## Journal of the American College of Cardiology

# Accuracy of Doppler Catheter Measurements: Effect of Inhomogeneous Beam Power Distribution on Mean and Peak Velocity

## Author + information

- Received June 6, 1996
- Revision received October 7, 1996
- Accepted October 25, 1996
- Published online February 1, 1997.

## Author Information

- Scott J Denardo, MD, FACCA,*,
- Lawrence Talbot, PhDB,
- Victor K Hargrave, BSA,
- Alan R Selfridge, PhDA,
- Thomas A Ports, MD, FACCA and
- Paul G Yock, MD, FACCA

- ↵*Dr. Scott J. Denardo, Cardiac Catheterization Laboratory, Moore Regional Hospital, Pinehurst, North Carolina 28374.

## Abstract

Objectives. We sought to determine the effect of inhomogeneous distribution of beam power produced by Doppler catheters on measurements of mean and peak velocity of coronary blood flow.

Background. Measurements of mean velocity of coronary blood flow by Doppler catheters have significant systematic errors that have not been completely characterized. We hypothesized that one error is the inhomogeneous distribution of the ultrasonic beam power and that this inhomogeneity makes measurements of mean, but not peak, velocity inaccurate.

Methods. We constructed a scaled-up model of a Doppler catheter to allow for accurate measurement of the distribution of beam power by miniature hydrophones. This catheter was placed in a model of coronary blood flow in which the fluid velocity was accurately measured by an external laser Doppler velocimeter. The laser Doppler measurements of mean velocity were compared with the measurements of mean velocity made by the catheter, using fast Fourier transform analysis, both without and with correction for inhomogeneous beam power distribution. Peak velocity measurements were also compared, as predicted from theory, without the need of correction for inhomogeneous beam power distribution. To investigate the clinical relevance of our results, we conducted studies using a clinical Doppler catheter both in a scaled model of coronary flow and in a series of eight patients. In the model and in each patient, we rotated the catheter without changing the axial position to systematically alter the relation of the beam power distribution to the local fluid dynamics.

Results. The measurement of beam power distribution revealed significant inhomogeneity. Comparison of the measured mean frequency shifts without correction for inhomogeneities in the distribution yielded a statistically significant difference. After correction for inhomogeneities, there was no statistically significant difference. Also, there was no significant difference for the peak frequency shifts. Rotation of the clinical catheter in the scaled model and in the patients changed the measured mean velocity (average change 18.8% and 20.6%, respectively), but not the measured peak velocity (average change 5.0% and 4.3%, respectively).

Conclusions. For signal analysis using a fast Fourier transform, the inhomogeneous distribution of power of the ultrasonic beam produced by Doppler catheters makes measurements of mean, but not peak, velocity inaccurate. Measurements of peak velocity may therefore prove superior to measurements of mean velocity in estimating the response to pharmacologic intervention and in estimating stenosis severity.

(J Am Coll Cardiol 1997;29:283–92)

Since the introduction of the first prototype by Hartley and Cole in 1977 ([1]), Doppler catheters have been used to measure velocity and flow reserve in studies of coronary physiology after both pharmacologic and mechanical interventions ([2–10]). Early validation studies demonstrated systematic errors in velocity measurements ([3, 11, 12]). These inaccuracies were attributed in part to the zero-crossing technique of analysis of the audio signal recorded by the Doppler catheter.

To improve the accuracy of measurements, an alternative technique for signal analysis, using a fast Fourier transform, was applied ([13]). Fast Fourier transforms produce a spectrum of Doppler-shifted frequencies based on the velocity of the individual scatterers (e.g., red blood cells) within the fluid. Because the Doppler spectrum reflects the velocity of the individual scatterers, the mean frequency shift of the spectrum should accurately reflect the mean velocity of the fluid flow. In fact, Yamagishi et al. ([14]) reported validation studies in which the mean frequency shift of the Doppler spectrum accurately predicted the measured mean velocity of fluid flow through a tube.

The measured mean velocity can be accurate only if the distribution of power of the ultrasonic beam is uniform, or homogeneous, over the entire vessel. However, Roth et al. ([15]) recently demonstrated that the power distribution for the Doppler catheter with an end-mounted transducer is *not*homogeneous. This inhomogeneity in power distribution is most likely a result of imperfections in the ultrasound crystal material and manufacturing steps required to mount the transducers. Such inhomogeneities can have a major impact on the accuracy of mean velocity measurements made by Doppler catheters. In particular, regions where the beam is stronger contribute more to the calculation of the mean velocity than regions where the beam is weaker. The peak velocity, however, should be unaffected by inhomogeneity because the measurement of peak velocity requires only that some part of the central beam insonifies the highest velocity portion of the flow stream. The theoretical accuracy of the peak velocity measurement, though widely accepted, has actually never been validated for the Doppler catheter.

We therefore hypothesized that the inhomogeneous distribution of power of the ultrasonic beam produced by a Doppler transducer makes measurements of mean, but not peak, velocity of fluid flow inaccurate. To test this hypothesis, we constructed a scaled-up model of a Doppler catheter with an end-mounted transducer to allow for accurate beam profile measurements and then plotted the distribution of beam power to assess inhomogeneity. We then placed this catheter in a model of coronary blood flow in which the velocity of both undisturbed and disturbed flow was accurately measured by using an external laser Doppler velocimeter. Taking these measurements as the predicted values, we compared them, both without and with correction for the beam power distribution, to mean flow velocity, as reflected by the mean frequency shift recorded by the catheter using fast Fourier transform analysis. Similarly, we compared predicted peak velocity to the peak frequency shift recorded by the catheter.

Finally, to investigate the clinical relevance of our results, we conducted both in vitro and in vivo studies where the relation of the beam power distribution produced by a clinical Doppler catheter to local fluid dynamics was altered. The in vitro studies involved placing the clinical catheter in a scaled model of coronary blood flow, and the in vivo studies involved placing the catheter into the coronary circulations of eight patients. For both the in vitro and in vivo studies, we rotated the clinical catheter to systematically alter the relation of the beam power distribution to local fluid dynamics. If the hypothesis about beam inhomogeneities is correct, then rotating the catheter should change the mean, but not peak, frequency shift.

## 1 Methods

### 1.1 In vitro studies: scaled-up model.

#### 1.1.1 Doppler catheter model.

The distribution of beam power transmitted by ultrasonic transducers can be measured using a hydrophone system ([15, 16]). However, no commercially available hydrophone system is small enough to allow for accurate, high resolution beam power measurements of clinical Doppler catheters, which have a wavelength in blood of 0.07 mm. We therefore constructed a scaled-up Doppler catheter (scale factor 12.7) (Fig. 1) that precisely mimicked the general design of a commercially available Millar Doppler catheter (Millar Instruments) (Fig. 1). In particular, the test catheter was constructed with an annular piezoelectric crystal at the tip, which faced downstream. The annular shape of the test crystal matched the design of clinical catheters. A 0.50-cm (outer diameter) aluminum rod modeled the central guide wire used to position clinical catheters. In addition, the material chosen for the transducer (modified lead titinate) had electromechanical properties that, when scaled, were very similar to those of the material used for the clinical catheters (PZT 5A). The beam power distribution produced by the test catheter was most likely more homogeneous than that produced by the clinical catheter because of three features: 1) The shape of the test transducer was more symmetric than that of the typical clinical catheter (Fig. 1). 2) The surface imperfections of the test transducer and the single electrical leads soldered to the front and back faces of this transducer were relatively smaller than those of the clinical catheter. 3) The crystal frequency of the test catheter (5.0 MHz) was, on a scale-relation basis, greater than that of the clinical catheter (20 MHz). Precise modeling for our system, including correction for differences in the speed of sound and viscosity of the test fluid compared with blood, would require a crystal frequency of 1.8 MHz. However, we chose the higher frequency because of the availability of a commercial 5.0-MHz Doppler transmitter/receiver system. The radial dimension of the annular transducer of the test catheter was therefore 11 wavelengths, whereas that of the clinical catheter was three wavelengths. These factors combined to produce a beam power distribution for the test catheter which was most likely narrower and more homogeneous than that of the clinical catheter.

#### 1.1.2 Coronary blood flow model.

The scaled-up, in vitro model of coronary blood flow (Fig. 2) was designed to deliver continuous flow at a constant perfusion pressure through the test section as measured by a mechanical flowmeter. The experimental fluid was a mixture of 52.2% glycerol in distilled water. This glycerol/water ratio was selected to maximize the Doppler shifts occurring at the test Reynolds numbers while avoiding signal aliasing as a result of exceeding the range–velocity product. From standard tables, the viscosity of this solution was determined to be 0.625 Newton-seconds (Ns)/m^{2}, the density 1,130 kg/m^{3}and the speed of sound 1,748 m/s. A 2.54-cm (internal diameter) acrylic tube was used as the test section, corresponding to a coronary artery with a lumen diameter of 2.0 mm. The mechanical flowmeter was calibrated by timing the collection of a set volume of the experimental fluid, converting volumetric flow to the Reynolds number and then performing a linear regression between the Reynolds number and flowmeter setting.

The catheter and guide wire were placed centrally in the acrylic test section (Fig. 3). A 10.0-cm long aluminum honeycomb screen was placed in the test section 130 cm upstream of the transducer to ensure that fully developed, annular laminar flow was achieved well upstream of the transducer. In addition, a stack of ten 4.0-mm thick, perforated paraffin discs (outer diameter 2.25 cm) was placed on the scaled-up guide wire downstream from the transducer. These discs absorbed the sound waves produced by the transducer and effectively circumvented the problem caused by the presence of multiple sample volumes beyond the primary sample volume of the transducer. An annular-shaped axisymmetric acrylic flow screen was placed 12.7 cm upstream from the transducer to generate disturbed flow patterns. This design ensured that, in addition to reproducible normal laminar flow patterns, reproducible disturbed flow patterns occurred at a position of 2.54 cm or further downstream from the transducer. Laser Doppler velocimeter and ultrasound data were obtained at axial intervals of 1.27 cm from 2.54 to 6.35 cm downstream from the transducer. This distance corresponds to range gate distances of 2.0 to 5.0 mm in the clinical setting.

Three different flow rates (corresponding to Reynolds numbers of 200, 300 and 400) were studied without and with the disturbance-producing flow screen. Thus, a total of six flow conditions were studied, modeling a range of physiologic and pathologic flow conditions.

#### 1.1.3 Beam power distribution data.

A hydrophone system (Specialty Engineering Associates) was used to measure the power distribution of the transmitted ultrasonic beam in the transverse plane as a function of axial position. A pulse signal generator (Hewlett Packard Model 8165) produced an input signal of 5.0 MHz. When this signal was applied to the transducer of the scaled-up Doppler catheter, the beam power distribution in the plane perpendicular to the axis of the catheter/guide wire was measured at the axial positions for which the laser Doppler velocimeter and ultrasound data were collected.

The diameter of the hydrophone transducer was 0.25 mm. The resolving power of the hydrophone system for the scaled-up Doppler catheter was therefore on the order of one wavelength ([1,748 m/s]/[5.0 MHz] ≈ 0.35 mm). To assess inhomogeneities in the beam power distribution at each axial position of interest, the hydrophone position was raster scanned to produce a two-dimensional topographic map of power as a function of position.

#### 1.1.4 Laser Doppler velocimeter and Doppler ultrasound measurements.

For predicted values of mean and peak fluid velocity, a side scatter laser Doppler velocimeter system was used to measure fluid velocity at specific points within the test section. The components of the system were a 1.5-W argon laser with a single color mode wavelength of 514.5 nm (Lexel, model 85), a beam splitter with appropriate transmitting and receiving optics (TSI, models 915 and 918, respectively) and a photomultiplier tube (RCA, model 4526) with DC power supply (Hewlett-Packard, model 6515A). Real-time, on-line data analysis of the amplified photomultiplier tube output (Keithley Instruments, pulse amplifier model 107) was performed using a signal processor (TSI, model 550 “Intelligent Flow Analyzer”) with microcomputer support (IBM PC/AT). Data were collected at each of the specified axial positions at radial intervals of 1.0 mm across the test section. The data analysis for measurements made at each point in the test section produced a mean velocity and standard deviation of fluid flow, reflecting the generally gaussian-shaped distribution of velocity fluctuations occurring at each point. This distribution became broader for increasing local flow disturbance. From the mean velocity data, individual velocity profiles were constructed by fitting a fifth-order polynomial to the individual data points (Fig. 4). Given the axisymmetry of the test section, the individual velocity profiles were assumed to be symmetric about the central guide wire. A combination of the mean fluid velocity and standard deviation was used to calculate the peak velocity for each point in the test section.

For measurement of mean and peak fluid velocity, the pulsed Doppler ultrasound equipment used consisted of a multifrequency Doppler unit (Vingmed, model SD 100, Oslo, Norway) and a spectrum analyzer (Medasonics Vasculab, model SP 100). The pulsed wave mode ultrasound provided the capability for range resolution—that is, the ability to make measurements in discrete sample volumes at various distances along the ultrasonic beam. The location of the primary sample volume was adjusted by altering the range delay interval. The Doppler unit transmission frequency was 5.0 MHz and the pulse duration was 2.25 ms. The sample volume length was set at 3.93 mm, corresponding to a sample volume for the clinical catheter of 0.31 mm.

The recorded audio output from the catheters was processed by means of a Medasonics spectrum analyzer, which performed a fast Fourier transform, producing a digital output of the Doppler power spectra. This spectrum analyzer is designed to compute 183 fast Fourier transformations (spectra), each composed of 256 frequency bins. For the coronary blood flow model, data were sampled for 4.0-s periods and stored in files of 40 kilobytes each, using the Medasonics data acquisition software. To reduce any effects of altered gain control, the gain was reset before each data collection period to maximize the visually displayed signal/noise ratio. For each flow condition and axial position, five data files were recorded after the gain control and flowmeter setting had been readjusted. Off-line analysis was performed using the IBM PC/AT computer. Noise was reduced through ensemble averaging of the 183 spectra for each of the five 4.0-s data files. Spectral moment analysis, in which standard definitions were used, was performed for the resulting ensemble-averaged frequency spectra. From this spectral moment analysis, the mean frequency shifts of the spectra were determined. Additionally, peak frequency shifts were determined from the ensemble-averaged spectra by scanning for the highest frequency data recorded with an amplitude greater than the experimentally determined background noise level. The five data sets for each flow condition and axial position were then averaged to allow comparison.

#### 1.1.5 Mathematic model.

To analyze the effect of ultrasonic beam power distribution in our scaled-up, in vitro system, we compared the mean frequency shift of the Doppler spectrum predicted by the laser Doppler velocimeter–measured velocity profiles, both without and with correction for the effect of inhomogeneous beam power distribution, to the mean frequency shift measured by the scaled-up Doppler catheter. The predicted mean frequency shifts without correction were determined directly from the velocity profiles with spatial averaging and using the Doppler equation. The predicted mean frequency shifts with correction were obtained by means of a mathematic model that combined the beam power distribution data with the velocity profile data. The details of this mathematic model are presented elsewhere ([17]). The qualitative interpretation of the final result is that the mean frequency shift of the ultrasound spectrum is proportional to the sum, for all points within the sample volume, of the fluid velocity at each point weighted by the normalized beam power at that point. The assumed axisymmetry of the velocity profiles allowed simplifying the application of the mathematic model. In particular, we divided the cross section of each velocity profile into a series of 20 concentric rings (Fig. 5). Each ring had a width of 0.51 mm and, by definition, constant velocity. The velocity associated with each ring corresponded to a specific frequency shift on the Doppler spectrum, as given by the Doppler equation. The amplitude at this frequency shift was determined by the net beam power occurring within the dimensions of the particular ring. The mean frequency shift of the composite Doppler spectrum was then determined using standard statistical techniques.

The predicted peak frequency shift of the Doppler spectrum was obtained directly from the fluid velocity data of the laser Doppler velocimeter. In particular, the maximal peak velocity at each specified axial position for each flow condition was multiplied by a constant, as specified by the Doppler equation, to generate the predicted peak frequency shift for that axial position and flow condition. This model predicts that the peak frequency would be unaffected by inhomogeneities in beam profile. Qualitatively, this prediction is consistent with the concept that as long as the highest velocity component in the flow field is insonated by some portion of the beam at an intensity level greater than the signal-noise level, the peak velocity will be accurately measured.

Comparison of the predicted mean and peak frequency shifts of the Doppler spectrum with the experimental values was performed by means of linear regression. The Student paired *t*test was used to compare correlations without and with correction for beam power distribution.

### 1.2 In vitro studies: scaled model.

#### 1.2.1 Coronary blood flow model.

The scaled, in vitro model of coronary blood flow was designed to replicate the scaled-up model (Fig. 2). In particular, the scaled model was designed to deliver continuous flow of an experimental fluid through a test section at a constant perfusion pressure. The experimental fluid was distilled water lightly seeded with cornstarch. From standard tables, the viscosity of this solution was estimated to be 0.068 Ns/m^{2}, the density 1,000 kg/m^{3}and the speed of sound 1,490 m/s. Tygon tubing of 2.5 mm (internal diameter) and 40 cm length was used as the test section. The Reynolds number of the experimental fluid was determined by timing the collection of a set volume of the experimental fluid, and then converting volumetric flow to the Reynolds number.

#### 1.2.2 Doppler ultrasound measurements.

A 3F Doppler catheter with an end-mounted transducer used for clinical studies was advanced over a 0.014-in. (0.035 cm) guide wire to terminate 25 cm beyond the entry point into the test section. Similar to the scaled-up model, this position ensured that fully developed flow was achieved well upstream of the transducer. Multiple sample volumes was not a problem in the scaled model because the ultrasound signal was effectively attenuated by the experimental fluid beyond the location of the primary sample volume. The signal generator (Millar Instruments, model MDV-20) had a carrier frequency of 20 MHz and a pulse repetition frequency of 62.5 kHz. For this system, the sample volume length was set at 0.46 mm and the location of the primary sample volume was adjusted to 5.0 mm downstream from the catheter tip. The audio signal returning from the Doppler catheter first passed through a phase quadrature detector and then through a gain controller to the Medasonics spectrum analyzer for processing through digital fast Fourier transform.

The Doppler catheter and guide wire were positioned adjacent to the wall of the test section, ensuring that the velocity profile of fluid flow was not axisymmetric. Data were sampled as for the scaled-up model, but at eight different Reynolds numbers ranging from 100 to 700. Subsequently, the Doppler catheter was rotated without a change in radial or axial position by increments of ∼60°. In this system, there was a complete transmission of rotation along the shaft of the catheter from the proximal to distal end, as confirmed by direct visual inspection. The rotation of the catheter without a change in radial or axial position systematically altered the relation of the beam power distribution produced by the Doppler catheter to the velocity profile of fluid flow, which was assumed to remain unchanged. Data were sampled after each rotation at the same Reynolds numbers. Using spectral analysis, the mean and peak frequency shifts of the spectra for each catheter position and Reynolds number were determined. Linear regression was then used to compare the mean and peak frequency shifts to the Reynolds numbers for each position. The standard deviations of the average slope of the resultant regression lines for both the mean and peak frequency shifts were then calculated to provide an estimate of the error associated with catheter rotation. Also, we used the Student unpaired *t*test to compare the slopes of the regression lines with the predicted slopes calculated from the known Reynolds number, specifics of the scaled model and use of the Doppler equation.

### 1.3 In vivo studies.

We studied eight patients (five men, three women; 39 to 79 years old, mean age 58) with documented coronary artery disease who had just undergone successful percutaneous transluminal coronary angioplasty. Written informed consent was obtained from all patients before angioplasty, and appropriate institutional guidelines were followed as set by the University of California, San Francisco, Committee on Human Research. After angioplasty, a 3F Doppler catheter with an end-mounted transducer (Millar Instruments, model DC-201) was passed over the previously placed 0.014-in. (0.035 cm) guide wire into the coronary circulation. The same signal generator used for the scaled, in vitro model studies (Millar Instruments, model MDV-20) was used for the in vivo studies. However, for the in vivo studies, the location of the primary sample volume was adjusted to 4.0 mm downstream from the catheter tip. Data were collected from the distal left main coronary artery in five patients, the proximal left circumflex coronary artery in two patients and the proximal right coronary artery in one patient. During the initial placement of the catheter, the device was manipulated to obtain an optimal audio signal. Data were then collected for 30 s. The catheter was then rotated ∼180° to a second position to alter the relation of the beam power distribution to the local fluid dynamics. This rotation was performed without a change in the axial location of the catheter, as confirmed by fluoroscopy. Data were then collected again for 30 s. In one patient, a 360° rotation was ultimately performed to confirm that the rotation at the proximal end of the catheter was indeed transmitted to the distal end without a change in axial position.

For each in vivo 30-s data sample, eight beats for which an optimal signal/noise ratio was obtained were selected for spectral analysis and subsequent comparison. The mean and peak frequency shifts for each of the five spectra produced during the 0.056-s period spanning peak diastole were determined. These five sets of values for each beat were then averaged. The data sets for precatheter and postcatheter rotation for all eight beats in each patient were then averaged for comparison. To compare these in vivo Doppler mean and peak velocities before and after catheter rotation, we used the Student unpaired *t*test.

## 2 Results

### 2.1 Beam power distribution.

The distribution of power of the transmitted ultrasonic beam produced by the scaled-up Doppler catheter in the transverse plane was inhomogeneous, and the degree of inhomogeneity varied as a function of the distance from the transducer (Fig. 6). For the more proximal axial positions, beam power was maximal in a ring between radii of 4.5 and 6.5 mm, corresponding to the peripheral region of the annular-shaped transducer. The power decreased by >30 dB below maximum at the guide wire boundary. Somewhat higher values (within 15 dB of maximum) occurred at the peripheral wall of the test section at all axial positions. Beam power was consistently lower in the region of the lead solder joint on the transducer surface (arrow in Fig. 6, B).

### 2.2 Comparison between predicted and experimental mean and peak frequency shifts.

The predicted values of the mean frequency shift uncorrected for the beam power distribution—that is, assuming a uniform power distribution—differed significantly from the experimental values derived from the scaled-up Doppler catheter (Fig. 7). In particular, the slope of the regression line comparing these predicted values to the experimental values was significantly less than the line of equality (0.80 ± 0.03 [mean ± SD] vs. 1.00 ± 0.00, p < 0.05, 95% confidence interval [CI] 0.74 to 0.86). In contrast, the predicted values corrected for the power distribution were more accurate: the slope of the regression line was not significantly different from the line of equality (0.92 ± 0.03 vs. 1.00 ± 0.00, p > 0.05, 95% CI 0.84 to 1.00). These results are consistent with the concept that those regions where the ultrasonic beam is stronger contribute more to the calculation of the mean velocity than those regions where the beam is weaker.

For the peak frequency data, the predicted values were also similar to the values obtained from the measured spectra (Fig. 8). The slope of the regression line here did not differ significantly from the line of equality (0.97 ± 0.08 vs. 1.00 ± 0.00, p > 0.20, 95% CI 0.79 to 1.14). These results are consistent with the concept that the measurement of peak velocity is accurate, provided that any part of the central beam insonifies the highest velocity portion of the flow stream.

### 2.3 Comparison of prerotation and postrotation clinical Doppler catheter data.

Rotation of the clinical Doppler catheter in the scaled, in vitro model caused significant changes in the measured mean frequency shift at each Reynolds number (Fig. 9). Although there was a high correlation between the mean frequency shift and the Reynolds number for each individual position of the catheter (minimal R value 0.969), the slopes of the regression lines differed significantly at baseline and after each rotation (average change 18.8%) (Table 1). Also, the average of the slopes of the regression lines differed significantly from the slope of the regression line when the predicted mean frequency shift calculated from the known Reynolds number, specifics of the scaled model and use of the Doppler equation were compared with the Reynolds number (p < 0.003) (Fig. 9, Table 1).

Rotation of the clinical Doppler catheter in the scaled model did not cause a significant change in the measured peak frequency shift at each Reynolds’ number (Fig. 9). In particular, the slopes of the regression lines did not differ significantly at baseline and after each rotation (average change 5.0%) (Table 1). Also, the average of the slopes of the regression lines did not differ significantly from the slope of the regression line when the predicted peak frequency shift calculated from the known Reynolds number (assuming a parabolic velocity profile), specifics of the scaled model and use of the Doppler equation were compared with the Reynolds number (p > 0.90) (Fig. 9, Table 1).

For the in vivo studies, rotation of the catheter caused a significant change in the measured mean velocity for seven of the eight patients (average change 3.4 cm/s [20.6%]; p < 0.05 for each patient except patient 7, where p > 0.05) (Fig. 10). In contrast, rotation did not cause a significant change in the measured peak velocity for seven of the eight patients (average change 1.3 cm/s [4.3%]; p > 0.05 for each patient except patient 6, where p < 0.05). In addition, further rotation of the catheter to its original orientation in patient 8 resulted in a return of mean velocity and peak velocity to the prerotation values (20.9 ± 2.5 vs. 18.5 ± 2.1 cm/s, p > 0.05 and 40.2 ± 2.0 vs. 40.8 ± 4.3 cm/s, p > 0.70, respectively).

## 3 Discussion

In this study, we used a scaled-up Doppler catheter with an end-mounted transducer in a model of coronary blood flow to show that the inhomogeneous distribution of power of the ultrasonic beam produced by the catheter makes measurements of mean, but not peak, velocity inaccurate. In particular, for signal analysis using a fast Fourier transform (such as used in the current commercially available Doppler catheters and guide wires), we show that the inhomogeneous beam power distribution makes the measurement of the mean velocity of fluid flow, as reflected by the mean frequency shift of the Doppler spectrum, inaccurate. The measurement of peak velocity, in contrast, is accurately reflected by the peak frequency shift of the Doppler spectrum and is thus independent of the distribution of beam power.

The finding in our scaled-up model that inhomogeneous beam power distribution makes the measurement of mean, but not peak, velocity of fluid flow inaccurate is supported by the results of our in vitro and in vivo studies using the clinical Doppler catheter. In these studies, rotating the catheter changed the measured value of the mean velocity. As suggested by our in vitro data, a principal reason for this change is that catheter rotation altered the relation between the inhomogeneous beam power distribution and local fluid dynamics. This phenomena should not affect the measurements of peak flow velocity. Indeed, we found no variation in peak velocity in seven of the eight patients, but peak velocity did vary in one patient (Patient 6). The reason that peak velocity varied in this patient likely involved poor signal quality and incomplete insonation of the vessel. In particular, if the region of maximal velocity was not sufficiently insonated before rotation in this patient, then the measured peak velocity would underestimate the true peak velocity.

### 3.1 Comparison with previous studies.

The degree of inhomogeneity of the distribution of beam power produced by the scaled-up Doppler catheter used in this study should be less than that for the clinical catheter. In particular, the more symmetrical shape of the scaled-up Doppler catheter, the relatively smaller area occupied by surface imperfections and solder joints for the electrical leads, the relatively higher frequency (considering the scale factor) and the consequent larger radial dimension of the annular transducer in the scaled-up catheter (in terms of wavelength) would each be expected to decrease beam inhomogeneity. However, the measured degree of inhomogeneity of the beam power distribution produced by the scaled-up Doppler catheter appeared greater than that recently demonstrated by Roth et al. ([15]) for the clinical catheter. Also, in contrast to the assumption made by Roth et al., this inhomogeneity was not axisymmetric. This disparity in degree of inhomogeneity may be explained by the greater than fivefold higher resolving power of the measuring system used in this study compared with that used by Roth et al.

The current results are also in conflict with those of Yamagishi et al. ([14]), who found that the mean frequency shift of the spectrum obtained from an end-mounted clinical Doppler catheter accurately predicted the measured mean velocity of fluid flow through a tube. Analysis of their fluid model, however, suggests that the profile of fluid flow was uniform or blunt. In the case of a blunt profile, the inhomogeneity of the distribution of beam power would not affect the measurement of mean velocity.

Our results may also help explain the conflicting results of earlier studies designed to validate the basic measurement of mean velocity using the zero-crossing technique ([3, 11]). For example, Sibley et al. ([3]) found that the Doppler catheter mean velocity systematically overestimated the known mean of velocity of fluid flow, whereas Tadaoka et al. ([11]) later found that the Doppler catheter mean velocity systematically underestimated the known mean velocity. The explanation of these conflicting results may well involve the fact that regions where the ultrasonic beam is stronger contribute more to the calculation of mean velocity than regions where the beam is weaker.

### 3.2 Implications.

Our results have implications for clinical studies using any Doppler catheter or guide wire with an end-mounted transducer. For example, in previous clinical studies that relied on measured mean velocity, a significant degree of error may have been introduced by the implied assumption of uniform beam power distribution produced by the Doppler catheter. However, studies in which the measured mean velocity was compared before and after an intervention and in which the catheter position was held constant would not have been affected by inhomogeneous beam power distribution. For example, the measured ratio of mean velocities to determine hyperemic response to coronary blood flow reserve would be accurate, provided that the catheter position was held constant.

The mathematic model used in our study can be applied to other ultrasound devices using fast Fourier transform analysis, such as the Doppler guide wire and the noninvasive, surface transducer. For example, the mathematic model can be used to explain the results of the recent study by Doucette et al. ([18]) using the Doppler guide wire in fully developed, undisturbed flow with an assumed parabolic velocity profile ([18]). In that study, the mean velocity was estimated by calculating one-half the measured peak velocity. These investigators showed that the product of this estimated mean velocity and the vessel cross-sectional area accurately predicted the measured volumetric flow. However, no mention was made of the accuracy of the product of the measured mean velocity and the cross-sectional area in predicting the measured flow. Based on our mathematic model, one would expect that one-half the measured peak velocity would indeed provide an accurate estimate of the true mean velocity, but that the measured mean velocity would not. Another important implication of our study is that attempts to measure disturbances in the pattern of blood flow (e.g., turbulence) using spectral analysis will be inaccurate, given the inhomogeneity of the beam power distribution.

### 3.3 Conclusions.

The inhomogeneous distribution of power of the ultrasonic beam produced by a clinical Doppler catheter with an end-mounted transducer makes the measurement of the mean velocity of fluid flow, as reflected by the mean frequency shift of the Doppler spectrum, inaccurate. The measurement of peak velocity, in contrast, is accurately given by the peak frequency shift of the Doppler spectrum and is thus independent of the beam power distribution. Regardless of the ultrasound device and the analytic technique used, measurements of blood flow velocity and flow reserve ratios, based on the measured mean velocity, may therefore have associated errors owing to inhomogeneities in the distribution of beam power. The peak velocity provides a more accurate measure of local fluid dynamics and is the preferred variable for coronary blood flow studies.

## Acknowledgements

We thank B. Pat Denardo for the design of the scaled-up, in vitro model, and Mimi Zeiger for assistance in preparation of the manuscript. We also thank Shirley Denardo for relentless support throughout the project.

## Footnotes

☆ This study was supported in part by Grant 88-N7 from the American Heart Association (California affiliate).

↵1 All editorial decisions for this article, including selection of referees, were made by a Guest Editor. This policy applies to all articles with authors from the University of California, San Francisco.

- Received June 6, 1996.
- Revision received October 7, 1996.
- Accepted October 25, 1996.

- The American College of Cardiology

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