Volume flow measurement using doppler and grey-scale decorrelation

Ultrasound in Med. & Biol., Vol. 27, No. 1, pp. 101–109, 2001 Copyright © 2001 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/01/$–see front matter

PII: S0301-5629(00)00291-X

● Original Contribution VOLUME FLOW MEASUREMENT USING DOPPLER AND GREY-SCALE DECORRELATION JONATHAN M. RUBIN, THERESA A. TUTHILL and J. BRIAN FOWLKES Department of Radiology, University of Michigan Medical Center, Ann Arbor, MI, USA (Received 28 February 2000; in final form 6 July 2000)

Abstract—A technique for volumetric blood flow measurement was developed by combining standard Doppler measurements with grey-scale decorrelation. Steered Doppler is used to determine the in-plane velocities, which are then used to extract the out-of-plane velocities from the temporal A-line decorrelation. As a result, a three-dimensional (3-D) vector flow field can be computed over the imaging plane using a single clinical transducer without knowledge of the vessel orientation. Volume flow is computed by integrating the out-of-plane flow over the vessel cross-section. The algorithm was tested using a scattering-enhanced fluid in a 6.4-mm diameter dialysis tubing. For a wide range of transducer angles, the volume flow was accurately measured to within 28% in these preliminary tests. (E-mail: [email protected]) © 2001 World Federation for Ultrasound in Medicine & Biology. Key Words: Volumetric blood flow, Medical ultrasound, Doppler, Grey-scale decorrelation.

two coplanar beams and trigonometric relations, the derived measured velocity is angle-independent. With current linear transducers, the beam from a single transducer can be steered in multiple directions. Maniatis et al. (1994) showed that a two-beam technique provided results comparable to more complex alternatives. Our proposed algorithm for volume flow estimation incorporates the two-beam Doppler approach for determining velocities in the scan plane. One of the first techniques to quantify the magnitude of the nonaxial flow components was developed by Newhouse et al. (1987), and is based on spectral broadening of the radiofrequency (RF) signal. As scatterers cross the focused ultrasound beam, the bandwidth of the Doppler spectrum increases. By combining standard Doppler with this traverse effect from an annular array, the Doppler angle can be estimated (Lee and Chiang 1999). Time-domain alternatives for measuring flow have also been extensively examined and implemented. Kasai et al. (1985) first demonstrated that the mean flow velocity and variance could be calculated in real-time using an autocorrelator on the quadrature components. In addition, improved resolution of the axial velocities can be computed from the correlation of consecutive A-lines, which eliminates the aliasing ambiguity of Doppler (Bonnefous and Pesque 1986). Expanding to 2-D, the

INTRODUCTION The quantification of volumetric blood flow would be beneficial for a number of clinical applications, including diagnosis of heart disease, carotid stenosis, coronary arteriosclerosis and renal failure. Doppler is the current clinical standard for measuring blood flow with ultrasound (US). Fluid motion toward or away from the transducer modifies the wavelength of the insonifying pulse. Assuming the angle between the beam and the vessel orientation are known, the flow velocity is then computed from the resulting frequency shift. Current techniques for volume flow measurement require the sonographer to orient the scan plane so that the axis of the vessel of interest lies within the scan plane, and then to calculate the total flow assuming a circularly symmetrical lumen. These assumptions, which are often not true, lead to large errors, making the method very hard to apply (Gill 1985). Consequently, the search for alternative velocity and volume-flow measurement techniques has been an active area of research. The use of multiple Doppler beams to determine in-plane flow velocities has been around for many decades (Wang and Yao 1982). Using

Address correspondence to: Theresa A. Tuthill, Ph.D., University of Michigan Medical Center, Dept of Radiology, 200 Zina Pitcher Place, Ann Arbor, MI 48109-0553 USA. E-mail: [email protected] 101

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temporal correlation of patterns between sequential frames, also known as speckle tracking, has been used to determine 1-D and 2-D flow vectors (Trahey et al. 1987). With the development of volumetric US scans, the correlation search algorithm has been applied in 3-D with some success (Morsy and von Ramm 1999). Many innovative techniques have been proffered for measuring motion in directions transverse to the US beam. Anderson (1998) used a spatial weighting of the point spread function to quantify the lateral motion. In a similar study, Jensen and Munk (1998) applied a transverse spatial modulation generated by apodization of the transducer elements to quantify flow in one or two directions transverse to the axial flow. Both of these techniques only determine 2-D flow. The estimation of blood velocity using the decorrelation of echo signals has also been fairly well documented. Using the time rate-of-change of A-lines, Bamber et al. (1988) demonstrated that decorrelation could be used to image tissue motion and blood flow. More quantitatively, Li et al. (1997) showed that the decorrelation of RF signals from an intravascular transducer was linearly related to the lateral displacement. The temporal decorrelation of power Doppler signals (Adler et al. 1995) and of the integrated power Doppler (Chen et al. 1996) have also been shown to be related to flow and can be used to estimate local tissue perfusion. More recently, the detection of variations in contrast-enhanced blood flow using grey-scale decorrelation has been shown in animal studies (Rubin et al. 1999). The proposed algorithm uses both traditional Doppler signals as well as grey-scale pixel decorrelation to determine total volume flow. The blood vessel may be oriented in any arbitrary direction as long as a cross sectional slice is visible in the imaging plane. The 3-D vector flow in relation to the imaging plane is calculated and the normal component to the plane is defined. The integration over this plane results in the total volume flow. The method should be directly applicable to processing the RF signals of a series of steered firings. Theory Our algorithm for measuring volumetric flow employs two of a clinical scanner’s operating modes: Doppler and B-scan imaging. First, conventional Doppler, steered in two directions, is used to compute the 2-D velocity vectors in the imaging plane. Second, the temporal decorrelation of intensity values is computed from the A-lines. The rate of decorrelation is related to the 3-D velocity vector, and the elevational (out-of-plane) velocity extracted. A simple summation of these velocities over the cross-section of the vessel provides the total volume flow.

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ជ , is Fig. 1. The flow tube with arbitrary vector flow direction, V shown in relation to the transducer geometry where the x-y plane is the transducer’s scan plane or in-plane. The Doppler steering angles for ⫺␪ and ⫹␪ are denoted by vectors kជ 1 and kជ 2, respectively.

In-plane velocities A schematic displaying flow direction and transducer orientation is shown in Fig. 1. By steering the Doppler beam within the imaging plane in two directions, ⫾ ␪, the two corresponding “axial” velocities, V1 and V2 can be measured. The in-plane velocity components, Vx and Vy can then be computed as follows, V 1 ⫽ kជ 1 䡠 Vជ ⫽ ⫺ V x sin␪ ⫹ V y cos␪

(1)

V 2 ⫽ kជ 2 䡠 Vជ ⫽ V x sin␪ ⫹ V y cos␪

(2)

Vx ⫽

V2 ⫺ V1 2 sin␪

and V y ⫽

V1 ⫹ V2 . 2 cos␪

(3)

Note that, due to the necessary angular independence for orthogonalization, the velocity estimate errors decrease as ␪ approaches 45° (2␪ ⫽ 90°). Decorrelation The rate of speckle decorrelation in a fluid is a function of flow velocity, pulse repetition frequency (PRF) or frame rate (depending on the processing method), and the beam characteristics of the transducer. Although a more detailed statistical analysis of speckle formation is given in a previous paper (Tuthill et al. 1998), the main points and assumptions are presented here. For fully developed speckle, at least 10 scatterers must be present in the sample volume defined by the 3-D point spread function (Oosterveld et al. 1985). The spatial probability density function of ultrasonic intensity should be an exponential distribution with a constant mean-to-standard deviation (MSD) ratio of 1.0. The

Volume flow measurement ● J. M. RUBIN et al.

amount of speckle change from pulse to pulse (or frame to frame) is directly related to the second order statistics of the speckle pattern. The derivation for the speckle correlation function in the lateral dimension is outlined here, and can easily be extended to the elevational and axial dimensions. For coherently formed speckle, the intensity correlation function is directly related to the amplitude correlation function which, in turn, is proportional to the point spread function (PSF) autocorrelation. Assuming a focued transducer, the beam pattern can then be approximated by a Gaussian that has a depth-dependent width as the beam goes in and out of the focal region. Consequently, the intensity autocorrelation in the lateral direction can also be written as a Gaussian function with respect to the fluid translation between acquired frames and will have a standard deviation of ␴x(z), the depth-dependent beam correlation width. The correlation width in the focus can be calculated by the transducer’s physical properties, or the correlation width for a longer range of depths can be calibrated using a phantom containing scatterers producing fully developed speckle. The temporal normalized intensity covariance, C, for a single pixel location then has a Gaussian shape (Wear and Popp 1987),

冉

冊

⫺共V x⌬t兲 2 C共⌬t, z兲 ⬀ exp , 2 ␴ x2共 z兲

(4)

where Vx is the lateral velocity and ␴ x(z) is the depthdependent beam correlation width as determined by the transducer properties. For a firing rate of Rf, the normalized covariance from a set of pixels at a specific depth acquired from consecutive A-lines can then be curve fit to a Gaussian as a function of the firing number, n,

冉

C共n兲 ⬀ exp

冊

⫺共Dn/R f兲 2 , 2

(5)

where D, the decorrelation value in units of inverse s, is equivalent to the velocity divided by the beam correlation width for that depth. The final result is that, by Gaussian curve-fitting, the correlation function for speckle regions from a set of A-lines or from a set of B-scan frames, the average velocity for that set can be calculated. For volume flow, the decorrelation can now be extended to include all 3 dimensions. Assuming an ellipsoidal sample volume, the curve-fitted decorrelation value, D, is directly related to the velocity components, D2 ⫽

V x2 V y2 V z2 ⫹ ⫹ , B x2 B y2 B z2

(6)

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where Bi is the beam correlation width (BCW) in the ith direction. The BCWs are calibrated using a speckle phantom and are dependent on depth and the transducer’s focusing parameters, but they are measurable throughout the imaging plane. 3-D flow vector and volume flow Having determined the in-plane velocities, Vx and Vy, from the Doppler measurements (or from speckle tracking), the magnitude of the velocity component normal to the scan plane, Vz, can be computed from eqn (6). Thus, the 3-D flow vector can be determined from a single transducer operating in two different modes for three measurements (for example, two Doppler and one decorrelation). The total volume flow through a vessel can also be computed. Gauss’ theorem states that the flux or volume flow out of a closed surface equals the integral of the divergence of the vector field over the enclosed volume. Thus, the total volume flow, F, is the normal velocity component integrated over the cross-sectional area,

F⫽

冕

共Vជ 䡠 nជ 兲ds

(7)

By summing up Vz, the velocity components normal to the imaging plane over the vessel area intersected by the imaging plane, the total volume flow can be calculated. MATERIALS AND METHODS A GE Logiq 700 clinical scanner (GE Medical Systems, Milwaukee, WI) with a 7.5-MHz linear array (L739) was used with a single focus. All internal postprocessing settings, such as edge enhancement and averaging, were turned off, and the depth was set to the minimum value of 3 cm to obtain the highest allowable frame rate of 30 Hz. The output power was set at the lowest level to reduce effects from additional decorrelation due to acoustic radiation force. For B-mode, a linear grey-scale mapping was applied and the scans were decompressed using manufacturer-supplied conversion curves to obtain images with pixel values proportional to amplitude. For the Doppler acquisition, the lowest velocity (3 cm/s) and lowest wall filter settings (12 Hz) were applied. All images were digitally stored on the scanner at 8 bits and transferred to a UNIX computer. The 3 cm ⫻ 4 cm digitized images were stored as 355 ⫻ 478 pixels for a square pixel size of length 84.5 ␮m. The transducer sample volume was calibrated by collecting a series of B-mode scans with incremental spacing in each direction (lateral, elevational and axial) over a tissue-mimicking phantom (CIRS Model

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Fig. 2. The experimental set-up is comprised of a water tank with the transducer mounted above. A syringe pump injects scattering medium into the dialysis tube at constant rates.

GUFL01; Computerized Imaging Reference Systems, Norfolk, VA). The phantom is comprised of densely packed, randomly distributed scatterers to create fully developed speckle. A linear micropositioner allowed for spacings of 50 ␮m for lateral and elevation directions, and 25 ␮m for axial. For each transducer orientation, a set of 60 images was acquired, and the corresponding beam correlation width was then computed as a function of depth. For the flow tube experiments, a 6.4-mm diameter molecularporous membrane tube (Spectrum Laboratories, Laguna Hill, CA) was placed in a water bath filled with degassed water (Fig. 2). A syringe pump (Model 22, Harvard Apparatus, Holliston, MA) was used to generate flows from 12 to 20 mL/min. Care was taken not to introduce air bubbles into the tube system. The outlet of the system was kept 10 cm above the tank to maintain pressure and ensure full expansion of the membrane tubing. The fluid was comprised of 1- to 35-␮m diameter polystyrene spheres (Cat #445, Duke Scientific, Palo Alto, CA) in a 5:1 water/glycerol mixture. A concentration of approximately 105 particles/mL was used to increase the backscatter for more uniform speckle. The transducer was fixed to allow both rotation about the y-axis and x-axis independently. The transducer was rotated about the y-axis, increasing ␾ (See Fig. 1) in 30° increments for each of three different volume flows. For each volume flow setting, a cine loop of 60 grey-scale images was collected first, followed by a set of color Doppler images. Ten uncorrelated images were collected for each of the two beam steering angles (⫾ 20°) and then averaged. The stored images were postprocessed using programs written in MATLAB (Mathworks, Natwick, MA). For the speckle decorrelation, the covariance function was computed for each pixel and averaged over a 5 ⫻ 5 pixel window. The covariance function was then normalized, and only the first lag was used for the Gaussian fit to determine the decorrelation

Fig. 3. The beam correlation width (BCW) at the focus of the 7.5-MHz probe was computed for all axial-rotated angles in 15° steps. Note that the elevational (or more generally the beam width) is much larger than for the lateral direction. The theoretical line is the ellipse computed from the lateral and elevational calibration.

value. The resulting decorrelation image was thresholded to include only decorrelation values faster than the slowmotion noise level of 20 s⫺1 (thus, excluding pixels that took more than 6 frames to decorrelate completely). Using eqn (6), the out-of-plane velocity was computed and summed up over the region defined by the thresholded decorrelation image to determine the total volume flow. RESULTS For the given scanner settings with a single focus, the GE L739 transducer had BCWs of 170 ␮m, 280 ␮m and 150 ␮m for the lateral, elevational and axial directions, respectively, near the focus. Figure 3 shows the measured BCWs for 15° increments about the elevational/lateral plane and the theoretical elliptical fit using only the original Bx (lateral) and By (elevational) values. The B-scan image of the flow tube at ␾ ⫽ 60° from longitudinal is shown in Fig. 4a. An enlargement of the region around the tube is also displayed (Fig. 4b) with the corresponding decorrelation image (Fig. 4c) for a volume flow of 16 mL/min. The corresponding Doppler images are shown in Fig. 5. Both the ⫺20° steering (Fig. 5b) and the ⫹ 20° steering (Fig. 5c) Doppler images are used to form the combined total in-plane velocity magnitude image shown in Fig. 6a. Figure 6b shows the resulting 2-D flow vectors. A lateral shift of 12 pixels, possibly due to the asymmetric apertures in the steered Doppler, was necessary to coregister the Doppler images from the two different look directions.

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Fig. 4. (a) The B-scan of the 6.4-mm dialysis tube at 60° from longitudinal is shown at left. (b) This enlarged section of the B-scan shows significant speckle in the tube from the polystyrene spheres. (c) The corresponding decorrelation image of the B-scan section shown in (b) for a flow rate of 16 mL/min. Brighter pixels represent rapid decorrelation.

The thresholded decorrelation image was applied as a mask, and the normal velocities summed up in the

enclosed region to compute the total volume flow. The decorrelation mask was chosen because it will provide a

Fig. 5. (a) The color Doppler image corresponding to the configuration for Fig. 4 and with the transducer steered at ⫺20° shows that a component of the flow is toward the transducer or to the left. (b) This enlarged view of the color flow image shows that the tube is not completely filled in due to the echo overwrite priority. (c) The corresponding Doppler image with the transducer steered 20° to the right shows flow moving away from the transducer or to the right.

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Fig. 6. (a) The in-plane velocity magnitude is determined from the Doppler images for the two different steering angles (Fig. 5b and c). The corresponding 2-D flow vector image (b) shows flow to the left.

detectable image of the vessel lumen regardless of flow angle, unlike the Doppler. The computed in-plane velocity image for the 16 mL/min example (Fig. 4) is shown in Fig. 7. The theoretical cross-sectional area for a circular tube at ␾ ⫽ 60° is also displayed. The summed volume flow in the masked cross-sectional area is 15.0 mL/min. Figure 8 shows the combined Doppler image, the decorrelation image, and the resulting out-of-plane velocity image for each of the three angles for the 16 mL/min flow rate. Examination of the in-plane velocities as determined from the Doppler showed a 20% to 30% increase over the theoretical values. This is attributed to the limited dynamic range of the scanner and the contrast enhancement necessary for fully developed speckle in B-mode imaging (see Discussion section). To account for the overestimation in the Doppler measurements, a scale factor was applied based on the ratio of the peak measured Doppler value to the theoretical angle-corrected peak velocity (assuming a parabolic flow profile) for the given input volume flow. Table 1 shows the measured volume flows and percent error for three different flow velocities. The flow range was limited at the high end by the B-mode decorrelation and at the low end by the measurable Doppler shifts. These constraints are due to the scanner used and are not a fundamental limit. The calculated volume flows for angles greater than 30° from longitudinal were within 28% of the actual rate. For angles less than or equal to

Fig. 7. (a) B-scan image. (b) The calculated out-of-plane velocity. Darker coloring represents higher flow. The solid line represents the theoretical tube outline.

30°, the decorrelation estimates were saturated due to the narrower BCW in the lateral direction. Between frames, the fluid would move almost completely through the sample volume and the corresponding pixels would be completely decorrelated. When this occurs in less than one lag, the result is an under-estimation of the true decorrelation and a much lower total volume flow estimate. However, this inaccuracy caused by the low frame rate should be eliminated with A-line processing. DISCUSSION AND SUMMARY Given the limitation from available frame rates, the Doppler/decorrelation volume flow estimation provided promising results for the allowable flow range. Higher frame rates and lower wall filters for the Doppler data should contribute to a wider range of measurable velocities. It should be noted that our technique can compute volume flow values without prior knowledge of the orientation of the vessel. Only the boundaries of the vessel must be visible in a cross-sectional view to ensure a closed region. For the current algorithm, the user needs only point at an area within the vessel for the total cross-sectional area for that vessel to be determined from

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Fig. 8. The total volume flow was computed for three different rotational angles (referenced from a longitudinal view of the tube) with an input volume flow of 16.0 mL/min. (a) The combined Doppler images show decreasing velocity with angle. Note that, for the cross-sectional view, 90°, there is no measurable Doppler velocity. (b) The decorrelation images show increased velocity in the center of the tube, although at 30° there is saturation due to the narrower beam traversed by the flow. (c) The computed out-of-plane velocity images are shaded red and overlaid on the original B-scan images. The total volume flow is computed from the integration of the colorized pixels. Note that, due to the underestimated decorrelation at 30°, the volume flow is also underestimated (see Table 1). The red ellipse shows the theoretical tube intersection.

the thresholded decorrelation image. Using decorrelation thresholding with its reduced angle dependence (Rubin et al. 1999) should provide a more reliable delineation of the flow boundaries than would Doppler.

Table 1. The measured total volume flow and percent error (in parentheses) for three different flow rates and three different transducer angles Actual volume flow (mL/min)

30°

60°

90°

12 16 20

15.3 (27%) 7.3* (⫺55%) 1.8* (⫺91%)

15.1 (25%) 15.0 (⫺6%) 14.5 (⫺28%)

12.1 (1%) 14.4 (⫺9%) 15.4 (⫺23%)

* Substantial portion of decorrelation image saturated due to limited frame rate.

The over-estimated Doppler velocities in our experiments are an artefact of the increased echo enhancement due to scattering from a high concentration of strong scatterers, and our results are consistent with the 20 to 45% increase reported by Forsberg et al. (1994) when using contrast agents. With the increased Doppler signal power, higher frequency shifts are detectable, yet the lower frequencies are still eliminated by the “wallthump” filter. The result is an apparent increase in velocity over the noise threshold. This artefact can be reduced with increased dynamic range of the scanner. Ideally, a fluid is needed with a scattering strength that would produce speckle in B-mode but would not override the color write priority in Doppler. The spatial resolution for the velocity estimates computed with our technique is primarily limited by the

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Doppler signal, which has a lower resolution than the B-mode images. The decorrelation technique is computed on each pixel in the B-scan or on each point of the A-line, and so the spatial resolution is determined by the axial point spread function and the digital sampling rate. Some spatial averaging is needed, however, to compute accurate correlation curves. The temporal resolution is determined by the number of sequential A lines needed for an accurate estimate of the decorrelation and Doppler frequency shift. In most clinical scanners, approximately 10 to 15 firing lines are used to compute the Doppler output. Blood flow in humans ranges from 30 L/min in the aorta during strenuous exercise to 10 nL/min in a single capillary (velocity on the order of mm/s). Our technique does have both upper and lower limits on the range of velocities that can be measured. Low flows are difficult to differentiate from soft tissue motion due to the similarity in decorrelation rates and the Doppler “wallthump” filter which eliminates signals from the relatively slow motion. At high velocities, the decorrelation component of the analysis breaks down, and a limit in Doppler PRF can be reached. If the flow movement is more than two BCWs between firings, the signals are completely decorrelated and no velocity estimate can be made. Thus, the PRF and the BCW of the sample volume determine the upper velocity limit: maximum velocity ⬍ (PRF ⫻ 2 ⫻ BCW). For example, with a 10-kHz firing rate and a correlation width of 400 ␮m, the maximum measurable velocity would be 800 cm/s. In the RF analysis, the axial BCW is an order of magnitude smaller than either the elevational or lateral component. However, this is basically the same limitation as Doppler (i.e., the PRF must be sufficiently high to avoid aliasing and maintain phase coherence). Contrary to Doppler measurements, flow perpendicular to the beam is in the preferred direction to detect higher velocities. The proposed technique also assumes all flow is in one direction in any sampling site during data acquisition. Shear motion or turbulent flow in a pixel may cause additional decorrelation which would upwardly bias the volume flow measurement. Another drawback of the technique is that the sign of flow cannot be determined in the decorrelation measurement. Thus the direction of out-of-plane flow remains unknown. This could be a problem with arterial flow where there may be reversal of flow during a heart cycle. One possible method to determine the flow directions would be a phase quadrature analysis in the out-of-plane direction with an array that can be steered in the elevational direction (termed a 1.75D array, Wildes et al. 1997). Future studies will examine the temporal resolution of this technique and test the algorithm with pulsatile

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flow. The current limit for real-time implementation is the number of firings used in the estimation of the decorrelation and for accurate Doppler measurement. Our technique has used contrast agents to monitor speckle decorrelation (Rubin et al. 1999); however, it is expected that, with blood flow, the decorrelation values may be estimated from a parameter derived from “Bflow” (GE Medical Systems, Milwaukee, WI). Thus, with only minor alterations to current clinical scanner architecture, our algorithm could be used to compute volumetric blood flow. Acknowledgements—This work was supported by a research gift from GE Medical Corporation. The authors also thank Anne Hall for helpful discussions.

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