm’. With the
55
50 0
1
2 3 4 5 Steps of Colour Gain Increase
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7
Fig. 2. The flow area as a function of colwr gain, which increasedin five stepsfrom its optimal value. The true flow areashouldbe 49.76 inn?.
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Fig. 3. Estimatedflow area after changingone instrument parameterat a time from the optimal (OP) setting(mean t standarddeviation). BG = B-mode gain; CEWP = colour vs. echowrite priority; UP = ultrasoundpower; P = persistence.
colour Doppler ultrasound, a flow area of 51.6 + 1.14 mm2 was obtained by using our optimal setting (3.6% larger than the true area). Keeping other parameters at their optimal setting, Fig. 2 shows how the flow area changes with the increase of the colour gain setting in five steps from the optimal value. It can be seen that significant overestimation was obtained with the increase of the colour gain. Figure 3 shows the flow area with variation of some other parameters. When the Bmode gain (BG) was decreased by 30%, the flow area increased to 56.2 2 1.76 mm’. Increasing the colour vs. echo write priority (CEWP) threshold by 50% increased the flow area to 6 1 t- 2.13 mm*. Doubling the ultrasound power (UP) resulted in an area of 61.5 t 2.16 mm’. A flow area of 46.55 + 2.04 mm* resulted by turning off the average (persistence [P] = 0). A paired t test showed that flow areas before and after changing the parameters are significantly different (p < 0.001). The results indicate the importance of choosing the parameter when quantitative analysis is required. 30 colour Doppler imaging
Using a colour map of red-toward/blue-away with yellow and aqua shades at the extreme ends of the colour bar, Fig. 4 shows a colour Doppler volume of the normal vessel with a flow rate of 8 n&/s (Re = 640). Fig. 4a shows a longitudinal cut in a plane near the vessel axis, and Fig. 4b a transverse cut. The expected parabolic flow behaviour can be seen with
Fig. 4. 3D colour Doppler imageof the normal vesselconsistingof 200 contiguoustransverseslices.The diameterof the vesselwas7.96 mm and the flow rate was 8 mL/s (Re = 640). (a) A longitudinal cut plane near the vesselaxis with flow from right to left. (b) A transverse cut plane of the samevolume.
the maximum velocity at the vessel centre and the minimum velocity close to the wail. The 3D image can be interactively rotated and cut in any arbitrary plane in real time to reveal a view in that plane, including views impossib!e to obtain using conventional techniques. Figure 5 shows the B-mode 3D image of the stenotic vessel, which provides the anatomical information of the tissue and vessel complex. Fig. 5a is a longitudinal cut and Fig. 5b-d are the transverse cuts. Figure 6 shows the colour Doppler volume image of the stenotic vessel with a flow rate of 10 mL/s (Re = 740). The four cuts correspond to those of Fig. 5. The same colour map used in Fig. 4 was used to generate this figure but the colour baseline had been changed. A high velocity flow can be seen at the stenosis and disturbed flow seen after the stenosis. Colour is confined approximately in the flow field. Accuracy of velocity and flow field measurement
Figure 7 shows the averaged 3D velocity distribution of one component of the 3D velocity vector field
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Fig. 5. B-mode 3D image of the stenotic vessel which provides only the anatomical information. ( a ) A longitudinal cut of the vessel; and (b)-(d) three transverse cuts distal, at as well as proximal to the stenosis.
Fig. 6. The colour Doppler 3D image of the stenotic vessel (flow rate = 10 mL/s). A complex flow pattern is shown in the zone after the stenosis; (a) - (d) correspond to the cut planes shown in Fig. 5.
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Fig. 7. The averaged 3D velocity distribution calculated from 200 slices of the volume shown in Fig. 4.
using the data of Fig. 4, which should have a maximum velocity of 32 cm/s for the flow rate of 8 mL/s. The PRF had been set to make the Nyquist velocity equal to 42 cm/s in this case. The parabolic surface fit resulted in a distribution with a maximum velocity of 31.06 cm/s (i.e., 0.94 cm/s lower than the expected velocity) and a diameter of 8.4 mm (i.e., 0.44 mm bigger than that of the actual vessel). The RMS error of the fit is 1.04 cm/s, or 2.5% of the Nyquist velocity. For all the flow rates tested, the RMS errors of the fits ranged between 2.35% and 3.25% of the Nyquist velocity. The velocity distributions for the condition of this study are thus in reasonable agreement with the parabolic distribution. Figure 8a shows the distribution of the standard deviations (SD) of Fig. 7 based on 200 transverse images. Values of the SD range between 0.2 cm/s to 7.9 cm/s (0.5% to 19% of the Nyquist velocity). For all the flow rates tested, the SD values ranged between 0.3% and 19% of the Nyquist velocity. These values agree well with those measured by Rickey et al. ( 1992)
(4
813
with a belt phantom. The residual errors between Fig. 7 and the theoretical parabolic distribution, created with the same flow rate, are shown in Fig. 8b. The residual errors over the whole cross-section were found to be less than 2.6 cm/s (6% of the Nyquist velocity). For all the flow rates tested, the residual errors were found to range between 5.3% and 7% of the Nyquist velocity. It can thus be concluded that, under the conditions described in this article, the velocity accuracy of our 3D colour Doppler system is better than 7% of the Nyquist velocity. Figure 9a shows the measured mean velocity from all flow experiments as a function of the true mean velocity in the normal vessel. There is an excellent agreement between these two velocities with a good correlation of r = 0.999. The accuracy was defined by the difference between the slope of the linear fit and the expected slope (= 1) and is equal to 0.9%. The maximum velocity as a function of the true mean velocity is plotted in Fig. 9b. An excellent agreement is also obtained with the correlation of r = 0.998. The linear regression results in a slope of 2.012, which is 1.2% larger than the expected value. The flow areas in the normal vessel are shown in Fig. 10 as a function of the Reynolds number. The true vessel area is also shown in this figure as the dotted line. It is clearly seen that the flow field is overestimated in all flow rates with the maximum difference of 6 mm2, which corresponds with the 0.48-mm overestimate in the vessel diameter. For the stenotic vessel, the transverse flow areas estimated at the eight locations by colour Doppler are plotted in Fig. 11 as a function of B-mode areas. The maximum diameter difference is found to be 0.5 mm at the neck of stenosis. Figures 10 and 11 also indicate that higher velocities result in more overestimation of
03
Fig. 8. (a) The distribution of the standard deviation of the velocity in Fig. 7, which indicates the precision of the velocity measurements. (b) The residual errors between the velocity distribution of Fig. 7 and a theoretical parabolic distribution calculated by using the flow rate of 8 mL/s and the true vessel diameter of 7.96 mm. These errors indicate the accuracy of velocity measurement.
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-+-Measured
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35
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(cm/s)
(b)
Fig. 9. (a) Plot illustrating the correlation between measured and true mean velocities of the flow in the normal vessel (mean 2 standard deviation). Error bars of the first two points are the size of the points. The accuracy of mean velocity measurement is given by the difference between the slope of the linear fit and the expected slope and is equal to 0.9%. (b) Plot showing the correlation between measured maximum velocity and the true mean velocity. For parabolic flow, the maximum velocity should be twice the mean velocity. The accuracy is defined as in (a) and is equal to 1.2%.
the flow field. Taking the worst situation, the spatial accuracy of our 3D colour Doppler system is still better than 0.5 mm. DISCUSSION
AND
CONCLUSION
techniques. Since blood flow is a 3D time-varying process, conventional 2D colour Doppler techniques present only a small fraction of the information necessary to characterise the whole process. Experimental work on the analysis of blood flow in 3D showed the poten-
With the advance of colour Doppler imaging, interest has grown in the development of methods for quantifying the severity of cardiovascular disease and for extracting useful information using colour Doppler
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600
700
800 Reynolds
900
1000
1100
1200
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Fig. 10. Measured flow area in the normal vessel as a function of Reynolds number. Large flow rates resulted in more overestimations. A maximum area of 55.8 mm2 indicates a 0.48~mm overestimation of vessel diameter.
20
25
30
B-mode
Area
35
40
45
(mm’)
Fig. 11. The flow areas measured using colour data versus those measured using B-mode images at eight locations of the stenotic vessel. The eight locations are equally distributed from L, to L8 as indicated over a distance of 5 mm. The yerror bars are due to measurements at different flow rates, and the x-error bars represent the variation in the area estimation obtained from 30 measurements of the B-mode areas. The maximum area difference corresponds to a 0.5mmdiameter overestimation.
In vitro
flow
with 3D colour
tial for acquiring additional clinical relevant information from 3D display of blood flow (Rindt et al. 1990). The advantage of using 3D colour Doppler is clear: it can localise a functional abnormality relative to the underlying anatomy. Some important information not previously available, such as the local velocity distribution and the high or low wall shear stress zone, may be measured by using 3D colour Doppler ultrasound. As a step toward the validation of the technique for determining the 3D velocity and 3D shear stress distributions, we validated the use of 3D colour Doppler ultrasound for estimating 3D velocity distributions of one component of the velocity vector field and quantified the accuracy of the velocity measurements using a simplified vascular and tissue mimicking phantom with constant flow. The results of this study show that our 3D colour Doppler system can be used to estimate the velocity with an accuracy better than 7% of the Nyquist velocity. These results can be further improved by directly acquiring the digital velocity data presented within the ultrasound machine instead of extracting from the video signal of the machine. In the present study, the spatial accuracy has been found to be better than 0.5 mm. As mentioned in the Introduction, the wall shear stress will be estimated by extrapolating the velocity profile which fits the measured velocity points. The accuracy and precision of the wall shear stress estimated using this approach are not straightforward but are dependent on the spatial resolution of the velocity estimates. Thus, with our present system having the accuracy measured in this study, the wall shear stress distribution can be expectedly estimated with acceptable accuracy in those medium to large vessels. The relative low spatial accuracy of colour Doppler system results in the encoding of the colour beyond the true flow field. This results in overestimates of the flow area as shown in Figs. 10 and 11. This problem could arise from the effects of the finite sample size (Tamura et al. 1991) . Even when the centre of the sample volume lies outside the flow field, a portion of the sample volume may lie within the vessel, depending on the sample volume dimensions. Improving the spatial accuracy by decreasing the dimension of the sample volume reduces Doppler sensitivity and the accuracy with which the velocity can be measured. This may partly explain why the colour Doppler imaging causes overestimation of the size of cardiac jets (Klewer et al. 1989). It has been noticed that the jet area depicted by colour imaging is likely to be more dependent on instrument parameters than on vascular anatomy or physiologic characteristics (Mitchell 1990 ) . The finite sample size could also be the reason
Doppler
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why there are relatively large and constant values along the wall on the SD distribution as shown in Fig. 8a. As pointed out previously, the blood flow in the cardiovascular system is a 3D time-varying process. The study described in this article only defines one component of the velocity vector. This information provides insights into the overall flow pattern and has significant clinical value, but it is only the first step in full flow field analysis. The full flow field can be obtained by imaging from more than one direction to reconstruct actual 3D three-component velocity vectors. Recently, various strategies for calculating 2D velocity vectors from noise-corrupted colour Doppler images obtained at multiple angles have been investigated by Maniatis et al. ( 1994). With the progress of our work, it is expected that the 3D blood velocity distribution as well as 3D wall shear stress distribution will be generated by 3D colour Doppler ultrasound to provide a functional description of the human artery. Acknowledgements-The authors are grateful for the financial support of the Medical Research Council of Canada. The first author gratefully acknowledge a postdoctoral fellowship of PCAR (Fonds pour la Formation de Chercheurs et L’ Aide a la Recherche of Quebec) and the second author gratefully acknowledge a FCAR doctoral fellowship. The fourth author is supported from a traineeship of the Heart and Stroke Foundation of Canada. We are grateful to ATL for providing us with an Ultramark 9 HDI colour Doppler system for these experiments. We thank Lori Gardi and Shane Dunne for their technical support and Shidong Tong and Richard Frayne for their helpful discussions during this project.
REFERENCES Assmann, P. E.; Roelandt, J. R. T. C. Two-dimensional and Doppler echocardiography in acute myocardial infarction and its complications. Ultrasound Med. Biol. 13507-517; 1987. Baumgartner, H.; Schima, H.; Kuhn, P. Importance of technical variables for quantitative measurements by colour Doppler Imaging. Am. J. Cardiol. 67:314-315; 1991. Care. C. G. Mechanical factors in atherosclerosis. In: Hwang, N. H. C.; Normann. N. A.. eds. Cardiovascular flow dynamics and measurements. Baltimore: University Park Press; 1977: 473. Duncan, D. D.; Bargeron, C. B.; Borchardt. S. E.; Deters, 0. J.; Gearhart, S. A.; Mark, F. F.; Friedman, M. H. The effect of compliance on wall shear in casts of a human aortic bifurcation. J. Biomech. Eng. 112:183-188; 1990. Evans, D. S.; McDicken, W. N.; Skidmore, R.; Woodcock, J. P. Doppler ultrasound: Physics, instrumentation, and clinical application. Chichester: John Wiley & Sons; 1989: 9. Fry, D. L. Certain histological and chemical responses of the vascular interface to acutely induced mechanical stress in the aorta of the dog. Circ. Res. 24:93; 1969. Grottum, P.; Svindland, A.; Walloe, L. Localization of atherosclerotic lesions in the bifurcation of the left main coronary artery. Atherosclerosis 4755-62; 1983. Holdsworth, D. W.; Rickey, D. W.; Drangova, M.; Miller, D. I. M.; Fenster, A. Computer-controlled positive displacement pump for physiological Row simulation. Med. Biol. Eng. Comput. 29:565570; 1991. Kitabatake, A.; Tanouchi, J.; Yoshida, Y.; Masuyama. T.; Uematsu, M.: Kamada. T. Quantitative colour flow imaging to measure the two-dimensional distribution of blood flow velocity and the flow rate. Japanese Circ. J. 54:304-308: 1990. Klewer. S. E.; Lloyd. T. R.; Goldberg. S. J. In vivo relation between
816
Ultrasound
in Medicine
and Biology
cineangiographic jet width and jet width imaged by colour-coded Doppler. Am. J. Cardiol. 64:13991401; 1989. Ku. D. N.; Giddens, D. P.; Zarins, C. K.; Glagov. S. Pulsatile flow and atherosclerosis in the human carotid bifurcation: Positive correlation between plaque location and low and oscillating shear stress. Atherosclerosis 5:293-302; 1985. Lou. Z.; Yang, W.; Stein, P. D. Errors in the estimation of arterial wall shear rates that result from curve fitting of velocity profiles. J. Biomech. 26:383-390; 1993. Maniatis, T. A.: Cobbold, R. S. C.; Johnston, K. W. Two-dimensional velocity reconstruction strategies for colour flow Doppler ultrasound images. Ultrasound Med. Biol. 20:137145; 1994. Mills, P. H.; Fuchs, H. 3D ultrasound display optical tracking. In: Proceedings of the I st Conference on Visualization in Biomedical Computing. Los Alamitos, CA: IEEE Computer Society Press; 1990:490-497. Mitchell. D. G. Colour Doppler imaging: Principles. limitations, and artifacts. Radiology 177: I- 10; 1990. Miyagi, Y.; Masaoka, H.; Akamatsu, N.; Sekiba, K. Development of a three-dimensional colour Doppler system. Med. Prog. Technol. 18:201-208; 1993. Ohbuchi. R.; Fuchs, H. Incremental 3D ultrasound imaging from a 2D scanner. In: Proceedings of the 1st Conference on Visualization in Biomedical Computing. Los Alamitos, CA: IEEE Computer Society Press; 1990:360-367. Perktold, K.; Thumer, E.; Kenner. T. Flow and stress characteristics in rigid walled and compliant carotid artery bifurcation models. Med. Biol. Eng. Comput. 32:19-26; 1994. Picot, P. A.; Rickey, D. W.; Mitchell, R.; Rankin, R. N.; Fenster, A. Three-dimensional colour Doppler imaging of the carotid artery. In: Image capture, formatting, and display. SPIE proceed-
Volume
21. Number
6. 1995
ings, Vol. 1444. Bellingham, WA: SPIE-The International Society for Optical Engineering: 1991:206-213 Picot. P. A.; Rickey. D. W.; Mitchell. R.: Rankin. R. N.: Fenstei. A. Three-dimensional colour Doppler imaging. Ultrasound Med Biol. l9:95-104; 1993. Pretorius, D. H.; Nelson. T. R.; Jaffe, J. S. Three-dimensional sono graphic analysis based on color flow Doppler and gray scale image data: A preliminary report, J. Ultrasound Med. 11:X-232; 1992. Rickey, D. W.; Rankin, R.; Fenster, A. A velocity evaluation phantom for colour and pulsed Doppler instruments. Ultrasound Med. Biol. 18:479-494; 1992. Rickey, D. W.; Picot, P. A.; Fenster. A. A wall-less vessel phantom for Doppler ultrasound studies. Ultrasound Med. Biol. [in press]. Rindt, C. C.; Steenhoven, A. A.; Janssen, J. D.; Reneman, R. S.; Segal. A. A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation. I. Biomech. 23:461-473; 1990. Ross, R. The pathogenesis of atherosclerosis: A perspective for the 1990’s. Nature 362801-809; 1993. Tamura, T.; Cobbold, R. S. C.; Johnston, K. W. Quantitative study of steady flow using colour Doppler ultrasound. Ultrasound Med. Biol. 17:595-605; 1991. Valdes-Cruz, L.; Tamura, T.; Dalton, N.; Elias, W. Color flow Doppler shunt areas as indicators of arterial septal defect shunting: Studies in an open chest animal model and initial clinical results. Circulation 74: 1 I - 145; 1986. Zierler, R. E.; Phillips, D. J.; Beach, K. W.; Primozich, J. F.; Strandness, D. E., Jr. Noninvasive assessment of normal carotid bifurcation hemodynamics with color flow ultrasound imaging. Ultrasound Med. Biol. 13:471-476: 1987.