In Vitro Doppler Ultrasound Investigation of Turbulence Intensity in Pulsatile Flow With Simulated Cardiac Variability

Ultrasound in Med. & Biol., Vol. 35, No. 1, pp. 120 –128, 2009 Copyright © 2008 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/09/$–see front matter

doi:10.1016/j.ultrasmedbio.2008.08.007

● Original Contribution IN VITRO DOPPLER ULTRASOUND INVESTIGATION OF TURBULENCE INTENSITY IN PULSATILE FLOW WITH SIMULATED CARDIAC VARIABILITY MEGHAN L. THORNE,*† TAMIE L. POEPPING,†‡ HRISTO N. NIKOLOV,* RICHARD N. RANKIN,§ DAVID A. STEINMAN,¶ and DAVID W. HOLDSWORTH*†储 *Robarts Research Institute, London, Ontario, Canada; †Departments of Medical Biophysics, ‡Physics and Astronomy, §Diagnostic Radiology and Nuclear Medicine, and 储Surgery, University of Western Ontario, London, Ontario, Canada; and ¶Biomedical Simulation Laboratory, University of Toronto, Toronto, Ontario, Canada (Received 25 March 2008; revised 24 July 2008; in final form 8 August 2008)

Abstract—An in vitro investigation of turbulence intensity (TI) associated with a severe carotid stenosis in the presence of physiological cardiac variability is described. The objective of this investigation was to determine if fluctuations due to turbulence could be quantified with conventional Doppler ultrasound (DUS) in the presence of normal physiological cycle-to-cycle cardiac variability. An anthropomorphic model of a 70% stenosed carotid bifurcation was used in combination with a programmable flow pump to generate pulsatile flow with a mean flow rate of 6 mL/s. Utilizing the pump, we studied normal, nonrepetitive cycle-to-cycle cardiac variability (ⴞ3.9%) in flow, as well as waveform shapes with standard deviations equal to 0, 2 and 3 times the normal variation. Eighty cardiac cycles of Doppler data were acquired at two regions within the model, representing either laminar or turbulent flow; each measurement was repeated six times. Turbulence intensity values were found to be 11 times higher (p < 0.001), on average, in the turbulent region than in the laminar region, with a mean difference of 24 cm/s. Twenty cardiac cycles were required for confidence in TI values. In conclusion, these results indicate that it is possible to quantify TI in vitro, even in the presence of normal and exaggerated cycle-to-cycle cardiac variability. (E-mail: [email protected]) © 2008 World Federation for Ultrasound in Medicine & Biology. Key Words: Doppler ultrasound, Carotid artery bifurcation, Flow phantom, Blood flow velocity, Spectral analysis, Ensemble average, Coherent fluctuation, Incoherent fluctuation, Turbulence intensity, Cardiac variability.

first-line imaging technique of choice (Osarumwense et al. 2005; Tahmasebpour et al. 2005; Titi et al. 2007), partly due to its recognized cost-effectiveness, and has replaced angiography in many centres, often being the sole imaging test prior to carotid endarterectomy surgery (Hathout et al. 2005). When the diagnosis is based entirely on peak systolic velocity measurements in the stenosis, DUS is used as a surrogate for lumenography in a manner that does not take advantage of its full potential. Indeed, in its current clinical implementation, Doppler ultrasound of the carotid provides only moderate sensitivity (89%) and specificity (84%) for detection of stenoses appropriate for surgery (Wardlaw et al. 2006). This inability to obtain precise diagnoses with an inherently quantitative technique like Doppler ultrasound suggests fundamental limitations in the way that DUS data are acquired and interpreted. Investigations employing other Doppler velocity-derived parameters (Poepping et

INTRODUCTION Stroke is the third major cause of death and the main cause of invalidity in industrialized countries, and extracranial carotid artery atherosclerosis disease is suspected to account for between 20% and 50% of all strokes and transient ischemic attacks (De Fabritiis et al. 2002; Fragata et al. 2006; Nandalur et al. 2006). Doppler ultrasound (DUS) is the most widely performed noninvasive test in the evaluation of a patient suspected of having carotid arterial disease (Gaitini and Soudack 2005) and is typically used to identify patients with high velocity jets within the internal carotid, indicative of vessel narrowing (Sigel 1998). Doppler ultrasound is the Address correspondence to: David W. Holdsworth, Imaging Research Laboratories, Robarts Research Institute, P.O. Box 5015, 100 Perth Drive, London, Ontario, N6A 5K8, Canada. E-mail: [email protected] 120

Turbulence in variable pulsatile flow ● M. L. THORNE et al.

al. 2007) may produce more reliable hemodynamic information for accurate diagnosis. Quantification of turbulence near carotid stenoses may provide additional diagnostic information, which could enhance the performance of DUS for diagnosis. (Ku 1997; May et al. 2001). Disturbed flow is characterized by transient fluctuations in an otherwise laminar flow field, which causes the flow to deviate from streamlined motion. As described by Yellin (1966), a region of disturbed flow may be described as turbulent, but true turbulence is self-preserving, rather than transient. Turbulence is defined as flow with irregular (random, chaotic) temporal and spatial disturbances of velocity and pressure (Yongchareon and Young 1979). Turbulence near a stenosis generates resistance that causes a sharp decrease in flow rate, leading to areas of recirculation in the flow field with higher values of vorticity, helicity and negative wall shear stress, which can promote clotting (Banks and Bressloff 2007; Birchall et al. 2006; Hademenos 1997) and significant thrombus production (Smith et al. 1972; Stein and Sabbah 1974; Yip et al. 2006). Turbulence near a plaque surface also results in pressure fluctuations that may cause plaque rupture (Loree et al. 1991; Tang et al. 1999). For these reasons, quantification of turbulence may improve the diagnosis of vulnerable plaque (Li et al. 2006). Doppler ultrasound was first proposed as a clinical technique to measure turbulence over 30 years ago (Sigel et al. 1970). Doppler techniques to characterize turbulence by spectral width using either stenosis index (STI) or spectral broadening index (SBI) have been proposed. These indices are not commonly used, possibly because of the confounding effects of machine specific factors that result in inherent spectral broadening (Hoskins et al. 1999; Keeton et al. 1997). The most promising method to characterize turbulence using ultrasound may be by direct measurement of the mean and fluctuating velocity components (Casty and Giddens 1984; Mann et al. 1987; Tarbell et al. 1986; Walburn et al. 1983). These approaches typically characterize turbulence in pulsatile flow by performing an ensemble average and measuring fluctuations between successive cardiac cycles. However, fluctuations in mean velocities between subsequent cardiac cycles may arise not only from turbulence but also from inherent physiological variations. The human heart is not a perfectly regular pump but exhibits beatto-beat variations that are also manifested in the carotid flow waveform (Holdsworth et al. 1999). These normal cycle-to-cycle variations may confound the calculation of turbulence intensity; if the added fluctuation due to cycle-to-cycle cardiac variability is great enough, it could potentially mask the turbulence associated with a carotid stenosis.

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Described here is an in vitro investigation of Doppler ultrasound measurements of turbulence intensity associated with severe carotid stenosis, in the presence of physiological pulsatility (including normal and exaggerated cycle-to-cycle variability). This investigation aims to demonstrate the feasibility of pulsed Doppler measurements of turbulence intensity for in vivo applications. It is hypothesized that quantification of turbulence, distal to a severely stenosed carotid bifurcation, is possible with conventional DUS, even in the presence of cycleto-cycle cardiac variability. MATERIALS AND METHODS Turbulence quantification As discussed, turbulence is manifested as incoherent velocity fluctuations about the mean. Measurements of turbulence in steady flow are easily made by recording the fluctuation of velocities around the mean velocity (Hinze 1959). The pulsatility of the heart complicates this measurement, requiring the measurement of incoherent turbulent fluctuations in the presence of underlying coherent fluctuations. It is possible to remove the average coherent cyclic fluctuations due to cardiac pulsatility through gating and ensemble averaging (Casty and Giddens 1984; Walburn et al. 1983). Removal of the underlying periodic fluctuations will leave only the random components, including: (1) ␴system, the inherent Doppler velocity measurement noise (which is typically about 5%); (2) ␴turb, due to turbulent fluctuations and (3) ␴physiol, random cycle-to-cycle fluctuations due to cardiac variability. Assuming that these random independent components add in quadrature, this gives the following expression for total velocity fluctuation, ␴total: 2 ␴2total ⫽ ␴2physiol ⫹ ␴2turb ⫹ ␴system

(1)

The primary goal of this study is to determine if turbulent velocity fluctuations (␴turb) can be quantified from Doppler ultrasound in the presence of physiological cardiac variability (␴physiol). The approach that we have taken is to perform in vitro measurements in a stenosed carotid flow model, with varying amounts of added cardiac variability introduced. Pulsatile flow simulation Pulsatile flow waveforms are produced in our in vitro flow facility by a computer-controlled flow simulator (UHDC Flow System, Shelley Medical Imaging Technologies, London, ON, Canada) (Holdsworth et al. 1991). This flow simulator produces a prescribed flow waveform, based on an operator-specified waveform file. The typical common carotid flow waveform (mean 6 mL/s) is based on the results of a previous study in normal volunteers where a normal averaged carotid flow

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cycle was derived from Doppler spectral analysis of 3560 human cardiac cycles measured in the common carotid artery (Holdsworth et al. 1999). The programmed waveform was then adjusted to compensate for system dampening, which is dependent on the tubing used in the in vitro set-up (Frayne et al. 1992; Poepping et al. 2002). The computer-controlled flow simulator also has the capability to mimic cardiac variability by producing a waveform consisting of consecutive nonrepetitive cycles with degrees of variability between each cycle. Random variations can be added to either the cycle length (time) or to the mean flow rate (amplitude) within each cycle. For this study, degrees of variability to the mean flow (where normal physiological cycle-to-cycle variability is 3.9%) were introduced while maintaining the cycle length of 0.92 s for each cycle (Holdsworth et al. 1999). Variability was achieved by multiplying the idealized cardiac cycle by a random point within a Gaussian distribution that had a mean of one and a user-specified standard deviation. This was repeated for each cycle making up the flow waveform. To investigate the effect of added cardiac variability on our turbulence measurements, four separate flow waveforms with standard deviations equal to 0, 1, 2 and 3 times the reported normal variation were created, corresponding to ⫾0%, ⫾3.9%, ⫾7.8% and ⫾11.7% cycle-to-cycle variability, respectively. Figure 1 demonstrates 11 cycles of each of the repetitive pulsatile flow waveform and the nonrepetitive waveform with exaggerated, ⫾11.7% cycle-to-cycle variability that was programmed into the in vitro flow system. In vitro facility The computer-controlled pump is part of a previously described flow facility, which allowed us to investigate turbulence within a stenosed carotid artery bifurcation, in the presence of cycle-to-cycle cardiac variability, in a controlled in vitro environment (Poepping et al. 2002, 2004). An anthropomorphic model of a severe 70% (in terms of diameter reduction by the North American Symptomatic Carotid Endarterectomy Trial) (Collaborators NASCET 1991; Fox 1993) concentric stenosed carotid bifurcation, with a common carotid artery (CCA) diameter of 8.0 mm and an internal carotid artery diameter of 5.6 mm (Smith et al. 1996 ) was used to mimic the turbulence that may be produced distal to a stenosis. With accurate geometry and flow resistance, this model produced velocity patterns similar to that found in a diseased human carotid artery with a corresponding stenosis (Steinman et al. 2000). The acoustic properties of the tissue, vessel wall and blood were matched with appropriate tissue-mimicking materials (Poepping et al. 2004). A well-established blood-mimicking fluid (BMF), originally developed by Ramnarine

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Fig. 1. Two flow rate waveforms, with a mean flow rate of 6 mL/s, produced by UHDC computer-controlled flow simulator representing (a) repetitive, 0% nonvarying waveform and (b) nonrepetitive, 11.7% exaggerated variability waveform.

et al. (1998) for use with Doppler ultrasound, and later modified and tested by Thorne et al. (2008) under conditions of turbulence, was used for all experiments. The blood-mimicking fluid has a dynamic viscosity of 4.1 ⫾ 0.1 mPa · s and a density of 1037 ⫾ 2 kg · m⫺3. Using a fresh batch of BMF, the flow system was operated for at least 1 h before the acquisition of each data-set to purge the system of any air bubbles. The BMF was pumped through the carotid artery bifurcation model, using the four sets of flow waveforms described above. Data acquisition Measurements were made within the phantom using a clinical duplex Doppler ultrasound machine (Ultramark 8, Advanced Technology Laboratories – ATL, Bothell, WA, USA) with a 5-MHz mechanical probe Doppler transducer (Access 10-PV, ATL). The Doppler probe was mounted on a mechanical arm, which was positioned by a computer-controlled three-dimensional (3D) stage and located above the phantom placed in a water bath. Doppler parameters were selected as follows: a pulse

Turbulence in variable pulsatile flow ● M. L. THORNE et al.

Fig. 2. Seventy-percent concentric carotid artery model with a common carotid artery (CCA) diameter of 8 mm and an internal carotid artery (ICA) diameter of 5.6 mm showing regions of acquisition: laminar flow acquired within the CCA, 2 cm proximal to the bifurcation apex; and turbulent flow acquired within the ICA, 1.3 cm distal to the bifurcation apex and 1.0 cm away from the CCA central axis.

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Data analysis Acquired DUS data were digitized at 44.1 kHz for off-line analysis and analyzed at 79 time-points per cardiac cycle using a 1024-point fast Fourier transform (FFT) with a 1024-point Hanning window and 50% overlap between FFTs. This produced an estimate of the instantaneous power spectrum every 12 ms, with a frequency resolution of 43 Hz. Using the Doppler frequency of the transducer (ft, MHz), the speed of sound through water (c, m/s) and the cosine angle of the transducer to the direction of flow (␪, °), the resulting Doppler shifted frequencies (fd, MHz) were converted to velocities (␯, m/s), via the Doppler equation: v⫽

repetition frequency of 25 kHz producing a Nyquist velocity of 380 cm/s, power set to 100%, gain of 60%, wall filter of 50 Hz, Doppler angle of 60° and samplevolume depth of 2.1 cm. Eighty sequential cycles of gated, demodulated in-phase and quadrature DUS data were acquired using a 1.5-mm sample-volume length from within two regions: the common carotid artery (CCA), representing a region of laminar flow and the internal carotid artery (ICA), representing a region of turbulent flow. Note that for these measurements, the sample volume length was reduced to the minimum available, in order to maximize the sensitivity to instantaneous fluctuations at one location within the vessel and reduce confounding spectral broadening (due to the underlying velocity distribution across the vessel). The laminar flow region (within the CCA) was selected centrally and located 2 cm proximal to the bifurcation apex and the turbulent region (within the ICA) was selected between the high velocity jet and the zone of recirculation (Hutchison and Karpinski 1985), at a point 1.3 cm distal to the bifurcation apex and 1.0 cm away from the central axis of the CCA, as demonstrated in Fig. 2. Acquisitions were repeated six times at each site for each of the four different flow waveforms (one nonvarying, one normal physiological flow variability and two exaggerated amounts of variability). Womersley numbers (␣, dimensionless) were calculated using the radius (R, cm), rate of pulsatility (␻, rad/s), fluid density (␳, kg · m⫺3) and the dynamic viscosity of the BMF (␮, Pa · s), as follows:

冑

␣⫽R

␻␳ ␮

(2)

The Womersley number was calculated as 5.2 within the CCA, 3.7 within the ICA and 1.1 within the stenosis.

fd · c 2 · f t · cos␪

(3)

From these velocity spectra, the instantaneous intensity-weighted mean velocity of each spectrum was calculated and traced out as a function of time covering 80 cardiac cycles (equivalent to 74 s). Sectioning individual cardiac cycles for the ensemble average was simplified since the carotid waveform had a constant periodic cycle length of 0.92 s. Turbulence intensity (TI) was determined by measuring fluctuations from one cycle to the next, calculated over a specified time window within the cardiac cycle. For this experiment, TI was calculated using time-points on the down-slope of peak systole, from 0.20 s to 0.25 s of the cardiac cycle, because previous investigations have indicated that turbulence is most prominent during this part of the cardiac cycle (Casty and Giddens 1984). Although the acquisition of 80 cardiac cycles using the in vitro facility was successful, in clinical implementations it may not be possible to acquire clinical Doppler data for such a long period. In this case, turbulence intensity would necessarily be calculated based on a smaller number of cycles. Thus, to study the effect that the number of cardiac cycles used for the ensemble averaging has on the statistical confidence in turbulence intensity calculations, turbulence was calculated based on an analysis of varying numbers of cardiac cycles using 5, 10, 15, 20, 25, 50, 75 and 80 cycles. Turbulence intensity is traditionally calculated as the root-mean-squared population standard deviation in averaged mean velocity but this calculation may underestimate fluctuations due to turbulence, especially when only a few cardiac cycles are used in the average. Thus, turbulence intensity (TI, cm/s) was calculated as the root-mean-squared sample standard deviation about the averaged mean velocity (u៮ , cm/s): TI ⫽

冑共

⌺ u ⫺ u៮ 兲2 n⫺1

(4)

For each site, turbulence intensity was calculated

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for each of the six trials and then averaged. Note that while only turbulence intensity was investigated in this article, it is important to distinguish TI from turbulence intensity level, where turbulence intensity level (To, dimensionless) is typically normalized by the mean velocity (eqn 5): T0 ⫽

TI u៮

(5)

There is a possibility that a short-term coherence exists between subsequent cardiac cycles, i.e. that the fluctuating velocity patterns in one cycle may have an effect on the next few cycles. This short-term “turbulence memory” could act to reduce apparent fluctuations (variability), especially when only a small number of cardiac cycles (n) are available for calculation (Bevilaqua and Lykoudis 1978). To investigate the effect of short-term turbulence memory, a separate analysis of TI calculated for small n (5, 10, 15, 20, 25) was performed, where the cycles analyzed were nonsequential. For this analysis, the cycles were selected from throughout the entire 80-cycle acquisition, with equal spacing of 16, 8, 5, 4 and 3 cycles, respectively. Again, turbulence intensity was calculated for each of the six trials and then averaged, for each site. We also studied the effect of increasing cycle-tocycle cardiac variability on calculations of turbulence intensity, within the region of laminar flow (CCA) and within the region of turbulent flow (ICA) mentioned above. Twenty-five cycles were acquired at each site with four different flow waveforms: one repeated flow waveform (⫾0% cycle-to-cycle variability added), a normal physiological flow waveform (⫾3.9% cycle-to-cycle variability) and two exaggerated flow waveforms (⫾7.8% and ⫾11.7% cycle-to-cycle variability). Turbulence intensity was calculated on the down slope of systole (i.e., 0.20 s to 0.25 s after peak systole) and calculations were averaged for six trials at each site. From this investigation the system error, ␴system, was calculated as the TI within the laminar flow region with no cycle-to-cycle variability introduced, divided by the mean velocity within the same region. A one-way repeated-measures ANOVA and Tukey post-hoc test were performed on turbulence intensity values when calculated using 5, 10, 15, 20, 25, 50, 75 and 80 cycles in order to determine if there was significant matching and to determine if there were statistical differences in turbulence intensity when calculated using different numbers of cardiac cycles. Secondly, linear regressions were performed on average turbulence intensity data acquired with increasing cycle-to-cycle variability, within the laminar flow and turbulent flow regions. A t-test was also performed on this data to deter-

Fig. 3. Calculated mean velocity waveform from Doppler acquisitions in the common carotid artery under (a) repetitive, 0% nonvarying pulsatile flow and (b) pseudo-random, 11.7% exaggerated variability pulsatile flow.

mine if there was a significant difference between average turbulence intensity measurements made at each acquisition site (laminar and turbulent flow regions). Statistical calculations were performed using commercially available software (Prism 4.0, GraphPad Software Inc., San Diego, CA, USA). RESULTS Pulsatile mean velocity Mean velocities were calculated from Doppler ultrasound data acquired within a laminar flow region within the CCA with a repetitive, nonvarying waveform pumped through the carotid flow loop, as shown in Fig. 3a and with a physiological waveform with exaggerated (⫾11.7%) cycle-to-cycle variability pumped through the carotid flow loop, as shown in Fig. 3b. Figure 3a demonstrates small variability between cycles (most noticeable at peak systole) due to system error because there is no turbulence within the laminar flow region and there is no added physiological variability. Figure 3b demonstrates a significantly larger variability (noticeable at

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physiological cardiac variability. Note that the cycle length in both Figs. 4a and 4b was maintained at 0.92s.

Fig. 4. Calculated mean velocity waveform from Doppler acquisitions in the internal carotid artery under (a) repetitive, 0% nonvarying pulsatile flow and (b) pseudo-random, 11.7% exaggerated variability pulsatile flow.

peak systole) within the laminar flow region due to both system error and cardiac variability since ⫾11.7% cycleto-cycle cardiac variability has been added. Note that in both Figs. 3a and 3b, the cycle length in each case was maintained at 0.92 s. Mean velocities calculated from data acquired within a turbulent flow region within the ICA for the repetitive, nonvarying waveform are shown in Fig. 4a and for the physiological waveform with ⫾11.7% exaggerated cycle-to-cycle cardiac variability are shown in Fig. 4b. Figure 4 demonstrates significantly larger fluctuations and higher mean velocities from within the turbulent flow region than seen in Fig. 3 for a laminar flow region. Figure 4a demonstrates variances due to both system error and turbulence; note that although there is no cycle-to-cycle variability introduced into the system an increase in variability between cycles can be seen, which is particularly apparent at peak systole. Figure 4b demonstrates combined fluctuations due to system error, cycle-to-cycle cardiac variability and turbulence. Increasing amounts of fluctuating velocities can be seen from Fig. 4a with no cardiac variability and Fig. 4b with

Number of ensemble averaged cycles Figure 5 shows average turbulence intensity calculations (averaged over six trials) on the down-slope of systole (i.e., 0.20 s to 0.25 s after peak systole) within a region of laminar flow (within the CCA) and within a region of turbulent flow (within the ICA). Since the accuracy of the value of turbulence intensity is dependent on the number of cardiac cycles used, the influence of the number of cardiac cycles on turbulence intensity calculations was investigated in the extreme case with the presence of ⫾11.7% cycle-to-cycle cardiac variability. Figure 5 demonstrates that turbulence intensity calculated from measurements made in the distal ICA were significantly higher, even in the presence of exaggerated cycle-to-cycle variability. From this figure, a minimum of 20 cardiac cycles is required for confidence in the estimate of turbulence intensity in the presence of exaggerated, ⫾11.7%, cycle-to-cycle variability. Finally, Fig. 5 also demonstrates an unexpected finding that the estimate of turbulence intensity is biased to a reduced value (by 30%) when only a small number of cardiac cycles (less than 20) are used in the ensemble average. To investigate the source of the observed bias, turbulence intensity measurements were calculated using the same number of cardiac cycles (for 5, 10, 15, 20, 25) but using nonsequential cardiac cycles, where cycles were selected with a minimum of three cycles separation (i.e., 25

Fig. 5. Mean (and standard error) turbulence intensity values averaged on the down-slope of peak systole with cardiac variability of 11.7%, measured within a laminar flow region (common carotid artery [CCA]) and turbulent flow region (internal carotid artery [ICA]) with ensemble averages incorporating 5 to 80 cycles of data. The circles indicate calculations of turbulence intensity using sequential cycles and the triangles indicate calculations of turbulence intensity using nonsequential cycles.

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the four different flow waveforms were found to be significantly different (p ⫽ 0.0001), with a mean TI difference of 24 cm/s. DISCUSSION

Fig. 6. Mean (and standard error) turbulence intensity values averaged on the down-slope of peak systole using 25 cardiac cycles with different amounts of cycle-to-cycle variability, measured in a laminar flow region (common carotid artery [CCA]) and turbulent flow region (internal carotid artery [ICA]).

cardiac cycles were chosen, each three cycles apart). Interestingly, this appears to eliminate the underestimation of turbulence intensity when using a small number of cardiac cycles. Results of a one-way repeated measures ANOVA and Tukey post-hoc test indicated that there was no significant difference between the six trials (p ⬍ 0.0001) and that there is a significant difference (p ⬍ 0.01) in TI values when 15 cardiac cycles were used in the calculation of TI versus 20 cycles. Thus, 20 cardiac cycles is required for confidence in TI values in the presence of exaggerated, ⫾11.7%, cycle-to-cycle variability. Cardiac variability Figure 6 demonstrates the effect of increasing cardiac variability on the calculation of average turbulence intensity (averaged over six trials) at peak systole within a region of laminar flow (within the CCA) and turbulent flow (within the ICA). We found turbulence intensity to be 11 times greater, on average, in the turbulent flow region, than in the laminar flow region. Also, in both turbulent and laminar flow regions, turbulence intensity increases as a function of added cardiac variability. From the acquired data within the laminar flow region, using a repetitive flow waveform, system error was calculated as 4.6%. Linear regression of data acquisitions within the laminar flow region found that the slope significantly deviates from zero (p ⬍ 0.05) and linear regression of data acquisitions within the turbulent flow region found that the slope does not significantly deviate from zero (p ⫽ 0.08). Finally, a t-test comparing average turbulence intensity values at each site (laminar and turbulent) with

Our investigation has demonstrated unequivocally that quantification of turbulence distal to a severely stenosed carotid bifurcation is possible with conventional Doppler ultrasound, even in the presence of underlying cycle-to-cycle cardiac variability, with up to three times the standard deviation in reported normal variation (Holdsworth et al. 1999). Turbulence intensity measured within the turbulent flow region was found to be significantly greater (11 times on average) than in the laminar flow region for all cases (see Fig. 6). This includes the challenging case where TI was calculated under conditions of 11.7% cardiac variability and only five cardiac cycles were used in the ensemble average (see Fig. 5). Our study demonstrates that, of the contributing fluctuations in the turbulent region (including variances due to physiological variability, turbulent fluctuations, and system error), turbulent fluctuations were found to be the predominant fluctuation even when a modest number of cardiac cycles were used in the calculation. In the turbulent flow region, within the ICA, fluctuations due to system error and physiological variability have no effect on the measurement of TI (see Fig. 6). In the laminar flow region, within the CCA, there was a significant increase in TI as we increased physiological variability because there are essentially no fluctuations due to turbulence; also at this reduced velocity scale, the relatively small fluctuations due to physiological variability have a significant effect on measured TI. Average turbulence intensity distal to a 70% concentric stenosis was found to be 29 ⫾ 1 cm/s, when measured on the down-slope of peak systole and the system error was found to be 4.6%, which is in the range expected for DUS measurements (Rickey et al. 1992). Although this study has shown that we are capable of calculating turbulence intensity using as few as five sequential cardiac cycles in the ensemble average, we suggest using at least 20 sequential cardiac cycles to provide adequate confidence in the turbulence intensity value. Calculations based on fewer cycles appear to artifactually reduce the estimate of turbulence intensity. This can be overcome by analyzing nonsequential cycles (i.e., cycles separated by a gap), as shown in Fig. 5, which indicates that turbulence manifested in the in vitro system of a severe carotid stenosis under conditions of pulsatile flow is a deterministic process where sequential cycles cannot be considered independent of one another due to short-term turbulence memory in self-preserving flow (Townsend 1976). While analysis of nonsequential

Turbulence in variable pulsatile flow ● M. L. THORNE et al.

cycles removed the artifactual underestimation of TI, this would not be feasible in clinical implementation, as this would unreasonably increase patient-examination time. To avoid this, one should strive to acquire a minimum of 20 cardiac cycles but, if this is not possible, one may consider implementing an empirically derived correction factor that would boost TI values obtained with a small number of cycles. A previous Doppler ultrasound investigation by Casty and Giddens reported the ability to quantify turbulence intensity by ensemble averaging distal to a moderate carotid stenosis in vivo, employing a specialized Doppler ultrasound machine (Casty and Giddens 1984). As their study was performed in vivo, information regarding the amount of inherent fluctuations due to cycleto-cycle variability was not available and, therefore, fluctuations due to turbulent flow versus cycle-to-cycle variability could not be distinguished. Our in vitro investigation provides a controlled environment where the extent of cardiac variability could be modified and fluctuations due to turbulent flow and cycle-to-cycle variability could be separated. Another previous investigation, using the same in vitro experimental set-up and analysis tools as the current study, calculated TI under conditions of a repetitive carotid waveform within a moderate stenosed carotid artery (Poepping et al. 2002). This investigation demonstrated regions of increased TI distal to the moderate stenosis when compared to the common carotid artery, reaching maximum values of 20 cm/s. Not only is there interest in the quantification of TI distal to carotid stenoses but previous investigations have measured TI using the ensemble-average method in other areas of the body that contain turbulence, such as aortic valve disease (Isaaz et al. 2003; Walburn et al. 1983), lower limb arterial disease and near a ventricular assist device (Mann et al. 1987). Our study utilized a clinical Doppler ultrasound machine for the acquisition and calculation of TI, which invokes the possibility of acquiring DUS velocity data in a clinical environment for studies of advanced velocitybased indices. Additional confounding factors will be encountered when this approach is implemented in clinical studies, including vessel tortuosity, lumen irregularity and vessel movement (due to respiration) during the examination. In our experience, these limitations can be overcome by skilled operators, through careful positioning of the sample volume within the vessel lumen, acquisition during periods of shallow breathing and stable positioning of the transducer. One limitation of our investigation is that the length of the cardiac waveform was maintained while fluctuations were added to the amplitude only but it is known that in vivo the cardiac waveform inherently fluctuates both in amplitude and length (Holdsworth et al. 1999).

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This should not have an effect on the amount of turbulence intensity measured, as fluctuations in length only occur as an extension of end diastole and the rest of the features of the cardiac cycle are maintained with the same period length. Our measurements of TI are made on the down-slope of peak systole, which would require the addition of an electrocardiogram (ECG) to perform similar ensemble averaging during clinical studies. Unfortunately, the acquisition of the ECG signal is not currently part of the standard protocol for routine clinical carotid artery examinations. Alternatively, frequency-domain analysis of mean velocities could be used, where the implementation of a high-pass filter could remove coherent cyclic variations, which are likely to occur between 0 and 15 Hz (Holdsworth et al. 1999). The removal of this lower frequency band would result in a waveform comprised mainly of higher frequencies, produced by turbulent flow. Previous studies have shown that high-pass filtering of the velocity waveform may be more accurate than using the ensemble-average method in a clinical implementation (Walburn et al. 1983). Another limitation of the current study is that we did not test the lower limits of quantifying turbulence intensity in the presence of cycle-to-cycle cardiac variability. We have shown that we can calculate turbulence intensity distal to a severe stenosis with physiological variability but this approach has not been tested in mild to moderate stenoses. It may be important in the future to quantify turbulence in the presence of mild to moderate stenosis in order to evaluate the hemodynamic phenomena associated with mild to moderate stenoses in the presence of cardiac variability. CONCLUSIONS By comparing variable and nonvariable flow conditions, we found that the variability contributed by physiological variations is small compared with the variability contributed by turbulence, distal to a carotid bifurcation stenosis. Thus, we are able to quantify turbulence intensity in an in vitro model, even in the presence of exaggerated cycle-to-cycle variations. We suggest averaging 20 sequential cardiac cycles for confidence in the turbulence intensity measurements. This investigation demonstrates the feasibility of pulsed Doppler measurements of turbulence intensity for in vivo applications. Acknowledgments—The authors acknowledge ATL (Advanced Technology Laboratories, Philips, Bothell, WA, USA) for the UM8 ultrasound unit. Financial support has been provided by the Heart and Stroke Foundation of Ontario (Grant # T-6427). Vessel models were fabricated with support from the Canadian Institutes for Health Research (group grant #MOP-77964). Drs. Holdsworth and Steinman are Career Investigators supported by the Heart and Stroke Foundation of Ontario.

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