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Comparison of CW Doppler ultrasound spectra with the spectra derived from a flow visualization model
Ultrasound in Med. & Biol Vol. 12, No. 2, pp. 125-133, 1986 Printed in the U.S.A.
0301-5629/86 $3.00 + .00 © 1986 Pergamon Press Ltd.
OOriginal Contribution COMPARISON THE SPECTRA
OF CW DERIVED
DOPPLER ULTRASOUND SPECTRA FROM A FLOW VISUALIZATION
WITH MODEL
J. K . POOTS, K . W . J O H N S T O N , R . S. C. C O B B O L D a n d M . K.ASSAM Institute of Biomedical Engineering, University of Toronto, Toronto, M5S I A4, Canada (Received 29 October 1984; in final form 26 July 1985) Abstract--The methods and results of a study to determine the accuracy of continuous wave (CW) Doppler spectral recordings by comparison to the spectra derived from the flow profiles photographed simultaneously in a pulsatile flow visualization model are reported in this paper. A pulsatile pump produced a flow velocity waveform, similar to that seen in the human femoral artery, in a quartz glass tube. The velocity profiles, which were made visible by using a photochromic dye/laser technique, were photographed, and at the same time the instantaneous Doppler spectra were recorded. A comparison of the Doppler data and the photographed profiles gave the following results. The Doppler spectrograms and those reconstructed from the flow visualization data were quite similar. Excellent agreement was observed between the instantaneous maximum and mean Doppler waveforms. Individual spectra showed some differences and these differences were quantified by the novel application of certain statistical shape descriptor coefficients that are based on the estimation of the higher order moments of the spectra. The Doppler spectra are generally more skewed towards higher frequencies, narrower, and more peaked than the flow visualization spectra. Analysis of the assumptions and various sources of error lead to the conclusion that the differences were probably caused by ultrasound beam nonuniformity and the effects of refraction, causing a reduction of the beam field response at the tube edges. It is concluded that provided certain precautions are taken in the measurement technique, the CW Doppler ultrasound spectra fairly accurately represent the true velocity profile. Key Words: Doppler Ultrasound, Flow visualization, Doppler spectrum. 1. I N T R O D U C T I O N
detecting minor carotid arterial disease (Douville et al., 1983a). There are m a n y factors which may affect the ideal relationship between the true blood flow velocity profile and the transduced Doppler spectrum and these may affect the diagnostic accuracy of Doppler assessment. They include: axial streaming of blood cells (Cox and Mason, 1971) and red cell aggregation (rouleaux or linear clumping) (Goldsmith and Skalak, 1975); the statistical nature of the ultrasound signal; incomplete or non-uniform insonation of the vessel (Lunt, 1975; Cobbold et al., 1983); equipment nonlinearities; errors introduced in the signal processing including, for example, the errors due to alteration of the spectrum by the use of a high pass filter to remove wall m o v e m e n t artifacts (Kassam et al., 1982) and inadequacies in the spectral estimate (Green et al., 1982). The effects of the above factors and others, on the relationship between the Doppler spectrum and the true blood flow velocity information are not necessarily separable. Consequently, as a first step in determining if the Doppler technique reliably transduces the blood flow velocity data, it is important to determine the cu-
Continuous wave (CW) Doppler techniques are widely used to diagnose arterial occlusive disease because they are noninvasive, relatively inexpensive and quite reliable. In clinical applications, the Doppler spectral waveform is recorded and from it, the m a x i m u m frequency waveform, the mean frequency waveform, or the instantaneous Doppler spectra are analyzed. For example, the instantaneous m a x i m u m and mean waveforms are dampened distal to arterial stenoses and quantitative analysis of these changes has proven to be of value in detecting peripheral arterial occlusive disease (Gosling and King, 1974; Johnston et al., 1978, 1984). Also, at the site of a carotid arterial stenosis, the peak Doppler frequency is increased, a measurement of which is of proven diagnosic value (Spencer and Reid, 1979; Brown et al., 1982). Just distal to an arterial stenosis, the blood flow is disturbed and the recorded abnormalities of the Doppler spectrum may be useful for Address correspondence to: Dr. R. S. C. Cobbold, Institute of Biomedical Engineering, Universityof Toronto, Toronto, M5S IA4 Canada. 125
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mulative error in the Doppler spectral data by comparing Doppler spectra to those obtained by an independent technique for obtaining flow velocity information. Thus, the purpose of this study is to determine the accuracy of the Doppler spectral recordings by comparison to spectra derived from flow velocity profiles which are photographed simultaneously in a pulsatile flow visualization model and to discuss the reasons for observed differences. 2. M E T H O D S The methods used in this study were quite complex and will be described under four headings: flow visualization model, Doppler technique, data analysis, and quantitative comparison of the flow profiles and Doppler spectra. 2.1 Flow visualization model Various methods for measuring the flow velocity profile have been described and these include hot film anemometry, laser Doppler, tracer dye injection, and the hydrogen bubble technique. The photochromic dye (flash photolysis) method was chosen for this study because it is non-invasive, it is relatively inexpensive to implement, it can be used for the measurement of turbulent flow, and, since the method was developed in our Chemical Engineering department (Popovich and Hummel, 1967; Smith and Hummel, 1973), advice was readily available. Figure 1 is a block diagram of the pulsatile photochromic dye visualization model which includes a pulsatile pump, a flow test section, a well-collimated laser light source, a photographic system, and a timing and control system. Since the details have been described elsewhere (Poots et al., 1986), only the principles will be described here. The pulsatile pump, similar in design to that described by Kiyose et al. (1977), was adjusted to produce a waveform which approximately resembles that seen in the human c o m m o n femoral artery. The test section, consisting of a 1.0 m long quartz tube of 5.00 m m inner diameter and wall thickness 1.0 m m , was connected to the p u m p by means of two 0.75 m lengths of Tygon tubing. The test fluid (kerosene) contained a photochromic dye and polystyrene beads (mean diameter 15 #m) to scatter the ultrasound. A well-collimated beam of ultraviolet light from a pulsed nitrogen laser ( ~ 5 0 0 kW for 5 ns) caused the tracer dye to undergo a reversible chemical reaction that changes it from a clear to a coloured form. This produced a narrow dye trace across the tube which subsequently moves with the fluid. Photographs were taken 5 ms after the laser was fired by a 35 m m camera with an electronically controlled shutter, bulk film
February1986, Volume 12, Number 2
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Comparison of CW Doppler ultrasound spectra• J. K. POOTSet aL and the tube was achieved by using a water bath. While the use of a kerosene bath would have eliminated beam refraction for rays along the probe axis (but not for offaxis rays), water was preferred to avoid possible damage to the probe. Refraction effects were taken into account in calculating the actual angle of incidence of the beam on the scattering particles. The insonated portion of the tube was approximately 30 cm distal to the region photographed, which in turn was approximately 30 cm from the inlet. Since the latter corresponds to just over one inlet length it is unlikely that there would be major differences in the velocity profiles at the two measurement points. The bidirectional Doppler signals were analyzed in real-time using a CCD-based spectrum analyzer (Zuech et al., 1982a,b) that was modified for these experiments. Upon receiving a request from the microcomputer, the spectrum analyzer provided one complete spectrum consisting of the forward (0-15 kHz) and reverse (0-5 kHz) components at +50 Hz resolution from data acquired over a l0 ms interval. A grey-scale video system was used to display the spectral waveforms, thus providing visual feedback during the experiments to facilitate proper alignment of the Doppler probe and ensure that the system was optimally adjusted. Simultaneously with the laser firing, a request was sent to the CCD analyzer to begin the analysis: l0 ms later this data was transferred to the Cromenco minicomputer to be stored on floppy disk. At the end of an experimental run, the spectral data was transferred to the PDP-11/34 minicomputer. It should be noted that the Doppler signal was extracted from the transreceiver prior to the lowpass (wall thump) filter--this avoided spectral distortion of the lower frequency components of the spectrum. During the calibration of the frequency analyzer, the various gains, off-sets and acceptable signal levels were optimized. The linearity between the input to the CCD analyzer and the output from the microcomputer was confirmed by tests using a variable frequency sinusoidal signal source. 2.3 Data analysis The data acquired in the experiments includes the photographed profiles and the corresponding Doppler spectra from the spectrum analyzer.
the piecewise linear fit. Generally an eighth degree polynomial was used but, in some cases, it was as low as three. The errors incurred in the digitization process were determined and found to be at the most, 1% of the peak velocity. The polynomial for each profile was used to predict the Doppler spectrum so that a comparison could be made to the corresponding measured Doppler spectrum. In order to calculate the Doppler spectrum it was assumed that the vessel was uniformly insonated, that the scattering particles were uniformly distributed and each contributed the same scattered power, and that the flow was axisymmetric.
Doppler spectra. The Doppler spectra from a realtime frequency analyzer vary from one cycle to another (Green et al., 1982) for a number of reasons, the most important of which are likely: the statistical nature of the Doppler signal itself, the noise and nonlinearities introduced by the CCD-based spectrum analyzer (which implements a Discrete Fourier Transform). In these experiments, ensemble averaging was used to reduce the variability between spectra (Bendat and Piersol, 1971 ). Spectra from 15 pump cycles were averaged to produce a mean spectrum for each time sample. 2.4 Quantitative comparison of spectra To quantitatively compare the recorded Doppler spectra with the spectra estimated from the flow visualization velocity profiles use was made o f certain standard statistically-based shape descriptors (Ott, 1977; Richmond, 1964). Specifically, the variance (describing the spectral width), the skewness (describing the degree of asymmetry), and the kurtosis (describing the degree of peakedness) were computed throughout a complete pump cycle. The Doppler and flow visualization data can be considered as being two-dimensional random vectors: functions of time and frequency (or velocity). To describe the shape of the instantaneous spectra from both sets of measurements, estimates of the first four moments were used, and time averages of moment-based parameters were then determined to describe the general trends throughout the pulse cycle. The nth moment of the sampled amplitude spectrum is given by
~. Flow visualization velocity profiles and spectra. The photographed profiles were digitized and fitted to a polynomial of variable degree. The degree of the polynomial used was selected by the computer program to minimize the RMS error of the fit, and to give a smooth transition between points by minimizing the midpoint RMS deviation of the polynomial fit from
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Ultrasound in Medicine and Biology
February1986, Volume 12, Number 2
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3.1 Doppler spectra Comparison of spectra recorded at the same time in different pump cycles illustrate the statistical fluctuations in the Doppler signal and possible fluctuations arising from short-time nature of the Fourier analysis. An individual amplitude spectrum taken close to the peak of the flow waveform is shown in Fig. 2(a). In addition, Fig. 2(b) shows the effect of averaging 15 spectra taken at the same time in successive pump cycles. It should be noted that the spectral amplitude scale used in these and subsequent figures extends from 0 to 255, corresponding to the 8 bits of resolution in the analog-digital conversion of the CCD spectrum analyzer output. From each spectrum taken throughout the 15 pump cycles, the mean frequency, standard deviation and the 95% T-statistic confidence intervals were determined. It was found that while the worst case 95% confidence intervals were _+43 about a mean amplitude of 128, a value of +20 was more typical. The instantaneous spectrogram of Fig. 3(a) consists of 55 spectra taken at 20 ms intervals over a full pump cycle, in which the spectral amplitudes (0-255) are represented in a linear manner by the colour scale purple, blue, green, yellow, red. To avoid the undesirable background, which arises from the low amplitude noise component that is evident in Fig. 2, a threshold of 15 was used. This corresponds to approximately the mean output, without a Doppler input, plus 2 standard deviations. The instantaneous and averaged spectrograms of Figs. 3(b) and (c) clearly demonstrate the improvement in display quality that results. Each spectrogram was displayed by the PDP 11/34 system driving a high resolution CRT graphics display system. An attempt was made to separate the observed variations due to the random nature of the Doppler signal from those due to the equipment used (princi-
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pally the CCD spectrum analyzer). The output from the 5 kHz "bin" of the CCD analyzer for a 5 kHz sinusoidal input signal was measured for various input signal amplitudes, and the standard deviation was obtained. In addition, using a Doppler signal from the pulsatile flow model the average output from all the frequency bins was determined for various input signal gains and the standard deviation was also obtained. Figure 4 compares the results. The output signal for a sinusoidal input varies somewhat, thus indicating that the spectrum analyzer likely introduces some statistical fluctuations in the observed results. However, it will be noted that these fluctuations are small compared to those arising from the statistical properties of the Doppler signal. 3.2 Flow visualization Figure 5 illustrates typical dye traces from an experimental run in which 55 photographs were taken at 20 ms intervals throughout a complete pump cycle. They show that the shape of the velocity profile changes throughout the pump cycle in a way similar to that expected for the femoral artery and that forward and reverse flow velocity components can coexist at the same sample time.
Comparison of CW Doppler ultrasound spectra • J. K. POOTS et al.
Fig. 3. Doppler spectrograms. For each, the amplitude scale (0-255) is represented by the colour scale: purple, blue, green, yellow, red. Also, each spectrogram is made up of spectra taken at 20 ms intervals: (a) without the use of a threshold; (b) with a threshold set to 15; (c) averaged spectrogram over 15 pump cycles.
Fig. 7. Comparison of (a) flow visualization, and (b) Doppler spectrograms. The amplitude scale (0-255) is shown as the computer generated colour scale on the left. The flow velocity scale ( 16 cm/s per division) and the frequency scale (200 Hz per division) are also computer generated.
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The individual Doppler spectra were estimated from the digitized traces in the manner previously described. Figure 6(a) shows two examples of estimated amplitude spectra derived from the flow visualization data. The corresponding averaged (over 15 cycles) Doppler spectra are shown in Fig. 6(b). Figure 7 enables the flow visualization and Doppler spectrograms to be compared. It will be noted that there is close qualitative agreement but as expected, the Doppler spectrogram shows evidence of a significant noise component which probably would have been further reduced if the averaging were performed over a greater number of cycles than 15, but this was not practical. Furthermore, it appears that the Doppler spectra have more power concentrated closer to the maximum. It should also be noted that correction for
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Fig. 6. Comparison of(a) flow visualization, and (b) Doppler spectra at two different times in the pump cycle. The flow spectra were estimated from the flow profiles and the Doppler spectra were averaged over 15 pump cycles. the refraction error arising from the fact that the probe was immersed in a water coupling medium (rather than kerosene), and with the assumption that c(kerosene) = 1342 m/s, and c(water) = 1480 m/s, the effective Doppler angle was 72.4 degrees. Thus, the Doppler frequency scale was found to be related to the flow velocity scale by the scaling factor of 2248 Hz/(m/s), and this is included in Fig. 7. Figure 8 compares the m a x i m u m and mean waveforms over a complete pump cycle for the flow visualization and Doppler data (averaged over 15 cycles). The criteria used for obtaining the m a x i m u m waveforms was simply to determine the highest frequency (or velocity) whose amplitude exceeded a threshold of 15. These waveforms are in fact the envelopes of the two spectrograms of Fig. 7. The means were obtained as the first m o m e n t s of each amplitude spectrum. While it will be observed that the overall agreement for both graphs is excellent, it should be pointed out that the degree of quantitative agreement for the maximum waveforms depends on the threshold chosen. The individual Doppler and flow visualization spectra were compared quantitatively by using the standard shape descriptors that were defined earlier. Figure 9 shows how the coefficients of variation, skewedness, and kurtosis vary throughout the pump cycle for both Doppler and flow visualization spectra.
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Ultrasound in Medicine and Biology
(flow visualization), indicating a tendency towards higher velocities (frequencies) for the Doppler spectra. The mean coefficients of kurtosis over the cycle were 2.506 (Doppler) vs 1.828 (flow visualization), indicating that the Doppler spectra are generally more peaked than the flow visualization spectra. 4. DISCUSSION A visual comparison of the flow visualization and Doppler spectrograms (Fig. 7) indicates qualitative agreement but also suggests that apart from the evidence of statistical fluctuations in the Doppler, there also exists differences in the shapes of individual spectra. These differences have been confirmed and quantified by the use of shape descriptors and by comparing the maximum and mean waveforms. The question remains as to whether these differences are as a result of errors that arise from the experimental and analytical techniques employed, or whether they truely exist. It is the primary purpose of this discussion to address this question through a consideration of the various errors and assumptions made in this study. The development of a computer controlled flow visualization system for characterizing Doppler spectral signals required the integration of a number of subsystems including a pulsatile pump, a medium powered ultraviolet laser, a photographic system, ultrasound Doppler instrumentation which provided real-time spectral analysis, and a microcomputer serving as a system controller and spectral data logger. In respect to the flow visualization system, errors arise from optical distortion, variations in the timing circuits, the finite trace thickness in relation to the tube diameter, refraction errors, and the absence of perfect symmetry in the flow velocity profile. It is estimated that the total error arising from all these sources is less than 5% of the maximum flow velocity. Distortion in the Doppler spectrum may be the result of one of several factors as discussed in the following paragraphs. The presence of a random component in the Doppler spectrum, which is quite apparent from the spectrograms of Fig. 3(a) and (b), may be the result of either or both the inherent statistically based process that gives rise to the Doppler signal or as a result of the short-time spectrum analysis using a CCD analyzer. For a sinewave input to the CCD analyzer, fluctuations of each spectral component was found to be typically _+10% of the mean (Zuech et al., 1982a). Thus, the major source of variation appears to be the inherent nature of the ultrasound scattering process. Nonetheless, since we used ensemble averaging together with the use of a threshold, it appears unlikely that the ob-
February1986, Volume 12, Number 2 served differences can be ascribed to statistical effects. This is supported by the observations that the shape descriptor results show consistent differences throughout the pump cycle when the data within 20 ms of the crossovers is ignored. Axial streaming of the polystyrene particles could be a possible source of the differences since it would result in a greater signal power from the central region of the tube. However, this appears to be unlikely since the concentration is small and the presence of a large pulsatile component in the flow with the resulting radial forces would tend to equalize the particle distribution. Although the beam pattern of the ultrasound Doppler probe used in this study was known, this was not used to correct the spectrum. It is possible that non-uniformities introduced errors in the transduced Doppler spectra. The observed Doppler probe beam pattern (Douville et al., 1983b) was that o f a Gaussian distribution with one standard deviation approximately equal to the vessel diameter. As reported by Cobbold et al. (1983), when this beam of this shape is directed at the center of the vessel, the higher frequencies will be accentuated, as observed in this study. The major cause of Doppler spectral distortion probably arises from the effects of refraction and wave mode conversion at the quartz tube/liquid interfaces. It should be noted that the critical angle for the water/ quartz interface is 16 ° for longitudinal waves and 25 ° for shear waves in quartz. Thus, since the probe is at 70.5 ° to the flow axis, transmission through the tube wall will be by shear waves only. Consequently, as the distance off-center increases there will be a rapid reduction of the transmitted beam power, and this will become zero when the second critical angle occurs. The net effect is to diminish the weighting of the Doppler components arising from off-axis flow, thereby causing spectral distortion.
5. C O N C L U S I O N S The results of this experimental study comparing Doppler spectral data and spectra estimated from the instantaneous flow visualization velocity profiles, show that there is close agreement between the spectrograms and excellent agreement between the instantaneous maximum and mean waveforms. Detailed quantitative analysis of the spectral shape has revealed some differences. The Doppler spectra are generally narrower, skewed towards the higher frequencies, and more peaked than the flow visualization spectra. It is believed that the differences were due to the ultrasound beam nonuniformity and refraction effects, but this will have to be confirmed.
Comparison of CW Doppler ultrasound spectra • J. K. POOTS et al. T h e o v e r a l l results g e n e r a l l y s u p p o r t t h e v a l i d i t y o f u s i n g D o p p l e r u l t r a s o u n d for t h e s t u d y o f d i l u t e s u s p e n d e d p a r t i c l e flow b u t also i n d i c a t e t h a t f u r t h e r w o r k is n e c e s s a r y to d e t e r m i n e t h e r e a s o n s for t h e o b s e r v e d d i s c r e p a n c i e s i f d e t a i l e d i n f o r m a t i o n is to b e e x t r a c t e d f r o m t h e D o p p l e r u l t r a s o u n d s p e c t r u m . Finally, results also e m p h a s i z e t h e p o t e n t i a l i m p o r t a n c e o f b e a m n o n u n i f o r m i t y i f c l i n i c a l l y useful i n f o r m a t i o n is to be e x t r a c t e d f r o m t h e i n d i v i d u a l o r e n s e m b l e ave r a g e d spectra. Acknowledgements--The authors wish to acknowledge the financial support from the Medical Research Council of Canada and wish to thank Mr. P. Zuech and Professor R. L. Hummel for assistance during various phases of this work.
REFERENCES Bendat J. S. and Piersol A. G. (1971) Random Data: Analysis and Measurement Procedures. Wiley Interscience, New York. Brown P. M., Johnston K. W., Kassam M. and Cobbold R. S. C. (1982) A critical study of ultrasound Doppler spectral analysis for detecting carotid disease. Ultrasound in Med.& Biol. 8, 515523. Cobbold R. S. C., Veltink P. H. and Johnston K. W. (1983) Influence of beam profile and degree of insonation on the CW Doppler ultrasound spectrum and mean velocity. IEEE Trans. Sonics Ultrasonics SU-30, 364-370. Cox R. G. and Mason S. G. (1971) Suspended particles in fluid flow through tubes. Ann. Rev. Fluid Mech. 3, 291-316. Douville Y., Johnston K. W., Kassam M., Zuech P., Cobbold R. S. C. and Jares A. (1983a) An in vitro model and its application for the study of carotid Doppler spectral broadening. Ultrasound in Med.& Biol. 9, 347-356. Douville Y., Arenson J. W., Johnston K. W., Cobbold R. S. C. and Kassam M. (1983b) Critical evaluation of continuous wave Doppler probes for carotid studies. J. Clin. Ultrasound 11, 8390. Goldsmith H. L. and Skalak R. (1975) Hemodynamics. Ann. Rev. Fluid Mech. 7, 213-247. Gosling R. G. and King D. H. (1974) Continuous wave ultrasound as an alternative and complement to X-rays in vascular examination. In Cardiovascular Applications of Ultrasound (Edited by
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R. E. Reneman), Chap. 22, pp. 226-285. North-Holland, Amsterdam. Green F. M., Beach K., Strandness D. E. and Phillips D. J. (1982) Computer based pattern recognition of carotid arterial disease using pulsed Doppler ultrasound. Ultrasound in Med. & Biol. 8, 161-176. Johnston K. W., Maruzzo B. C. and Cobbold R. S. C. (1978) Doppler methods for quantitative measurement and localization of peripheral arterial occlusive disease by analysis of the blood flow velocity waveform. Ultrasound in Med. & Biol. 4, 209-223. Johnston K. W., Kassam M., Koers J., Cobbold R. S. C. and MacHattie D. (1984) Comparative study of four methods for quantifying Doppler ultrasound waveforms from the femoral artery. Ultrasound in Med. & Biol. 10, 1-12. Kassam M. S., Cobbold R. S. C., Johnston K. W. and Graham C. M. (1982) Method for estimating the Doppler mean velocity waveform. Uhrasound in Med. & Biol. 8, 537-544. Lunt M. J. (1975) Accuracy and limitations of the ultrasonic Doppler blood velocimeter and zero crossing detector. Ultrasound in Med. & Biol. 2, 1-10. Kiyose T., Kusaba A., Kamori M., Inokuchi K., Takamatsu Y. and Takahara H. (1977) Development of pump system for experimental model simulation of blood flow in peripheral artery. Fucota Acta Med. 68, 86-91. Ott L. (1977) An Introduction to Statistical Methods and Data Analysis. Duxbury Press, North Scituate, Mass. Poots J. K., Cobbold R. S. C., Johnston K. W., Appugliese R., Kassam M., Zuech P. E. and Hummel R. L. (1986) A new pulsatile flow visualization method using a photochromic dye with application to Doppler ultrasound. Ann. Biomed. Engng. Popovich A. T. and Hummel R. L. (1967) A new method for nondisturbing turbulent flow measurement very close to a wall. Chem. Engng Sci. 22, 21-25. Richmond S. B. (1964) Statistical Analysis. Ronald Press, New York. Smith J. W. and Hummel R. L. (1973) Studies of fluid flow by photography using a non-disturbing light sensitive indicator. J. Soc. Mot. Pic. Tel Engng. 82, 278-281. Spencer M. P. and Reid J. M. (1979) Quantitation of carotid stenosis with continuous-wave (C-W) Doppler ultrasound. Stroke 10, 326330. Zuech P. E., Cobbold R. S. C., Kassam M. and Johnston K. W. (1982a) The application of CCD transversal filters for real-time spectral analysis of Doppler ultrasound arterial signals. Ultrasound in Med. & Biol. 8, 57-69. Zuech P. E., Cobbold R. R. C., Kassam M. and Johnston K. W. (1982b) Dual-channel CCD-based spectrum analyzer for Doppler ultrasound arterial assessment. Digest, 9th Canadian Med. Biol. Eng. Conf., pp. 73-74.
0301-5629/86 $3.00 + .00 © 1986 Pergamon Press Ltd.
OOriginal Contribution COMPARISON THE SPECTRA
OF CW DERIVED
DOPPLER ULTRASOUND SPECTRA FROM A FLOW VISUALIZATION
WITH MODEL
J. K . POOTS, K . W . J O H N S T O N , R . S. C. C O B B O L D a n d M . K.ASSAM Institute of Biomedical Engineering, University of Toronto, Toronto, M5S I A4, Canada (Received 29 October 1984; in final form 26 July 1985) Abstract--The methods and results of a study to determine the accuracy of continuous wave (CW) Doppler spectral recordings by comparison to the spectra derived from the flow profiles photographed simultaneously in a pulsatile flow visualization model are reported in this paper. A pulsatile pump produced a flow velocity waveform, similar to that seen in the human femoral artery, in a quartz glass tube. The velocity profiles, which were made visible by using a photochromic dye/laser technique, were photographed, and at the same time the instantaneous Doppler spectra were recorded. A comparison of the Doppler data and the photographed profiles gave the following results. The Doppler spectrograms and those reconstructed from the flow visualization data were quite similar. Excellent agreement was observed between the instantaneous maximum and mean Doppler waveforms. Individual spectra showed some differences and these differences were quantified by the novel application of certain statistical shape descriptor coefficients that are based on the estimation of the higher order moments of the spectra. The Doppler spectra are generally more skewed towards higher frequencies, narrower, and more peaked than the flow visualization spectra. Analysis of the assumptions and various sources of error lead to the conclusion that the differences were probably caused by ultrasound beam nonuniformity and the effects of refraction, causing a reduction of the beam field response at the tube edges. It is concluded that provided certain precautions are taken in the measurement technique, the CW Doppler ultrasound spectra fairly accurately represent the true velocity profile. Key Words: Doppler Ultrasound, Flow visualization, Doppler spectrum. 1. I N T R O D U C T I O N
detecting minor carotid arterial disease (Douville et al., 1983a). There are m a n y factors which may affect the ideal relationship between the true blood flow velocity profile and the transduced Doppler spectrum and these may affect the diagnostic accuracy of Doppler assessment. They include: axial streaming of blood cells (Cox and Mason, 1971) and red cell aggregation (rouleaux or linear clumping) (Goldsmith and Skalak, 1975); the statistical nature of the ultrasound signal; incomplete or non-uniform insonation of the vessel (Lunt, 1975; Cobbold et al., 1983); equipment nonlinearities; errors introduced in the signal processing including, for example, the errors due to alteration of the spectrum by the use of a high pass filter to remove wall m o v e m e n t artifacts (Kassam et al., 1982) and inadequacies in the spectral estimate (Green et al., 1982). The effects of the above factors and others, on the relationship between the Doppler spectrum and the true blood flow velocity information are not necessarily separable. Consequently, as a first step in determining if the Doppler technique reliably transduces the blood flow velocity data, it is important to determine the cu-
Continuous wave (CW) Doppler techniques are widely used to diagnose arterial occlusive disease because they are noninvasive, relatively inexpensive and quite reliable. In clinical applications, the Doppler spectral waveform is recorded and from it, the m a x i m u m frequency waveform, the mean frequency waveform, or the instantaneous Doppler spectra are analyzed. For example, the instantaneous m a x i m u m and mean waveforms are dampened distal to arterial stenoses and quantitative analysis of these changes has proven to be of value in detecting peripheral arterial occlusive disease (Gosling and King, 1974; Johnston et al., 1978, 1984). Also, at the site of a carotid arterial stenosis, the peak Doppler frequency is increased, a measurement of which is of proven diagnosic value (Spencer and Reid, 1979; Brown et al., 1982). Just distal to an arterial stenosis, the blood flow is disturbed and the recorded abnormalities of the Doppler spectrum may be useful for Address correspondence to: Dr. R. S. C. Cobbold, Institute of Biomedical Engineering, Universityof Toronto, Toronto, M5S IA4 Canada. 125
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mulative error in the Doppler spectral data by comparing Doppler spectra to those obtained by an independent technique for obtaining flow velocity information. Thus, the purpose of this study is to determine the accuracy of the Doppler spectral recordings by comparison to spectra derived from flow velocity profiles which are photographed simultaneously in a pulsatile flow visualization model and to discuss the reasons for observed differences. 2. M E T H O D S The methods used in this study were quite complex and will be described under four headings: flow visualization model, Doppler technique, data analysis, and quantitative comparison of the flow profiles and Doppler spectra. 2.1 Flow visualization model Various methods for measuring the flow velocity profile have been described and these include hot film anemometry, laser Doppler, tracer dye injection, and the hydrogen bubble technique. The photochromic dye (flash photolysis) method was chosen for this study because it is non-invasive, it is relatively inexpensive to implement, it can be used for the measurement of turbulent flow, and, since the method was developed in our Chemical Engineering department (Popovich and Hummel, 1967; Smith and Hummel, 1973), advice was readily available. Figure 1 is a block diagram of the pulsatile photochromic dye visualization model which includes a pulsatile pump, a flow test section, a well-collimated laser light source, a photographic system, and a timing and control system. Since the details have been described elsewhere (Poots et al., 1986), only the principles will be described here. The pulsatile pump, similar in design to that described by Kiyose et al. (1977), was adjusted to produce a waveform which approximately resembles that seen in the human c o m m o n femoral artery. The test section, consisting of a 1.0 m long quartz tube of 5.00 m m inner diameter and wall thickness 1.0 m m , was connected to the p u m p by means of two 0.75 m lengths of Tygon tubing. The test fluid (kerosene) contained a photochromic dye and polystyrene beads (mean diameter 15 #m) to scatter the ultrasound. A well-collimated beam of ultraviolet light from a pulsed nitrogen laser ( ~ 5 0 0 kW for 5 ns) caused the tracer dye to undergo a reversible chemical reaction that changes it from a clear to a coloured form. This produced a narrow dye trace across the tube which subsequently moves with the fluid. Photographs were taken 5 ms after the laser was fired by a 35 m m camera with an electronically controlled shutter, bulk film
February1986, Volume 12, Number 2
Doppler Frequency Analyzer
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Comparison of CW Doppler ultrasound spectra• J. K. POOTSet aL and the tube was achieved by using a water bath. While the use of a kerosene bath would have eliminated beam refraction for rays along the probe axis (but not for offaxis rays), water was preferred to avoid possible damage to the probe. Refraction effects were taken into account in calculating the actual angle of incidence of the beam on the scattering particles. The insonated portion of the tube was approximately 30 cm distal to the region photographed, which in turn was approximately 30 cm from the inlet. Since the latter corresponds to just over one inlet length it is unlikely that there would be major differences in the velocity profiles at the two measurement points. The bidirectional Doppler signals were analyzed in real-time using a CCD-based spectrum analyzer (Zuech et al., 1982a,b) that was modified for these experiments. Upon receiving a request from the microcomputer, the spectrum analyzer provided one complete spectrum consisting of the forward (0-15 kHz) and reverse (0-5 kHz) components at +50 Hz resolution from data acquired over a l0 ms interval. A grey-scale video system was used to display the spectral waveforms, thus providing visual feedback during the experiments to facilitate proper alignment of the Doppler probe and ensure that the system was optimally adjusted. Simultaneously with the laser firing, a request was sent to the CCD analyzer to begin the analysis: l0 ms later this data was transferred to the Cromenco minicomputer to be stored on floppy disk. At the end of an experimental run, the spectral data was transferred to the PDP-11/34 minicomputer. It should be noted that the Doppler signal was extracted from the transreceiver prior to the lowpass (wall thump) filter--this avoided spectral distortion of the lower frequency components of the spectrum. During the calibration of the frequency analyzer, the various gains, off-sets and acceptable signal levels were optimized. The linearity between the input to the CCD analyzer and the output from the microcomputer was confirmed by tests using a variable frequency sinusoidal signal source. 2.3 Data analysis The data acquired in the experiments includes the photographed profiles and the corresponding Doppler spectra from the spectrum analyzer.
the piecewise linear fit. Generally an eighth degree polynomial was used but, in some cases, it was as low as three. The errors incurred in the digitization process were determined and found to be at the most, 1% of the peak velocity. The polynomial for each profile was used to predict the Doppler spectrum so that a comparison could be made to the corresponding measured Doppler spectrum. In order to calculate the Doppler spectrum it was assumed that the vessel was uniformly insonated, that the scattering particles were uniformly distributed and each contributed the same scattered power, and that the flow was axisymmetric.
Doppler spectra. The Doppler spectra from a realtime frequency analyzer vary from one cycle to another (Green et al., 1982) for a number of reasons, the most important of which are likely: the statistical nature of the Doppler signal itself, the noise and nonlinearities introduced by the CCD-based spectrum analyzer (which implements a Discrete Fourier Transform). In these experiments, ensemble averaging was used to reduce the variability between spectra (Bendat and Piersol, 1971 ). Spectra from 15 pump cycles were averaged to produce a mean spectrum for each time sample. 2.4 Quantitative comparison of spectra To quantitatively compare the recorded Doppler spectra with the spectra estimated from the flow visualization velocity profiles use was made o f certain standard statistically-based shape descriptors (Ott, 1977; Richmond, 1964). Specifically, the variance (describing the spectral width), the skewness (describing the degree of asymmetry), and the kurtosis (describing the degree of peakedness) were computed throughout a complete pump cycle. The Doppler and flow visualization data can be considered as being two-dimensional random vectors: functions of time and frequency (or velocity). To describe the shape of the instantaneous spectra from both sets of measurements, estimates of the first four moments were used, and time averages of moment-based parameters were then determined to describe the general trends throughout the pulse cycle. The nth moment of the sampled amplitude spectrum is given by
~. Flow visualization velocity profiles and spectra. The photographed profiles were digitized and fitted to a polynomial of variable degree. The degree of the polynomial used was selected by the computer program to minimize the RMS error of the fit, and to give a smooth transition between points by minimizing the midpoint RMS deviation of the polynomial fit from
127
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February1986, Volume 12, Number 2
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3.1 Doppler spectra Comparison of spectra recorded at the same time in different pump cycles illustrate the statistical fluctuations in the Doppler signal and possible fluctuations arising from short-time nature of the Fourier analysis. An individual amplitude spectrum taken close to the peak of the flow waveform is shown in Fig. 2(a). In addition, Fig. 2(b) shows the effect of averaging 15 spectra taken at the same time in successive pump cycles. It should be noted that the spectral amplitude scale used in these and subsequent figures extends from 0 to 255, corresponding to the 8 bits of resolution in the analog-digital conversion of the CCD spectrum analyzer output. From each spectrum taken throughout the 15 pump cycles, the mean frequency, standard deviation and the 95% T-statistic confidence intervals were determined. It was found that while the worst case 95% confidence intervals were _+43 about a mean amplitude of 128, a value of +20 was more typical. The instantaneous spectrogram of Fig. 3(a) consists of 55 spectra taken at 20 ms intervals over a full pump cycle, in which the spectral amplitudes (0-255) are represented in a linear manner by the colour scale purple, blue, green, yellow, red. To avoid the undesirable background, which arises from the low amplitude noise component that is evident in Fig. 2, a threshold of 15 was used. This corresponds to approximately the mean output, without a Doppler input, plus 2 standard deviations. The instantaneous and averaged spectrograms of Figs. 3(b) and (c) clearly demonstrate the improvement in display quality that results. Each spectrogram was displayed by the PDP 11/34 system driving a high resolution CRT graphics display system. An attempt was made to separate the observed variations due to the random nature of the Doppler signal from those due to the equipment used (princi-
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pally the CCD spectrum analyzer). The output from the 5 kHz "bin" of the CCD analyzer for a 5 kHz sinusoidal input signal was measured for various input signal amplitudes, and the standard deviation was obtained. In addition, using a Doppler signal from the pulsatile flow model the average output from all the frequency bins was determined for various input signal gains and the standard deviation was also obtained. Figure 4 compares the results. The output signal for a sinusoidal input varies somewhat, thus indicating that the spectrum analyzer likely introduces some statistical fluctuations in the observed results. However, it will be noted that these fluctuations are small compared to those arising from the statistical properties of the Doppler signal. 3.2 Flow visualization Figure 5 illustrates typical dye traces from an experimental run in which 55 photographs were taken at 20 ms intervals throughout a complete pump cycle. They show that the shape of the velocity profile changes throughout the pump cycle in a way similar to that expected for the femoral artery and that forward and reverse flow velocity components can coexist at the same sample time.
Comparison of CW Doppler ultrasound spectra • J. K. POOTS et al.
Fig. 3. Doppler spectrograms. For each, the amplitude scale (0-255) is represented by the colour scale: purple, blue, green, yellow, red. Also, each spectrogram is made up of spectra taken at 20 ms intervals: (a) without the use of a threshold; (b) with a threshold set to 15; (c) averaged spectrogram over 15 pump cycles.
Fig. 7. Comparison of (a) flow visualization, and (b) Doppler spectrograms. The amplitude scale (0-255) is shown as the computer generated colour scale on the left. The flow velocity scale ( 16 cm/s per division) and the frequency scale (200 Hz per division) are also computer generated.
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The individual Doppler spectra were estimated from the digitized traces in the manner previously described. Figure 6(a) shows two examples of estimated amplitude spectra derived from the flow visualization data. The corresponding averaged (over 15 cycles) Doppler spectra are shown in Fig. 6(b). Figure 7 enables the flow visualization and Doppler spectrograms to be compared. It will be noted that there is close qualitative agreement but as expected, the Doppler spectrogram shows evidence of a significant noise component which probably would have been further reduced if the averaging were performed over a greater number of cycles than 15, but this was not practical. Furthermore, it appears that the Doppler spectra have more power concentrated closer to the maximum. It should also be noted that correction for
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Ultrasound in Medicine and Biology
(flow visualization), indicating a tendency towards higher velocities (frequencies) for the Doppler spectra. The mean coefficients of kurtosis over the cycle were 2.506 (Doppler) vs 1.828 (flow visualization), indicating that the Doppler spectra are generally more peaked than the flow visualization spectra. 4. DISCUSSION A visual comparison of the flow visualization and Doppler spectrograms (Fig. 7) indicates qualitative agreement but also suggests that apart from the evidence of statistical fluctuations in the Doppler, there also exists differences in the shapes of individual spectra. These differences have been confirmed and quantified by the use of shape descriptors and by comparing the maximum and mean waveforms. The question remains as to whether these differences are as a result of errors that arise from the experimental and analytical techniques employed, or whether they truely exist. It is the primary purpose of this discussion to address this question through a consideration of the various errors and assumptions made in this study. The development of a computer controlled flow visualization system for characterizing Doppler spectral signals required the integration of a number of subsystems including a pulsatile pump, a medium powered ultraviolet laser, a photographic system, ultrasound Doppler instrumentation which provided real-time spectral analysis, and a microcomputer serving as a system controller and spectral data logger. In respect to the flow visualization system, errors arise from optical distortion, variations in the timing circuits, the finite trace thickness in relation to the tube diameter, refraction errors, and the absence of perfect symmetry in the flow velocity profile. It is estimated that the total error arising from all these sources is less than 5% of the maximum flow velocity. Distortion in the Doppler spectrum may be the result of one of several factors as discussed in the following paragraphs. The presence of a random component in the Doppler spectrum, which is quite apparent from the spectrograms of Fig. 3(a) and (b), may be the result of either or both the inherent statistically based process that gives rise to the Doppler signal or as a result of the short-time spectrum analysis using a CCD analyzer. For a sinewave input to the CCD analyzer, fluctuations of each spectral component was found to be typically _+10% of the mean (Zuech et al., 1982a). Thus, the major source of variation appears to be the inherent nature of the ultrasound scattering process. Nonetheless, since we used ensemble averaging together with the use of a threshold, it appears unlikely that the ob-
February1986, Volume 12, Number 2 served differences can be ascribed to statistical effects. This is supported by the observations that the shape descriptor results show consistent differences throughout the pump cycle when the data within 20 ms of the crossovers is ignored. Axial streaming of the polystyrene particles could be a possible source of the differences since it would result in a greater signal power from the central region of the tube. However, this appears to be unlikely since the concentration is small and the presence of a large pulsatile component in the flow with the resulting radial forces would tend to equalize the particle distribution. Although the beam pattern of the ultrasound Doppler probe used in this study was known, this was not used to correct the spectrum. It is possible that non-uniformities introduced errors in the transduced Doppler spectra. The observed Doppler probe beam pattern (Douville et al., 1983b) was that o f a Gaussian distribution with one standard deviation approximately equal to the vessel diameter. As reported by Cobbold et al. (1983), when this beam of this shape is directed at the center of the vessel, the higher frequencies will be accentuated, as observed in this study. The major cause of Doppler spectral distortion probably arises from the effects of refraction and wave mode conversion at the quartz tube/liquid interfaces. It should be noted that the critical angle for the water/ quartz interface is 16 ° for longitudinal waves and 25 ° for shear waves in quartz. Thus, since the probe is at 70.5 ° to the flow axis, transmission through the tube wall will be by shear waves only. Consequently, as the distance off-center increases there will be a rapid reduction of the transmitted beam power, and this will become zero when the second critical angle occurs. The net effect is to diminish the weighting of the Doppler components arising from off-axis flow, thereby causing spectral distortion.
5. C O N C L U S I O N S The results of this experimental study comparing Doppler spectral data and spectra estimated from the instantaneous flow visualization velocity profiles, show that there is close agreement between the spectrograms and excellent agreement between the instantaneous maximum and mean waveforms. Detailed quantitative analysis of the spectral shape has revealed some differences. The Doppler spectra are generally narrower, skewed towards the higher frequencies, and more peaked than the flow visualization spectra. It is believed that the differences were due to the ultrasound beam nonuniformity and refraction effects, but this will have to be confirmed.
Comparison of CW Doppler ultrasound spectra • J. K. POOTS et al. T h e o v e r a l l results g e n e r a l l y s u p p o r t t h e v a l i d i t y o f u s i n g D o p p l e r u l t r a s o u n d for t h e s t u d y o f d i l u t e s u s p e n d e d p a r t i c l e flow b u t also i n d i c a t e t h a t f u r t h e r w o r k is n e c e s s a r y to d e t e r m i n e t h e r e a s o n s for t h e o b s e r v e d d i s c r e p a n c i e s i f d e t a i l e d i n f o r m a t i o n is to b e e x t r a c t e d f r o m t h e D o p p l e r u l t r a s o u n d s p e c t r u m . Finally, results also e m p h a s i z e t h e p o t e n t i a l i m p o r t a n c e o f b e a m n o n u n i f o r m i t y i f c l i n i c a l l y useful i n f o r m a t i o n is to be e x t r a c t e d f r o m t h e i n d i v i d u a l o r e n s e m b l e ave r a g e d spectra. Acknowledgements--The authors wish to acknowledge the financial support from the Medical Research Council of Canada and wish to thank Mr. P. Zuech and Professor R. L. Hummel for assistance during various phases of this work.
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