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The resolution of the ultrasound pulsed Doppler for blood velocity measurements
1. Biomechnnics,
1973, Vol. 6, pp. 701-710.
Pergamon Press.
Printed in Great Britain
THE RESOLUTION OF THE ULTRASOUND DOPPLER FOR BLOOD VELOCITY MEASUREMENTS”? RONALD L. MORRIS, MICHAEL
B. HISTAND and CHARLES
PULSED
W. MILLER
Colorado State University, Fort Collins, Colorado 80521, U.S.A. Abstract-Pulsed ultrasound Doppler velocity meters (PUDVM) permit noninvasive blood velocity measurements. The emitted ultrasound beam characteristics primarily determine the resolution of the instrument when recording velocity profiles. The sample volume, the small region over which velocity information data are detected, was found to be > 2.3 mm’ depending on the transducer disk dia., distance in front of the disk, sampling time increment, and pulse length. The shape of the sample volume approximates a cylinder in the near field and a frustrum of a cone in the far field. The end surfaces of the sample volume were affected by the emitted pulse shape. Ultrasonic beam cross-sections were found to be smaller than predicted by theory due to the finite threshold levels of the PUDVM. The variation of the sample volume with range was illustrated by steady laminar flow velocity profile measurements in rigid tubes. The accuracy of velocity measurements was within 5 ner cent with slightly larger deviations occurring near the walls due to the finite sample volume. INTRODUCTION CONSIDERABLE research has been directed toward improving techniques for the measurement of blood flow. Recently, the pulsed ultrasound Doppler velocity meter (PUDVM) has attracted the attention of physicians and medical researchers as a method to accurately record blood velocity and flow noninvasively. This paper describes the characteristics and defines the resolution of the PUDVM for blood velocity measurement. The PUDVM provides new methods for determination of cardiac output, diagnosis of peripheral arterial disease, evaluation of organ function by local flow comparisons, measurement of hormonal delivery to an organ when coupled with immunoassay techniques, and the assessment of the action of various vasoeff ector drugs. A salient feature of this method is the ability to measure instantaneous velocity, flow, and flow direction transcutaneously. Contemporary blood flow measurement generally requires insertion of a catheter or
17 July 1972. .-. f’l‘his work was supported
probe into a vessel or attachment of a cufftype flowmeter around a vessel. The catheter tip electromagnetic velocity probe (Mills, 1966, 1%7; Gabe, 1969) measures instantaneous flow although its size may seriously alter flow and velocity profiles. The cuff electromagnetic flowmeter (Denison, 1955; Schneider, 1968) measures instantaneous flow transmurally and has been used extensively by investigators. Drift and variations in zero levels, however, remain a problem during chronic applications. The hot-film anemometer (Ling, 1970) measures instantaneous velocities at various locations across a vessel lumen, but flow disturbance and surgical trauma remain a problem. Additional methods include thermal flowmeters (Leraand, 1968) and bristle flow meters (Bergel, 1968) which measure instantaneous flow. All of the methods described require surgery and are unsuitable for noninvasive chronic monitoring of blood flow, velocity, or velocity distributions. A continuous wave ultrasound Doppler veloc-
*Received
by USPHS Grant No. HE 14737. 701
702
R. L. MORRIS, M. B. HISTAND
ity meter (Satomura, 1960; Baker, 1964; McLeod, 1%7) can be used noninvasively, yielding the average instantaneous velocity over a cross-section. This method generally requires an in viuo calibration before quantitative data can be obtained since the vessel diameter is unknown. Recently developed pulsed Doppler systems (Baker, 1970, 1971; McLeod, 1971; Peronneau, 1970, 1971; Wells, 1969) permit measurement of local instantaneous blood velocity at discrete locations in an arterial crosssection. Velocity profiles can be constructed, and the vessel diameter determined from a velocity profile (Baker, 1970). Flow rates can be calculated by integration of the velocity profile over the diameter of the vessel. Strandness (1967) suggests a number of useful noninvasive applications of the PUDVM in diagnosis and evaluation of arterial and venous occlusive disease. Histand (1972) has demonstrated the application of the PUDVM for detailed transcutaneous measurement of velocity profiles in the peripheral arteries of the dog. Peronneau (1969) demonstrated the use of a PUDVM in viva with catheter-tip transducers in the dog. Miller (1972) used implantable cuffs at various locations on the arterial tree of dogs for the chronic study of atherogenesis. The PUDVM offers new possibilities in the study of hemodynamics both transcutaneously and transmurally. For applications of the PUDVM by medical researchers, it is important to determine its resolution by defining the sample volume, the small volume over which velocity data are averaged.
INSTRUMENT DESCRIPTION
The PUDVM used in this research was developed by McLeod (1971). It emits pulses of 7-10 MHz ultrasound 4, 8, or 16cycles in length at a repetition rate of 10, 20, or 40 kHz to drive the transducer. A fraction of the energy of the ultrasonic pulse is backscattered at interfaces with different acoustic impedances. (The acoustic impedance (2) is the
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product of the density of the medium (p) and the speed of sound (c) in the medium.) The backscattered signal is received by the same transmitting piezoelectric transducer during the latent period following emission, and an electronic gate is utilized to record only a short interval (1 p set or more) of the returned signal at a selected delay time following transmission. In effect, the delay and gate permit measuring Doppler frequency shift information in a small sample volume a known distance (range) in front of the transducer. A Doppler frequency shift occurs when an interface has a velocity relative to the transducer. The frequency of the backscattered signal will be altered in proportion to the relative velocity of that interface. The relative velocity (V) is calculated from the Doppler equation: v=
CAf 2fo cos e
where Af =Doppler frequency shift, c = velocity of sound in the medium, fO= transmitted ultrasound frequency, and 8 = angle between the velocity vector and the axis of the sound beam. Electronic variation of the range position (range-gating) permits the measurement of time varying flow velocities at sequential locations along the axis in front of the transducer. Velocity profiles in a tube or blood vessel can be conveniently constructed from this data. In blood vessels, the erythrocytes act as sound scatterers. A transmitted f. of 7-8 MHz results in Doppler frequency shifts up to 10 kHz for normal blood velocities. For recording purposes, the frequency shift is converted to an analog signal proportional to the velocity by a zero-crossing frequency to voltage converter. Adjustable threshold levels, specifying minimum amplitude and frequency recorded, reduce noise in the output. Proper trigger threshold adjustment is important for the detection of the dominant frequencies within the Doppler spectrum. The ultrasonic pulse and beam characteris-
PULSED
DOPPLER
BLOOD
tics largely define the volume over which the flow is sampled at a particular location. Ideally a very small sample volume is desirable for an approximate point measurement. The present instrument measures an average of frequency shifts over the sample volume. The sample volume should be sufficiently small so that no large velocity gradients exist within its boundaries. The composition, size, and shape of the piezoelectric disk are important parameters affecting the beam characteristics. The geometry and material will define the optimal resonating frequency (J,) and the mechanical Q (quality factor, which is a measure of the internal damping). The Q factor of a piezoelectric transducer can be determined by recording the amplitudes of two successive free vibration maximums, A, and AZ, and applying the empirical equation
Q=ln(A:,Az) where A,/AZ > 1. For pulsed ultrasound systems, low Q material (high internal damping) such as lead metaniobate (Q = 15) has the advantage of a wider frequency response and less ‘after ring’ (Blitz, 1963). However, a low Q crystal has the distinct disadvantage of a reduced output resulting in a less intense backscattered signal. The particular Q chosen will depend upon the application. The material used in this study was lead titanate zirconate (Q = 75) which has good response characteristics for blood velocity measurements. Beam divergence is primarily determined by transducer geometry. The larger the disk diameter, the farther the distance before beam divergence. This is the near field (Fresnel zone) whose length X0 is defined by:
VELOCITY
703
MEASUREMENT
The far field (Fraunhofer zone) can be represented as a diverging beam originating from the center of the transducer crystal with a half angle a, measured from the beam axis (Fig. I). The maximum intensity in the near field is constant, but decreases in the far field in proportion to the inverse square of the distance. The intensity distribution in a beam cross section has a maximum in the center and decreases toward the periphery (Lloyd, 1967). An effective beam exists within the boundaries of the actual beam since portions of the beam where the backscattered intensity is below the threshold level for the PUDVM are not detected. The quantity and quality of the signal returned to the transducer are functions of reflection, scattering, and attenuation. Generally, when a longitudinal pressure wave encounters interfaces of large cross-sectional diameter with respect to wave length (A), reflection and refraction occur. The percentage of energy transmitted and the amount reflected is dependent upon the angle of incidence and the ratio of the specific acoustic impedances (2) of the two media. When the cross-sectional diameter of the interface is on the order of a wave length or smaller, Rayleigh-type scattering occurs (Viktorov , ULTRASONIC BOUNDARIES
FAR
where r is the radius of a circular transducer, and A is the wave length of the ultrasound.
BEAM
FIELD
Fig. 1. Ultrasonic energy is emitted from disk as a collimated beam in the near field the region of the far field. The dimensions far fields are functions of disk radius (r) wavelength (A)
a piezoelectric but diverges in of the near and and ultrasound
704
R. L. MORRIS, M. B. HISTAND
1967). Rayleigh scattering occurs in all directions, and the energy loss of the beam (attenuation) is proportional to the volume of the scatterer and the fourth power of frequency (Hueter, 1955; Blitz, 1%3). Rayleigh scattering has been shown to be a valid assumption for ultrasound in blood (Reid, 1969; Fraser, 1970). Attenuation due to fractional heating also occurs. METHODS The PUDVM was evaluated to determine the relationship between sample volume and range. The gate and pulse length were held constant since they fix the sample volume length. The ultrasonic beam diameter was measured at predetermined distances in front of the piezoelectric disk. The effective diameter of the beam as a function of distance was found by mechanically scanning the transducer across the edge of a very thin magnetic tape which acts as a scattering surface. The tape moves at a constant velocity and is submerged in distilled water. The recorded velocity distribution approximates a square wave from which distinct beam boundaries can be found. A schematic of the measuring apparatus is shown in Fig. 2. The emitted frequency of the transducer was adjusted to obtain maximum returned amplitude by visualizing pulse re-
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flections from a flat plate. The transducer was held in position by a stereotaxic transducer holder which permits four degrees of freedom with vernier scales for each degree. The transducer was positioned at an angle of 60” with respect to the edge of the moving tape (Fig. 3). The tape velocity was 50 cmlsec * 2 cm/set. Vertical movement in increments of O-125 mm provided a distinct definition of the beam edge. For a correct definition of the portion of the beam used by the PUDVM for processing (effective beam diameter), simulated acoustic attenuation was used. The attenuation was adjusted to approximate amplitudes obtained in actual blood flow studies, where natural attenuation was used. To accomplish this, the signal between the transducer and the PUDVM was electronically attenuated, holding the signal to noise ratio constant. The pulse beam was visualized by the Schlieren optical method and compared with the previous measurements. The errors introduced by averaging over the sample volume are demonstrated by velocity profile measurements in tubes. For this investigation, velocity profile measurements were made using the 1.8 and 3.0 mm dia. transducers previously studied. These measurements were performed with a gate setting of 1 or 2 psec and pulse length of 16 cycles in a straight rigid butyrate tube (11.11 mm i.d.) during steady laminar flow (Reynolds numbers 2000). The PUDVM threshold levels were set just above the noise level at a zero flow condition. The apparatus (Fig. 4) consisted of recirculating water with a 0.2 per cent suspension of silicone spheres acting as sound scatterers. Prior to experimentation, the temperature of the recir-
CONSTANT SPEED &C. MOTOR
ULTRASONIC PULSE MAGNETIC TAPE ’ i ~-TAPE
rTAPE
GUIDE
P
GUIDE
rPlEZOELECTRlC
TRANSDUCER
DISK
DISTILLED
______--_ DIRECTION
OF
VELOCITY
StAN
WATER
__-_-_-_ PULSE
TAPE
POSITION
Fig. 2. Apparatus for measurement of sample volume diameter. Beam boundaries are determined by an edge scan of a continuous loop of magnetic tape moving at a constant velocity. When the tape is within the beam boundaries, a backscattered velocity signal is recorded.
DISTRIBUTION
Fig. 4. Schematic of steady flow recirculating apparatus for water suspended silicone scattering medium. The test section of the tube in the measurement tank is submerged in distilled water to insure acoustic coupling.
PULSED
DOPPLER
BLOOD VELOCITY
culating fluid was allowed to equilibrate, minimizing any viscosity variation, and the flow rate was adjusted to insure laminar flow. Small amounts of dye were injected at the tube inlet to check the absence of turbulence. Flow collections were made several times, and a mean velocity v was calculated. jF=
Flow (Q) Cross-sectional
area (Al’
The PUDVM transducer was positioned laterally over the tube axis by maximizing the returned signal with the transducer inclined at an angle of 60” with respect to the tube axis. Velocity measurements were made by range-gating in 0.925 psec increments (- 0.7 mm in range) across the flow stream with a constant gate and pulse length. The velocity information was plotted on an X-Y plotter. The instnment output was internally calibrated by input of a signal of known frequency channeled into the zero-crossing me@. Flow collections were repeated to provide a check on V.
705
MEASUREMENT
dent on the transducer beam characteristics. The pulse length is dependent on the number of cycles emitted at a particular frequency and the Q factor of the crystal. The back-scattered signal will be a superposition of small pressure waves of various amplitudes and frequencies (Fig. 6). The composite pressure waves represent information from a known sample volume when recorded with a particular delay and gate. The size of the incident pulse is much larger than the numerous sound scatterers (5 x lo6 red blood cells/mm3). It follows that the sample volume cross-section will be defined by the maximum pulse cross-section and, therefore, will be circular for the circular transducers used.
RESULTS AND DISCUSSION
The characteristics of the PUDVM and the emitted ultrasonic beam provide the basis for sample volume analysis. The emitted pulse has been shown to be a tear-drop shape by Baker (1971) and an actual photograph is shown in Fig. 5. The pulse diameter is depen,-EMlTTED
ULTRASONIC
t=o+ p
EMlTd’
ULTRASOUND SCKC’
t-t A
B
lANsDucER
A INITIAL FRONT ( $1
PULSE
t=
WAVE FROM “n’
tLAt
t=t,
t>t,
bEAM BOUNDARY
Fig. 6. Rayleigh scattering from red blood cells illustrated as overlapping pressure waves. The actual case would involve scattering from more than 5 x 10” red blood cells within an emitted pulse. The backscattered energy received by the transducer is the sum of all the pressure waves corresponding to a particular time and location.
Fig. 7. Relationship between sampling time and sample length. For a gate setting of 2Ax/c (set) the sample volume length will be Ax (mm). At time t = 0’ the ultrasonic pulse is emitted by the piezoelectric transducer. The two scatterers are located Ax apart. At t = f,+ scatterer A begins to scatter the ultrasound in all directions. I, represents the initial scattered wave front from A. IA and the ultrasonic pulse will reach point B simultaneously and IA will also be Ax from point A toward the transducer. Is will originate when I, (toward the transducer) is 2Ax from point B.
706
R. L. MORRIS, M. B. HISTAND SCATTERERS-ABC 9 I , DE t 1F ---_
BOUNDARIES
WAVE
SAMPLE VOLUME SURFACE SHAPES
FRONT
END
kAMPLE VOLUME LONGITUDINAL CROSS SECTION
Fig. 8. Sample volume end surface shapes. Considering one pulse, initial wave fronts from points A, B, and C, fixed with respect to the conducting medium, combine to produce the plane wave front indicated, A short time later additional backscattered ultrasound from D, E and F will also superpose with this returning wave front. Therefore, for any instant in time the backscattered ultrasound arriving at the piezoelectric transducer will contain information from a small volume bounded, for example, by the scatterine noints A. B. C. D. E and F’. The shaue of this small voru-me is die to the ‘pulse shape and velocity of conduction in medium. In a similar fashion a combined wave front is formed from points G, H, I, J, K and L. Therefore, for a finite gate length, the sample volume end surface shapes are defined by the points D, E, F and G, H, I.
The length of the sample volume is determined by the time the gate is open (At) and the length of the emitted pulse (R). The effects of the gate and pulse length on the sample volume length are illustrated in Figs. 7 and 8. To determine the effect of the gate length on the sample volume length, consider an infinitely small pulse transmitted through the flow stream and the backscattered information recorded with a finite gate length (At = 1 psec). During 1 p set sound travels - l-5 mm in water or tissue. However to convert a 1 psec gate
and C. W. MILLER
time to sample length, account must be made for the additional time it takes for the incident pulse to be scattered at the far end of the sample volume and return. This implies that the gate time is actually twice the sample volume length; therefore, the 1 Fsec gate corresponds to 0.75 mm sample volume length (Fig. 7). Generally, the gate contribution to sample volume length is l,= cAtI2. The effect of the pulse length is found by considering a finite pulse length (PI) and an infinitesimally small gate time. In this case the combined wave front of backscattered ultrasound at any one point and time on the pulse beam axis will include backscattered information over a sample length (1,) of CR /2. A/2 is the time (distance of CR/~) it takes for backscattered ultrasound to travel from the leading edge of the incident pulse to the trailing edge; and, therefore, information from other scatterers in that interval is superposed. Combining the equations, the sample volume length is then the sum of the two components: l,, = lP+ I, = c(P, +At)/2. The sample volume shape for a gate = 0 will be the same shape as the incident pulse except with a length of 4(cpI). The actual sample volume shape for a finite gate will resemble a cylinder in the near field or a cone frustrum in the far field. The proximal and distal ends of the sample volume will retain the incident pulse shape as in the gate =0 case (Fig. 8). It should also be clear that the total scattered ultrasonic energy will be greater from the beam axis than the beam boundaries due to the incident pulse shape. The velocity profiles obtained from edge scans of the moving tape have steep slopes at the extremes indicating a distinct beam boundary. A typical edge scan velocity distribution is shown in Fig. 9. Figure 10 is a composite of results of effective beam diameter variations as a function of range for the four transducers tested. Theoretical predictions of the near and far fields are indicated. The measured beam is the portion of the beam above the threshold level of the PUDVM. The measured beams are narrower due to the effects of attenuation
(Facing p.
Fig. 5. A photograph of a reflected ultrasound pulse recorded on a high frequency oscilloscope. I.8 mm, frequency = 7.45 MHz, pulse duration of 16 cycles.
Transducer diameter =
Fig. 11. Schlieren photograph of an ultrasound beam from a transducer visualized in a 4 in. Schlieren optical system.
PULSED
DOPPLER
BLOOD
RANGE= IO mm TAPE vELOCITY=53*2&
VELOCITY
MEASUREMENT -BEAM
--
707 MEWJREMENTbYJRVE FIT) PREDICTION
-THEORETICAL
60r
5“1 0’.
-1.5
L2.03mm.J.
y
40
VERTICAL
-.5 POSITION
I
0 FROM
.5 TAPE
11
,
b
1.5
PLANE(mm)
Fig. 9. Typical sample volume diameter data. The beam boundaries are defined by the transducer position when the moving tape velocity is detected. The velocity profile shapes were extrapolated to determine the zero velocity intersections which were assumed to be the beam boundaries.
causing returned signals below the PUDVM threshold. The Schlieren photographs (Fig. 11) showed good correlation with the measured diameters. To minimize the dispersion error the beam boundaries were approximated by a curve fit prior to calculation of the crosssectional area. The calculated results are shown in Fig. 12. The sample volume is the product of the measured beam area and the sample length. The measurements from two l-8 mm dia. transducers show very close agreement. Figure 12 indicates that the larger the diameter of the piezoelectric disk the longer the near field length and the greater the sample volumes in the near field. The 3-O mm transducer data illustrates that higher frequency ultrasound implies longer near fields and smaller sample volumes, in agreement with theory. Further reduction in beam cross-sectional area can be accomplished by the use of acoustic lenses for beam focusing, although beyond the point of focus, resolution would suffer. The results of the tube flow measurements were compared with the theoretical velocity
Fig. 10. Beam diameter variation with range. The solid lines are the measured ultrasonic beam boundaries resulting from a curve fit of the data points taken at various ranges. The dashed lines represent the theoretical prediction of the beam for a particular transducer diameter and frequency. The region between the measured and theoretical beam is the portion of the beam where the backscattered amplitude or frequency is below the PUDVM threshold levels..
profile in a rigid tube assuming steady laminar flow. The velocity distribution is therefore parabolic: V(r) = V,,,(l-
r2/R02)
where r is the radial position of the velocity measured from the tube longitudinal axis, R. is the tube radius, and V,,,,, is the centerline velocity in the tube (V,,, = 2 V). In the figures the velocities were normalized with respect to V..__^ rn”“.The velocitv . nrofiles measured for the 1
708
R. L. MORRIS, M. B. HISTAND
1.9-~~~~7.4
B
2.6---7.6 -..
5
16r
ti
01 0
3.0----713 3.Q-----7.9
.‘/
I
5
IO RANGE
15
20
25
(mm)
Fig. 12. The sample volume will be the product of the sample volume cross sectional area (above) and the sample length which is fixed by the gate setting of the PUDVM. A 1 psec gate setting will give sample lengths of 0.75 mm and 2 ysec of 1.5 mm.
3-O mm transducer with gate settings of 1 and 2 psec are shown in Fig. 13 along with the known velocity profile for a steady laminar flow. These data show good correlation with the actual profile except at the walls. The profile measured with a gate setting of 1 psec is more accurate than the profile measured %=5.55mm V,,,&36.2 cmhec o GATE= I p see B GATP2paec
I
NEAR WALL
R/R., J %xL
Fig. 13. Steady flow tube velocity profile data measured with the 3.0 mm dia. transducer.
and C. W. MILLER
with a gate of 2 psec at the near wall, due to the smaller sample volume. At the far wall both profiles differ from the actual profile with a gradual taper to zero velocity. This effect is due to the sample volume size and its increase with distance as the following analysis illustrates. A digital computer simulation of blood velocity profile measurements in tubes was developed. Each sample volume was divided into 250 equal volume increments. The average velocity at each incremental volume was calculated, and the 250 samples were then averaged over the sample volume to give a predicted PUDVM velocity measurement. Using greater than 250 incremental volumes does not increase the accuracy significantly. The simulation assumed that each incremental volume of scatterers had equal incident and scattered energy. Weighing factors can be incorporated to account for pulse shape and intensity distribution, once these factors are accurately determined. This simulation was used to predict a steady laminar flow velocity profile in a tube. The simulation assumed the beam divergence characteristics previously determined for the 1G3mm transducer, a transducer angle of 60”, a parabolic velocity profile in the tube, and a cylindrical sample volume shape in the near field and a frustrum of a cone in the far field. The effects of the velocity variation in three dimensions across the sample volume, due to its finite size, were taken into consideration. The result of this analysis was a prediction of the measured velocity profile with the 1.8 mm dia. transducer (gate = 2 psec, pulse length = 16 cycles, f. = 7.5 MHz). These data are presented in Fig. 14, together with an actual velocity profile measured with the PUDVM (same gate, A, and fO) and the parabolic profile. The predicted profile illustrates the wall effect observed in the 3-O mm transducer profiles and is due to the finite size of the sample volume and the beam divergence characteristics in the far field. The magnitude of the measured velocity profile is 2 per cent smaller
PULSED
DOPPLER
BLOOD VELOCITY
%=5.55 mm V,,=35Acdsec A GATE = 2 LLsec
.B
v
.6
V max A
I
NiAR WALL
R/R.
I FhR WALL
Fig. 14. Steady flow tube velocity profiles predicted by sample volume analysis and measured with the 1.8 mm diameter transducer with a gate setting of 2 gsec.
than the predicted profile at the centerline. This discrepancy is possibly due to the assumption of a flat ended sample volume for the analytical model or a slight transducer inclination angle error. A one degree error is equal to a 4 per cent velocity error at an inclination angle of 60” (Gill, 1972). Comparisons of the velocity profiles measured using the 1.8 and 3.0 mm dia. transducers with the theoretical profile indicate that the 3-O mm transducer is approximately 5 per cent more accurate at the tube centerline and far wall. However, the 1-8 mm transducer allows more accuracy at the near wall since the beam diameter is 30 per cent smaller at that location. The 3.0 mm transducer offers the least variation in sample volume for a tube dia. of 11 mm and, therefore, would produce a more accurate measurement.
predict the actual beam characteristics; however, they do not correspond exactly to the portion of the backscattered beam detected by the PUDVM. The trigger threshold levels are crucial in determining the portion of the beam being detected. Each transducer must be tested with a particular PUDVM to determine sample volumes and divergence characteristics. This information will define the resolution for a particular application of the PUDVM. Without this information, unsymmetrical, skewed, or magnitude errors in velocity profiles could be misinterpreted. A knowledge of the sample volume variation as a function of range for various sizes and types of transducers (Fig. 12) will aid in proper transducer selection. The sample volume shape has been shown to approximate a cylinder in the near field and a frustrum of a cone in the far field. The surface proximal to the transducer is due to the pulse trailing shape and the far surfaces is due to the pulse leading surface shape. The length of the sample volume is determined by the gate and the pulse length. The attainable resolution of the current instrumentation provides a sample volume of 2.3 mm3 or larger, depending on the pulse length, gate duration, and beam characteristics. Present indications are that velocity disturbances or skewed velocity profiles caused by protuberances such as atherosclerotic plaques may be detected in arteries noninvasively. Velocity contours could be mapped along a vessel, thereby allowing determination of plaque locations and thicknesses. Additional applications of the PUDVM in transmural and transcutaneous measurement of hemodynamics in investigative and diagnostic medicine also exist.
SUMMARY AND CONCLUSIONS
The preceeding analysis and experimental results clearly show the variation of sample volume due to transducer design parameters is an essential factor to know prior to making measurements with a PUDVM. Theory can
709
MEASUREMENT
NOMENCLATURE Z
acoustic impedance (g cm’/sec) P density of a medium (g/cm’) velocity of ultrasound (mm/set) ; relative velocity (cmlsec) Af Doppler frequency shift (Hz) f0 transmitted ultrasound frequency
(Hz)
710
R. L. MORRIS. M. B. HISTAND
e angle between velocity vector and axis of sound beam (degrees) A1 amplitude of undriven vibration maximum (V) Al succeeding undriven amplitude maximum (V) Q factor quality factor (transducer internal damping, nondimensional) X0 near field length (mm) radius of circular transducer (mm) : wave length of transmitted ultrasound (mm) @ half angle of beam divergence (degrees) Reynolds Number vd/v (nondimensional) kinematic viscosity (cm*/sec) ; mean velocity (cm/set) tube dia. (cm) : flow (mm’lsec) A cross-sectional area (mm’) V(r) velocity at position r from the tube axis (cmlsec) tube centerline velocity (cm/set) VRCI tube radius (mm) I.4 initial pressure wave front from point A backscattered toward the transducer Z, initial pressure wave front from point B backscattered toward the transducer 1, sample volume length component due to the gate (mm) 1, sample voIume length component due to the pulse length (mm) 1 total sample length (mm) r;; gate length (set) PI pulse length (see). REFERENCES Baker, D. W. and Stegell, H. F. (1964) A sonic transcutaneous blood flowmeter. Proc. 17th Ann. Conf. Engr. Med. Biol,, p. 76. Baker, D. W. (1970) Pulsed ultrasonic Doppler blood-flow sensing. IEEE Trans. on Sonics and Ultrasonics. SU-17; 3, 170-182. Baker, D. W., Jorgensen, J. E. and Campau, D. N. (1971) The characteristics of the pulsed ultrasonic Doppler flowmeter. Symposium on Flow, Pittsburgh. Bergel, D. (1968) The bristle flowmeter. New Findings in Blood Flowmetry, (Edited by Cappelen, Chr., Jr.), p. 22. AAS & WAHLS Boktrykkeri, Oslo. Blitz, J. (1963) Fundamentals of Ultrasonics, pp. 9; 152. Butterworth, London. Carlin, B. (1969) Ultrasonics, p. 64. McGraw-Hill, New York. Denison, A. B., Jr., Spencer, M. P. and Green, H. D. (195.5) A square wave electromagnetic flowmeter for application to intact blood vessels. Circ. Res. 3.39-46. Fraser, M. P. (1970) Transcutaneous spectral bloodflowmeter. Technical Note 1970-7, Lincoln Laboratory, Mass. Inst. Tech., Lexington, Mass. Gabe, I. T., Gault, J. H., Ross, J., Jr., Mason, D. T., Mills, D. J., Schillingford, J. P. and Braunwald, E. (1969) Measurement of instantaneous blood flow velocity and
and C. W. MILLER
pressure in conscious man with a catheter-tip velocity probe. Circulation 40, 603-614. Gill, R. W. and Meindl, J. D. (1972) Optimal design of the pulsed Doppler ultrasonic flowmeter. Proc. 25th Ann. Conf. Engr. Med. Biol.. D. 34. Bal Harbour. FLa. Histaid, My B., Miller, d. -W. and Mcieod, fi. D. (1973) The Transcutaneous measurement of blood velocity profiles and flow. Cardiovasc. Res. (in press). Hueter, T. F. and Bolt, R. H. (1955) Sonics, pp. 63-72. Wiley, New York. Leraand, S. (1968) Thermal flowmeters. New Findings in Blood Flowmetry. (Edited by Cappelen, Chr., Jr.), pp. 15-17. AAS & WAHLS Boktrykkeri, Oslo. Ling, S. C., Atabek, H. B. and Carmody, J. J. (1970) Pulsatile flows in arteries. Znt. Appl. Mech. Conf. Lloyd, E. A. (1967) Energy measurement. Ultrasonic Techniques in Biology and Medicine. (Edited by Brown, B. and Gordon, D.), p. 52. Thomas, Springfield, Ill. McLeod, F. D., Jr. (1967) A directional Doppler flowmeter. DiPest 7th Zntl. Conf. Med. Biol. Enar. (Edited bv Jacobson, Bertil), pp. 13-14, Stockholm._ McLeod, F. D. and Anliker, M. (1971) A multiple gate pulse Doppler flowmeter. IEEE Ultrasonics Symposium, p. 51. Miami. Miller, C. W., Nealeigh, R. C. and Histand, M. B. (1972) The effect of arterial location upon arterial velocity distributions. Proc. 9th Ann. Rocky Mtn. Bioengineering Symposium, pp. 129-132. Mills, C. J. and Shillingford, J. P. (1967) A catheter tip electromagnetic velocity probe and its evaluation. Cardiovasc. Res. 1, 263-273. Mills, C. J. (1963) A catheter tip electromagnetic velocity probe. Phys. Med. Biol. II, 323-324. Peronneau, P. A. and Leger, F. (1969) Doppler ultrasonic pulsed blood flowmeter. 8th Zntl. Conf. Med. Biol. Engr. pp. 10-11. Chicago. Peronneau, P., Hinglais, J., Pellet, M. and Leger, F. (1970) Velocimetre sanguin par effet Doppler a emission ultrasonore pulsee. L’Onde Electrique 50, 3-23. Peronneau, P. A., Pellet, M. M., Xhaard, M. C. and Hinglais, J. R. (1971) Pulsed Doppler ultrasonic blood flowmeter real-time instaneaneous velocity profiles. Symposium on Flow, Pittsburgh. Reid. J. M.. Siaelmann. R. A.. Nasser, M. G. and Baker, D. WI (1969) Tie scattering of ultrasound by human blood. 8th Zntl. Conf. Med. Biol. Engr. pp. 10-17. Chicago. Satomura, S. and Kaneko, Z. (1960) Ultrasound blood rheograph. Report of 3rd Znt. Conf. Med. Elect., pp. 254-258. London. Schneider, H., Wieberdink, J. and Reneman, R. S. (1968) Physical aspects of electromagnetic flowmetry. New Findings in Blood Flowmetry. (Edited by Cappelen, Chr., Jr.), pp. 32-35. AAS & WAHLS Boktrykkeri, Oslo. Strandness, D. E., Jr., Schultz, R. D., Sumner, D. S. and Rushmer, R. F. (1967) Ultrasonic flow detection. A useful technique in the evaluation of peiipheral vascular disease. Am. J. Slrrg. 113, 311-320. Viktorov, I. A. (1967) Rayleigh and Lamb Waves, pp. 63-64. Plenum Press, New York. Wells, P. N. T. (1969) A ranged-gated ultrasonic Doppler System. Med. Biol. Engr. 7, 641-652.
1973, Vol. 6, pp. 701-710.
Pergamon Press.
Printed in Great Britain
THE RESOLUTION OF THE ULTRASOUND DOPPLER FOR BLOOD VELOCITY MEASUREMENTS”? RONALD L. MORRIS, MICHAEL
B. HISTAND and CHARLES
PULSED
W. MILLER
Colorado State University, Fort Collins, Colorado 80521, U.S.A. Abstract-Pulsed ultrasound Doppler velocity meters (PUDVM) permit noninvasive blood velocity measurements. The emitted ultrasound beam characteristics primarily determine the resolution of the instrument when recording velocity profiles. The sample volume, the small region over which velocity information data are detected, was found to be > 2.3 mm’ depending on the transducer disk dia., distance in front of the disk, sampling time increment, and pulse length. The shape of the sample volume approximates a cylinder in the near field and a frustrum of a cone in the far field. The end surfaces of the sample volume were affected by the emitted pulse shape. Ultrasonic beam cross-sections were found to be smaller than predicted by theory due to the finite threshold levels of the PUDVM. The variation of the sample volume with range was illustrated by steady laminar flow velocity profile measurements in rigid tubes. The accuracy of velocity measurements was within 5 ner cent with slightly larger deviations occurring near the walls due to the finite sample volume. INTRODUCTION CONSIDERABLE research has been directed toward improving techniques for the measurement of blood flow. Recently, the pulsed ultrasound Doppler velocity meter (PUDVM) has attracted the attention of physicians and medical researchers as a method to accurately record blood velocity and flow noninvasively. This paper describes the characteristics and defines the resolution of the PUDVM for blood velocity measurement. The PUDVM provides new methods for determination of cardiac output, diagnosis of peripheral arterial disease, evaluation of organ function by local flow comparisons, measurement of hormonal delivery to an organ when coupled with immunoassay techniques, and the assessment of the action of various vasoeff ector drugs. A salient feature of this method is the ability to measure instantaneous velocity, flow, and flow direction transcutaneously. Contemporary blood flow measurement generally requires insertion of a catheter or
17 July 1972. .-. f’l‘his work was supported
probe into a vessel or attachment of a cufftype flowmeter around a vessel. The catheter tip electromagnetic velocity probe (Mills, 1966, 1%7; Gabe, 1969) measures instantaneous flow although its size may seriously alter flow and velocity profiles. The cuff electromagnetic flowmeter (Denison, 1955; Schneider, 1968) measures instantaneous flow transmurally and has been used extensively by investigators. Drift and variations in zero levels, however, remain a problem during chronic applications. The hot-film anemometer (Ling, 1970) measures instantaneous velocities at various locations across a vessel lumen, but flow disturbance and surgical trauma remain a problem. Additional methods include thermal flowmeters (Leraand, 1968) and bristle flow meters (Bergel, 1968) which measure instantaneous flow. All of the methods described require surgery and are unsuitable for noninvasive chronic monitoring of blood flow, velocity, or velocity distributions. A continuous wave ultrasound Doppler veloc-
*Received
by USPHS Grant No. HE 14737. 701
702
R. L. MORRIS, M. B. HISTAND
ity meter (Satomura, 1960; Baker, 1964; McLeod, 1%7) can be used noninvasively, yielding the average instantaneous velocity over a cross-section. This method generally requires an in viuo calibration before quantitative data can be obtained since the vessel diameter is unknown. Recently developed pulsed Doppler systems (Baker, 1970, 1971; McLeod, 1971; Peronneau, 1970, 1971; Wells, 1969) permit measurement of local instantaneous blood velocity at discrete locations in an arterial crosssection. Velocity profiles can be constructed, and the vessel diameter determined from a velocity profile (Baker, 1970). Flow rates can be calculated by integration of the velocity profile over the diameter of the vessel. Strandness (1967) suggests a number of useful noninvasive applications of the PUDVM in diagnosis and evaluation of arterial and venous occlusive disease. Histand (1972) has demonstrated the application of the PUDVM for detailed transcutaneous measurement of velocity profiles in the peripheral arteries of the dog. Peronneau (1969) demonstrated the use of a PUDVM in viva with catheter-tip transducers in the dog. Miller (1972) used implantable cuffs at various locations on the arterial tree of dogs for the chronic study of atherogenesis. The PUDVM offers new possibilities in the study of hemodynamics both transcutaneously and transmurally. For applications of the PUDVM by medical researchers, it is important to determine its resolution by defining the sample volume, the small volume over which velocity data are averaged.
INSTRUMENT DESCRIPTION
The PUDVM used in this research was developed by McLeod (1971). It emits pulses of 7-10 MHz ultrasound 4, 8, or 16cycles in length at a repetition rate of 10, 20, or 40 kHz to drive the transducer. A fraction of the energy of the ultrasonic pulse is backscattered at interfaces with different acoustic impedances. (The acoustic impedance (2) is the
and C. W. MILLER
product of the density of the medium (p) and the speed of sound (c) in the medium.) The backscattered signal is received by the same transmitting piezoelectric transducer during the latent period following emission, and an electronic gate is utilized to record only a short interval (1 p set or more) of the returned signal at a selected delay time following transmission. In effect, the delay and gate permit measuring Doppler frequency shift information in a small sample volume a known distance (range) in front of the transducer. A Doppler frequency shift occurs when an interface has a velocity relative to the transducer. The frequency of the backscattered signal will be altered in proportion to the relative velocity of that interface. The relative velocity (V) is calculated from the Doppler equation: v=
CAf 2fo cos e
where Af =Doppler frequency shift, c = velocity of sound in the medium, fO= transmitted ultrasound frequency, and 8 = angle between the velocity vector and the axis of the sound beam. Electronic variation of the range position (range-gating) permits the measurement of time varying flow velocities at sequential locations along the axis in front of the transducer. Velocity profiles in a tube or blood vessel can be conveniently constructed from this data. In blood vessels, the erythrocytes act as sound scatterers. A transmitted f. of 7-8 MHz results in Doppler frequency shifts up to 10 kHz for normal blood velocities. For recording purposes, the frequency shift is converted to an analog signal proportional to the velocity by a zero-crossing frequency to voltage converter. Adjustable threshold levels, specifying minimum amplitude and frequency recorded, reduce noise in the output. Proper trigger threshold adjustment is important for the detection of the dominant frequencies within the Doppler spectrum. The ultrasonic pulse and beam characteris-
PULSED
DOPPLER
BLOOD
tics largely define the volume over which the flow is sampled at a particular location. Ideally a very small sample volume is desirable for an approximate point measurement. The present instrument measures an average of frequency shifts over the sample volume. The sample volume should be sufficiently small so that no large velocity gradients exist within its boundaries. The composition, size, and shape of the piezoelectric disk are important parameters affecting the beam characteristics. The geometry and material will define the optimal resonating frequency (J,) and the mechanical Q (quality factor, which is a measure of the internal damping). The Q factor of a piezoelectric transducer can be determined by recording the amplitudes of two successive free vibration maximums, A, and AZ, and applying the empirical equation
Q=ln(A:,Az) where A,/AZ > 1. For pulsed ultrasound systems, low Q material (high internal damping) such as lead metaniobate (Q = 15) has the advantage of a wider frequency response and less ‘after ring’ (Blitz, 1963). However, a low Q crystal has the distinct disadvantage of a reduced output resulting in a less intense backscattered signal. The particular Q chosen will depend upon the application. The material used in this study was lead titanate zirconate (Q = 75) which has good response characteristics for blood velocity measurements. Beam divergence is primarily determined by transducer geometry. The larger the disk diameter, the farther the distance before beam divergence. This is the near field (Fresnel zone) whose length X0 is defined by:
VELOCITY
703
MEASUREMENT
The far field (Fraunhofer zone) can be represented as a diverging beam originating from the center of the transducer crystal with a half angle a, measured from the beam axis (Fig. I). The maximum intensity in the near field is constant, but decreases in the far field in proportion to the inverse square of the distance. The intensity distribution in a beam cross section has a maximum in the center and decreases toward the periphery (Lloyd, 1967). An effective beam exists within the boundaries of the actual beam since portions of the beam where the backscattered intensity is below the threshold level for the PUDVM are not detected. The quantity and quality of the signal returned to the transducer are functions of reflection, scattering, and attenuation. Generally, when a longitudinal pressure wave encounters interfaces of large cross-sectional diameter with respect to wave length (A), reflection and refraction occur. The percentage of energy transmitted and the amount reflected is dependent upon the angle of incidence and the ratio of the specific acoustic impedances (2) of the two media. When the cross-sectional diameter of the interface is on the order of a wave length or smaller, Rayleigh-type scattering occurs (Viktorov , ULTRASONIC BOUNDARIES
FAR
where r is the radius of a circular transducer, and A is the wave length of the ultrasound.
BEAM
FIELD
Fig. 1. Ultrasonic energy is emitted from disk as a collimated beam in the near field the region of the far field. The dimensions far fields are functions of disk radius (r) wavelength (A)
a piezoelectric but diverges in of the near and and ultrasound
704
R. L. MORRIS, M. B. HISTAND
1967). Rayleigh scattering occurs in all directions, and the energy loss of the beam (attenuation) is proportional to the volume of the scatterer and the fourth power of frequency (Hueter, 1955; Blitz, 1%3). Rayleigh scattering has been shown to be a valid assumption for ultrasound in blood (Reid, 1969; Fraser, 1970). Attenuation due to fractional heating also occurs. METHODS The PUDVM was evaluated to determine the relationship between sample volume and range. The gate and pulse length were held constant since they fix the sample volume length. The ultrasonic beam diameter was measured at predetermined distances in front of the piezoelectric disk. The effective diameter of the beam as a function of distance was found by mechanically scanning the transducer across the edge of a very thin magnetic tape which acts as a scattering surface. The tape moves at a constant velocity and is submerged in distilled water. The recorded velocity distribution approximates a square wave from which distinct beam boundaries can be found. A schematic of the measuring apparatus is shown in Fig. 2. The emitted frequency of the transducer was adjusted to obtain maximum returned amplitude by visualizing pulse re-
and C. W. MILLER
flections from a flat plate. The transducer was held in position by a stereotaxic transducer holder which permits four degrees of freedom with vernier scales for each degree. The transducer was positioned at an angle of 60” with respect to the edge of the moving tape (Fig. 3). The tape velocity was 50 cmlsec * 2 cm/set. Vertical movement in increments of O-125 mm provided a distinct definition of the beam edge. For a correct definition of the portion of the beam used by the PUDVM for processing (effective beam diameter), simulated acoustic attenuation was used. The attenuation was adjusted to approximate amplitudes obtained in actual blood flow studies, where natural attenuation was used. To accomplish this, the signal between the transducer and the PUDVM was electronically attenuated, holding the signal to noise ratio constant. The pulse beam was visualized by the Schlieren optical method and compared with the previous measurements. The errors introduced by averaging over the sample volume are demonstrated by velocity profile measurements in tubes. For this investigation, velocity profile measurements were made using the 1.8 and 3.0 mm dia. transducers previously studied. These measurements were performed with a gate setting of 1 or 2 psec and pulse length of 16 cycles in a straight rigid butyrate tube (11.11 mm i.d.) during steady laminar flow (Reynolds numbers 2000). The PUDVM threshold levels were set just above the noise level at a zero flow condition. The apparatus (Fig. 4) consisted of recirculating water with a 0.2 per cent suspension of silicone spheres acting as sound scatterers. Prior to experimentation, the temperature of the recir-
CONSTANT SPEED &C. MOTOR
ULTRASONIC PULSE MAGNETIC TAPE ’ i ~-TAPE
rTAPE
GUIDE
P
GUIDE
rPlEZOELECTRlC
TRANSDUCER
DISK
DISTILLED
______--_ DIRECTION
OF
VELOCITY
StAN
WATER
__-_-_-_ PULSE
TAPE
POSITION
Fig. 2. Apparatus for measurement of sample volume diameter. Beam boundaries are determined by an edge scan of a continuous loop of magnetic tape moving at a constant velocity. When the tape is within the beam boundaries, a backscattered velocity signal is recorded.
DISTRIBUTION
Fig. 4. Schematic of steady flow recirculating apparatus for water suspended silicone scattering medium. The test section of the tube in the measurement tank is submerged in distilled water to insure acoustic coupling.
PULSED
DOPPLER
BLOOD VELOCITY
culating fluid was allowed to equilibrate, minimizing any viscosity variation, and the flow rate was adjusted to insure laminar flow. Small amounts of dye were injected at the tube inlet to check the absence of turbulence. Flow collections were made several times, and a mean velocity v was calculated. jF=
Flow (Q) Cross-sectional
area (Al’
The PUDVM transducer was positioned laterally over the tube axis by maximizing the returned signal with the transducer inclined at an angle of 60” with respect to the tube axis. Velocity measurements were made by range-gating in 0.925 psec increments (- 0.7 mm in range) across the flow stream with a constant gate and pulse length. The velocity information was plotted on an X-Y plotter. The instnment output was internally calibrated by input of a signal of known frequency channeled into the zero-crossing me@. Flow collections were repeated to provide a check on V.
705
MEASUREMENT
dent on the transducer beam characteristics. The pulse length is dependent on the number of cycles emitted at a particular frequency and the Q factor of the crystal. The back-scattered signal will be a superposition of small pressure waves of various amplitudes and frequencies (Fig. 6). The composite pressure waves represent information from a known sample volume when recorded with a particular delay and gate. The size of the incident pulse is much larger than the numerous sound scatterers (5 x lo6 red blood cells/mm3). It follows that the sample volume cross-section will be defined by the maximum pulse cross-section and, therefore, will be circular for the circular transducers used.
RESULTS AND DISCUSSION
The characteristics of the PUDVM and the emitted ultrasonic beam provide the basis for sample volume analysis. The emitted pulse has been shown to be a tear-drop shape by Baker (1971) and an actual photograph is shown in Fig. 5. The pulse diameter is depen,-EMlTTED
ULTRASONIC
t=o+ p
EMlTd’
ULTRASOUND SCKC’
t-t A
B
lANsDucER
A INITIAL FRONT ( $1
PULSE
t=
WAVE FROM “n’
tLAt
t=t,
t>t,
bEAM BOUNDARY
Fig. 6. Rayleigh scattering from red blood cells illustrated as overlapping pressure waves. The actual case would involve scattering from more than 5 x 10” red blood cells within an emitted pulse. The backscattered energy received by the transducer is the sum of all the pressure waves corresponding to a particular time and location.
Fig. 7. Relationship between sampling time and sample length. For a gate setting of 2Ax/c (set) the sample volume length will be Ax (mm). At time t = 0’ the ultrasonic pulse is emitted by the piezoelectric transducer. The two scatterers are located Ax apart. At t = f,+ scatterer A begins to scatter the ultrasound in all directions. I, represents the initial scattered wave front from A. IA and the ultrasonic pulse will reach point B simultaneously and IA will also be Ax from point A toward the transducer. Is will originate when I, (toward the transducer) is 2Ax from point B.
706
R. L. MORRIS, M. B. HISTAND SCATTERERS-ABC 9 I , DE t 1F ---_
BOUNDARIES
WAVE
SAMPLE VOLUME SURFACE SHAPES
FRONT
END
kAMPLE VOLUME LONGITUDINAL CROSS SECTION
Fig. 8. Sample volume end surface shapes. Considering one pulse, initial wave fronts from points A, B, and C, fixed with respect to the conducting medium, combine to produce the plane wave front indicated, A short time later additional backscattered ultrasound from D, E and F will also superpose with this returning wave front. Therefore, for any instant in time the backscattered ultrasound arriving at the piezoelectric transducer will contain information from a small volume bounded, for example, by the scatterine noints A. B. C. D. E and F’. The shaue of this small voru-me is die to the ‘pulse shape and velocity of conduction in medium. In a similar fashion a combined wave front is formed from points G, H, I, J, K and L. Therefore, for a finite gate length, the sample volume end surface shapes are defined by the points D, E, F and G, H, I.
The length of the sample volume is determined by the time the gate is open (At) and the length of the emitted pulse (R). The effects of the gate and pulse length on the sample volume length are illustrated in Figs. 7 and 8. To determine the effect of the gate length on the sample volume length, consider an infinitely small pulse transmitted through the flow stream and the backscattered information recorded with a finite gate length (At = 1 psec). During 1 p set sound travels - l-5 mm in water or tissue. However to convert a 1 psec gate
and C. W. MILLER
time to sample length, account must be made for the additional time it takes for the incident pulse to be scattered at the far end of the sample volume and return. This implies that the gate time is actually twice the sample volume length; therefore, the 1 Fsec gate corresponds to 0.75 mm sample volume length (Fig. 7). Generally, the gate contribution to sample volume length is l,= cAtI2. The effect of the pulse length is found by considering a finite pulse length (PI) and an infinitesimally small gate time. In this case the combined wave front of backscattered ultrasound at any one point and time on the pulse beam axis will include backscattered information over a sample length (1,) of CR /2. A/2 is the time (distance of CR/~) it takes for backscattered ultrasound to travel from the leading edge of the incident pulse to the trailing edge; and, therefore, information from other scatterers in that interval is superposed. Combining the equations, the sample volume length is then the sum of the two components: l,, = lP+ I, = c(P, +At)/2. The sample volume shape for a gate = 0 will be the same shape as the incident pulse except with a length of 4(cpI). The actual sample volume shape for a finite gate will resemble a cylinder in the near field or a cone frustrum in the far field. The proximal and distal ends of the sample volume will retain the incident pulse shape as in the gate =0 case (Fig. 8). It should also be clear that the total scattered ultrasonic energy will be greater from the beam axis than the beam boundaries due to the incident pulse shape. The velocity profiles obtained from edge scans of the moving tape have steep slopes at the extremes indicating a distinct beam boundary. A typical edge scan velocity distribution is shown in Fig. 9. Figure 10 is a composite of results of effective beam diameter variations as a function of range for the four transducers tested. Theoretical predictions of the near and far fields are indicated. The measured beam is the portion of the beam above the threshold level of the PUDVM. The measured beams are narrower due to the effects of attenuation
(Facing p.
Fig. 5. A photograph of a reflected ultrasound pulse recorded on a high frequency oscilloscope. I.8 mm, frequency = 7.45 MHz, pulse duration of 16 cycles.
Transducer diameter =
Fig. 11. Schlieren photograph of an ultrasound beam from a transducer visualized in a 4 in. Schlieren optical system.
PULSED
DOPPLER
BLOOD
RANGE= IO mm TAPE vELOCITY=53*2&
VELOCITY
MEASUREMENT -BEAM
--
707 MEWJREMENTbYJRVE FIT) PREDICTION
-THEORETICAL
60r
5“1 0’.
-1.5
L2.03mm.J.
y
40
VERTICAL
-.5 POSITION
I
0 FROM
.5 TAPE
11
,
b
1.5
PLANE(mm)
Fig. 9. Typical sample volume diameter data. The beam boundaries are defined by the transducer position when the moving tape velocity is detected. The velocity profile shapes were extrapolated to determine the zero velocity intersections which were assumed to be the beam boundaries.
causing returned signals below the PUDVM threshold. The Schlieren photographs (Fig. 11) showed good correlation with the measured diameters. To minimize the dispersion error the beam boundaries were approximated by a curve fit prior to calculation of the crosssectional area. The calculated results are shown in Fig. 12. The sample volume is the product of the measured beam area and the sample length. The measurements from two l-8 mm dia. transducers show very close agreement. Figure 12 indicates that the larger the diameter of the piezoelectric disk the longer the near field length and the greater the sample volumes in the near field. The 3-O mm transducer data illustrates that higher frequency ultrasound implies longer near fields and smaller sample volumes, in agreement with theory. Further reduction in beam cross-sectional area can be accomplished by the use of acoustic lenses for beam focusing, although beyond the point of focus, resolution would suffer. The results of the tube flow measurements were compared with the theoretical velocity
Fig. 10. Beam diameter variation with range. The solid lines are the measured ultrasonic beam boundaries resulting from a curve fit of the data points taken at various ranges. The dashed lines represent the theoretical prediction of the beam for a particular transducer diameter and frequency. The region between the measured and theoretical beam is the portion of the beam where the backscattered amplitude or frequency is below the PUDVM threshold levels..
profile in a rigid tube assuming steady laminar flow. The velocity distribution is therefore parabolic: V(r) = V,,,(l-
r2/R02)
where r is the radial position of the velocity measured from the tube longitudinal axis, R. is the tube radius, and V,,,,, is the centerline velocity in the tube (V,,, = 2 V). In the figures the velocities were normalized with respect to V..__^ rn”“.The velocitv . nrofiles measured for the 1
708
R. L. MORRIS, M. B. HISTAND
1.9-~~~~7.4
B
2.6---7.6 -..
5
16r
ti
01 0
3.0----713 3.Q-----7.9
.‘/
I
5
IO RANGE
15
20
25
(mm)
Fig. 12. The sample volume will be the product of the sample volume cross sectional area (above) and the sample length which is fixed by the gate setting of the PUDVM. A 1 psec gate setting will give sample lengths of 0.75 mm and 2 ysec of 1.5 mm.
3-O mm transducer with gate settings of 1 and 2 psec are shown in Fig. 13 along with the known velocity profile for a steady laminar flow. These data show good correlation with the actual profile except at the walls. The profile measured with a gate setting of 1 psec is more accurate than the profile measured %=5.55mm V,,,&36.2 cmhec o GATE= I p see B GATP2paec
I
NEAR WALL
R/R., J %xL
Fig. 13. Steady flow tube velocity profile data measured with the 3.0 mm dia. transducer.
and C. W. MILLER
with a gate of 2 psec at the near wall, due to the smaller sample volume. At the far wall both profiles differ from the actual profile with a gradual taper to zero velocity. This effect is due to the sample volume size and its increase with distance as the following analysis illustrates. A digital computer simulation of blood velocity profile measurements in tubes was developed. Each sample volume was divided into 250 equal volume increments. The average velocity at each incremental volume was calculated, and the 250 samples were then averaged over the sample volume to give a predicted PUDVM velocity measurement. Using greater than 250 incremental volumes does not increase the accuracy significantly. The simulation assumed that each incremental volume of scatterers had equal incident and scattered energy. Weighing factors can be incorporated to account for pulse shape and intensity distribution, once these factors are accurately determined. This simulation was used to predict a steady laminar flow velocity profile in a tube. The simulation assumed the beam divergence characteristics previously determined for the 1G3mm transducer, a transducer angle of 60”, a parabolic velocity profile in the tube, and a cylindrical sample volume shape in the near field and a frustrum of a cone in the far field. The effects of the velocity variation in three dimensions across the sample volume, due to its finite size, were taken into consideration. The result of this analysis was a prediction of the measured velocity profile with the 1.8 mm dia. transducer (gate = 2 psec, pulse length = 16 cycles, f. = 7.5 MHz). These data are presented in Fig. 14, together with an actual velocity profile measured with the PUDVM (same gate, A, and fO) and the parabolic profile. The predicted profile illustrates the wall effect observed in the 3-O mm transducer profiles and is due to the finite size of the sample volume and the beam divergence characteristics in the far field. The magnitude of the measured velocity profile is 2 per cent smaller
PULSED
DOPPLER
BLOOD VELOCITY
%=5.55 mm V,,=35Acdsec A GATE = 2 LLsec
.B
v
.6
V max A
I
NiAR WALL
R/R.
I FhR WALL
Fig. 14. Steady flow tube velocity profiles predicted by sample volume analysis and measured with the 1.8 mm diameter transducer with a gate setting of 2 gsec.
than the predicted profile at the centerline. This discrepancy is possibly due to the assumption of a flat ended sample volume for the analytical model or a slight transducer inclination angle error. A one degree error is equal to a 4 per cent velocity error at an inclination angle of 60” (Gill, 1972). Comparisons of the velocity profiles measured using the 1.8 and 3.0 mm dia. transducers with the theoretical profile indicate that the 3-O mm transducer is approximately 5 per cent more accurate at the tube centerline and far wall. However, the 1-8 mm transducer allows more accuracy at the near wall since the beam diameter is 30 per cent smaller at that location. The 3.0 mm transducer offers the least variation in sample volume for a tube dia. of 11 mm and, therefore, would produce a more accurate measurement.
predict the actual beam characteristics; however, they do not correspond exactly to the portion of the backscattered beam detected by the PUDVM. The trigger threshold levels are crucial in determining the portion of the beam being detected. Each transducer must be tested with a particular PUDVM to determine sample volumes and divergence characteristics. This information will define the resolution for a particular application of the PUDVM. Without this information, unsymmetrical, skewed, or magnitude errors in velocity profiles could be misinterpreted. A knowledge of the sample volume variation as a function of range for various sizes and types of transducers (Fig. 12) will aid in proper transducer selection. The sample volume shape has been shown to approximate a cylinder in the near field and a frustrum of a cone in the far field. The surface proximal to the transducer is due to the pulse trailing shape and the far surfaces is due to the pulse leading surface shape. The length of the sample volume is determined by the gate and the pulse length. The attainable resolution of the current instrumentation provides a sample volume of 2.3 mm3 or larger, depending on the pulse length, gate duration, and beam characteristics. Present indications are that velocity disturbances or skewed velocity profiles caused by protuberances such as atherosclerotic plaques may be detected in arteries noninvasively. Velocity contours could be mapped along a vessel, thereby allowing determination of plaque locations and thicknesses. Additional applications of the PUDVM in transmural and transcutaneous measurement of hemodynamics in investigative and diagnostic medicine also exist.
SUMMARY AND CONCLUSIONS
The preceeding analysis and experimental results clearly show the variation of sample volume due to transducer design parameters is an essential factor to know prior to making measurements with a PUDVM. Theory can
709
MEASUREMENT
NOMENCLATURE Z
acoustic impedance (g cm’/sec) P density of a medium (g/cm’) velocity of ultrasound (mm/set) ; relative velocity (cmlsec) Af Doppler frequency shift (Hz) f0 transmitted ultrasound frequency
(Hz)
710
R. L. MORRIS. M. B. HISTAND
e angle between velocity vector and axis of sound beam (degrees) A1 amplitude of undriven vibration maximum (V) Al succeeding undriven amplitude maximum (V) Q factor quality factor (transducer internal damping, nondimensional) X0 near field length (mm) radius of circular transducer (mm) : wave length of transmitted ultrasound (mm) @ half angle of beam divergence (degrees) Reynolds Number vd/v (nondimensional) kinematic viscosity (cm*/sec) ; mean velocity (cm/set) tube dia. (cm) : flow (mm’lsec) A cross-sectional area (mm’) V(r) velocity at position r from the tube axis (cmlsec) tube centerline velocity (cm/set) VRCI tube radius (mm) I.4 initial pressure wave front from point A backscattered toward the transducer Z, initial pressure wave front from point B backscattered toward the transducer 1, sample volume length component due to the gate (mm) 1, sample voIume length component due to the pulse length (mm) 1 total sample length (mm) r;; gate length (set) PI pulse length (see). REFERENCES Baker, D. W. and Stegell, H. F. (1964) A sonic transcutaneous blood flowmeter. Proc. 17th Ann. Conf. Engr. Med. Biol,, p. 76. Baker, D. W. (1970) Pulsed ultrasonic Doppler blood-flow sensing. IEEE Trans. on Sonics and Ultrasonics. SU-17; 3, 170-182. Baker, D. W., Jorgensen, J. E. and Campau, D. N. (1971) The characteristics of the pulsed ultrasonic Doppler flowmeter. Symposium on Flow, Pittsburgh. Bergel, D. (1968) The bristle flowmeter. New Findings in Blood Flowmetry, (Edited by Cappelen, Chr., Jr.), p. 22. AAS & WAHLS Boktrykkeri, Oslo. Blitz, J. (1963) Fundamentals of Ultrasonics, pp. 9; 152. Butterworth, London. Carlin, B. (1969) Ultrasonics, p. 64. McGraw-Hill, New York. Denison, A. B., Jr., Spencer, M. P. and Green, H. D. (195.5) A square wave electromagnetic flowmeter for application to intact blood vessels. Circ. Res. 3.39-46. Fraser, M. P. (1970) Transcutaneous spectral bloodflowmeter. Technical Note 1970-7, Lincoln Laboratory, Mass. Inst. Tech., Lexington, Mass. Gabe, I. T., Gault, J. H., Ross, J., Jr., Mason, D. T., Mills, D. J., Schillingford, J. P. and Braunwald, E. (1969) Measurement of instantaneous blood flow velocity and
and C. W. MILLER
pressure in conscious man with a catheter-tip velocity probe. Circulation 40, 603-614. Gill, R. W. and Meindl, J. D. (1972) Optimal design of the pulsed Doppler ultrasonic flowmeter. Proc. 25th Ann. Conf. Engr. Med. Biol.. D. 34. Bal Harbour. FLa. Histaid, My B., Miller, d. -W. and Mcieod, fi. D. (1973) The Transcutaneous measurement of blood velocity profiles and flow. Cardiovasc. Res. (in press). Hueter, T. F. and Bolt, R. H. (1955) Sonics, pp. 63-72. Wiley, New York. Leraand, S. (1968) Thermal flowmeters. New Findings in Blood Flowmetry. (Edited by Cappelen, Chr., Jr.), pp. 15-17. AAS & WAHLS Boktrykkeri, Oslo. Ling, S. C., Atabek, H. B. and Carmody, J. J. (1970) Pulsatile flows in arteries. Znt. Appl. Mech. Conf. Lloyd, E. A. (1967) Energy measurement. Ultrasonic Techniques in Biology and Medicine. (Edited by Brown, B. and Gordon, D.), p. 52. Thomas, Springfield, Ill. McLeod, F. D., Jr. (1967) A directional Doppler flowmeter. DiPest 7th Zntl. Conf. Med. Biol. Enar. (Edited bv Jacobson, Bertil), pp. 13-14, Stockholm._ McLeod, F. D. and Anliker, M. (1971) A multiple gate pulse Doppler flowmeter. IEEE Ultrasonics Symposium, p. 51. Miami. Miller, C. W., Nealeigh, R. C. and Histand, M. B. (1972) The effect of arterial location upon arterial velocity distributions. Proc. 9th Ann. Rocky Mtn. Bioengineering Symposium, pp. 129-132. Mills, C. J. and Shillingford, J. P. (1967) A catheter tip electromagnetic velocity probe and its evaluation. Cardiovasc. Res. 1, 263-273. Mills, C. J. (1963) A catheter tip electromagnetic velocity probe. Phys. Med. Biol. II, 323-324. Peronneau, P. A. and Leger, F. (1969) Doppler ultrasonic pulsed blood flowmeter. 8th Zntl. Conf. Med. Biol. Engr. pp. 10-11. Chicago. Peronneau, P., Hinglais, J., Pellet, M. and Leger, F. (1970) Velocimetre sanguin par effet Doppler a emission ultrasonore pulsee. L’Onde Electrique 50, 3-23. Peronneau, P. A., Pellet, M. M., Xhaard, M. C. and Hinglais, J. R. (1971) Pulsed Doppler ultrasonic blood flowmeter real-time instaneaneous velocity profiles. Symposium on Flow, Pittsburgh. Reid. J. M.. Siaelmann. R. A.. Nasser, M. G. and Baker, D. WI (1969) Tie scattering of ultrasound by human blood. 8th Zntl. Conf. Med. Biol. Engr. pp. 10-17. Chicago. Satomura, S. and Kaneko, Z. (1960) Ultrasound blood rheograph. Report of 3rd Znt. Conf. Med. Elect., pp. 254-258. London. Schneider, H., Wieberdink, J. and Reneman, R. S. (1968) Physical aspects of electromagnetic flowmetry. New Findings in Blood Flowmetry. (Edited by Cappelen, Chr., Jr.), pp. 32-35. AAS & WAHLS Boktrykkeri, Oslo. Strandness, D. E., Jr., Schultz, R. D., Sumner, D. S. and Rushmer, R. F. (1967) Ultrasonic flow detection. A useful technique in the evaluation of peiipheral vascular disease. Am. J. Slrrg. 113, 311-320. Viktorov, I. A. (1967) Rayleigh and Lamb Waves, pp. 63-64. Plenum Press, New York. Wells, P. N. T. (1969) A ranged-gated ultrasonic Doppler System. Med. Biol. Engr. 7, 641-652.