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A triangulation method for the quantitative measurement of arterial blood velocity magnitude and direction in humans
Ultrasoundin Med. & BioL Vol. 16, No. 5, pp. 499-509, 1990
0301-5629/90 $3.00 + .00 © 1990 Pergamon Press plc
Printed in the U.S.A.
QOriginal Contribution A TRIANGULATION MEASUREMENT MAGNITUDE
METHOD FOR THE QUANTITATIVE OF ARTERIAL BLOOD VELOCITY AND DIRECTION IN HUMANS
E. S C H R A N K , t D . J. PHILLIPS,* W . E. M O R I T Z t a n d D . E. STRANDNESS, JR.* *Department of Electrical Engineering, University of Washington, Seattle, WA 98195, U.S.A. *Department of Surgery, University of Washington, School of Medicine, Seattle, WA 98195, U.S.A. (Received 9 M a y 1989; in final f o r m 17 January 1990)
Abstract--A triangulation method has been applied to a duplex ultrasound scanner to quantify blood flow velocities in two dimensions. A position locating system (PLS) connected to the scanhead locates the sample volume (SV) in 3-D space to a precision of 1 mm. The PLS is used to obtain flow velocity data from two independent lines of sight in the human femoral artery. Data are gathered from anatomic sites of interest along one line of sight. Later the computer directs the SV to interrogate the same points in space from a second line of sight. Water tank studies using both constant velocity and pulsatile string targets were used to validate the method. Velocity magnitudes could be calculated to within 5% error for Doppler angles below 75 degrees for various string depths and speeds; the error in Doppler angle calculation was usually less than 3 degrees. Results from the superficial femoral artery show flow velocity vectors are nearly parallel to the vessel walls. Peak systolic velocity magnitudes range from 63-66 cm/s in three presumed normal individuals. Following the validation studies addressed in this paper, this triangulation approach is intended in future work to document the complex nonaxial character of blood flow that occurs normally at branch points and in regions of intraluminal disease. Key Words: Triangulation, Non-axial blood flow, Quantifying blood flow velocities, Position locating systems.
INTRODUCTION
formed by the transducer axis and flow velocity vector can only be estimated. It has been c o m m o n practice to estimate the Doppler angle between the transducer axis and the blood vessel axis from the duplex image. T h i s D o p p l e r angle m e a s u r e m e n t is frequently used in "angle correction" protocols incorporated into duplex scanners in order to report results of Doppler studies in units o f velocity (Zwiebel 1987). This does not, in general, provide a correct value for the flow velocity magnitude and can lead to serious errors. O f particular concern is the use o f such velocity estimates in serial clinical studies (Phillips et al. 1989). T h e new t w o - d i m e n s i o n a l color flow d u p l e x scanners generate flow images using only one c o m p o nent of the flow velocity vectors. Although the flow images appear to show streamlines and flow velocity direction, the observer should not be misled. There are m a n y possible flow regimes in the blood vessel that could have produced the observed color image. Only one c o m p o n e n t of the flow velocity vector at each image pixel was used to construct the image. The two-dimensional color flow images can be m o r e
Pulsed Doppler ultrasound has been used for several decades for the detection and quantification of blood flow velocities within h u m a n b l o o d vessels. Currently, all commercially available ultrasound duplex scanners acquire pulsed Doppler flow velocity data from a transducer oriented along a single line of sight. Since the detected flow velocity is the blood velocity c o m p o n e n t along the transducer axis, only one component of the three dimensional flow velocity vector is obtained. Multitransducer pulsed Doppler systems have previously been used, however, to investigate blood velocity patterns in animals (Peronneau et al. 1977). In-vitro flow model studies (Ku et al. 1985) and our knowledge o f h e m o d y n a m i c s (Caro 1978) indicate that the orientation of flow vectors in h u m a n arteries is variable and generally not axial at branch points, bifurcations, curves, and at sites o f intraluminal disease. These, in fact, are all sites of clinical interest. T h e D o p p l e r angle, defined as the angle A d d r e s s for reprints: W. E. M o r i t z , D e p a r t m e n t o f Electrical E n g i n e e r i n g , FT- 10, U n i v e r s i t y o f W a s h i n g t o n , Seattle, W A 98195. 499
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difficult to interpret since the operator must be constantly aware o f the orientation of the sound b e a m relative to the assumed direction o f flow velocity vectors within a region o f interest. It is essential to rem e m b e r that detected flow velocities are those along the sound b e a m axis and that both the orientation of the sound b e a m and the blood flow velocity vectors are changing over space and in time. Quantitation of flow velocity parameters using color flow can be misleading and is difficult at best (Daigle 1989). This paper presents a m e t h o d by which a triangulation procedure is i m p l e m e n t e d to obtain the two c o m p o n e n t s o f a blood flow velocity vector within an image plane. Referring to Fig. 1, velocity V I is obtained at the sample volume location along the line of sight L1 and velocity V2 is obtained along an independent line of sight L2. The only flow velocity vector within the image plane that produces the projections VI and V2 onto L1 and L2, respectively, is the vector V. The position locator first determines the spatial locations where flow velocities are recorded along one line of sight, and then permits data to be taken at the same points in space from a second, independent line o f sight. In this way, the magnitude and direction o f the flow velocity vector at a point in space and time can be determined in two dimensions as a function of time. This represents a significant step toward quantification o f flow velocities within blood vessels. This paper describes the position locator system, how data is acquired and processed by the triangulation procedure, m e t h o d validation studies, and preliminary two-dimensional flow velocity pro-
Fig. 1. Schematic representation of the triangulation method. Flow velocity V 1 is obtained from the sample volume location, SV, along the line of sight L1. The ultrasound scan head is then moved to obtain V2 at the same site within the artery along an independent line of sight L2. The vector V is the only vector within the image plane that could produce the flow velocity vectors V1 and V2 along L1 and L2, respectively.
Volume 16, Number 5, 1990 files from h u m a n femoral arteries. The technique described below permits a more complete assessment of the velocity o f blood flow within a region of interest than current methods. MATERIALS AND METHODS
Position locator system A position locator system (PLS) was used for acquiring the directional information necessary for the triangulation velocity studies. This locator system was developed in our laboratory (Moritz and Shreve 1976, 1977; Moritz et al. 1983; Wong 1988) and has been previously used for two- and three-dimensional imaging of the heart. The PLS uses an acoustic ranging technique for locating the position and orientation of the ultrasound scan head. Figure 2 illustrates the basic acoustic ranging principle of the PLS. Three small (0.8 m m ) spark gap electrodes (SGI, SG2, SG3 of Fig. 2) are affixed to a circular plate which is precision m o u n t e d to the ultrasound transducer. The position and orientation of the electrodes relative to the u l t r a s o n i c i m a g e is k n o w n . W h e n a s p a r k gap is "fired," a high voltage pulse is generated across the electrodes producing an electrical arc. A sound wave is generated which propagates spherically from the spark gap. T h r e e piezoelectric h e m i s p h e r i c transducers m o u n t e d on an " L " shaped arm function as point m i c r o p h o n e s to detect the generated sound wave. Each of the three spark gaps are sequentially fired and the propagation delay times for the sound waves to reach each of the microphones are measured. The delay times (along with the speed of sound in air at the current temperature) are used to find the spark gap to m i c r o p h o n e distances (Ra, Rb, and Rc o f Fig. 2). F r o m these distances the location of the spark gaps, and hence the location and orientation of the transducer and scan plane are determined. The location of the sample volume (SV) is found by measuring the SV angle and depth voltages generated by the potentiometers on the ultrasound scan head. In addition, the SV can be positioned at any location within the ultrasound image by relaying PLS generated sample volume angle and depth voltages b a c k to the u l t r a s o u n d scan head. This capability allows us to place the SV at the same point in space to gather Doppler information from a second line of sight in the triangulation experiments. The PLS is capable of directing the SV back to its original location within approximately 1 m m when the scan head is positioned to a second scanning position (Schrank 1989). The PLS is interfaced to an Advanced Technology Laboratories M a r k 600 duplex scanner with a 5
Triangulation method for the quantitative measurement of arterial blood velocity • E. SCHRANK et al.
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Fig. 2. Acoustic ranging technique used in the position location system. The three spark gap electrodes are labeled SG 1, SG2 and SG3. Each of the spark gaps is fired sequentially generating a series of spherically radiating sound waves. The sound waves are detected by three orthogonally placed microphone point receivers Ma, Mb and Mc. The spark gap to microphone distances Ra, Rb and Rc are determined by measuring the time required for the sound wave to reach each of the microphones.
M H z short focus scan head (Advanced Technology Laboratories, ATL, Bothell, WA). An I B M - A T personal c o m p u t e r serves as the system controller unit and the PLS is under the control of software running on the AT. System programs were written in the C p r o g r a m m i n g language. A PLS adapter card containing customized circuitry for controlling operation of the PLS resides in one of the backplane I/O slots of the I B M - A T computer.
Triangulation methods Triangulation experiments were performed on string p h a n t o m velocity reference targets a n d on h u m a n subjects. The general experimental protocol used by both the string p h a n t o m and in-vivo studies is described in the following section. Experimental procedures specific to the string p h a n t o m or in-vivo experiments are given in the sections following the general procedures section.
General procedures The triangulation experiments were initiated by p o s i t i o n i n g the ultrasoiJnd scan head to the first scanning position and imaging the target area (Fig. 3a). The scan head position was held fixed and the Doppler SV was placed by the operator at one or m o r e positions where velocity information was to be gathered. At each o f these locations the 3-D position coordinates of the SV were recorded with the PLS so
that the SV could later be directed back to the same points. The direction of the Doppler b e a m and the orientation of the ultrasound scan plane relative to a fixed reference coordinate system were also determined using the PLS. Forward and reverse Doppler channels were recorded onto the two audio channels of a tape recorder (Sony m o d e l VO-2600) after switching the ultrasound scanning system into D o p p l e r m o d e . Once data collection from the first scanning position was completed the scan head was repositioned to the second scanning position in the scan plane (Fig. 3b). During repositioning, the spark gaps were fired continuously, and operator repositioning guidance directions were displayed on the I B M - A T monitor. These c o m m a n d s directed the operator to correctly position the scan head so that the scan plane was maintained. U p o n repositioning the scan head position was held fixed while the sample volume was directed successively to each of the previously selected sample volu m e locations by the PLS. At each SV location the D o p p l e r signals were recorded and the ultrasound b e a m direction vectors measured. Data analysis was performed off-line after c o m pletion of the data collection process. Analysis was performed using a set of programs to digitize, analyze, and display the triangulation data. Each triangulation velocity vector was calculated by first determining the projection velocity vectors corresponding
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Fig. 3. Femoral artery study. Doppler recordings made from the same region of space from two independent lines of sight. (a) and (b) illustrate the typical procedures used in the in-vivo experiments. The femoral artery was imaged and the scan head was positioned to the first scanning position (a). The sample volume was placed at four different locations within the arterial lumen (indicated by circles). After recording from these areas the scan head was repositioned to the second scanning position (b). The sample volume was directed back to each of the original locations by the position locator system and the second set of Doppler recordings were taken. L 1 and L2 indmate the direction of the Doppler ultrasound beam at the two scanning locations. Using this method, Doppler data were acquired from points in space from two independent lines of observation.
to V1 and V2 o f Fig. 1, and then solving a set of equations to quantify the triangulation velocity vector, V. The projection velocity vectors V1 and V2 were found by performing a spectral analysis on the r e c o r d e d D o p p l e r signals a n d using the D o p p l e r b e a m direction information obtained from the PLS. During the data analysis process, D o p p l e r recordings m a d e from each of the two scanning positions were replayed and digitized. Forward and reverse Doppler channels were each digitized at a sampling rate of approximately 30 k H z with an Analog Devices AD7824 A / D converter. Resolution o f the digitized data was 8 bits. A 512 point F F T was performed on the digitized data to decompose the signals into their discrete frequency components. A m e a n velocity estimator algorithm was used to evaluate the magnitudes o f the velocity projection vectors V1 and V2 (eqn 1). Equation (1) computes the average particle velocity within the region of the SV by c o m p u t i n g the m e a n of the c o m b i n e d forward and reverse power spectra: IV,,=l = c { 2 [ ~
• P(~i)]-
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powers o f the ith frequency c o m p o n e n t of the forward and reverse Doppler spectra, respectively. Particles within the SV are likely to travel at different velocities; an estimate o f the m e a n particle velocity within the SV was obtained using eqn (1) which simply calculates the m e a n particle velocity within the SV using a frequency analysis o f the pulsed Doppler signal. Equation ( 1) was derived by assuming that the power P ( f ) backscattered between the frequency f a n d f + d f i s proportional to the n u m b e r of particles moving within a velocity range vi and vi + dr, where frequency and velocity are related by the Doppler equation constant, (2fo)/c (see, Atkinson and Woodcock 1982, for derivation). To reduce biasing of the m e a n velocity estimate caused by noise in the spectra, frequency c o m p o n e n t s of the Doppler power spectra below 150 Hz and less than 10% of the m a x i m u m spectrum power were set equal to zero prior to evaluating eqn ( 1). The projection velocity vectors V 1, and V2 were d e t e r m i n e d by using d i r e c t i o n a l i n f o r m a t i o n obtained from the PLS and the c o m p u t e d velocity magnitudes: V1 = IV1 ]UI
where IVI,21 is the magnitude of V1 or V2, c is the speed o f sound in tissue or water, fo is the transducer transmission frequency, ffi and J~i are the ith discrete frequency c o m p o n e n t s o f the forward and reverse D o p p l e r spectra, while P ( f f / ) a n d P(fri) are the
V2 = I V 2 l U 2 where IV 1 I and ]V2 ] were evaluated from eqn (1), and U 1 and U2 were the unit direction vectors indi-
Triangulation method for the quantitative measurement of arterial blood velocity• E. SCHRANKet al. cating the D o p p l e r b e a m direction from the two scanning positions. The triangulation velocity vector, V, was evaluated from V1 and V2 by simultaneously solving the following set of linear equations: V I . ( V 1 - V) = 0 V 2 . ( V 2 - V) = 0 V - ( V l x V2) -- 0 where V 1 • V2 and V1 X V2 denotes the dot product and cross product, respectively, o f the vectors V1 and V2.
String phantom experiments Two different string phantoms served as velocity reference targets for the triangulation studies. The first o f these p h a n t o m s provided a u n i f o r m speed string target. A loop of fine surgical thread (Ethicon, 4.0 surgical silk) was immersed in a water tank and driven by a small precision m o t o r (Micro Mo H E series m i n i a t u r e motor). An electronic calibrated output signal, generated by the motor, was used to measure string speed. The velocity of the uniform speed string p h a n t o m could be varied between approximately 10-60 cm/s by controlling the voltage supplying the precision motor. T h e string speed and direction were used to compute a reference velocity vector, Vr, to which the triangulation velocity measurements could be compared. The direction o f the string was measured by placing the sample volume at 10 different locations on the string target and determining the position of the points using the position locator system. A least squares best fit line was calculated through the 10 points to give the string unit direction. The string reference velocity vector, Vr, was found by multiplying the string speed by the string unit directional vector. A second study utilized a pulsatile string. A linear piecewise approximation to a c o m m o n carotid flow velocity waveform was digitized and used to drive a stepping motor. The velocity direction was determined as above while an independent measure of string displacement as a function of time was provided by an optical encoder (see Fig. 8). The velocity waveform voltage from the pulsatile string phantom was relayed to the ECG trigger circuitry used in the in-vivo experiments to provide a trigger pulse signal indicating the onset of the velocity waveform. Approximately 0.8 s blocks o f Doppler data were digitized and the triangulation velocity vectors were calculated at 20-ms intervals.
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In-vivo experiments D u r i n g the h u m a n in-vivo triangulation experiments, the subjects reclined comfortably on a hospital bed while Doppler recordings were taken from the femoral artery of the upper thigh region on three different subjects. Since b l o o d velocities changed throughout the cardiac cycle, ECG activity was used as a timing reference to examine the Doppler signals at specific times during the cardiac cycle. Referencing the Doppler signals to the cardiac cycle was essential since velocity information from the same interrogation site had to be acquired over different heart cycles when the scan head was placed at the first and second scanning positions. Prior to the triangulation measurements, electrodes were placed on the fight arm and right leg of the subjects studied. The amplified ECG signal was relayed to an ECG trigger circuit which produced a brief trigger pulse at the onset of the QRS wave. The ECG signal was encoded and recorded on the video channel of the tape recorder simultaneously with the forward and reverse Doppler signals on the audio tracks. During the off-line analysis both the forward and reverse Doppler channels were digitized in 25 Kbyte blocks, corresponding to approximately 0.8 s of digitized data. Within the 0.8 s time period, triangulation velocity vectors were evaluated at 20-ms time intervals. An ECG averaging feature was incorporated into the in-vivo analysis software, and was used to compensate for variability in blood flow patterns over different ECG cycles. To implement ECG averaging, the pulsed Doppler signal was recorded over several ECG cycles and the Doppler spectra were evaluated at 20-ms time intervals for each o f the ECG cycles. At each evaluated 20°ms time interval the Doppler spectra from the selected ECG cycles were s u m m e d and the resulting forward and reverse Doppler spectra were evaluated using eqn (1). Averaging over two ECG cycles appeared sufficient, and was used for the in-vivo data analysis. No significant changes in the triangulation velocities occurred with additional averaging.
RESULTS
String phantom experiments The magnitude and direction of the triangulation velocities for the uniform string phantom experiments were measured while systematically varying: (a) string speed, (b) sample volume depth, and (c) Doppler angle (Fig. 4). During the string phantom experiments an effort was made to keep the two lines o f sight, L1 and L2, essentially symmetrical to the
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mental trials. The upper and lower error bars indicate the m a x i m u m and m i n i m u m values, respectively, for the five experimental trials. Figure 5 graphs the percent magnitude error and directional error of the triangulation velocity vectors vs. string velocities. The Doppler angle and sample volume depths were maintained between 49-51 degrees and 2.1-2.6 cm, respectively. Over the range of string speeds tested (15-52 cm/s) the m e a n percent magnitude error did not exceed 5% (indicated by the pair of dashed lines). The m e a n of the angle between the reference velocity vector and the triangulated ve-
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experimental trials, and the upper and lower error bars represent the m a x i m u m and m i n i m u m values from the five trials. The triangulation velocity magnitudes were calculated at 20-ms intervals. The data o f Fig. 8 show that the triangulation velocity magnitudes effectively track the string speed throughout the pulsatile cycle of the string.
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locity vector (directional error) was less than 3 degrees (shown by the dashed line). Larger velocities could not be tested due to speed limitations o f the string phantom motor. Figure 6 is a plot o f percent magnitude error and directional error vs. sample volume depth. During this experiment the Doppler angle was kept between 49-51 degrees, and the string speed was maintained at 44 cm/s. The effect o f Doppler angle on the percent magnitude error and directional error of the triangulation velocities is shown in Fig. 7. String speed was maintained at 44 cm/s and sample volume depth was kept between 1.9-2.7 cm while the angle between the string and Doppler ultrasound beam was varied between 40 and 80 degrees. Within the Doppler angle range o f 40-70 degrees the percent magnitude error and directional error remained relatively small; the mean of the magnitude error did not exceed 5% and the mean directional error was less than 3 degrees. For larger Doppler angles o f 75 and 80 degrees however, the mean magnitude error increased (17% and 9%, respectively) and there was a much wider spread o f the magnitude error values for each o f the five experimental trials. T h e results o f the t r i a n g u l a t i o n e x p e r i m e n t s using the pulsatile string p h a n t o m are shown in Fig. 8. The solid line in the figure indicates the magnitude o f the string velocity measured using an output voltage generated by a calibration encoder wheel attached to the phantom. String velocity magnitude measured using the triangulation m e t h o d is indicated by the filled circles. The circles represent the mean o f five
In-vivo e x p e r i m e n t s Data from the i n - v i v o studies were analyzed from five experimental trials using three different subjects (subjects A, B and C). These subjects had no known circulatory or cardiovascular problems. The velocity measurements were taken from the superficial femoral artery of the upper thigh region. This region of the femoral artery was chosen because of the ease of access. Blood flow in this area was expected to be undisturbed, laminar and relatively parallel to the vessel axis. The large size of the artery also simplified the data acquisition. Velocity i n f o r m a t i o n was averaged over two nonsuccessive ECG cycles. T h e n u m b e r o f heart cycles recorded for e a c h sample v o l u m e location ranged from approximately 10-40 cycles for the different subjects. The time to collect data for a single experimental trial ranged from about 3-7 minutes. The data acquisition time did not appear to affect the computed triangulation velocities. The experimental results from each of the three subjects is depicted graphically in Figs. 9, 10 and 11. Each of the figures consists of eight drawings labeled a-h. Each of these drawings represents both a two-dimensional view o f the interrogated region of the femoral artery as it would appear in a 2-D scan, and the triangulation velocity vectors measured at specific times within the E C G cycle. T h e circles in each drawing represent the sites within the femoral artery at which the vessel was interrogated, and the lines emanating from the circles represent the respective triangulation velocity vectors. The length of the velocity vectors is, o f course, proportional to the velocity magnitudes, and the direction of the vectors indicates the direction of velocity within the scan plane. The broad curved lines appearing above and below each set of velocity vectors represents the boundary of the arterial wall. The numbers appearing below each set o f vectors is the time after the onset of the ECG QRS wave at which the measurements were taken. The upper and lower scale bars appearing in the lower left hand corner o f Figs. 9-11 indicate the scale for distance and velocity magnitude, respectively. The eight time periods of the ECG cycle which are displayed in the figures were selected to show the triphasic character of blood flow in the femoral ar-
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tery. The waveform consisted of (a) forward systolic flow followed by (b) reverse flow and (c) subsequent forward flow component. The velocity vectors were calculated at 20-ms intervals. Flow velocity vectors calculated at times intermediate to those shown displayed the same parallel flow pattern with a gradual transition o f the blood flow velocities throughout the three phases of flow within the femoral artery. The three major phases of blood flow can be clearly seen for each of the subjects in Figs. 9, 10 and 11. The large systolic forward flow c o m p o n e n t (Figs. 9(b), 10(b) and 1 l(b)) was followed by a reverse flow c o m p o n e n t (Figs. 9(d)(e)(f), 10(d)(e) and 1 l(d)(e)(f)) and subsequently followed by a smaller forward flow c o m p o n e n t (Figs. 9(g)(h), 10(f)(g)(h), 1 l(g)(h)). DISCUSSION All commercially available ultrasound duplex scanners c u r r e n t l y e m p l o y pulsed D o p p l e r techniques to obtain flow velocity data along a single line of observation. This means that only one c o m p o n e n t of a three dimensional blood flow velocity vector that changes with time is detected. Current attempts toward quantifying the Doppler signals include angle correction wherein a Doppler angle must be assumed in order to report results in units of velocity (cm/s). In all cases, only one c o m p o n e n t of the blood flow velocity vector is detected and the Doppler angle must be estimated by some method. One of three assumptions regarding the direction of the blood flow vector is usually made: (a) the blood flow vector is coaxial to the ultrasound beam, in which case the Doppler angle is zero degrees; (b) the blood flow vector is parallel to the blood vessel axis, with the Doppler angle estimated from the intersection of the vessel axis with the ultrasound beam; or (c) using the new duplex color flow scanners, the display of color shades provides the impression o f flow streamlines which might be taken to be parallel to the directions of the flow vectors. Our knowledge about the complex flow patterns at normal bifurcations due to changes in vascular geometry (Ku et ai. 1985) and the fact that intraluminal disease is an encroachment of the normal flow lumen, indicate that the directions of the flow velocity vectors in these regions are not known with any degree of certainty. Errors of 10-30 degrees in the Doppler angle can result in large errors of reported velocities (Phillips et al. 1989). The ability to appreciate and define the direction of the flow velocity vector in two dimensions within the plane o f the ultrasound image is a significant c o n t r i b u t i o n to the understanding o f h u m a n blood flow. A triangulation method for quantifying the twodimensional character of flow velocity vectors de-
Volume16, Number 5, 1990 tected by diagnostic ultrasound has been developed. While the ultimate goal is to define the flow velocity vector in three dimensions, the technical and practical problems to be solved suggest that this problem is best addressed in a stepwise fashion. Thus, the results reported here represent the component velocities in a plane. The PLS has evolved to the point where blood flow velocities can be documented in two dimensions at selected anatomic sites. The superficial femoral artery was chosen for the initial h u m a n studies because of the well-behaved flow patterns known to exist and the ease of positioning the duplex scanhead to acquire two independent lines of sight required by the triangulation procedure. The spark gap platform mounted to the ultrasound scan head does not interfere with operator ability to perform a clinical study. The array of point microphone receivers is positioned above the patient and the lack of intervening reflectors assures an accurate position measurement. Careful engineering analysis demonstrates the ability of the PLS to specify a point in three dimensions to an accuracy of 1 mm. This paper has reported the ability to specify the magnitude of a flow vector to within 5% and the direction of the vector to within 3 degrees within the plane of the ultrasound image for a moving string target. Referring to Fig. 7, the magnitude error estimate for the flow velocity vector increased markedly for Doppler angles above 70 degrees. The reasons for this include a decreased velocity resolution in the frequency analysis algorithm because of the unfavorable Doppler angle, and the increased susceptibility to errors from geometrical considerations (i.e., referring to Fig. 1, the magnitude of the triangulation vector, V, will change markedly for small changes in either of the two measured vectors V1 or V2). While the limitation of Doppler angle may present problems in repositioning of the scan head in some anatomical sites, we did not find this to be a problem in the in-vivo experiments, although some attention to scan head positioning was required to avoid recording at excessively large Doppler angles. The flow velocity vectors in Figs. 10-11 are remarkably parallel during most of the cardiac cycle. It should be kept in mind that the "line segments" represent flow velocities and not particle paths. Crossings of the flow velocity vectors do not indicate the mixing of fluid elements. Deviation of the vectors from the axial direction could be due to: local secondary blood flow patterns caused by changes in vascular geometry, radial components associated with compliant vessels and the pulsatile character of flow, unfavorable Doppler angles during the transitions between forward and reverse flow, and/or the possibility
Triangulation method for the quantitative measurement of arterial blood velocity • E. SCHRANK el aL
that hemodynamic events were not the same for all of the cardiac cycles used in the triangulation measurements. Considering these aspects it is remarkable that the flow velocity vectors are as uniform as shown. The triangulation measurements made using the pulsatile string phantom (Fig. 8) demonstrated a relatively high degree of accuracy over most of the pulsatile waveform. However, during the initial acceleration phase of the waveform of Fig. 8 the errors in the triangulation measurements were considerably more pronounced than at the later portions of the waveform. This is a result of the finite length of time the Doppler signal must be analyzed to compute the Doppler spectra. For example, in this study the period over which the Doppler signal was analyzed to compute a Doppler spectrum was approximately 17 ms. If the target velocity (and hence Doppler frequency) changes significantly within the 17-ms period corresponding errors will occur in the frequency estimation values and hence the triangulation velocity vectors. Decreasing the period over which the Doppler signal is analyzed is not necessarily a solution since this would, in turn, result in a decrease in frequency resolution in the Doppler spectra. Overall, however, the general form of the pulsatile waveform of Fig. 8 is quite well represented by the triangulation velocity values. Several limitations of the triangulation method using the PLS result from the nonsimultaneous nature of the data collection. For example, although not shown in the figures, the triangulated flow velocity vectors became markedly distorted in late diastole. This situation is believed to be artifact caused by beat to beat variations of the cardiac cycle leading to significant errors in the triangulation method during this time of the cardiac cycle, since data had to be acquired over different ECG cycles for the two lines of sight, L1 and L2. Other problems which can arise include sample volume repositioning errors due to limitations of the PLS, and patient movement or mechanical distortion of the vessel during scan head repositioning. Vessels exhibiting complex flow patterns due to branch points or stenosis, and vessels which are relatively small in size, will naturally present a greater challenge to the triangulation method than the site of the femoral artery chosen in this study. Errors in measured triangulation velocity vectors resulting from SV repositioning errors will be more pronounced in regions of blood flow where there are large changes in blood velocity vectors over a small region of space, than in regions where the velocity vector field remains relatively uniform. The approximately 1 mm 3 dimension of the sample volume itself also becomes a limiting factor in smaller vessels, and
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in regions where velocity vectors vary significantly within a small region. Studies examining the performance of the triangulation method using the PLS in these more challenging and clinically relevant anatomical sites have yet to be performed. The goal of the current study was to evaluate the basic triangulation technique as a means to study blood velocity vectors in humans. A method of documenting the nonaxial character of blood flow at clinical sites of interest is not yet available. Further quantification and understanding of blood flow character in states of health and disease require a more complete description of the flow velocity vectors. The technique described here offers the opportunity to provide a clearer picture of the nature of blood flow. We have demonstrated the ability to determine the magnitude and direction of moving targets accurately using a duplex scanner and transducer locating system. While much more work remains to be done, a new tool for use in the study of blood flow has been developed. Acknowledgement--This work was supported by Grant HL-20898 from The National Institutes of Health and the Graduate School Research Fund of the University of Washington.
REFERENCES Atkinson, J.; Woodcock, J. P. Doppler ultrasound and its use in clinical measurement. New York: Academic Press; 1982. Caro, C. G.; Pedley, T. J.; Schroter, R. C.; Seed, W. A. The mechanics of the circulation. New York: Oxford University Press; 1978. Daigle, R. E. Quantitative aspects of color flow imaging. In: Manda, N. C., ed. Textbook of color Doppler echocardiography. Philadelphia: Lea and Febiger; 1989. Ku, D. N., et al. Hemodynamics of the normal carotid bifurcation: in vitro and in vivo studies. Ultrasound Med. Biol. 11:13-26; 1985. Moritz, W. E.; Shreve, P. L. A microprocessor based spatial locating system for use with diagnostic ultrasound. Proc. IEEE 64:966-974; 1976. Moritz, W. E.; Shreve, P. L. A system for locating points, lines and planes in space. IEEE Trans. Instrum. Meas. 26:5-10; 1977. Moritz, W. E.; Pearlman, A. S.; McCabe, D. H.; Medema, D. K.; Ainsworth, M. E.; Boles, M. S. An ultrasonic technique for imaging the ventricle in three dimensions and calculating its volume. IEEE Trans. Biomed. Eng. BME-30:482-492; 1983. Peronneau, P.; Sandman, W.; Xhaard, M. Blood flow patterns in large arteries. In: White, D. N.; Brown, R. E., ed., Ultrasound in Medicine. New York: Plenum Press; 1977:1193-1208. Phillips, D. J.; Beach, K. W.; Primozich, J.; Strandness, D. E. Should results of ultrasound studies be reported in units of frequency or velocity? Ultrasound Med. Biol. 15:205-212; 1989. Schrank, E. E. Triangulation method for the quantitative measurement of arterial blood velocity magnitude and direction in humans. Master's thesis, University of Washington, Seattle, Washington; 1989. Wong, S. Y. IBM PC/AT based diagnostic ultrasound imaging system. Master's thesis, University of Washington, Seattle, Washington; 1988. Zwiebel, W. J. Spectrum analysis in carotid sonography. Ultrasound Med. Biol. 13:625-636; 1987.
0301-5629/90 $3.00 + .00 © 1990 Pergamon Press plc
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QOriginal Contribution A TRIANGULATION MEASUREMENT MAGNITUDE
METHOD FOR THE QUANTITATIVE OF ARTERIAL BLOOD VELOCITY AND DIRECTION IN HUMANS
E. S C H R A N K , t D . J. PHILLIPS,* W . E. M O R I T Z t a n d D . E. STRANDNESS, JR.* *Department of Electrical Engineering, University of Washington, Seattle, WA 98195, U.S.A. *Department of Surgery, University of Washington, School of Medicine, Seattle, WA 98195, U.S.A. (Received 9 M a y 1989; in final f o r m 17 January 1990)
Abstract--A triangulation method has been applied to a duplex ultrasound scanner to quantify blood flow velocities in two dimensions. A position locating system (PLS) connected to the scanhead locates the sample volume (SV) in 3-D space to a precision of 1 mm. The PLS is used to obtain flow velocity data from two independent lines of sight in the human femoral artery. Data are gathered from anatomic sites of interest along one line of sight. Later the computer directs the SV to interrogate the same points in space from a second line of sight. Water tank studies using both constant velocity and pulsatile string targets were used to validate the method. Velocity magnitudes could be calculated to within 5% error for Doppler angles below 75 degrees for various string depths and speeds; the error in Doppler angle calculation was usually less than 3 degrees. Results from the superficial femoral artery show flow velocity vectors are nearly parallel to the vessel walls. Peak systolic velocity magnitudes range from 63-66 cm/s in three presumed normal individuals. Following the validation studies addressed in this paper, this triangulation approach is intended in future work to document the complex nonaxial character of blood flow that occurs normally at branch points and in regions of intraluminal disease. Key Words: Triangulation, Non-axial blood flow, Quantifying blood flow velocities, Position locating systems.
INTRODUCTION
formed by the transducer axis and flow velocity vector can only be estimated. It has been c o m m o n practice to estimate the Doppler angle between the transducer axis and the blood vessel axis from the duplex image. T h i s D o p p l e r angle m e a s u r e m e n t is frequently used in "angle correction" protocols incorporated into duplex scanners in order to report results of Doppler studies in units o f velocity (Zwiebel 1987). This does not, in general, provide a correct value for the flow velocity magnitude and can lead to serious errors. O f particular concern is the use o f such velocity estimates in serial clinical studies (Phillips et al. 1989). T h e new t w o - d i m e n s i o n a l color flow d u p l e x scanners generate flow images using only one c o m p o nent of the flow velocity vectors. Although the flow images appear to show streamlines and flow velocity direction, the observer should not be misled. There are m a n y possible flow regimes in the blood vessel that could have produced the observed color image. Only one c o m p o n e n t of the flow velocity vector at each image pixel was used to construct the image. The two-dimensional color flow images can be m o r e
Pulsed Doppler ultrasound has been used for several decades for the detection and quantification of blood flow velocities within h u m a n b l o o d vessels. Currently, all commercially available ultrasound duplex scanners acquire pulsed Doppler flow velocity data from a transducer oriented along a single line of sight. Since the detected flow velocity is the blood velocity c o m p o n e n t along the transducer axis, only one component of the three dimensional flow velocity vector is obtained. Multitransducer pulsed Doppler systems have previously been used, however, to investigate blood velocity patterns in animals (Peronneau et al. 1977). In-vitro flow model studies (Ku et al. 1985) and our knowledge o f h e m o d y n a m i c s (Caro 1978) indicate that the orientation of flow vectors in h u m a n arteries is variable and generally not axial at branch points, bifurcations, curves, and at sites o f intraluminal disease. These, in fact, are all sites of clinical interest. T h e D o p p l e r angle, defined as the angle A d d r e s s for reprints: W. E. M o r i t z , D e p a r t m e n t o f Electrical E n g i n e e r i n g , FT- 10, U n i v e r s i t y o f W a s h i n g t o n , Seattle, W A 98195. 499
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difficult to interpret since the operator must be constantly aware o f the orientation of the sound b e a m relative to the assumed direction o f flow velocity vectors within a region o f interest. It is essential to rem e m b e r that detected flow velocities are those along the sound b e a m axis and that both the orientation of the sound b e a m and the blood flow velocity vectors are changing over space and in time. Quantitation of flow velocity parameters using color flow can be misleading and is difficult at best (Daigle 1989). This paper presents a m e t h o d by which a triangulation procedure is i m p l e m e n t e d to obtain the two c o m p o n e n t s o f a blood flow velocity vector within an image plane. Referring to Fig. 1, velocity V I is obtained at the sample volume location along the line of sight L1 and velocity V2 is obtained along an independent line of sight L2. The only flow velocity vector within the image plane that produces the projections VI and V2 onto L1 and L2, respectively, is the vector V. The position locator first determines the spatial locations where flow velocities are recorded along one line of sight, and then permits data to be taken at the same points in space from a second, independent line o f sight. In this way, the magnitude and direction o f the flow velocity vector at a point in space and time can be determined in two dimensions as a function of time. This represents a significant step toward quantification o f flow velocities within blood vessels. This paper describes the position locator system, how data is acquired and processed by the triangulation procedure, m e t h o d validation studies, and preliminary two-dimensional flow velocity pro-
Fig. 1. Schematic representation of the triangulation method. Flow velocity V 1 is obtained from the sample volume location, SV, along the line of sight L1. The ultrasound scan head is then moved to obtain V2 at the same site within the artery along an independent line of sight L2. The vector V is the only vector within the image plane that could produce the flow velocity vectors V1 and V2 along L1 and L2, respectively.
Volume 16, Number 5, 1990 files from h u m a n femoral arteries. The technique described below permits a more complete assessment of the velocity o f blood flow within a region of interest than current methods. MATERIALS AND METHODS
Position locator system A position locator system (PLS) was used for acquiring the directional information necessary for the triangulation velocity studies. This locator system was developed in our laboratory (Moritz and Shreve 1976, 1977; Moritz et al. 1983; Wong 1988) and has been previously used for two- and three-dimensional imaging of the heart. The PLS uses an acoustic ranging technique for locating the position and orientation of the ultrasound scan head. Figure 2 illustrates the basic acoustic ranging principle of the PLS. Three small (0.8 m m ) spark gap electrodes (SGI, SG2, SG3 of Fig. 2) are affixed to a circular plate which is precision m o u n t e d to the ultrasound transducer. The position and orientation of the electrodes relative to the u l t r a s o n i c i m a g e is k n o w n . W h e n a s p a r k gap is "fired," a high voltage pulse is generated across the electrodes producing an electrical arc. A sound wave is generated which propagates spherically from the spark gap. T h r e e piezoelectric h e m i s p h e r i c transducers m o u n t e d on an " L " shaped arm function as point m i c r o p h o n e s to detect the generated sound wave. Each of the three spark gaps are sequentially fired and the propagation delay times for the sound waves to reach each of the microphones are measured. The delay times (along with the speed of sound in air at the current temperature) are used to find the spark gap to m i c r o p h o n e distances (Ra, Rb, and Rc o f Fig. 2). F r o m these distances the location of the spark gaps, and hence the location and orientation of the transducer and scan plane are determined. The location of the sample volume (SV) is found by measuring the SV angle and depth voltages generated by the potentiometers on the ultrasound scan head. In addition, the SV can be positioned at any location within the ultrasound image by relaying PLS generated sample volume angle and depth voltages b a c k to the u l t r a s o u n d scan head. This capability allows us to place the SV at the same point in space to gather Doppler information from a second line of sight in the triangulation experiments. The PLS is capable of directing the SV back to its original location within approximately 1 m m when the scan head is positioned to a second scanning position (Schrank 1989). The PLS is interfaced to an Advanced Technology Laboratories M a r k 600 duplex scanner with a 5
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Fig. 2. Acoustic ranging technique used in the position location system. The three spark gap electrodes are labeled SG 1, SG2 and SG3. Each of the spark gaps is fired sequentially generating a series of spherically radiating sound waves. The sound waves are detected by three orthogonally placed microphone point receivers Ma, Mb and Mc. The spark gap to microphone distances Ra, Rb and Rc are determined by measuring the time required for the sound wave to reach each of the microphones.
M H z short focus scan head (Advanced Technology Laboratories, ATL, Bothell, WA). An I B M - A T personal c o m p u t e r serves as the system controller unit and the PLS is under the control of software running on the AT. System programs were written in the C p r o g r a m m i n g language. A PLS adapter card containing customized circuitry for controlling operation of the PLS resides in one of the backplane I/O slots of the I B M - A T computer.
Triangulation methods Triangulation experiments were performed on string p h a n t o m velocity reference targets a n d on h u m a n subjects. The general experimental protocol used by both the string p h a n t o m and in-vivo studies is described in the following section. Experimental procedures specific to the string p h a n t o m or in-vivo experiments are given in the sections following the general procedures section.
General procedures The triangulation experiments were initiated by p o s i t i o n i n g the ultrasoiJnd scan head to the first scanning position and imaging the target area (Fig. 3a). The scan head position was held fixed and the Doppler SV was placed by the operator at one or m o r e positions where velocity information was to be gathered. At each o f these locations the 3-D position coordinates of the SV were recorded with the PLS so
that the SV could later be directed back to the same points. The direction of the Doppler b e a m and the orientation of the ultrasound scan plane relative to a fixed reference coordinate system were also determined using the PLS. Forward and reverse Doppler channels were recorded onto the two audio channels of a tape recorder (Sony m o d e l VO-2600) after switching the ultrasound scanning system into D o p p l e r m o d e . Once data collection from the first scanning position was completed the scan head was repositioned to the second scanning position in the scan plane (Fig. 3b). During repositioning, the spark gaps were fired continuously, and operator repositioning guidance directions were displayed on the I B M - A T monitor. These c o m m a n d s directed the operator to correctly position the scan head so that the scan plane was maintained. U p o n repositioning the scan head position was held fixed while the sample volume was directed successively to each of the previously selected sample volu m e locations by the PLS. At each SV location the D o p p l e r signals were recorded and the ultrasound b e a m direction vectors measured. Data analysis was performed off-line after c o m pletion of the data collection process. Analysis was performed using a set of programs to digitize, analyze, and display the triangulation data. Each triangulation velocity vector was calculated by first determining the projection velocity vectors corresponding
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Fig. 3. Femoral artery study. Doppler recordings made from the same region of space from two independent lines of sight. (a) and (b) illustrate the typical procedures used in the in-vivo experiments. The femoral artery was imaged and the scan head was positioned to the first scanning position (a). The sample volume was placed at four different locations within the arterial lumen (indicated by circles). After recording from these areas the scan head was repositioned to the second scanning position (b). The sample volume was directed back to each of the original locations by the position locator system and the second set of Doppler recordings were taken. L 1 and L2 indmate the direction of the Doppler ultrasound beam at the two scanning locations. Using this method, Doppler data were acquired from points in space from two independent lines of observation.
to V1 and V2 o f Fig. 1, and then solving a set of equations to quantify the triangulation velocity vector, V. The projection velocity vectors V1 and V2 were found by performing a spectral analysis on the r e c o r d e d D o p p l e r signals a n d using the D o p p l e r b e a m direction information obtained from the PLS. During the data analysis process, D o p p l e r recordings m a d e from each of the two scanning positions were replayed and digitized. Forward and reverse Doppler channels were each digitized at a sampling rate of approximately 30 k H z with an Analog Devices AD7824 A / D converter. Resolution o f the digitized data was 8 bits. A 512 point F F T was performed on the digitized data to decompose the signals into their discrete frequency components. A m e a n velocity estimator algorithm was used to evaluate the magnitudes o f the velocity projection vectors V1 and V2 (eqn 1). Equation (1) computes the average particle velocity within the region of the SV by c o m p u t i n g the m e a n of the c o m b i n e d forward and reverse power spectra: IV,,=l = c { 2 [ ~
• P(~i)]-
2fo [ 2 P ( f f i )
2[J)', • P(fr,)]} (1) + 2P(Jk~)]
powers o f the ith frequency c o m p o n e n t of the forward and reverse Doppler spectra, respectively. Particles within the SV are likely to travel at different velocities; an estimate o f the m e a n particle velocity within the SV was obtained using eqn (1) which simply calculates the m e a n particle velocity within the SV using a frequency analysis o f the pulsed Doppler signal. Equation ( 1) was derived by assuming that the power P ( f ) backscattered between the frequency f a n d f + d f i s proportional to the n u m b e r of particles moving within a velocity range vi and vi + dr, where frequency and velocity are related by the Doppler equation constant, (2fo)/c (see, Atkinson and Woodcock 1982, for derivation). To reduce biasing of the m e a n velocity estimate caused by noise in the spectra, frequency c o m p o n e n t s of the Doppler power spectra below 150 Hz and less than 10% of the m a x i m u m spectrum power were set equal to zero prior to evaluating eqn ( 1). The projection velocity vectors V 1, and V2 were d e t e r m i n e d by using d i r e c t i o n a l i n f o r m a t i o n obtained from the PLS and the c o m p u t e d velocity magnitudes: V1 = IV1 ]UI
where IVI,21 is the magnitude of V1 or V2, c is the speed o f sound in tissue or water, fo is the transducer transmission frequency, ffi and J~i are the ith discrete frequency c o m p o n e n t s o f the forward and reverse D o p p l e r spectra, while P ( f f / ) a n d P(fri) are the
V2 = I V 2 l U 2 where IV 1 I and ]V2 ] were evaluated from eqn (1), and U 1 and U2 were the unit direction vectors indi-
Triangulation method for the quantitative measurement of arterial blood velocity• E. SCHRANKet al. cating the D o p p l e r b e a m direction from the two scanning positions. The triangulation velocity vector, V, was evaluated from V1 and V2 by simultaneously solving the following set of linear equations: V I . ( V 1 - V) = 0 V 2 . ( V 2 - V) = 0 V - ( V l x V2) -- 0 where V 1 • V2 and V1 X V2 denotes the dot product and cross product, respectively, o f the vectors V1 and V2.
String phantom experiments Two different string phantoms served as velocity reference targets for the triangulation studies. The first o f these p h a n t o m s provided a u n i f o r m speed string target. A loop of fine surgical thread (Ethicon, 4.0 surgical silk) was immersed in a water tank and driven by a small precision m o t o r (Micro Mo H E series m i n i a t u r e motor). An electronic calibrated output signal, generated by the motor, was used to measure string speed. The velocity of the uniform speed string p h a n t o m could be varied between approximately 10-60 cm/s by controlling the voltage supplying the precision motor. T h e string speed and direction were used to compute a reference velocity vector, Vr, to which the triangulation velocity measurements could be compared. The direction o f the string was measured by placing the sample volume at 10 different locations on the string target and determining the position of the points using the position locator system. A least squares best fit line was calculated through the 10 points to give the string unit direction. The string reference velocity vector, Vr, was found by multiplying the string speed by the string unit directional vector. A second study utilized a pulsatile string. A linear piecewise approximation to a c o m m o n carotid flow velocity waveform was digitized and used to drive a stepping motor. The velocity direction was determined as above while an independent measure of string displacement as a function of time was provided by an optical encoder (see Fig. 8). The velocity waveform voltage from the pulsatile string phantom was relayed to the ECG trigger circuitry used in the in-vivo experiments to provide a trigger pulse signal indicating the onset of the velocity waveform. Approximately 0.8 s blocks o f Doppler data were digitized and the triangulation velocity vectors were calculated at 20-ms intervals.
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In-vivo experiments D u r i n g the h u m a n in-vivo triangulation experiments, the subjects reclined comfortably on a hospital bed while Doppler recordings were taken from the femoral artery of the upper thigh region on three different subjects. Since b l o o d velocities changed throughout the cardiac cycle, ECG activity was used as a timing reference to examine the Doppler signals at specific times during the cardiac cycle. Referencing the Doppler signals to the cardiac cycle was essential since velocity information from the same interrogation site had to be acquired over different heart cycles when the scan head was placed at the first and second scanning positions. Prior to the triangulation measurements, electrodes were placed on the fight arm and right leg of the subjects studied. The amplified ECG signal was relayed to an ECG trigger circuit which produced a brief trigger pulse at the onset of the QRS wave. The ECG signal was encoded and recorded on the video channel of the tape recorder simultaneously with the forward and reverse Doppler signals on the audio tracks. During the off-line analysis both the forward and reverse Doppler channels were digitized in 25 Kbyte blocks, corresponding to approximately 0.8 s of digitized data. Within the 0.8 s time period, triangulation velocity vectors were evaluated at 20-ms time intervals. An ECG averaging feature was incorporated into the in-vivo analysis software, and was used to compensate for variability in blood flow patterns over different ECG cycles. To implement ECG averaging, the pulsed Doppler signal was recorded over several ECG cycles and the Doppler spectra were evaluated at 20-ms time intervals for each o f the ECG cycles. At each evaluated 20°ms time interval the Doppler spectra from the selected ECG cycles were s u m m e d and the resulting forward and reverse Doppler spectra were evaluated using eqn (1). Averaging over two ECG cycles appeared sufficient, and was used for the in-vivo data analysis. No significant changes in the triangulation velocities occurred with additional averaging.
RESULTS
String phantom experiments The magnitude and direction of the triangulation velocities for the uniform string phantom experiments were measured while systematically varying: (a) string speed, (b) sample volume depth, and (c) Doppler angle (Fig. 4). During the string phantom experiments an effort was made to keep the two lines o f sight, L1 and L2, essentially symmetrical to the
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Fig. 4. Schematic illustration of uniform string phantom experiment. During the uniform string phantom triangulation experiments the string was imaged with the ultrasound scanner and the sample volume (SV) was placed on the moving string target. The sample volume depth, d, Doppler angle, O, and string speed, v, were monitored and systematically varied during the string experiments. The string was driven using a set of pulleys and a precision miniature motor (M). T indicates the ultrasound transducer element. string target. In this way two o f the parameters (for example, sample volume depth and Doppler angle) could be held nearly constant, or within a narrow range of values, while the effects o f the third parameter (in this case string speed) could be examined. (The condition o f symmetrical lines of sight is, of course, not a requirement of the triangulation method.) The three parameters, string speed, sample volume depth and Doppler angle were varied to test the triangulation technique over a range of experimental conditions which could likely occur later in the i n - v i v o experiments. The results o f the uniform speed string p h a n t o m e x p e r i m e n t s are s u m m a r i z e d in Figs. 5, 6 a n d 7. Errors in the triangulation velocity magnitude (percent m a g n i t u d e error) a n d direction (directional error) were estimated by comparing the magnitude and direction of the triangulation velocity vector, Vt, to the reference velocity vector, Vr.Vr was determined by observing a calibrated output voltage indicating the string speed and measuring the string direction. T h e p e r c e n t m a g n i t u d e e r r o r o f the t r i a n g u l a t i o n v e l o c i t y v e c t o r s was c a l c u l a t e d as (]Vt] - IVr I )/I Vr I X 100, where IVt I and IVr ] represent the magnitude o f the triangulation and reference velocity vectors, respectively. The directional error is the calculated angle between the triangulation and reference velocity vectors. Complete agreement between the triangulation and reference velocity vectors would be indicated by a percent magnitude error of 0% and a directional error of 0 °. Each data point in Figs. 5, 6 and 7 represents the m e a n o f five experi-
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locity vector (directional error) was less than 3 degrees (shown by the dashed line). Larger velocities could not be tested due to speed limitations o f the string phantom motor. Figure 6 is a plot o f percent magnitude error and directional error vs. sample volume depth. During this experiment the Doppler angle was kept between 49-51 degrees, and the string speed was maintained at 44 cm/s. The effect o f Doppler angle on the percent magnitude error and directional error of the triangulation velocities is shown in Fig. 7. String speed was maintained at 44 cm/s and sample volume depth was kept between 1.9-2.7 cm while the angle between the string and Doppler ultrasound beam was varied between 40 and 80 degrees. Within the Doppler angle range o f 40-70 degrees the percent magnitude error and directional error remained relatively small; the mean of the magnitude error did not exceed 5% and the mean directional error was less than 3 degrees. For larger Doppler angles o f 75 and 80 degrees however, the mean magnitude error increased (17% and 9%, respectively) and there was a much wider spread o f the magnitude error values for each o f the five experimental trials. T h e results o f the t r i a n g u l a t i o n e x p e r i m e n t s using the pulsatile string p h a n t o m are shown in Fig. 8. The solid line in the figure indicates the magnitude o f the string velocity measured using an output voltage generated by a calibration encoder wheel attached to the phantom. String velocity magnitude measured using the triangulation m e t h o d is indicated by the filled circles. The circles represent the mean o f five
In-vivo e x p e r i m e n t s Data from the i n - v i v o studies were analyzed from five experimental trials using three different subjects (subjects A, B and C). These subjects had no known circulatory or cardiovascular problems. The velocity measurements were taken from the superficial femoral artery of the upper thigh region. This region of the femoral artery was chosen because of the ease of access. Blood flow in this area was expected to be undisturbed, laminar and relatively parallel to the vessel axis. The large size of the artery also simplified the data acquisition. Velocity i n f o r m a t i o n was averaged over two nonsuccessive ECG cycles. T h e n u m b e r o f heart cycles recorded for e a c h sample v o l u m e location ranged from approximately 10-40 cycles for the different subjects. The time to collect data for a single experimental trial ranged from about 3-7 minutes. The data acquisition time did not appear to affect the computed triangulation velocities. The experimental results from each of the three subjects is depicted graphically in Figs. 9, 10 and 11. Each of the figures consists of eight drawings labeled a-h. Each of these drawings represents both a two-dimensional view o f the interrogated region of the femoral artery as it would appear in a 2-D scan, and the triangulation velocity vectors measured at specific times within the E C G cycle. T h e circles in each drawing represent the sites within the femoral artery at which the vessel was interrogated, and the lines emanating from the circles represent the respective triangulation velocity vectors. The length of the velocity vectors is, o f course, proportional to the velocity magnitudes, and the direction of the vectors indicates the direction of velocity within the scan plane. The broad curved lines appearing above and below each set of velocity vectors represents the boundary of the arterial wall. The numbers appearing below each set o f vectors is the time after the onset of the ECG QRS wave at which the measurements were taken. The upper and lower scale bars appearing in the lower left hand corner o f Figs. 9-11 indicate the scale for distance and velocity magnitude, respectively. The eight time periods of the ECG cycle which are displayed in the figures were selected to show the triphasic character of blood flow in the femoral ar-
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tery. The waveform consisted of (a) forward systolic flow followed by (b) reverse flow and (c) subsequent forward flow component. The velocity vectors were calculated at 20-ms intervals. Flow velocity vectors calculated at times intermediate to those shown displayed the same parallel flow pattern with a gradual transition o f the blood flow velocities throughout the three phases of flow within the femoral artery. The three major phases of blood flow can be clearly seen for each of the subjects in Figs. 9, 10 and 11. The large systolic forward flow c o m p o n e n t (Figs. 9(b), 10(b) and 1 l(b)) was followed by a reverse flow c o m p o n e n t (Figs. 9(d)(e)(f), 10(d)(e) and 1 l(d)(e)(f)) and subsequently followed by a smaller forward flow c o m p o n e n t (Figs. 9(g)(h), 10(f)(g)(h), 1 l(g)(h)). DISCUSSION All commercially available ultrasound duplex scanners c u r r e n t l y e m p l o y pulsed D o p p l e r techniques to obtain flow velocity data along a single line of observation. This means that only one c o m p o n e n t of a three dimensional blood flow velocity vector that changes with time is detected. Current attempts toward quantifying the Doppler signals include angle correction wherein a Doppler angle must be assumed in order to report results in units of velocity (cm/s). In all cases, only one c o m p o n e n t of the blood flow velocity vector is detected and the Doppler angle must be estimated by some method. One of three assumptions regarding the direction of the blood flow vector is usually made: (a) the blood flow vector is coaxial to the ultrasound beam, in which case the Doppler angle is zero degrees; (b) the blood flow vector is parallel to the blood vessel axis, with the Doppler angle estimated from the intersection of the vessel axis with the ultrasound beam; or (c) using the new duplex color flow scanners, the display of color shades provides the impression o f flow streamlines which might be taken to be parallel to the directions of the flow vectors. Our knowledge about the complex flow patterns at normal bifurcations due to changes in vascular geometry (Ku et ai. 1985) and the fact that intraluminal disease is an encroachment of the normal flow lumen, indicate that the directions of the flow velocity vectors in these regions are not known with any degree of certainty. Errors of 10-30 degrees in the Doppler angle can result in large errors of reported velocities (Phillips et al. 1989). The ability to appreciate and define the direction of the flow velocity vector in two dimensions within the plane o f the ultrasound image is a significant c o n t r i b u t i o n to the understanding o f h u m a n blood flow. A triangulation method for quantifying the twodimensional character of flow velocity vectors de-
Volume16, Number 5, 1990 tected by diagnostic ultrasound has been developed. While the ultimate goal is to define the flow velocity vector in three dimensions, the technical and practical problems to be solved suggest that this problem is best addressed in a stepwise fashion. Thus, the results reported here represent the component velocities in a plane. The PLS has evolved to the point where blood flow velocities can be documented in two dimensions at selected anatomic sites. The superficial femoral artery was chosen for the initial h u m a n studies because of the well-behaved flow patterns known to exist and the ease of positioning the duplex scanhead to acquire two independent lines of sight required by the triangulation procedure. The spark gap platform mounted to the ultrasound scan head does not interfere with operator ability to perform a clinical study. The array of point microphone receivers is positioned above the patient and the lack of intervening reflectors assures an accurate position measurement. Careful engineering analysis demonstrates the ability of the PLS to specify a point in three dimensions to an accuracy of 1 mm. This paper has reported the ability to specify the magnitude of a flow vector to within 5% and the direction of the vector to within 3 degrees within the plane of the ultrasound image for a moving string target. Referring to Fig. 7, the magnitude error estimate for the flow velocity vector increased markedly for Doppler angles above 70 degrees. The reasons for this include a decreased velocity resolution in the frequency analysis algorithm because of the unfavorable Doppler angle, and the increased susceptibility to errors from geometrical considerations (i.e., referring to Fig. 1, the magnitude of the triangulation vector, V, will change markedly for small changes in either of the two measured vectors V1 or V2). While the limitation of Doppler angle may present problems in repositioning of the scan head in some anatomical sites, we did not find this to be a problem in the in-vivo experiments, although some attention to scan head positioning was required to avoid recording at excessively large Doppler angles. The flow velocity vectors in Figs. 10-11 are remarkably parallel during most of the cardiac cycle. It should be kept in mind that the "line segments" represent flow velocities and not particle paths. Crossings of the flow velocity vectors do not indicate the mixing of fluid elements. Deviation of the vectors from the axial direction could be due to: local secondary blood flow patterns caused by changes in vascular geometry, radial components associated with compliant vessels and the pulsatile character of flow, unfavorable Doppler angles during the transitions between forward and reverse flow, and/or the possibility
Triangulation method for the quantitative measurement of arterial blood velocity • E. SCHRANK el aL
that hemodynamic events were not the same for all of the cardiac cycles used in the triangulation measurements. Considering these aspects it is remarkable that the flow velocity vectors are as uniform as shown. The triangulation measurements made using the pulsatile string phantom (Fig. 8) demonstrated a relatively high degree of accuracy over most of the pulsatile waveform. However, during the initial acceleration phase of the waveform of Fig. 8 the errors in the triangulation measurements were considerably more pronounced than at the later portions of the waveform. This is a result of the finite length of time the Doppler signal must be analyzed to compute the Doppler spectra. For example, in this study the period over which the Doppler signal was analyzed to compute a Doppler spectrum was approximately 17 ms. If the target velocity (and hence Doppler frequency) changes significantly within the 17-ms period corresponding errors will occur in the frequency estimation values and hence the triangulation velocity vectors. Decreasing the period over which the Doppler signal is analyzed is not necessarily a solution since this would, in turn, result in a decrease in frequency resolution in the Doppler spectra. Overall, however, the general form of the pulsatile waveform of Fig. 8 is quite well represented by the triangulation velocity values. Several limitations of the triangulation method using the PLS result from the nonsimultaneous nature of the data collection. For example, although not shown in the figures, the triangulated flow velocity vectors became markedly distorted in late diastole. This situation is believed to be artifact caused by beat to beat variations of the cardiac cycle leading to significant errors in the triangulation method during this time of the cardiac cycle, since data had to be acquired over different ECG cycles for the two lines of sight, L1 and L2. Other problems which can arise include sample volume repositioning errors due to limitations of the PLS, and patient movement or mechanical distortion of the vessel during scan head repositioning. Vessels exhibiting complex flow patterns due to branch points or stenosis, and vessels which are relatively small in size, will naturally present a greater challenge to the triangulation method than the site of the femoral artery chosen in this study. Errors in measured triangulation velocity vectors resulting from SV repositioning errors will be more pronounced in regions of blood flow where there are large changes in blood velocity vectors over a small region of space, than in regions where the velocity vector field remains relatively uniform. The approximately 1 mm 3 dimension of the sample volume itself also becomes a limiting factor in smaller vessels, and
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in regions where velocity vectors vary significantly within a small region. Studies examining the performance of the triangulation method using the PLS in these more challenging and clinically relevant anatomical sites have yet to be performed. The goal of the current study was to evaluate the basic triangulation technique as a means to study blood velocity vectors in humans. A method of documenting the nonaxial character of blood flow at clinical sites of interest is not yet available. Further quantification and understanding of blood flow character in states of health and disease require a more complete description of the flow velocity vectors. The technique described here offers the opportunity to provide a clearer picture of the nature of blood flow. We have demonstrated the ability to determine the magnitude and direction of moving targets accurately using a duplex scanner and transducer locating system. While much more work remains to be done, a new tool for use in the study of blood flow has been developed. Acknowledgement--This work was supported by Grant HL-20898 from The National Institutes of Health and the Graduate School Research Fund of the University of Washington.
REFERENCES Atkinson, J.; Woodcock, J. P. Doppler ultrasound and its use in clinical measurement. New York: Academic Press; 1982. Caro, C. G.; Pedley, T. J.; Schroter, R. C.; Seed, W. A. The mechanics of the circulation. New York: Oxford University Press; 1978. Daigle, R. E. Quantitative aspects of color flow imaging. In: Manda, N. C., ed. Textbook of color Doppler echocardiography. Philadelphia: Lea and Febiger; 1989. Ku, D. N., et al. Hemodynamics of the normal carotid bifurcation: in vitro and in vivo studies. Ultrasound Med. Biol. 11:13-26; 1985. Moritz, W. E.; Shreve, P. L. A microprocessor based spatial locating system for use with diagnostic ultrasound. Proc. IEEE 64:966-974; 1976. Moritz, W. E.; Shreve, P. L. A system for locating points, lines and planes in space. IEEE Trans. Instrum. Meas. 26:5-10; 1977. Moritz, W. E.; Pearlman, A. S.; McCabe, D. H.; Medema, D. K.; Ainsworth, M. E.; Boles, M. S. An ultrasonic technique for imaging the ventricle in three dimensions and calculating its volume. IEEE Trans. Biomed. Eng. BME-30:482-492; 1983. Peronneau, P.; Sandman, W.; Xhaard, M. Blood flow patterns in large arteries. In: White, D. N.; Brown, R. E., ed., Ultrasound in Medicine. New York: Plenum Press; 1977:1193-1208. Phillips, D. J.; Beach, K. W.; Primozich, J.; Strandness, D. E. Should results of ultrasound studies be reported in units of frequency or velocity? Ultrasound Med. Biol. 15:205-212; 1989. Schrank, E. E. Triangulation method for the quantitative measurement of arterial blood velocity magnitude and direction in humans. Master's thesis, University of Washington, Seattle, Washington; 1989. Wong, S. Y. IBM PC/AT based diagnostic ultrasound imaging system. Master's thesis, University of Washington, Seattle, Washington; 1988. Zwiebel, W. J. Spectrum analysis in carotid sonography. Ultrasound Med. Biol. 13:625-636; 1987.