478

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-24, NO. 5, SEPTEMBER 1977

-Communications Transducer

Geometrical Spectrum Broadening in Ultrasonic Doppler Systems VERNON L. NEWHOUSE, L. WILLIAM VARNER, AND PHILLIP J. BENDICK Abstract-The bandwidth of the output spectrum of blood flow meters may prove of value in estimating flow parameters such as the degree of turbulence. It is therefore important to determine the various factors which affect this bandwidth. It is shown that scatterers moving in the near field of the sound beam generated by a single transducer ultrasound Doppler system produce a spectrum whose breadth is primarily determined by the range of angles over which backscattered ultrasound is received by the transducer. An empirical method of calculating the bandwidth of the output spectrum is described, and the results are compared with direct Doppler measurements. Since the spectrum broadening depends on the angle between the target path and the ultrasound beam, it is suggested that the phenomenon may be usable to provide an independent measure of this angle.

INTRODUCTION Under various conditions the bandwidth of the output spectrum of Doppler flow measurement systems can be used to estimate various important flow parameters such as maximum flow velocity [11, turbulence [2], or the angle 0 between flow direction and the ultrasound beam [31]. In view of the information which may be obtained from the Doppler spectrum bandwidth it is clearly important to determine the factors which produce broadening of this spectrum. In previous work attention has been concentrated on spectral broadening caused by the transit time of ultrasound scatterers moving through the ultrasound beam [4, 51. These effects become progressively more important the larger the distance between the transducer and the flow being measured. In the present work a thread moving in the near field of an unfocused transducer was used to simulate uniform velocity flow of random scatterers carried by a liquid. It is shown that under these circumstances Doppler output spectrum broadening is due mainly to the range of angles over which ultrasound is backscattered to the transducer. The effect of this phenomenon on the output spectrum will be called "geometrical broadening". For flow measurement in the near field, this geometrical broadening effect is found to be much stronger than the transit time effects investigated previously. It is also shown that the spectral bandwidth due to geometrical broadening varies strongly with 0, and that its dependence on 0 is different from that of the Doppler frequency, defined in the usual way as that frequency at which the Doppler output spectrum has its peak energy.

SPECTRAL BROADENING MECHANISMS The bandwidth of the Doppler spectrum is affected by a number of mechanisms. Spectral broadening due to Brownian Manuscript received March 1, 1976; revised September 13, 1976. This work was supported by the National Science Foundation. V. L. Newhouse is with the School of Electrical Engineering, Purdue University, West Lafayette, IN 47907. L. W. Varner was with the School of Electrical Engineering, Purdue University, West Lafayette, IN 47907. He is now with Electromagnetic Systems Laboratories, Vienna, VA 22180. P. J. Bendick was with the School of Electrical Engineering, Purdue University, West Lafayette, IN 47907. He is now with Wishard Memorial Hospital, Indianapolis, IN 46202.

r Path

Ultrasound Beam Edges Fig. L. Model for geometric broadening in near field.

motion has been shown to be negligible for random scatterers such as blood cells [6] . Spatial or temporal velocity gradients will also cause spectral broadening. For a single constant velocity flow stream such as a jet, no broadening arises from these factors. The effect of velocity gradients can also be made negligible by a suitable choice of geometry, such as by arranging for the Doppler system range cell to be much smaller than the vessel diameter. (The range cell is here defined as that region of the beam from which echoes originate which are coherent with the Doppler reference signal.) Spectral broadening can occur due to the finite transit time of the scatterers passing through the range cell. If these flow sufficiently parallel to the ultrasound beam so that their transit time through the range cell is determined by those boundaries of the range cell which are normal to the beam axis, then the Doppler output spectrum bandwidth has been shown to be proportional to that of the transmitted spectrum [ 5] . However if the flow is at a sufficiently large angle to the beam and if the extent of the range cell along the beam is sufficiently long, the scatterer transit time through the range cell is determined by the beam edges. In that case it has been calculated [7] that the Doppler output bandwidth will be the inverse of the scatterer transit time, given by 2v sin 0 B

(1)

w

where w is the effective beam width. In the derivation of the above result it was assumed that the scatterers are Poisson distributed in space and that rays leaving and being reflected to the transducer do so over a very small range of angles. For an ultrasound beam width of 1 cm with a transmitted center frequency of 5 MHz, eq. (1) predicts a Doppler bandwidth much smaller than is actually observed when the flow being measured is in the near field of the transducer. This indicates that the transit time effect is not the predominant broadening factor under these circumstances. GEOMETRICAL BROADENING

This phenomenon may be understood from the simplified two dimensional near-field representation shown in Fig. 1. We will compute the order of magnitude of this effect by making the following simplifying assumptions: a. The intensity of the sound beam emitted by the transducer falls abruptly to zero outside the beam boundaries shown in the figure.

479

COMMUNICATIONS

o

EXPERIMENTAL DATA,i930°

+

EXPERIMENTAL DATA,9=60

angle 0 with the ultrasound beam. Also, Bg is directly portional to the transmitted frequency. Finally, Bg function of range r from transducer to target path. range dependence may be easily seen by noting from 1 that 01 and 02 decrease with increasing range.

EXPERIMENTAL DATA,8-45°

prois a This Fig.

EXPERIMENTAL RESULTS

For examining the effects of geometrical broadening on - CALCULATED VALUES the Doppler spectrum experimentally, it is desirable to miniRANGE 3cm mize the effect of fluid velocity gradients within the range cell. This was achieved by observing the Doppler spectrum produced by a nylon thread moving at constant velocity in water. The irregularities on the thread surface provide a good simulation of fluid suspended scatterers, and the motion of ex 30, the thread simulates uniform velocity flow. Specifically, the frequency of the peak energy density of the output spectrum is found to be proportional to v c os 0 as predicted by the conventional Doppler equation. Here v stands for the thread velocity and 0 for the angle between the thread and the ultrasound beam. To calculate the degree of geometrical spectrum broadening, a semi-empirical procedure was used, which takes transducer directivity into account. In this technique a small lead sphere of 3.2 mm diameter was fastened to the same thread that was used for the flow simulation, and was then slowly moved through the ultrasound beam at some angle 0 to its axis. The angles As and 02 shown in Fig. I were then measured experimentally, being taken as those angles for which the transducer just received detectable echoes from the lead sphere. Thus for a given 0 and r defined as in Fig. 1, the geometrical broadening contribution to the Doppler .1 .2 .3 .4 .5 .6 .7 .8 .9 bandwidth could be calculated using eq. (2). The Doppler spectrum bandwidths calculated- with this -VELOCITY, m/sec empirical spectrum estimation technique are shown as solid Fig. 2. Doppler bandwidth as a function of velocity. lines in Fig. 2 for comparison with spectrum bandwidths measured directly, using the moving thread. The transmitted b. All rays emitted by the transducer are parallel to the center frequency fo and the transducer diameter were 5 MHz and 1.2 cm respectively, and the range r of the thread was 3 beam boundaries. cm, placing it well within the near field of the transducer. Also c. The directivity of the transducer may be taken into account by assuming the maximum angular spread of received shown are calculations of the transit time spectral broadening ultrasound to which the transducer is sensitive to occur when using eq. (1). It can be seen that this effect is negligibly small compared to the geometrical broadening. The scatter in the a ray is transmitted along a beam edge and received at the data points is accounted for by two sources of experimental midpoint of the transducer face. With these assumptions we may establish upper and lower error: there may be as much as a 1 0% error in the determinalimits on the range of Doppler frequencies received by the tion of bandwidth from spectrum analyzer photographs; and there may also be a 10% error in the previously described transducer as follows: spectral estimation technique. In addition, the data were taken over a period of several days-data for a single day Upper limit: fd (upper) = - [cos 0 + cos (0 k2 )I show much less variation. Inspection of the figure shows that the theoretical prediction lines lie approximately 15% vf0 above lines fitted to the data points. This discrepancy seems [cos 0 + Cos (6+ )J. Lower limit: fd (lower) = acceptable in view of the assumptions made in the development of the theoretical model. The data clearly lend strong Thus the Doppler bandwidth due to geometric effects may be support to our explanation of the observed spectral broadening defined to be the difference between the upper and lower in the near field. limits, or Figure 3 shows a verification of the prediction that Bg decrease with increasing range. The aforementioned should Bg fd (upper) fd (lower) sources of error explain the discrepancy between experimental and calculated values. vf0 (2) The equations for both geometrical and transit time broaden--[Cos (0 - 02) - COS( + 01 ing predict a maximum effect at 0 = 900. This has been where fo is the transmitted center frequency and c is the observed experimentally, suggesting a technique for flow measurement at right angles, which has long been a problem speed of sound. Although eq. (2) is based on somewhat simplified assump- due to the zero Doppler center frequency produced under these tions, its behavior serves to qualitatively account for the circumstances. experimental results observed. First, Bg does not vary with DISCUSSION 0 in the same manner as does the Doppler output spectrum Simulated Doppler flow measurements using a moving thread. center frequency. Thus by measuring the bandwidth and center frequency of this spectrum, it may be possible to have been presented and analyzed, demonstrating "geometrical" independently estimate both the flow velocity v and its spectrum broadening which is much larger than that due to -

a

a

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-24, NO. 5, SEPTEMBER 1977

480

[5] Newhouse, V. L., P. J. Bendick and L. W. Varner, "Analysis of Transit Time Effects on Doppler Flow Measurement," IEEE Trans. Biomed. Eng., Vol. BME-23, pp. 381-387, Sept. 1976. Green, P. S., "Spectral Broadening of Acoustic Reverberation in Doppler-Shift Fluid Flowmeters," Jour. Acoust. Soc. Am., 36, No. 7, pp. 1383-1390, 1964.

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"Transit Time Broadening in Ultrasonic Doppler

L.,

Flow Measurement Systems," Internal Report, Purdue University, Nov. 1973.

2000 I 1800

An Inexpensive Modular Pulse Generating System

F 1600 3 1400

JOHN NOLTE AND THEODORE J. TARBY

z

Il

1200

Abstract-A multiple channel pulse generator is described, consisting of a clock module and several identical output modules. Clock frequency can be varied continuously from 0.003 Hz to 100 Hz. Output pulses have continuously variable duration, can be positioned anywhere within the timing cycle, and their amplitude is variable from +5 to -5 V.

1000

800 600

400 200 0_

1

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It is frequently necessary in biological and other experiments to program sequences of events, such as oscilloscope sweeps and various stimuli. The apparatus called for must allow for repetition of the sequence at some selectable frequency, as well as allowing the experimenter to vary the relative positions

6

-RANGE, cm Fig. 3. Doppler bandwidth

f

as a function of

of the events within the

range.

transit time effects. Rough calculations in(dicate that this geometrical broadening will always dominate a for targets in the near field of the transducer. However, ince geometrical idening due to broadening decreases with range and transit time effects is independent of range as long as the )ossible to find beam width remains constant, it may This was conditions where the two effects are compar ffith and Brody probably the case for the experiments in which only transit time effects were consider red [4]. As pointed out above, geometrical broa(dening may be usable as a means of estimating the beltween the ultraa technique for sound beam and the flow direction, measuring flow at right angles to an beam. Whether or not these techniques are in fact il for real time blocity gradients pulsatile blood flow measurements whereve exist and where possibly only 20 ms are available for 1- In any event, spectrum estimation remains to be established the geometrical broadening effects described I ere will have to be taken into account in the design ins intended to measure Doppler bandwidth for the i of factors such as velocity gradient or turbulence. si

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of

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sequence.

accuracy is usually not necessary, since the events, or some

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chart recorder. We describe here

a

are

displayed

on

an

oscilloscope

simple modular system which

or

offers low

cost and maximum ease of operation. The circuits are based on the widely used type 555 timer. The master frequency control is a single potentiometer by of which the repetition rate can be varied over about five orders of magnitude. No range switches are involved, but the resolution is means

good

throughout

the

entire

range

changes logarithmically with the output channel there are single

since

the

repetition rate

control resistance. For each controls for pulse duration,

amplitude and delay (with respect to the clock pulse). A seven-channel unit is presently used in the senior author's laboratory, controlling two electromechanical shutters, two

electrode

resistance

testers,

current

injection

micropipette

through two

electrodes and a calibration pulse generator. clock output triggers the oscilloscope sweep, and seven events may be positioned at any desired

within the

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each of the temporal location

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estimatiol

ACKNOWLEDGMENT

The authors

are grateful to E. S.

Furgason

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discussions.

REFERENCES Arts, M. G. J. and J. M. J. G. Roevros, "On the Instantaneous Measurement of Blood Flow by Ultrasonic ins", Med. & Biol. XEngng., Vol. IO, pp. 23-24, 1972. 121b lbright, R. J. and J. H. Harris, "Diagnosis Urethral on B Flow [1

Mea

tvarameters Vol.

3 [4]

by Ultrasonic

BME-22,

pp.

of

Backscatter",

IEEE

7'rans.

lamed.

1-91,1975.

CLOCK CIRCUIT

Figure1 is a schematic diagram of the clock circuit, which is simplified from a previously published design (1). If greater wider range of operating frequencies temperature stability are required, the original description should be consulted. The base voltage of Q1 is fixed at 9.1 V by the1N757 zener diode. When the wiper of R3 is at the upper end of its range the emitter voltage of 1Q is Q (shorted to the base of 1), or a

fixed at some value near 9.7 V by the 1N746-ICl feedback loop. Since the emitter-base voltage of 1Q is fixed, a constant collector current flows, charging the 5 pF capacitor. Rotating

Manuscript received August 9, 1976; revised December 2, 1976. This work was supported by Grants EY 01155 (National Eye Blooa Velocity and Angle", Poc. 28th A CEMB, p. 76, Sept. 1975. Institute) and BMS75-17638 (National Science Foundation). The authors are with the Department of Anatomy, University of in UltraGriffith, J. M., and Brody, W. R., "Velocityesolution Re 1975. Colorado Medical School, Denver, CO 80262. sonic Doppler Flowmeters," Proc. 28th ACEMBI p.r- 75,Sept. I --I-

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L. W., V. L. Newhouse and P. J. Ben4lick, "Application transit Time Effects to the Independent Measurement of

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Geometrical spectrum broadening in ultrasonic Doppler systems.

478 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-24, NO. 5, SEPTEMBER 1977 -Communications Transducer Geometrical Spectrum Broadening in U...
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