Ultrasound in Med. & Biol.. Vol. 2. pp. 1-10. Pergamon Press. 1975. Printed in Great Britain.

A C C U R A C Y A N D LIMITATIONS OF THE ULTRASONIC DOPPLER BLOOD VELOCIMETER A N D ZERO CROSSING DETECTOR M. J. LUNT Department of Medical Electronics, St. Bartholomew's Hospital, London E.C. 1., England (First received 12 October 1973, and in revised .form 17 December 1974)

Abstract--The zero crossing detector processes blood velocity signals from a Doppler ultrasonic velocimeter to give an output that can be recorded on paper. Although this output gives an indication of the instantaneous velocity averaged across the vessel the system does have limitations when used for quantitative work. This paper explains the working of the zero crossing detector and illustrates how errors can arise due to changes in amplitude and frequency content of the signal. Suggestions are made for reducing the errors, and other more accurate methods of analysis are discussed. Key words: Ultrasonics, Blood flow velocity.

INTRODUCTION

The Doppler velocimeter was developed in the early 1960's (Satomura et al., 1960; Franklin et al., 1961) and by 1964 a transcutaneous version had been developed for clinical work (Baker et al., 1964). The instrument transmits a beam of ultrasound of constant frequency from a crystal and ultrasound scattered from irradiated structures is received by a second crystal adjacent to the transmitter. If the irradiated structures are moving, the frequency of the received ultrasound will be changed by an amount proportional to their velocities, (the Doppler effect). The transmitted and received frequencies are compared and an electrical signal with a frequency equal to the difference is obtained. This frequency will therefore be proportional to the velocity of the structure. If moving blood is irradiated, ultrasound will be scattered from the corpuscles and the conditions are such that the difference frequency is usually in the audible range. Most instruments have an audio output, either headphones or loudspeaker, so that the operator can hear the resulting audio tones. Many clinical uses of the velocimeter have now become routine, including the accurate measurement of blood pressure in diseased limbs (Kirby et al., 1969), the detection of deep vein thrombosis (Evans et al., 1969) and the detection of carotid artery occlusion (Muller, 1972). In all these applications however the instrument is used as a flow detector, a decrease in the pitch of the audio signal indicating a reduction in blood

velocity. In order to measure blood velocity a frequency meter is required, and nearly all commercial Doppler velocimeters use zero crossing detectors for this because they are simple and cheap. They do, however, have limitations, due mainly to the complexity of the audio signal, that make accurate blood velocity measurements hard to achieve.

A. T H E A U D I O SIGNAL

If a single moving blood corpuscle is irradiated by ultrasound, the Doppler equation

f=

2fo V cos0 ¢

will apply, where .f = frequency of audio signal .[o = frequencyoftransmitted ultrasound V cos0 = component of corpuscular velocity along the ultrasound beam c = velocity of ultrasound in blood. The audio signal obtained when a single corpuscle is irradiated would therefore be a sine wave of frequency .f In a blood vessel there are many blood cells moving at different velocities, each of which will give rise to an audio signal, and the resulting audio output will be the sum of the signals from the individual cells. This resulting output signal has variable peak height

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Fig. 3. An ideal zero crossing detector with noise on the input. The low amplitude sine wave represents noise and illustrates its effect.With signal and noise together, occasional additional pulses are emitted (e.g. the last pulse) but when the signal falls to zero, many pulses are emitted. An offset trigger level (at voltage + A) can give no pulses when the signal falls to zero, but additional pulses are still produced when signal is present (e.g. the last pulse with level + A).

B. THE ZERO CROSSING DETECTOR

The ideal zero crossing detector consists of a c o m p a r a t o r that gives an o u t p u t pulse every time the voltage of the electrical signal crosses the zero line going from negative to positive (Fig. 2). T h e o u t p u t f r o m the detector is n o r m a l l y obtained by averaging the n u m b e r of pulses over a b o u t 50 msee. This ideal zero crossing detector is unusable in practice because of electrical noise causing additional o u t p u t pulses, especially if the signal falls to zero (Fig. 3). W h e n flow is present, additional pulses are occasionally emitted resulting in an o u t p u t level that is slightly high, but when the flow falls to zero, as it can in an artery during diastole, the c o m p a r a t o r triggers off the electrical noise resulting in a very high output level when it should be zero. T h e p r o b l e m of triggering from noise can be o v e r c o m e by using an offset trigger level (Fig. 3) but additional pulses are still p r o d u c e d with signal and noise together.

Most c o m m e r c i a l zero crossing detectors use the S E T - R E S E T system (Fig. 4) which can give the correct frequency of a pure sine wave b o t h with and without noise present (Fig. 5). With a sine wave input the output is the correct frequency provided the trigger level is a b o v e the peak noise level and below the amplitude of the sine wave. This m e a n s that if the trigger level is kept constant the S E T - R E S E T system will give a constant (correct) o u t p u t over a range of signal and noise amplitudes. Summarising, the S E T - R E S E T system has the following properties provided that the input signal is a pure sine wave and that the trigger level is a b o v e the peak noise amplitude: (a) With signal plus noise, the output is proportional to the signal frequency; (b) With noise alone the output is zero; (c) T h e output is constant over a range of input amplitudes.

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The audio signal from the Doppler velocimeter is not a pure sine wave but a mixture of many frequencies, which means that the output from the zero crossing detector will depend on the amplitude of the input and also its frequency content. These will be considered in turn.

B.1 Effect of signal amplitude It has been shown that with a sine wave input the zero crossing detector is insensitive to changes in signal amplitude, but with the more complex signal from a blood vessel the number of output pulses depends on the trigger level (Fig. 6). For constant trigger level the output therefore depends on the signal amplitude and this effect has been neatly demonstrated by Flax (1973). The implications of this have been investigated by replaying a signal from a blood vessel at

different amplitudes through the zero crossing detector. Three different signals were analysed: pulsatile flow in the radial artery (recording 1, Fig. 7), pulsatile flow in the radial artery with the fist clenched to give zero diastolic flow (recording 2, Fig. 7) and steady flow from a syringe in a plastic tube (recording 3). The results showed that the way in which the number of zero crossing pulses varied with amplitude was different for each of the recordings (Fig. 8). In order to explain these results it is necessary to consider the relative amplitudes of signal, noise and trigger level of the SET-RESET system. The detailed analysis is beyond the scope of this paper, but Fig. 8 can be used to illustrate some important points. Recordings 1 and 3 have plateaux where the counts are approximately constant, hence it is possible to state a characteristic number of counts for each

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M. J. LUNT

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Fig. 7. Waveforms for the radial artery recordings. Both recordings were replayed at a mean amplitude of -40dB (see Fig. 8). Note the absence of diastolic flow in recording 2.

recording. Theoretical analysis suggests that an improvement in signal to noise ratio is required in order to obtain a plateau with recording 2. Recordings 1 and 2 were both obtained with the same equipment on the same vessel, which shows that for quantitative measurements a lower noise level is necessary if the signal at any time falls to zero but there is still a need for a more detailed study of this. Meanwhile, users of the instrument should ensure they have adequate signal to noise ratios and are obtaining signals with plateaux. Automatic gain control circuits which adjust their gain to give a constant mean output amplitude can be used but in our experience, although these circuits improve accuracy when a plateau is present, they require detailed calibration if there is no plateau.

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The zero crossing detector is sensitive to the frequency content of the signal as well as its amplitude. The frequency content can be changed by the apparatus, by electrical noise or by signals from moving structures but before these effects can be examined in detail a method for describing the frequency content must be found. Since a signal from blood consists of a continuous band of frequencies, it is meaningless to consider any particular frequency, and so it is usual to state the electrical energy contained within a narrow band of frequencies between f and f + Af. The energy will be proportional to Af, and so an energy density E(.f) can be defined such that the electrical energy between frequencies f and f + A f is E(.f)A/: The symbolism E(f) shows that E will vary as f varies, and a graph of E(.f) against f is called a frequency spectrum (Fig. 9). When a signal with frequency spectum E(f) is passed into a zero crossing detector, the zero crossing frequency N is given theoretically by r,o

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Accuracy and limitations of the ultrasonic Doppler blood velocimeter and zero crossing detector

Doppler signal. The theory is strictly only applicable to true zero crossing detectors and not to the SET-RESET system, and also requires some assumptions as to the nature of the scattering of ultrasound by blood cells. Flax et al. (1970) showed that the frequency spectrum of the audio output was consistent with the necessary assumptions, but the main point of argument is whether there is a definite phase relation between contributions from different cells. This has not yet been proved, but since the theory does seem to be a good approximation it will be used without further comment. 2a. Frequency response of the apparatus. The received signal must be processed before it reaches the zero crossing detector, and this processor will have a non-uniform frequency response. One method of measuring the response requires a radio frequency oscillator in which the output can be amplitude modulated by an audio signal controlled by a second oscillator. The transmitter in the Doppler is switched off and an amplitude modulated signal at the transmitter frequency is connected into its receiver. This generates an audio signal at the frequency of the modulating oscillator, and the frequency response of the processor can be plotted. A non-uniform response can affect the frequency spectrum of the received signal, so

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Fig. 10. Changing frequency spectrum. The upper spectrum is the undistorted signal, with zero crossing frequency shown by the thick line. If the apparatus amplifies low frequencies more than high, the spectrum is distorted (centre diagram) and the zero crossing frequency is lower. Similarly. over amplification of high frequencies gives too high an output (bottom diagram).

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Fig. 11. Effect of changing frequency spectrum. The frequency response of the Doppler was changed by introducing filters before the zero crossing detector. For each response the output against velocity curve was plotted by ejecting a known volume of blood from a syringe at constant velocity and counting the number of zero crossing pulses at each velocity.

changing the zero crossing detector output for a given blood velocity (Fig. 10). The effect of altering the response can be investigated by introducing filters between the audio output of the Doppler and the input to the zero crossing detector (Fig. 11). The ideal frequency response is one that does not affect the signal but reduces noise to a minimum: that is a high frequency cut just above the maximum frequency in the signal. In practice a low frequency cut is also required to reduce the effects of vessel wall movement. The optimum frequency response has been discussed by Flax et aL (1973). 2b. Vessel wall movement. The wall of a blood vessel moves out during systole and returns during diastole, and this will produce a Doppler shifted reflection. Carotid artery wall velocities can be five millimetres per second during systole giving a Doppler frequency shift of about 70 Hz at normal incidence with a l0 MHz transmitter. The reflection from the vessel wall will be of high amplitude, and this will reduce the measured zero crossing frequency (Fig. 12). Zero crossing detectors usually incorporate filters with low frequency cuts to reduce the amplitude of the wall movement signals while only affecting the lower frequencies in the signal from the blood. In our analyser this filter is effective in removing the diastolic wall movements, but the higher velocity systolic movements still distort the trace (Fig. 12). The artifact can be heard in the

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headphones as a pre-systolic "thump" which can often be reduced by slight probe movement. 2c. Blood flow profile in the vessel. Because the zero crossing detector measures the root mean square frequency and not the mean, a change in flow profile will affect the output from the detector even if the mean velocity remains constant. For steady flow in a rigid tube, theory shows that the flow profile is parabolic (i.e. a graph of fluid velocity against distance from the centre of the vessel is a parabola). Pulsatile pressure in the body causes the flow profile to be

non-parabolic, and in the great arteries it can become flat with all the blood moving at the same velocity (Schultz et al., 1969). Very asymmetric and peaky profiles can be expected close to bifurcations and just distal to stenoses. For each of the various flow profiles, the number of cells travelling in each velocity range can be calculated assuming that the cells are evenly distributed across the vessel. Thus the expected Doppler shift frequency spectrum can be derived provided that each cell scatters the same amount of ultrasonic energy. From this

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Fig. 13. Effect of changing flow profile. For parabolic profile the theoretical zero crossing is proportional to 1.16 times the mean velocity while for fiat profile the frequency is proportional to the mean velocity. Hence, a change in profile can alter the zero crossing frequency by 16 per cent while the mean velocity remains constant.

Accuracy and limitations of the ultrasonic Doppler blood velocimeter and zero crossing detector

spectrum the mean frequency and the theoretical zero crossing frequency can be calculated and compared (Fig. 13). With a flat profile the zero crossing frequency (f=c) is equal to the mean frequency (f), with a parabolic profile f=c increases to 1.16f and with the more peaky profiles found near stenoses f=c can increase still further. Hence, even well away from bifurcations or stenoses, if the mean velocity of blood in a vessel remains constant the output from the zero crossing detector can theoretically change by 16 per cent due to changes in flow profiles. The flow profile can be determined by frequency analysing the Doppler shift signal (Woodcock et al., 1972). Since the profile depends on the pulsatility of the flow it may be possible to use frequency analysis to derive correction factors based on the ratio of systolic to diastolic velocity. The simpler zero crossing detector could then be used routinely and the output corrected with these factors. 2d. Not irradiating the whole vessel. If there is parabolic flow in the vessel and the ultrasonic beam does not irradiate the whole vessel, then the zero crossing frequency will change as the beam scans across the vessel. Assuming that there is parabolic flow, that the ultrasonic intensity is uniform across the beam, and that transmitter and receiver have the same geometry, the theoretical zero crossing frequency can be calculated for different probe positions (Fig. 14).

7

Experimental results support the theory and show a decrease in zero crossing frequency as the beam gets close to the edge of the vessel (Fig. 15). The error can be reduced by always listening for the strongest signal while positioning the probe and this will be done automatically by most operators. In addition a wide beam has the advantage of covering the whole vessel with a more uniform ultrasonic intensity than a narrow beam. Thus all moving cells are irradiated with similar energy and the central, fast moving cells do not dominate the result. In practice the beam should be wide enough if the crystal is at least as wide as the expected diameter of the vessel. With rectangular crystals the beam width across the vessel will depend on the orientation of the probe and should be as wide as possible without picking up neighbouring vessels. 2e. Mixed arterial and venous signals. Veins and arteries often run close together and it is possible to obtain combined venous and arterial signals (Gosling et al., 1969). The effect of unwanted venous signals is to reduce the measured arterial velocity, since the venous signals are generally lower frequency than the arterial (Fig. 16). A directional Doppler can indicate reverse flow due to a vein and warn the operator that he has a mixed signal, but the only method that can be used quantitatively in this situation is frequency analysis (Light, 1974; Coghlan, 1973). C. THE DIRECTIONAL ZERO CROSSING ANALYSER

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Fig. 14. Effect of not irradiating the whole vessel. Assuming a beam width equal to the vessel radius and parabolic flow, the frequency spectrum (right) can be calculated for different beam positions (left). The boM lines indicate the zero crossing frequency for each spectrum. Note how the theoretical zero crossing frequency decreases as the beam moves from the

centre of the vessel.

So far very little mention has been made of directional Doppler instruments but they are coming to be regarded as essential for any research project. The zero crossing analyser has been adapted by McLeod (1967) to detect the direction of flow, but the method as used in most commercial instruments does have some fundamental limitations. The McLeod system generates two audio signals (A and B), identical except that if flow is towards the probe signal A leads B in phase, and if flow is away from the probe B leads A. There is azero crossing detector for each channel, consisting of Schmidt triggers which are the basis of the SET-RESET system outlined above. When the signal passes level + X going from below the Schmidt trigger output goes up and returns only when the signal crosses level - X going from above. These Schmidt triggers feed pulse generating circuits, and the pulse generator in channel A gives out a pulse whenever Schmidt A goes from negative to positive provided that. Schmidt B is negative at the time. Similarly, generator B only gives pulses

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when Schmidt A is negative and Schmidt B goes from negative to positive (Fig. 17). C.1 Effect of signal amplitude In order to register the direction of flow correctly, this system has to be carefully set up, and in particular the two zero crossing detectors must be set at the same trigger levels. When different, variation in the peak height in the signal can cause misrepresentation of flow direction (Fig. 18). C.2 Effect of mixed signals The directional Doppler will also be inaccurate when both directions of flow are simultaneously present. The situation can be illustrated more easily by examples than by theoretical analysis. The directional Doppler

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measures the same number of zero crossings as the non-directional Doppler but it distributes the pulses between the two channels, and the ratio of pulses in the channels is roughly the same as the ratio of the velocities in the two directions. With mixed arterial and venous signals the total number of zero crossings is less than the true number for the arterial flow (Fig. 16). The directional Doppler will distribute these pulses between the two channels giving even fewer to the arterial one, so although the ratios may be correct, the actual zero crossing frequencies for the channels will be reduced. The McLeod system is very useful because it indicates if forward and reverse flow are both present and so

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Fig. 17. The directional zero crossing analyser. The McLeod system is illustrated with a sine wave input, channel A leading channel B in phase. When Schmidt A goes positive, Schmidt B is negative, and so an output pulse is produced from channel A. When B goes positive A is already positive and so there are no output pulses from channel B.

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Fig. 18. The directional system when set up incorrectly. The signal here changes amplitude, and the trigger level in A is greater than in B. Although signal A leads signal B in phase, the second peak does not reach the trigger level of A and so when signal B reaches trigger level B Schmidt A is still negative, and an output pulse is produced from channel B. Since channel A leads B in phase, the output should be restricted to channel A. The error can be eliminated by setting both trigger levels the same.

enables the operator to eliminate the unwanted signal, but it should not be used quantitatively when flows in both directions are simultaneously present. D. ALTERNATIVE METHODS OF ANALYSIS

The zero crossing detector obviously has fundamental limitations when used with the Doppler velocimeter and at least three other methods of analysis are used. Light e t al. (1974) use 18 bandpass filters to split the audio signal into its component frequencies, and the output is displayed using a special recorder. This system was originally developed for monitoring aortic blood velocity, and works very well in the presence of noise since the final separation of signal and noise is performed by eye from the trace. This on-line system is directional and not only indicates when bidirectional flow is present but separates the two signals and displays them both. Since all the information in the audio signal is displayed, wall movement artefact and unwanted signal from neighbouring vessels can be identified on the trace. Disadvantages are that the instrumentation is complex, it needs a special recorder, and it is difficult to analyse the trace automatically. Coghlan et al. (1973) have developed a more sophisticated spectrum analyser which gives a display similar to that of the commercially available spectrograph (Kay Elemetrics CorU . M . B . Vol. 2 NO. 1 B

poration) with the major advantage that their system works on line whereas the Kay instrument takes approx. 1 min to analyse 3 sec of record. Coghlan's analyser gives a similar output to Light's but with a finer frequency separation, and so has the same advantages and disadvantages. These two systems display audio signal information, giving the maximum instantaneous velocity, but so far do not attempt to measure the instantaneous velocity averaged across the vessel. The system developed by Arts e t al. (1972) does measure this velocity and is therefore much closer to the zero crossing system. It uses multipliers, adders and dividers to calculate the mean frequency of the audio signal and not the root mean square. The main advantages over zero crossing detection are that the output does not depend on the flow profile, and that when used on two vessels simultaneously it registers the mean velocity. However, since it processes the signal and only displays a single mean frequency at any one time it does have the other disadvantages of the zero crossing detector (sensitive to noise, to equipment frequency response, to uneven insonation of the target, to vessel wall movement) and in addition it cannot indicate when artery and vein are simultaneouly irradiated. CONCLUSION

The zero crossing detector is available in most of the commercial Doppler velocimeters, and those working with the instrument might achieve better results when they know how it works and realise the errors and limitations inherent in this form of analysis. In spite of the limitations, the instrument should be capable of measuring blood velocity to about 20 per cent, and can detect changes in velocity of about 5 per cent. Most of the errors arise because of the wide frequency spectrum of the blood flow signal, but with the introduction of pulsed Doppler flowmeters the received signal can be limited to a narrower frequency range. The zero crossing detector will be much more accurate in this situation, and measurements of blood velocity and flow should be possible. Meanwhile, we must accept the zero crossing detector with all its limitations and recognise the advantages of being able to measure blood velocity to within 20 per cent with no discomfort to the subject. REFERENCES

Arts, M. G. J. and Roevros, J. M. J. (1972) On the instantaneous measurement of blood flow by ultrasonic means. Med. Biol. Engng 10, 23-42.

M. J. LIJNT

10

Baker, D. W., Steggal, H. F. and Schlegel, W. A. (1974) A sonic transcutaneous blood flowmeter. Proc. 17th Conf. Engng. Med. Biol. p. 76.

Coghlan, B. A., Taylor, M. G. and King, D. H. (1973) Online display of Doppler shift spectra by a new time compressiar&nalyser. Cardiovascular Applications of Ultrasound(Edited by Reneman. R.), pp.55-56. North-Holland, Amsterdam. Evans, D. S. and Cockett, F. B. (1969) Diagnosis of deep vein thrombosis with an ultrasonic Doppler technique. Br. Med. J. 2. 802.

Flax, S. W., Webster, J. G. and Updike, S. J. (1970) Statistical evaluation of the Doppler ultrasonic blood flowmeter. Biomed. Sci. Instrum. 7. 201-222. Flax, S. W., Webster, J. G. and Updike, S. J. (1973) Pitfalls using Doppler ultrasound to transduce blood Row. I.E.E.E.

Trans. Biomed. Engng 20. 306-309.

Franklin, D. L., Schlegal, W. A. and Rushmer, R. F. (1961) Flow measured by Doppler frequency of back scattered sound. Science 134,564. Gosling, R. H., King, D. H., Newman, D. L. and Woodcock, J. P. (1969) Transcutaneous measurement of arterial blood velocity by ultrasound. Ultrasonics for Industry 19.69, pp. 16-23. Iliffe Science & Technology Publications Ltd. Hansen, P. L., Cross, G. and Light, L. H. (1974) Beam angle independent Doppler velocity measurement in superficial vessels. Clinical Blood Flow Measurements. Sector, London.

Kato, K., Motomiya. M., Izumi, T., Kaneko, Z., Shiraishi, J., Omizo, H. and Nakano, S. (1965) Linearity of readings on ultrasonic flowmeter. Dig. 6th Inr. Conf. Med. Elecl. Biol. Engng. p. 284. Kirby, R. R.. Kemmerer, W. T. and Morgan, J. L. (1969) Transcutaneous Doppler measurement of blood pressure. Anoesthesiol. 31, 86.

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