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LaPlace transform analysis of femoral artery doppler signals: The state of the art
Ultrasound in Med. & Biol. Vol. 15. No, 1, pp. 13-20, 1989 Prinled in the U.S.A.
0301-5629/89 $3.00 + .00 Pergamon Press plc
OOriginal Contribution LAPLACE TRANSFORM ANALYSIS OF FEMORAL ARTERY SIGNALS: THE STATE OF THE ART
DOPPLER
J. DENNIS BAKER, ROBERT SKIDMORE a n d SUSAN E. A. COLE Department of Medical Physics, Bristol Royal Infirmary, Bristol, UK, and the Vascular Surgery Section, VA Medical Center, Sepulveda, CA (Received 9 September 1987;in final form 4 July 1988) Abstract--A followup study was conducted to validate our previous experience with the LaPlace Transform Analysis (LTA) method for processing Doppler ultrasound signals from the common femoral artery to detect significant stenosis of the aorto-iliac segment. The first phase used the same instantaneous mean velocity signal processor as used in the prior study. A comparison of the Doppler examinations with angiograms in 98 legs yielded a sensitivity = 92% and sensitivity = 94% in the identification of 50% or greater stenosis of the aorta-iliac segment, results almost identical to the last study. Because of theoretical disadvantages of using the instantaneous mean velocity signal we carried out a second phase using a peak velocity detector. In 148 limbs sensitivity = 87% and specificity = 98%. The presence or absence of superficial femoral artery occlusion did not affect the accuracy of the waveform analysis in the detection of proximal disease. The LTA parameter related to distal resistance, G, was not found to have clinical value in the assessment of the femoral-popliteal segment.
Key Words: Ultrasound, Doppler, Waveform analysis, LaPlace transform, Diagnosis, Arterial occlusive disease, Iliac artery.
INTRODUCTION
waveform was described in terms of a third-owner transform of the form:
The noninvasive detection of severe occlusive disease of the distal aorta and the iliac arteries is a clinically important but difficult problem. Although simple segmental pressure measurements are useful in the leg, they have not been found to be accurate enough in determining inflow disease, particularly in the presence of superficial femoral artery (SFA) disease. A number of investigators have turned to analysis of the Doppler velocity waveform from the common femoral artery as a method of assessing proximal disease. The simplest method has been to determine whether or not there is reverse flow in early diastole. Some of the quantitative methods of classifying the velocity waveform include pulsatility index and principle component analysis. In 1979 Skidmore introduced the LaPlace transform analysis (LTA), which processed the waveform in the frequency domain (Skidmore, 1979; Skidmore et al., 1980). Initial evaluation of the method showed that the common femoral artery velocity could be described using a 3 pole, 1 zero model. The arterial
H(S) = 1/(Sa + 2D W O + W 0 2 ) ( S + G). The theoretical model upon which the method was based predicted that the coefficients of the transform were related to proximal stenosis (D or damping value), arterial wall stiffness (WO), and distal impedance (G). The solution of the equation yielded two complex poles related to D and W O and a real pole related to G. These can be expressed on an Argand diagram, a graphic representation of complex numbers, where the real values are plotted on the X axis and imaginary values on the Y axis (Fig. 1). In LTA the magnitude on the X axis = D . W O and the Y axis = W O (1 - DE)1/2. A significant proximal stenosis reduced both D and W O , shifting the positions of the complex poles from X 1 to X2. Normal values of D ranged from 0.20 to 0.40. Increasing proximal stenosis produced an increase in D, and with severe damping of the waveform the complex poles became real and D reached a maximum of 1.00. W O was related to proximal vessel wall stiffness; normal arteries had values above 15 and lower values resulted from proximal stenosis. G was related to the radius of the distal
Address correspondenceand reprint requeststo: Dr. Baker, 112G, VA MedicalCenter, Sepulveda,CA 91343. 13
14
UltrasoundinMedicineandBiology Volume15,Number1,1989 NORMAL
STENOTIC
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Fig. 1. Argand diagram representation of the two complex poles (X1) and the real pole (X3) obtained from the analysis. Proximal stenosis decreases both D and WO, shifting the complex poles from X 1 to X2. or runoff system. The model predicted that D and WO were independent of distal impedance, i.e., unaffected by the status of the SFA. The initial clinical evaluation of LTA focused upon the diagnostic value of D and found that a value >0.60 had an 85% sensitivity and an 84% specificity in identifying an iliac stenosis of >50% diameter reduction (Baird et al., 1980). These encouraging resuits led to further evaluation and development of the method. The original Doppler system had a maximum frequency follower which employed the multiple filter method. Processing was done on a MINC computer (Digital Equipment Co.) and required eight minutes to analyze each set of waveforms. This system, with its expensive research computer and slow processing, was clumsy and not really practical for routine use in a clinical setting, so a second setup was developed using an Apple II+ computer. An analog mean frequency processor, based upon the design of Arts and Roevros (1972), was built to replace the maximum follower with its large size and complexity and its requirement for manual threshold adjustment. The initial study of femoral artery signals carried out with this new system produced excellent resuits in the diagnosis of inflow stenosis >50% (Baker et al., 1984). In addition, the hardware was compact and simple to use, making it practical for routine clinical examinations.
We were concerned whether the use of the mean frequency might result in errors due to the requirement for complete insonation of the vessel. A pilot study by Campbell comparing the multiple-filter maximum frequency detector with the analog mean frequency detector showed no significant difference in the values obtained for femoral artery D and WO (Campbell et al., 1984). In spite of these findings we were interested in evaluating peak frequency measurements. Because of practical problems with the multiple-filter processor, we developed an analog maximum frequency detector. The present report comprises two separate phases of our work with LTA for assessment of lower extremity disease. The first was a validation study using the same equipment (including the mean frequency signal processor) as in the initial evaluation reported in 1984. The second phase was carded out in a separate group of patients using the new analog maximum frequency detector. PATIENTS AND METHODS Common femoral artery Doppler velocity signals were obtained using a 10 MHz directional, continuous wave detector featuring a high signal-to-noise ratio. This unit was designed and built in our laboratory and was the same one used in the previous studies (Baker et al., 1984). In the first phase the quadrature output was connected to an analog detector which provided an instantaneous mean frequency signal. This device was based on the design of Arts and Roevros (1972). For the second phase we designed and built an analog maximum frequency processor based on a servo-loop controlled variable filter which tracked the peak frequency. The unit had two sections, one for forward and one for reverse flow signals, The two outputs were added together to produce a single bidirectional signal. An 8-bit analog-todigital converter provided the interface for the Apple II+ computer (Apple Computer, Inc., Cupertino, Calif.). The computer screen displayed a real-time trace of the velocity signal, which could be frozen once an optimal waveform was obtained. A cursor was used to select three waveforms to be averaged for the analysis, and the data were stored on disk. Usually all the samples from a patient were stored and then analyzed after the end of the examination. The computer program, written in compiled Basic for faster execution, calculated D, WO, and G. Increased processing speed was achieved by using an accelerator card based upon an ADM 9511B arithmetic processor unit (California Computer Systems model 7811), permitting computation for each record in 50 s.
LaPlace transform analysis of Doppler signals • J. D. BAKER et al.
This study, carded out in the Vascular Studies Unit, Bristol Royal Infirmary, included Doppler recordings from limbs of patients for whom satisfactory arteriograms were available displaying the segment from the distal abdominal aorta to the knee. Patients with cardiac dysrhythmias or heart rates above 100 were excluded. Patients with prior operations involving the femoral artery were not studied to avoid potential problems which can be caused by scar tissue and by prosthetic materials. Recordings with artifacts or with substantial difference between cardiac cycles were excluded. In each phase approximately 10% of limbs with satisfactory angiograms were excluded for this reason. Table 1 summarizes the characteristics of the patients included in each phase. In some patients only one leg was included in the study because of major leg amputation or unsuitable Doppler or arteriographic studies on one side. Prior to obtaining the Doppler recordings the patient rested on the examining table for 15 min. Common femoral velocity tracings were obtained just below the inguinal ligament, which was identified from bony landmarks rather than from the groin crease. The examiner used both the analog trace on the screen and the audio output to adjust the probe, and considerable care was required to achieve optimal insonation of the vessel while avoiding venous signal contamination. All stenoses in the arota-iliac segment and in the superficial femoral artery were identified on each arteriogram. The residual lumen and the diameter of the normal adjacent segment were measured in order to calculate the percent diameter reduction for each lesion. If there was more than one stenosis in a segment, the most severe was measured. We focused on the detection of significant inflow disease, defined as 50% or greater diameter reduction proximal to the common femoral artery. For most of the analysis the proximal segments were grouped by category of stenosis: no stenosis, 1-19%, 20-49%, 50-99%, and 100%. The superficial femoral arteries were divided into patent or occluded vessels. These groupings were the same as used on our previous study to permit comparison of results. Receiver operator characteristic (ROC) analysis was used to determine the effects on sensitivity and specificity resulting from different T a b l e 1. Characteristics o f patients. Signal processor Mean Maximum
No. limbs
No. patients
Mean age (S.D.)
Male
Indication % critical ischemia
98 148
65 101
62.1 62.5
77% 77%
31% 32%
15
threshold values of D. Differences between categories was studied with the unpaired t-test. RESULTS The primary goals of the study were (a) to determine how well LTA could diagnose the presence of a significant stenosis and (b) to evaluate whether there was any difference in results obtained by using the two different methods of Doppler signal processing, mean versus peak frequency. Figure 2 shows the values of D in each category of proximal stenosis. In both phases of the study there was a highly significant difference (p < 0.00 l) between the mean values of D obtained for inflow stenosis above and below 50% (Table 2). The variance within each group was high enough so there was no significant difference between the subgroups of inflow disease above or below 50% except for a difference between 50-99% and 100% in the patients studied with the peak velocity detector (17 -- 0.04). The difference resulted from the occurrence of three cases with very low D; if these outliers are excluded, there is no difference between the two subgroups. The results of ROC analysis are summarized in Fig. 3. For both phases the best diagnosis of inflow stenosis >50% is achieved with a threshold D of 0.60, the same as found in our original study. Using this cutoff point yielded a sensitivity of 92% and a specificity of 94% for the patients studied with the mean frequency system. Of note is the fact that the only false positives occurred in patients with proximal aneurysms. The second phase using the maximum frequency processor yielded a sensitivity of 87% and a specificity of 98%. Early work with the waveform analysis suggested that the damping value might help to grade the severity of stenosis below 50%. The plots in Fig. 2 show no distinguishable difference for the three categories of early disease. When D is plotted against the measured percent stenosis there is a rising trend, but linear regression showed poor correlation. The theoretical model suggested that the diagnosis of proximal disease should not be affected by the status of the superficial femoral artery. Figure 2 identifies the legs with open and occluded SFAs. The mean D values for the occluded ones were slightly higher than for the patent ones, however, the differences were not statistically significant. The ROC curves computed for the groups with open and occluded SFAs were essentially the same as for the entire group. The relation of WO to proximal disease was evaluated both for measure of percent stenosis and
16
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for category of stenosis, but neither approach improved the diagnosis. There was a decrease in WO of the common femoral artery with increasing severity of proximal lesions, but there was more overlap between groups than with D. We evaluated Campbell's suggestion that the ratio of femoral to ankle WO provides as assessment of patency of the superficial femoral artery (Campbell et al., 1983). In our patients the ratio did not separate open vessels from occlusions in any of the categories of iliac disease. Review of the data from the prior study indicated that plotting the positions of the complex poles, which are determined by both D and I410, might provide more information than either parameter individually. Figure 4 shows the plots for one of each pair of complex poles on the Argand diagram for the patients studied with the mean frequency system. We established four zones corresponding to categories of proximal stenosis. These were: (A) normal or early disease (defined by D < 0.45 and WO > 13), (B) <50% stenosis (0.45 < D < 0.60 and 13 > I410 > 11.5), (C) 50-99% stenosis (D > 0.60 and 11.5 > WO > 9.0), and (D) occlusion (WO < 9.0). The plot of the results from the present study yielded a high degree of correspondence to the zones defining categories of disease. Only 6 values are off by more than one category, and 5 of these are the patients with aneurysmal disease. Although this approach yielded a good result in the first place, it did not provide satisfactory separation in the group studied with maximum velocity signal processing. In the theoretical model, G is related to distal resistance. We initially thought that this value might be clinically relevant in terms of identifying superficial femoral artery occlusion from the proximal waveform. In this study both the legs with open and with occluded superficial femorals had a wide range of G and no separation between the two groups was afforded by this parameter. DISCUSSION
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Fig. 2. Relation of D to the category of stenosis determined from the angiogram. (a) Studies with mean velocity signal. (b) Studies with peak velocity signal.
In both groups ROC analysis showed that the best identification of significant stenosis was achieved with a threshold ofD = 0.60, the same value obtained on previous studies. Overall, the results obtained with the two methods of signal processing are similar (Table 2). The main difference was the somewhat lower sensitivity obtained with the maximum velocity processor: 87% versus 92% with the mean velocity signal. Figure 1B shows that there were 3 legs in the 50-99% stenosis category with D in the clearly normal range. In each case the femoral waveforms had a normal, triphasic appearance, so that the result of the
LaPlace transform analysis of Doppler signals • J. D. BAKER el al.
17
Table 2. Mean damping values by category of stenosis. Current study
Prior study~
Mean freq.
Max freq.
Stenosis category
No. limbs
D (mean)
No, limbs
D (mean)
No. limbs
D (mean)
0% 1-19% 2O-49% 5O-99% 100%
33 7 5 11 6
0.39 0.38 0.67 0.82 0.89
40 6 16 16 20
0.43 0.51 0.44 0.78 0.79
43 5 40 31 29
0.43 0.38 0.42 0.73 0.82
Identification of stenosis >50% Sensitivity Specificity
100% 93%
92% 94%
87% 98%
Baker et al., 1984.
LTA corresponded with the appearance of the signal. One stenosis measured 50% and may have actually belonged in the lower category. (Such borderline cases represent a limit to angiographic measurements.) The other two were measured as 60 and 70% stenosis. We have no explanation for these two outliers. The other errors, both false positives and false negative, fall close to the threshold and are similar to the errors found in previous studies. Extensive experience with LTA of femoral artery waveforms has shown that obtaining an optimal Doppler signal is the key to accurate diagnostic data. Complete insonation of the vessel is important, especially when using the mean velocity system. Tangen-
tial insonation or attempting to study a femoral artery of an obese person where part of the vessel is beyond the range of the probe may produce an aberrant waveform, the analysis of which can produce substantial errors. Campbell (1983) has shown that even small deflections from the optimal probe position can produce substantial error in waveform shape in normal subjects. Figure 5 shows some of the distorted signals which can be obtained from normal femoral arteries. Analysis of these signals often yields D in the abnormal range. An additional source of error may be the presence of proximal aneurysmal disease. In the study with the mean velocity processor all four false posi-
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U l t r a s o u n d in Medicine a n d Biology
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Fig. 4. Complex poles plotted on Argand diagram. For simplicity only the upper part of the diagram with the positive pole is shown. Areas of diagram corresponding to severityof proximal stenosis: (a) normal, (b) <50%, (c) >50%, (d) occlusion. Circles indicate proximal aneurysms.
tives were found in these patients. These waveforms were analyzed individually and all were found to show marked attenuation, which can result from the energy loss in a saccular aneurysm. Not all patients with aneurysms have attenuated waveforms. The extent of damping is probably related to the size of the actual flow lumen through the laminated thrombus in the aneurysm. The group studied with the peak frequency system did not have any cases with marked attenuation associated with aneurysms, however, the experience with the first phase warned that care is required in the interpretation ofwaveform analysis in the presence of proximal aneurysms. A normal value of D indicates that there is no major upstream steno-
sis, however, an abnormal value does not necessarily diagnose occlusive disease. There have been few centers to study LTA, due in part to the lack of a suitable commercial device. Our equipment was designed and built in our laboratory. The only other group to evaluate LTA with mean velocity was Capper et al. (1986) using a mean velocity processor and computer analysis similar to ours. The overall results were a sensitivity of 88% but a specificity of only 63%. This problem was certainly the result of including patients studied in the initial period of use of the technique, for distorted waveforms often yield an abnormally high D. The imorovement occurring with increased experience was
LaPlace transform analysis of Doppler signals • J. D. BAKER el al.
reflected by the sensitivity of 100% and specificity of 89% obtained by analyzing the 28 limbs from the latter part of Capper's study. Table 3 summarizes the diagnostic results of other studies which employed peak velocity signal processing. The first study represents the initial clinical experience with LTA (Baird et al., 1980). Subsequent experience with the method has shown that great care is required to obtain optimal waveforms, and some of the errors probably resulted from inclusion of records with artifacts. Johnston et al. (1984) obtained a good sensitivity but a somewhat lower specificity, possibly the result of performing the curve-fitting in the time domain rather than the frequency domain. MacPherson et al. (1984) had poor results with the technique, but it is not possible to determine whether this problem resulted from inclusion of records with artifacts or from some factor in the analysis. Of note is the fact that none of these reports related proximal aneurysms to false positive results. In the development of LTA, Skidmore considered that G might provide an assessment of the status of the superficial femoral artery based upon the proximal Doppler signal, however, this parameter has not proven to have any diagnostic value. It is probable that G reflects the entire distal resistance, with the superficial femoral artery contributing an unknown part of the total. We conclude that it is not worth pursuing the evaluation of G as a measure of large vessel disease. We had hoped that changing from the instantaneous mean signal to the maximum would improve the results by reducing problems which might arise with incomplete insonation of the common femoral artery, however, the sensitivity is lower with the peak velocity data. Since the two methods were studied in different patients, we cannot know whether the difference in sensitivity is clinically significant. The wide
(a)
19
Table 3. Comparison with previous studies which used maximum frequency signal. Detection of proximal stenosis >50%
Threshold for D Sensitivity Specificity
Baird (1980)
Johnston (1984)
MacPherson (1984)
0.60 85% 84%
0.63 87% 84%
58% 76%
a
Present study 0.60 87% 98%
"No ROC analysis given--threshold of 0.60 used for comparison.
variability of D prevented identification of subgroups based on this parameter. Data obtained with the mean processor showed that separation into subcategories of stenosis was achieved by plotting the complex poles (which are related to both D and WO) on an Argand diagram, however, with the maximum detector there is too much overlap to permit meaningful separation of subgroups. Although theoretically the peak signal should be superior, better results appear to be achieved with the mean signal. It may be that it is not possible to obtain as good a curve fit for the more oscillatory maximum signal so that there would be more problem results of LTA. Further evaluation of LTA is needed to clarify some of the problems identified in this study. We are currently carrying out a detailed study of the curve-fit obtained with different arterial waveforms in order to define more completely the limitations of this technique. Initially, we considered that the LTA method would be simple and easily mastered, but experience has shown that great care must be taken to obtain a suitable waveform. Signals with positive or negative offsets will result in errors (Fig. 4). We are trying to develop other guidelines to help identify artifactual waveforms. In addition, we have a new Doppler unit incorporating both peak and mean processors so that we can obtain both types of signals on each patient. This will permit direct comparison between the two processing systems in order to determine whether there is any advantage of one over the other.
(b) Acknowledgement--This study was supported in part by the Joash Medical Foundation.
(e)
(d)
Fig. 5. Distorted signals obtained from normal common femoral arteries, The positive (a, b) or negative offset (c) is not the result of a baseline shift on the Doppler unit but is present in the detected signal. The truncated signal (d) reflects poor probe placement.
REFERENCES Arts, M. G. J.; Roevros, J. M. J. G. On the instantaneous measurement of bloodflow by ultrasonic means. Med. Biol. Engng. 10:23-24; 1972. Baker, J. D.; Machleder, H. I.; Skidmore, R. Analysis of femoral artery Doppler signals by the LaPlace transform damping method. J. Vase. Surg. 1:520-524; 1984.
20
Ultrasound in Medicine and Biology
Baird, R. N.; Bird, D. R.; Clifford, P. C.; Lusby, R. J.; Skidmore, R.; Woodcock, J. P. Upstream stenosis--its diagnosis by Doppler signals from the femoral artery. Arch. Surg. 115:1316-1322; 1980. Campbell, W. B. LaPlace transform analysis of Doppler waveforms in lower limb arterial disease. University of London; 1983. MS thesis. Campbell, W. B.; Baird, R. N.; Cole, S. E. A.; Evans, J. M.; Skidmore, R.; Woodcock, J. P. Physiologic interpretation of Doppler shift waveforms: the femoro distal segment in combined disease. Ultrasound in Med. & Biol. 9:265-269; 1983. Campbell, W. B.; Skidmore, R.; Baird, R. N. Variability and reproducibility of arterial Doppler waveforms. Ultrasound in Med. & Biol. 10:601-606: 1984. Capper, W. L.; Amoore, J. N.; Clifford, P. C.; lmmelman, E. J.; Harries-Jones, E. P. A system for rapid analysis of the femoral
Volume 15, Number 1, 1989 blood velocity waveform at the bedside. Ultrasound in Med. & Biol. 12:31-38; 1986. Johnston, K. W.; Kassam, M.; Koers, J.; Cobbold, R. S. C.; MacHattie, D. Comparative study of four methods for quantifying Doppler ultrasound waveforms from the femoral artery. Ultrasound in Med. & Biol. 10:1-12; 1984. MacPherson, D. S.; Evans, D. H.; Bell, P. R. F. Common femoral artery wave-forms: a comparison of three methods of objective analysis with direct pressure measurements. Br. J. Surg. 71:4649; 1984. Skidmore, R. The use of the transcutaneous ultrasonic tlowmeter in the dynamic analysis of blood flow. University of Bristol; 1979. Ph.D. thesis. Skidmore, R.; Woodcock, J. P.; Wells, P. N. T.; Bird, D.; Baird, R. N. Physiological interpretation of Doppler-shift waveforms --II1 clinical results. Ultrasound in Med. & Biol. 6:227-231; 1980.
0301-5629/89 $3.00 + .00 Pergamon Press plc
OOriginal Contribution LAPLACE TRANSFORM ANALYSIS OF FEMORAL ARTERY SIGNALS: THE STATE OF THE ART
DOPPLER
J. DENNIS BAKER, ROBERT SKIDMORE a n d SUSAN E. A. COLE Department of Medical Physics, Bristol Royal Infirmary, Bristol, UK, and the Vascular Surgery Section, VA Medical Center, Sepulveda, CA (Received 9 September 1987;in final form 4 July 1988) Abstract--A followup study was conducted to validate our previous experience with the LaPlace Transform Analysis (LTA) method for processing Doppler ultrasound signals from the common femoral artery to detect significant stenosis of the aorto-iliac segment. The first phase used the same instantaneous mean velocity signal processor as used in the prior study. A comparison of the Doppler examinations with angiograms in 98 legs yielded a sensitivity = 92% and sensitivity = 94% in the identification of 50% or greater stenosis of the aorta-iliac segment, results almost identical to the last study. Because of theoretical disadvantages of using the instantaneous mean velocity signal we carried out a second phase using a peak velocity detector. In 148 limbs sensitivity = 87% and specificity = 98%. The presence or absence of superficial femoral artery occlusion did not affect the accuracy of the waveform analysis in the detection of proximal disease. The LTA parameter related to distal resistance, G, was not found to have clinical value in the assessment of the femoral-popliteal segment.
Key Words: Ultrasound, Doppler, Waveform analysis, LaPlace transform, Diagnosis, Arterial occlusive disease, Iliac artery.
INTRODUCTION
waveform was described in terms of a third-owner transform of the form:
The noninvasive detection of severe occlusive disease of the distal aorta and the iliac arteries is a clinically important but difficult problem. Although simple segmental pressure measurements are useful in the leg, they have not been found to be accurate enough in determining inflow disease, particularly in the presence of superficial femoral artery (SFA) disease. A number of investigators have turned to analysis of the Doppler velocity waveform from the common femoral artery as a method of assessing proximal disease. The simplest method has been to determine whether or not there is reverse flow in early diastole. Some of the quantitative methods of classifying the velocity waveform include pulsatility index and principle component analysis. In 1979 Skidmore introduced the LaPlace transform analysis (LTA), which processed the waveform in the frequency domain (Skidmore, 1979; Skidmore et al., 1980). Initial evaluation of the method showed that the common femoral artery velocity could be described using a 3 pole, 1 zero model. The arterial
H(S) = 1/(Sa + 2D W O + W 0 2 ) ( S + G). The theoretical model upon which the method was based predicted that the coefficients of the transform were related to proximal stenosis (D or damping value), arterial wall stiffness (WO), and distal impedance (G). The solution of the equation yielded two complex poles related to D and W O and a real pole related to G. These can be expressed on an Argand diagram, a graphic representation of complex numbers, where the real values are plotted on the X axis and imaginary values on the Y axis (Fig. 1). In LTA the magnitude on the X axis = D . W O and the Y axis = W O (1 - DE)1/2. A significant proximal stenosis reduced both D and W O , shifting the positions of the complex poles from X 1 to X2. Normal values of D ranged from 0.20 to 0.40. Increasing proximal stenosis produced an increase in D, and with severe damping of the waveform the complex poles became real and D reached a maximum of 1.00. W O was related to proximal vessel wall stiffness; normal arteries had values above 15 and lower values resulted from proximal stenosis. G was related to the radius of the distal
Address correspondenceand reprint requeststo: Dr. Baker, 112G, VA MedicalCenter, Sepulveda,CA 91343. 13
14
UltrasoundinMedicineandBiology Volume15,Number1,1989 NORMAL
STENOTIC
O~
X2¢
xs% X2
~
" =
C08
~ O~
O ×1
Fig. 1. Argand diagram representation of the two complex poles (X1) and the real pole (X3) obtained from the analysis. Proximal stenosis decreases both D and WO, shifting the complex poles from X 1 to X2. or runoff system. The model predicted that D and WO were independent of distal impedance, i.e., unaffected by the status of the SFA. The initial clinical evaluation of LTA focused upon the diagnostic value of D and found that a value >0.60 had an 85% sensitivity and an 84% specificity in identifying an iliac stenosis of >50% diameter reduction (Baird et al., 1980). These encouraging resuits led to further evaluation and development of the method. The original Doppler system had a maximum frequency follower which employed the multiple filter method. Processing was done on a MINC computer (Digital Equipment Co.) and required eight minutes to analyze each set of waveforms. This system, with its expensive research computer and slow processing, was clumsy and not really practical for routine use in a clinical setting, so a second setup was developed using an Apple II+ computer. An analog mean frequency processor, based upon the design of Arts and Roevros (1972), was built to replace the maximum follower with its large size and complexity and its requirement for manual threshold adjustment. The initial study of femoral artery signals carried out with this new system produced excellent resuits in the diagnosis of inflow stenosis >50% (Baker et al., 1984). In addition, the hardware was compact and simple to use, making it practical for routine clinical examinations.
We were concerned whether the use of the mean frequency might result in errors due to the requirement for complete insonation of the vessel. A pilot study by Campbell comparing the multiple-filter maximum frequency detector with the analog mean frequency detector showed no significant difference in the values obtained for femoral artery D and WO (Campbell et al., 1984). In spite of these findings we were interested in evaluating peak frequency measurements. Because of practical problems with the multiple-filter processor, we developed an analog maximum frequency detector. The present report comprises two separate phases of our work with LTA for assessment of lower extremity disease. The first was a validation study using the same equipment (including the mean frequency signal processor) as in the initial evaluation reported in 1984. The second phase was carded out in a separate group of patients using the new analog maximum frequency detector. PATIENTS AND METHODS Common femoral artery Doppler velocity signals were obtained using a 10 MHz directional, continuous wave detector featuring a high signal-to-noise ratio. This unit was designed and built in our laboratory and was the same one used in the previous studies (Baker et al., 1984). In the first phase the quadrature output was connected to an analog detector which provided an instantaneous mean frequency signal. This device was based on the design of Arts and Roevros (1972). For the second phase we designed and built an analog maximum frequency processor based on a servo-loop controlled variable filter which tracked the peak frequency. The unit had two sections, one for forward and one for reverse flow signals, The two outputs were added together to produce a single bidirectional signal. An 8-bit analog-todigital converter provided the interface for the Apple II+ computer (Apple Computer, Inc., Cupertino, Calif.). The computer screen displayed a real-time trace of the velocity signal, which could be frozen once an optimal waveform was obtained. A cursor was used to select three waveforms to be averaged for the analysis, and the data were stored on disk. Usually all the samples from a patient were stored and then analyzed after the end of the examination. The computer program, written in compiled Basic for faster execution, calculated D, WO, and G. Increased processing speed was achieved by using an accelerator card based upon an ADM 9511B arithmetic processor unit (California Computer Systems model 7811), permitting computation for each record in 50 s.
LaPlace transform analysis of Doppler signals • J. D. BAKER et al.
This study, carded out in the Vascular Studies Unit, Bristol Royal Infirmary, included Doppler recordings from limbs of patients for whom satisfactory arteriograms were available displaying the segment from the distal abdominal aorta to the knee. Patients with cardiac dysrhythmias or heart rates above 100 were excluded. Patients with prior operations involving the femoral artery were not studied to avoid potential problems which can be caused by scar tissue and by prosthetic materials. Recordings with artifacts or with substantial difference between cardiac cycles were excluded. In each phase approximately 10% of limbs with satisfactory angiograms were excluded for this reason. Table 1 summarizes the characteristics of the patients included in each phase. In some patients only one leg was included in the study because of major leg amputation or unsuitable Doppler or arteriographic studies on one side. Prior to obtaining the Doppler recordings the patient rested on the examining table for 15 min. Common femoral velocity tracings were obtained just below the inguinal ligament, which was identified from bony landmarks rather than from the groin crease. The examiner used both the analog trace on the screen and the audio output to adjust the probe, and considerable care was required to achieve optimal insonation of the vessel while avoiding venous signal contamination. All stenoses in the arota-iliac segment and in the superficial femoral artery were identified on each arteriogram. The residual lumen and the diameter of the normal adjacent segment were measured in order to calculate the percent diameter reduction for each lesion. If there was more than one stenosis in a segment, the most severe was measured. We focused on the detection of significant inflow disease, defined as 50% or greater diameter reduction proximal to the common femoral artery. For most of the analysis the proximal segments were grouped by category of stenosis: no stenosis, 1-19%, 20-49%, 50-99%, and 100%. The superficial femoral arteries were divided into patent or occluded vessels. These groupings were the same as used on our previous study to permit comparison of results. Receiver operator characteristic (ROC) analysis was used to determine the effects on sensitivity and specificity resulting from different T a b l e 1. Characteristics o f patients. Signal processor Mean Maximum
No. limbs
No. patients
Mean age (S.D.)
Male
Indication % critical ischemia
98 148
65 101
62.1 62.5
77% 77%
31% 32%
15
threshold values of D. Differences between categories was studied with the unpaired t-test. RESULTS The primary goals of the study were (a) to determine how well LTA could diagnose the presence of a significant stenosis and (b) to evaluate whether there was any difference in results obtained by using the two different methods of Doppler signal processing, mean versus peak frequency. Figure 2 shows the values of D in each category of proximal stenosis. In both phases of the study there was a highly significant difference (p < 0.00 l) between the mean values of D obtained for inflow stenosis above and below 50% (Table 2). The variance within each group was high enough so there was no significant difference between the subgroups of inflow disease above or below 50% except for a difference between 50-99% and 100% in the patients studied with the peak velocity detector (17 -- 0.04). The difference resulted from the occurrence of three cases with very low D; if these outliers are excluded, there is no difference between the two subgroups. The results of ROC analysis are summarized in Fig. 3. For both phases the best diagnosis of inflow stenosis >50% is achieved with a threshold D of 0.60, the same as found in our original study. Using this cutoff point yielded a sensitivity of 92% and a specificity of 94% for the patients studied with the mean frequency system. Of note is the fact that the only false positives occurred in patients with proximal aneurysms. The second phase using the maximum frequency processor yielded a sensitivity of 87% and a specificity of 98%. Early work with the waveform analysis suggested that the damping value might help to grade the severity of stenosis below 50%. The plots in Fig. 2 show no distinguishable difference for the three categories of early disease. When D is plotted against the measured percent stenosis there is a rising trend, but linear regression showed poor correlation. The theoretical model suggested that the diagnosis of proximal disease should not be affected by the status of the superficial femoral artery. Figure 2 identifies the legs with open and occluded SFAs. The mean D values for the occluded ones were slightly higher than for the patent ones, however, the differences were not statistically significant. The ROC curves computed for the groups with open and occluded SFAs were essentially the same as for the entire group. The relation of WO to proximal disease was evaluated both for measure of percent stenosis and
16
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for category of stenosis, but neither approach improved the diagnosis. There was a decrease in WO of the common femoral artery with increasing severity of proximal lesions, but there was more overlap between groups than with D. We evaluated Campbell's suggestion that the ratio of femoral to ankle WO provides as assessment of patency of the superficial femoral artery (Campbell et al., 1983). In our patients the ratio did not separate open vessels from occlusions in any of the categories of iliac disease. Review of the data from the prior study indicated that plotting the positions of the complex poles, which are determined by both D and I410, might provide more information than either parameter individually. Figure 4 shows the plots for one of each pair of complex poles on the Argand diagram for the patients studied with the mean frequency system. We established four zones corresponding to categories of proximal stenosis. These were: (A) normal or early disease (defined by D < 0.45 and WO > 13), (B) <50% stenosis (0.45 < D < 0.60 and 13 > I410 > 11.5), (C) 50-99% stenosis (D > 0.60 and 11.5 > WO > 9.0), and (D) occlusion (WO < 9.0). The plot of the results from the present study yielded a high degree of correspondence to the zones defining categories of disease. Only 6 values are off by more than one category, and 5 of these are the patients with aneurysmal disease. Although this approach yielded a good result in the first place, it did not provide satisfactory separation in the group studied with maximum velocity signal processing. In the theoretical model, G is related to distal resistance. We initially thought that this value might be clinically relevant in terms of identifying superficial femoral artery occlusion from the proximal waveform. In this study both the legs with open and with occluded superficial femorals had a wide range of G and no separation between the two groups was afforded by this parameter. DISCUSSION
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In both groups ROC analysis showed that the best identification of significant stenosis was achieved with a threshold ofD = 0.60, the same value obtained on previous studies. Overall, the results obtained with the two methods of signal processing are similar (Table 2). The main difference was the somewhat lower sensitivity obtained with the maximum velocity processor: 87% versus 92% with the mean velocity signal. Figure 1B shows that there were 3 legs in the 50-99% stenosis category with D in the clearly normal range. In each case the femoral waveforms had a normal, triphasic appearance, so that the result of the
LaPlace transform analysis of Doppler signals • J. D. BAKER el al.
17
Table 2. Mean damping values by category of stenosis. Current study
Prior study~
Mean freq.
Max freq.
Stenosis category
No. limbs
D (mean)
No, limbs
D (mean)
No. limbs
D (mean)
0% 1-19% 2O-49% 5O-99% 100%
33 7 5 11 6
0.39 0.38 0.67 0.82 0.89
40 6 16 16 20
0.43 0.51 0.44 0.78 0.79
43 5 40 31 29
0.43 0.38 0.42 0.73 0.82
Identification of stenosis >50% Sensitivity Specificity
100% 93%
92% 94%
87% 98%
Baker et al., 1984.
LTA corresponded with the appearance of the signal. One stenosis measured 50% and may have actually belonged in the lower category. (Such borderline cases represent a limit to angiographic measurements.) The other two were measured as 60 and 70% stenosis. We have no explanation for these two outliers. The other errors, both false positives and false negative, fall close to the threshold and are similar to the errors found in previous studies. Extensive experience with LTA of femoral artery waveforms has shown that obtaining an optimal Doppler signal is the key to accurate diagnostic data. Complete insonation of the vessel is important, especially when using the mean velocity system. Tangen-
tial insonation or attempting to study a femoral artery of an obese person where part of the vessel is beyond the range of the probe may produce an aberrant waveform, the analysis of which can produce substantial errors. Campbell (1983) has shown that even small deflections from the optimal probe position can produce substantial error in waveform shape in normal subjects. Figure 5 shows some of the distorted signals which can be obtained from normal femoral arteries. Analysis of these signals often yields D in the abnormal range. An additional source of error may be the presence of proximal aneurysmal disease. In the study with the mean velocity processor all four false posi-
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U l t r a s o u n d in Medicine a n d Biology
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tives were found in these patients. These waveforms were analyzed individually and all were found to show marked attenuation, which can result from the energy loss in a saccular aneurysm. Not all patients with aneurysms have attenuated waveforms. The extent of damping is probably related to the size of the actual flow lumen through the laminated thrombus in the aneurysm. The group studied with the peak frequency system did not have any cases with marked attenuation associated with aneurysms, however, the experience with the first phase warned that care is required in the interpretation ofwaveform analysis in the presence of proximal aneurysms. A normal value of D indicates that there is no major upstream steno-
sis, however, an abnormal value does not necessarily diagnose occlusive disease. There have been few centers to study LTA, due in part to the lack of a suitable commercial device. Our equipment was designed and built in our laboratory. The only other group to evaluate LTA with mean velocity was Capper et al. (1986) using a mean velocity processor and computer analysis similar to ours. The overall results were a sensitivity of 88% but a specificity of only 63%. This problem was certainly the result of including patients studied in the initial period of use of the technique, for distorted waveforms often yield an abnormally high D. The imorovement occurring with increased experience was
LaPlace transform analysis of Doppler signals • J. D. BAKER el al.
reflected by the sensitivity of 100% and specificity of 89% obtained by analyzing the 28 limbs from the latter part of Capper's study. Table 3 summarizes the diagnostic results of other studies which employed peak velocity signal processing. The first study represents the initial clinical experience with LTA (Baird et al., 1980). Subsequent experience with the method has shown that great care is required to obtain optimal waveforms, and some of the errors probably resulted from inclusion of records with artifacts. Johnston et al. (1984) obtained a good sensitivity but a somewhat lower specificity, possibly the result of performing the curve-fitting in the time domain rather than the frequency domain. MacPherson et al. (1984) had poor results with the technique, but it is not possible to determine whether this problem resulted from inclusion of records with artifacts or from some factor in the analysis. Of note is the fact that none of these reports related proximal aneurysms to false positive results. In the development of LTA, Skidmore considered that G might provide an assessment of the status of the superficial femoral artery based upon the proximal Doppler signal, however, this parameter has not proven to have any diagnostic value. It is probable that G reflects the entire distal resistance, with the superficial femoral artery contributing an unknown part of the total. We conclude that it is not worth pursuing the evaluation of G as a measure of large vessel disease. We had hoped that changing from the instantaneous mean signal to the maximum would improve the results by reducing problems which might arise with incomplete insonation of the common femoral artery, however, the sensitivity is lower with the peak velocity data. Since the two methods were studied in different patients, we cannot know whether the difference in sensitivity is clinically significant. The wide
(a)
19
Table 3. Comparison with previous studies which used maximum frequency signal. Detection of proximal stenosis >50%
Threshold for D Sensitivity Specificity
Baird (1980)
Johnston (1984)
MacPherson (1984)
0.60 85% 84%
0.63 87% 84%
58% 76%
a
Present study 0.60 87% 98%
"No ROC analysis given--threshold of 0.60 used for comparison.
variability of D prevented identification of subgroups based on this parameter. Data obtained with the mean processor showed that separation into subcategories of stenosis was achieved by plotting the complex poles (which are related to both D and WO) on an Argand diagram, however, with the maximum detector there is too much overlap to permit meaningful separation of subgroups. Although theoretically the peak signal should be superior, better results appear to be achieved with the mean signal. It may be that it is not possible to obtain as good a curve fit for the more oscillatory maximum signal so that there would be more problem results of LTA. Further evaluation of LTA is needed to clarify some of the problems identified in this study. We are currently carrying out a detailed study of the curve-fit obtained with different arterial waveforms in order to define more completely the limitations of this technique. Initially, we considered that the LTA method would be simple and easily mastered, but experience has shown that great care must be taken to obtain a suitable waveform. Signals with positive or negative offsets will result in errors (Fig. 4). We are trying to develop other guidelines to help identify artifactual waveforms. In addition, we have a new Doppler unit incorporating both peak and mean processors so that we can obtain both types of signals on each patient. This will permit direct comparison between the two processing systems in order to determine whether there is any advantage of one over the other.
(b) Acknowledgement--This study was supported in part by the Joash Medical Foundation.
(e)
(d)
Fig. 5. Distorted signals obtained from normal common femoral arteries, The positive (a, b) or negative offset (c) is not the result of a baseline shift on the Doppler unit but is present in the detected signal. The truncated signal (d) reflects poor probe placement.
REFERENCES Arts, M. G. J.; Roevros, J. M. J. G. On the instantaneous measurement of bloodflow by ultrasonic means. Med. Biol. Engng. 10:23-24; 1972. Baker, J. D.; Machleder, H. I.; Skidmore, R. Analysis of femoral artery Doppler signals by the LaPlace transform damping method. J. Vase. Surg. 1:520-524; 1984.
20
Ultrasound in Medicine and Biology
Baird, R. N.; Bird, D. R.; Clifford, P. C.; Lusby, R. J.; Skidmore, R.; Woodcock, J. P. Upstream stenosis--its diagnosis by Doppler signals from the femoral artery. Arch. Surg. 115:1316-1322; 1980. Campbell, W. B. LaPlace transform analysis of Doppler waveforms in lower limb arterial disease. University of London; 1983. MS thesis. Campbell, W. B.; Baird, R. N.; Cole, S. E. A.; Evans, J. M.; Skidmore, R.; Woodcock, J. P. Physiologic interpretation of Doppler shift waveforms: the femoro distal segment in combined disease. Ultrasound in Med. & Biol. 9:265-269; 1983. Campbell, W. B.; Skidmore, R.; Baird, R. N. Variability and reproducibility of arterial Doppler waveforms. Ultrasound in Med. & Biol. 10:601-606: 1984. Capper, W. L.; Amoore, J. N.; Clifford, P. C.; lmmelman, E. J.; Harries-Jones, E. P. A system for rapid analysis of the femoral
Volume 15, Number 1, 1989 blood velocity waveform at the bedside. Ultrasound in Med. & Biol. 12:31-38; 1986. Johnston, K. W.; Kassam, M.; Koers, J.; Cobbold, R. S. C.; MacHattie, D. Comparative study of four methods for quantifying Doppler ultrasound waveforms from the femoral artery. Ultrasound in Med. & Biol. 10:1-12; 1984. MacPherson, D. S.; Evans, D. H.; Bell, P. R. F. Common femoral artery wave-forms: a comparison of three methods of objective analysis with direct pressure measurements. Br. J. Surg. 71:4649; 1984. Skidmore, R. The use of the transcutaneous ultrasonic tlowmeter in the dynamic analysis of blood flow. University of Bristol; 1979. Ph.D. thesis. Skidmore, R.; Woodcock, J. P.; Wells, P. N. T.; Bird, D.; Baird, R. N. Physiological interpretation of Doppler-shift waveforms --II1 clinical results. Ultrasound in Med. & Biol. 6:227-231; 1980.