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Department of Medical Imaging, Medical Ultrasound Imaging Center, Radboud University Medical Center, Nijmegen, The NetherlandsDepartment of Medical Physics, Catharina Hospital, Eindhoven, The Netherlands
Address correspondence to: Chris L. de Korte, Department of Medical Imaging, Radboud University Medical Center, Geert Grooteplein Zuid 10, 6525 GA Nijmegen, The Netherlands.
Department of Medical Imaging, Medical Ultrasound Imaging Center, Radboud University Medical Center, Nijmegen, The NetherlandsPhysics of Fluid Group, TechMed Centrum, University of Twente, Enschede, The Netherlands
Ultrasound-based local pulse wave velocity (PWV) estimation, as a measure of arterial stiffness, can be based on fast focused imaging (FFI) or plane wave imaging (PWI). This study was aimed at comparing the accuracy of in vivo PWV estimation using FFI and PWI. Ultrasound radiofrequency data of carotid arteries were acquired in 14 healthy volunteers (25–57 y) by executing the FFI (12 lines, 7200 Hz) and PWI (128 lines, 2000 Hz) methods consecutively. PWV was derived at two time-reference points, dicrotic notch (DN) and systolic foot (SF), for multiple pressure cycles by fitting a linear function through the positions of the peaks of low-pass filtered wall acceleration curves as a function of time. The accuracy of PWV estimation was determined for various cutoff frequencies (10–200 Hz). No statistically significant difference was observed between PWVs estimated by both approaches. The PWV and R2 at DN were higher, on average, than those at SF (PWV/R2: FFI SF 5.5/0.92, FFI DN 6.1/0.92; PWI SF 5.4/0.89, PWI DN 6.3/0.95). The use of cutoff frequencies between 40 and 80 Hz provided the most accurate PWVs. Both methods seemed equally suitable for use in clinical practice, although we have a preference for the PWV at DN given the higher R2 values.
). The PWV is defined as the velocity at which pressure waves, generated by the systolic contraction of the heart, propagate along the arterial tree, and it is assessed by measuring transit distance and transit time between two sites in the arterial system and taking their ratio (
The gold standard for measuring large artery stiffness is obtaining the PWV between the common carotid artery and femoral artery (cfPWV); asymptomatic vascular damage is indicated by cfPWV values >10 m/s (
). Assuming an infinitely long, straight, isolated and cylindrical vessel with elastic, isotropic and homogeneous walls, containing a homogenous, incompressible and non-viscous fluid, the PWV is quantitatively related to the Young's modulus of the artery by the Moens–Korteweg equation (
). Although most of these assumptions are only approximately valid in vivo, the qualitative relationship between stiffness and PWV remains valid in vivo (
). The cfPWV is a representation of the average velocity between the two measurement sites and consequently gives no information about small local arterial abnormalities, as is seen in early stage of atherosclerosis disease (
). Assessment of the local PWV could be of great value, as it represents the velocity over a length of 5 cm most commonly obtained at the common carotid artery caudal to the bifurcation. Also, a good correlation is found between the regional cfPWV and local PWV for arterial stiffness measurements (
). Local PWV values are lower compared with regional cfPWV values, as PWV increases with distance from the heart, along with elastic condition of the arterial wall (
). No generally accepted gold standard for in vivo local stiffness measurements exists.
Today the local PWV is obtained using two different ultrasound methods: high-frame-rate focused transmission with reduced imaging line density, which will be referred to as fast focused imaging (FFI), and ultrafast plane wave imaging (PWI). In FFI, the piezoelectric elements in the transducer are activated in subgroups per imaging line according to a certain delay profile, which ensures the ultrasound pulses transmitted by each element are perfectly in sync at a certain focal spot. These focused pressure waves insonify a narrow tissue region. PWI, on the other hand, is obtained by activating all piezoelectric elements simultaneously. One unfocused pressure front is transmitted by the transducer which insonifies a wide tissue region, and reflected waves are received. Hence, to insonify a certain tissue region, FFI requires more transmit events than PWI and, therefore, has a lower temporal resolution. However, because of the focusing in transmit, FFI provides images with a higher signal-to-noise ratio and better spatial resolution.
reported that the local PWV can be accurately determined from images obtained with FFI at a frame rate of 651 Hz. The images consisted of 16 echo lines spanning a total width of 15.86 mm.
investigated the influence of the time-reference points on the obtained PWV for FFI. They reported that the dicrotic notch (DN) should be preferred to the systolic foot (SF), as SF is affected by early wave reflections and has, in contrast to DN, no significant correlation with the relative distension and local distensibility coefficient. PWI has also been found to provide accurate PWV measurements (
concluded that optimal PWI performance was found at frame rates between 1667 and 2778 Hz for in vivo pulse wave tracking.
Previous studies focused on the optimization using one of the two ultrasound methods. However, PWV estimation using FFI and PWI has not yet been compared head-to-head in vivo. In the study described here, we investigated the accuracy of the estimated PWV using FFI and PWI in healthy volunteers. PWV was estimated for both the SF and DN time-reference points.
Methods
In vivo measurements
Three sets of ultrasound data of the right carotid artery were acquired in 15 healthy volunteers for PWV analysis (see Table 1). The volunteers were scanned after 3 min of rest lying supine with the head turned away from the imaging side. The carotid artery was imaged caudal from the bifurcation, to minimize effects from reflections. The blood pressure and heart rate were determined before every measurement (M6 Comfort HEM/FL31, Omron, Kyoto, Japan). The mean blood pressure was obtained as follows: mean blood pressure = ⅓ × systolic blood pressure + ⅔ × diastolic blood pressure. The protocol was in accordance with the World Medical Association Declaration of Helsinki on Ethical Principles for Medical Research Involving Human Subjects, and ethical approval was obtained for this study from the medical ethical committee region Arnhem–Nijmegen, The Netherlands; informed consent was obtained from all human participants.
Two-dimensional beamformed ultrasound in-phase and quadrature (IQ) data of each carotid artery were acquired using a Vantage 256 ultrasound research imaging system (Verasonics Inc., Kirkland, WA, USA) with a linear array transducer (ATL L12-5 50 mm, Philips, Bothell, WA, USA). The transducer contained 256 elements, had a pitch of 0.1953 mm and the transmit center frequency was set to 8.9 MHz. The system was controlled by a custom-made acquisition script, developed in MATLAB R2015b (The MathWorks, Natick, MA, USA). Images of the carotid artery in the longitudinal direction were obtained using both FFI and PWI. These methods were executed sequentially in one recording (3.5 s each). A full acquisition with both the FFI and PWI method lasted 7 s, during which the participants were instructed to hold their breath. A total of three acquisition series were obtained per participant. The parameters of both methods were chosen in such a way that a PWV up to 16 m/s could be measured, according to the Nyquist sampling criterion. Acquisition was performed covering a 25-mm-wide, 24-mm-deep field-of-view using both FFI and PWI (see Table 2). The common carotid artery was imaged in the longitudinal direction; both the anterior and posterior wall were within the field-of-view. The frequency content of the acceleration curve at –6 dB frequency content never exceeded 150 Hz; therefore, a frame rate of at least 300 Hz was required based on a Fourier analysis. FFI was performed with 12 imaging lines, a focal depth of 12 mm (between posterior and anterior wall) and a pulse repetition frequency (PRF) of 7200 Hz (resulting in 600 frames/s. PWI was performed with a PRF of 2000 Hz. The mechanical index (MI) and the spatial-peak pulse-average intensity (ISPPA.3) were 0.93 and 120.45 W/cm2, respectively, which are well within the international safety limits for ultrasound imaging of peripheral vessels (
American Institute of Ultrasound in Medicine (AIUM)/National Electrical Manufacturers Association (NEMA). Acoustic Output Measurement Standard for Diagnostic Ultrasound Equipment, 2004.
International Electrotechnical Commission (IEC) IEC Standard 61157—Standard means for the reporting of the acoustic output of medical diagnostic ultrasonic equipment.
The PWV was determined at the SF and DN time-reference points for each pressure cycle. The time-reference points were defined as the time points at which the wall acceleration waveform reached a maximum before and after the systolic peak of the distension waveform (
). The wall acceleration waveform was obtained by manually segmenting the anterior and posterior wall of the carotid artery in the first image obtained, followed by estimation of the interframe displacement of the walls using autocorrelation of IQ data of successive frames and thereafter calculation of the second derivative (see Fig. 1). The anterior and posterior wall acceleration waveforms were low-pass filtered, after which the slope of a linear fit through the time points of maximal acceleration versus position provided a PWV estimate at the SF and DN time-reference points. All estimations were repeated multiple times for a range of Butterworth low-pass filter cutoff frequencies (10–200 Hz) to additionally investigate the filter setting effect on the PWV estimates (
). Measurements with R2 < 0.6 (where R2 is the coefficient of determination of the linear fit) or a PWV smaller than 1 m/s or larger than 16 m/s were excluded (
). The PWV and R2 values of each volunteer were obtained by first calculating the median value of the obtained values within one measurement of 3.5 s, and then calculating the mean value of the three 3.5 s measurements.
Fig. 1Overview of data processing steps used to obtain the pulse wave velocity (PWV) value from the original arterial displacement curves.
A statistical analysis was performed on the obtained average pulse wave velocities with FFI and PWI. The distribution of continuous variables was tested using the Kolmogorov–Smirnov test for normality, with statistical significance set at p ≤ 0.05. The PWVs obtained using the FFI and PWI methods were compared using a two-sided Wilcoxon signed rank test for each participant. Pearson's correlation coefficient was used to measure the association between PWVs and blood pressure values.
Results
Images from the right carotid artery were successfully acquired in 14 of the 15 volunteers (25–57 y) (see Table 1) using FFI and PWI, with on average 16 heartbeats per volunteer. The data set of one volunteer was excluded, as the posterior wall of the carotid artery was not fully visible within the 24-mm-deep window. The PWVs and R2 values were estimated for all heartbeats, using the unfiltered or low-pass filtered wall-acceleration curves with cutoff frequencies ranging from 10 to 200 Hz (Fig. 2). Comparable PWVs and R2 values were found in case cutoff frequencies between 40 to 200 Hz were used. Between these cutoff frequencies, the PWVs and R2 values at the DN were on average higher compared those at the SF (PWV/R2: FFI SF 5.5/0.92, FFI DN 6.1/0.92, PWI SF 5.4/0.89, PWI DN 6.3/0.95). The number of PWVs that matched the inclusion criteria (PWV 1–16 m/s and R2 > 0.6) when applying a low-pass filter with a cutoff frequency between 20 and 200 Hz was similar to those for the FFI and PWI methods, 85.4% and 88.6%, respectively (Fig. 3). Without filtering the wall-acceleration curves, the number of PWVs that matched the inclusion criteria was less for both methods, but higher for FFI than for PWI: 74.2% and 52.5%, respectively.
Fig. 2(a) Mean PWVs and (b) mean R2 coefficients of 14 volunteers using the fast focused imaging (FFI) and plane wave imaging (PWI) methods at the systolic foot (SF) and dicrotic notch (DN) with and without low-pass filters with cutoff frequencies of 0–200 Hz.
Fig. 3Estimated PWVs outside the inclusion criteria (PWV of 1–16 m/s and R2 > 0.6) at the systolic foot (SF) and dicrotic notch (DN) for both the fast focused imaging (FFI) and plane wave imaging (PWI) methods with and without low-pass filter with cutoff frequencies of 0–200 Hz.
The most accurate PWVs, that is, those with the highest R2 values and a small number of excluded data points, were acquired at cutoff frequencies between 40 and 80 Hz. The PWVs at DN were on average higher than those at SF (PWV/R2: FFI SF 5.6/0.94, FFI DN 6.3/0.93, PWI SF 5.6/0.93, PWI DN 6.4/0.96) (Fig. 4). At a cutoff frequency of 60 Hz, the average PWV value for FFI was 5.6 ± 1.8 m/s at SF and 6.3 ± 1.1 m/s at DN, with R2 values of 0.95 ± 0.04 and 0.93 ± 0.05, respectively. Comparable values were obtained for the PWI method, with PWVs of 5.6 ± 2.2 m/s at SF and 6.4 ± 1.2 m/s at DN, and R2 values of 0.93 ± 0.05 and 0.96 ± 0.07, respectively. No statistically significant bias was found between the PWVs estimated by the two approaches (p > 0.05), as illustrated in Fig. 5. The percentages of PWVs that matched the inclusion criteria at 60 Hz were 93.7% and 85.3% for FFI at the SF and at DN, respectively, and 92% and 98.2% for PWI at the SF and at DN, respectively. A positive relation was observed between age and PWVs with both the FFI and PWI methods at the dicrotic notch, although only a significant correlation (p = 0.006) was found between age and PWVs with the PWI method at the dicrotic notch.
Fig. 4Boxplot of the pulse wave velocities (PWVs) obtained in the right carotid artery of 14 volunteers at the systolic foot (SF) and dicrotic notch (DN) for both the fast focused imaging (FFI) and plane wave imaging (PWI) methods (a) without using a low-pass filter and (b) using a 60 Hz low-pass filter.
Fig. 5Bland–Altman plot of the pulse wave velocity (PWV) in the right carotid artery of 14 volunteers using the fast focused imaging (FFI) and plane wave imaging (PWI) methods with a 60 Hz low-pass filter at the (a) systolic foot and (b) dicrotic notch.
Both approaches produced similar R2 values over the range of cutoff frequencies (Fig. 2). Only when no low-pass filter was applied were the PWVs estimated with a higher accuracy (indicated by the larger R2 value) for FFI compared with PWI (average R2 at SF, 0.89 vs. 0.71; at DN, 0.90 vs. 0.76). In addition, lower PWVs were obtained without a low-pass filter, compared with those obtained with low-pass filter with a cutoff frequency of 60 Hz (Fig. 6).
Fig. 6Bland–Altman plot of the pulse wave velocity (PWV) in the right carotid artery of 14 volunteers at the dicrotic notch (DN) with and without 60 Hz low-pass filter using the (a) fast focused imaging (FFI) and (b) plane wave imaging (PWI) methods.
A positive correlation was observed between PWVs at either the SF or DN and the mean blood pressure (Fig. 7). The strongest correlations were observed for PWV values (low-pass filtered with 60 Hz) at the DN reference point for both the FFI and PWI methods with the mean blood pressure, with correlation values of 0.09 and 0.18, respectively. However, the relation between the mean blood pressure and PWVs obtained with FFI and PWI at the DN was not statistically significant (p = 0.30 and 0.13). In addition, no statistically significant correlation was found between the PWVs and heart rate.
Fig. 7Pulse wave velocity (PWV) in the right carotid artery of 14 volunteers at the dicrotic notch obtained with a 60 Hz low-pass filter using the fast focused imaging (FFI) and plane wave imaging (PWI) methods versus mean blood pressure at the (a) systolic foot and (b) dicrotic notch.
We successfully obtained and compared the local PWV in the carotid artery using both the FFI and PWI methods in a group of 14 healthy volunteers. We observed that both methods provided similar PWVs and comparable R2 values with the use of a low-pass filter with a cutoff frequency between 40 and 200 Hz, with the most accurate PWVs between 40 and 80 Hz. Compared with PWI, FFI provided more accurate PWVs at lower filter frequencies and without a low-pass filter and, therefore, seems to be less sensitive to filter settings.
The PWV values obtained in our study are comparable with previously reported velocities in the carotid artery (4–6 m/s) (
reported the use of a low-pass filter with a cutoff frequency of 80 Hz on the distension waveforms and, thereafter, a first-order high-pass derivative filter with a cutoff frequency of 100 Hz on the acceleration waveform to obtain the PWV with FFI at the DN. The PWV values obtained at the DN (5.0 ± 0.7 m/s, age 26 ± 4 y) are lower compared with the results in our study, which could be caused by the younger age of the volunteers.
In the analysis, the accuracy of the PWV values was quantified using the R2 values as true, or ground truth, PWV values are unknown. However, the R2 value is not necessarily an indicator of accuracy, but (by definition) indicates the quality of the fit to the provided data. Large R2 values indicate a precise fit, but are not necessarily an indicator of an accurate model because one could be overfitting the data. The model under consideration is linear, so overfitting is not possible, which means that the R2 value is an indicator of both the accuracy and the precision of the model under consideration, but this topic could be addressed in more depth in future work.
In this study a depth up to 24 mm is used for imaging. In practice, the carotid artery could be present at greater depth, which hampers the analysis. When choosing a larger depth for acquisition, the achievable frame rate will be lower. This will affect the FFI method more than the PWI method, as the echo lines are recorded one by one.
Further research could include the acquisition of pulse wave velocities in patients with atherosclerotic diseases, for instance, in the presence of a plaque in the carotid artery. The FFI method suffers less from side lobes and has a higher echographic signal-to-noise ratio and therefore could have an advantage in tracking of the vessel wall with presence of plaques. On the other hand, the PWI method provides more information over the full length of the imaged width, compared with the few lines in the FFI method.
Conclusions
On the basis of the results, there is no clear difference in estimated PWVs and the accuracy of the estimates using FFI or PWI, when using a low-pass filter with a cutoff frequency between 40 and 200 Hz. The most accurate PWVs were obtained using a cutoff frequency between 40 and 80 Hz. On average, the PWVs estimated using FFI are less sensitive to filtering parameters compared with those estimated using PWI. Higher R2 values are obtained when estimating the PWV at the DN compared with the systolic foot. Therefore, it seems that the FFI and PWI methods are equally suitable for use in clinical practice, although we have a preference for measurement of the PWV at the dicrotic notch.
Conflict of interest disclosure
The authors declare that there are no conflicts of interest.
References
American Institute of Ultrasound in Medicine (AIUM)/National Electrical Manufacturers Association (NEMA). Acoustic Output Measurement Standard for Diagnostic Ultrasound Equipment, 2004.
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