Characteristics and Correlations of Wall Shear Stress and Flow Turbulence in the Carotid Bifurcation Evaluated Using an Ultrasound Vector Flow Imaging.

INTRODUCTION: The aim of the study was to evaluate characteristics and provide the normal values of wall shear stress (WSS) and flow turbulence (Tur), and the relationship between them in the carotid bifurcation based on an ultrasound vector flow imaging (V Flow) in healthy adults. METHODS: Max and mean WSS and Tur values at three segments (initial segments of internal and external carotid arteries [IICA and IECA]; distal segment of common carotid artery [DCCA]), both in anterior and posterior walls, were successfully obtained in 56 healthy adults, using ultrasound V Flow function. Relationship between mean WSS and Tur was further explored. RESULTS: The mean WSS value was 0.71 Pa, 0.86 Pa, and 0.96 Pa at IICA, IECA, and DCCA, respectively (IICA < IECA < DCCA, p < 0.05). The mean Tur value was 13.85%, 5.46%, and 4.17% at IICA, IECA, and DCCA, respectively (IICA > IECA > DCCA, p < 0.05). A cutoff value (WSS = 0.4 Pa) was selected and Tur values were significantly higher in group with WSS cutoff value <0.4 Pa than group with WSS cutoff value ≥0.4 Pa (p < 0.01). CONCLUSION: WSS and Tur are moderately negatively correlated, which can be used in the quantitative evaluation of carotid bifurcation and could be a potential dual-parameter tool in the clinical research for early detection of carotid atherosclerosis.

[Application Research of Vector Flow Technique on Convex Array Ultrasonic Probe of Abdomen].

Vector flow imaging (VFI) is an innovative ultrasound flow measurement technology. Compared with the traditional color Doppler and spectral Doppler, VFI has the advantages of independence of angle correction and direct acquisition of real-time amplitude and direction of flow. Transverse oscillation (TO) method is one of the effective methods for vector flow imaging. However, a complete and detailed algorithm validation process based on commercial ultrasound machines is still lacking due to more complex convex probes. This study starts with introducing the imaging process and principle of transverse oscillation vector flow technique, and calculates the error between the set velocity value and the measured velocity value through the simulation experiment, and verifies the error between the set velocity value and the measured velocity value through the Doppler flow phantom experiment. Among them, the velocity value measured by the TO vector flow technique in the simulation experiment is 0.48 m/s and the preset value is 0.50 m/s, the error between them is -4%. The velocity values are 8.33, 11.14, 14.44 and 16.67 cm/s measured by the Doppler flow phantom experiment, the actual velocity values are 7.97, 10.78, 14.06 and 17.34 cm/s, the errors between them are all within ±5%. Both experiments verify the feasibility of using vector flow technique on abdominal convex probe.

Blood Flow Turbulence Quantification of Carotid Artery With a High-Frame Rate Vector Flow Imaging.

OBJECTIVES: To assess the feasibility and performance of Turbulence (Tur) index as a quantitative tool for carotid artery flow turbulence; to detect and compare the blood flow patterns of common carotid artery (CCA) and carotid bulb (CB) at different ages and cardiac phases in healthy adults, and thus interpret the evolvement of etiology difference between CCA and CB. METHODS: Carotid flow characteristics of 40 healthy volunteers were evaluated quantitatively by a high-frame rate vector flow imaging. Three types of flow patterns were defined depending on the distributive range of complex flow during systole in CB. Comparison of mean Tur value in CCA and CB at different age groups and cardiac phases was performed. And the correlation between Tur value and the diameter ratio of proximal internal carotid artery to common carotid artery (DRpro-ica/cca) was tested. RESULTS: Mean Tur values in CB were remarkably higher than that in CCA, whether during systole or diastole (P < .001). Meanwhile Tur values in CB during systole were significantly higher than that during diastole (P < .001). Flow complexity of CB showed variations among 40 participants especially in systole, whereas the flow pattern of CCA was relatively consistent. Mean Tur values were positively correlated with DRpro-ica/cca in CB (ρ = 0.69, P < .05). CONCLUSIONS: V Flow imaging provided a reliable method-Tur, for quantitative analysis of carotid blood flow. It had potential to be further applied in distinguishing complex hemodynamic characteristics in high-risk people of carotid diseases for the risk stratification of cardiovascular events.

First experiences of ultrasound vector flow imaging at the femoropopliteal artery in peripheral arterial disease.

Background: The femoropopliteal artery (FPA) plays a central role in diagnosing and treating peripheral arterial disease (PAD). FPA lesions are the most frequent cause of intermittent claudication, and no other artery of the lower extremities is recanalised more frequently. Generally, ultrasound is the primary imaging tool in PAD, particularly FPA. With the development of high-frame-rate ultrasound technology in addition to traditional ultrasound modes, vector flow imaging (VFI) has provided deeper haemodynamic insights when used in the carotid artery. Here, we report the use of VFI at the FPA level in routine PAD examinations. Patients and methods: In this single-centre prospective study, we evaluated consecutive patients with PAD using B-mode imaging, colour Doppler, pulsed wave Doppler (PW) and vector flow. Hemodynamic parameters at predefined locations at the carotid artery and FPA were compared. Results: Qualitatively adequate VFI at all sites was possible in 76% of the patients with PAD. With decreasing volume flow from the common carotid artery to the internal carotid artery and from the common femoral artery via the superficial femoral artery to the popliteal artery, the correlation between VFI- and PW-derived-volume flow was high at every site. Based on different techniques, the VFI-derived values were significantly lower than the PW-derived values. The mean wall shear stress was significantly lower at all femoropopliteal sites than at the carotid sites, whereas the oscillatory shear index at the femoral site was higher than that at the carotid sites rather than at the popliteal location. Conclusions: Our findings suggest that vector flow data acquisition in the FPA is feasible in most patients with PAD. Therefore, with knowledge of the method and its limitations, VFI provides haemodynamic information beyond traditional ultrasound techniques and is a promising new tool for flow analysis in PAD.

Precise evaluation of blood flow patterns in human carotid bifurcation based on high-frame-rate vector flow imaging.

PURPOSE: To investigate the feasibility of high-frame-rate vector flow imaging (HiFR-VFI) compared to ultrasound color Doppler flow imaging (CDFI) for precisely evaluating flow characteristics in the carotid bifurcation (CB) of presumed healthy adults. METHODS: Forty-three volunteers were assessed for flow characteristics and their extensions using HiFR-VFI and CDFI in CBs. The flow patterns were classified according to the streamlines in HiFR-VFI and quantitatively measured using an innovative turbulence index (Tur-value). Interobserver agreement was also assessed. RESULTS: HiFR-VFI was consistent with CDFI in detecting laminar and nonlaminar flow in 81.4% of the cases; however, in 18.6% of the cases, only HiFR-VFI identified the nonlaminar flow. HiFR-VFI showed a larger extension of complex flow (0.37 ± 0.26 cm2 ) compared to CDFI (0.22 ± 0.21 cm2 ; p < 0.05). The flow patterns were classified into four types: 3 type-I (laminar flow), 35 type-II (rotational flow), 27 type-III (reversed flow), and 5 type-IV (complex flow). The Tur-value of type-IV (50.03 ± 14.97)% is larger than type-III (44.57 ± 8.89)%, type-II (16.30 ± 8.16)%, and type-I (1.48 ± 1.43)% (p < 0.05). Two radiologists demonstrated almost perfect interobserver agreement on recognizing the change of streamlines (κ = 0.81, p < 0.001). The intraclass correlation coefficient of the Tur-value was 0.98. CONCLUSION: HiFR-VFI can reliably characterize complex hemodynamics with quantitative turbulence measurement and may be an auxiliary diagnostic tool for assessing atherosclerotic arterial disease.

Phasicity and resistance of the arterial spectral Doppler waveform in a canine femoral focal artery stenosis model.

INTRODUCTION: This study aims to evaluate changes in the arterial spectral Doppler waveform in a canine artery stenosis model. METHODS: Canine femoral artery stenosis models were established in 12 beagle dogs. Doppler waveforms were recorded in the femoral artery preoperatively and postoperatively in the femoral artery and at the ankle after formation of a 50%, 70%, and 90% stenosis or occlusion. Major descriptors for arterial Doppler waveform were used to analyse waveforms. RESULTS: The proportion of multiphasic waveforms proximal to a moderate stenosis decreased compared to normal baseline, although the difference was not statistically significant, whereas the decreases at the stenosis, distal to the stenosis, and at the ankle were significant (p < 0.05). The decreases in arteries with a more severe stenosis or occlusion were significant at all locations (p < 0.05). The proportion of high resistive waveforms decreased significantly at the ankle in the arteries with a moderate stenosis (50%) (p = 0.002), but the decreases proximal to, at, and distal to the stenosis were not significant. The decreases were significant at all locations in the arteries with a more severe stenosis (p < 0.05). The decrease was significant at the ankle in the arteries with an occlusion (p < 0.001) but not significant pre, at, and post an occlusion. CONCLUSIONS: Phasicity and resistance of Doppler waveforms alter in canine femoral arteries with a stenosis. Phasicity change seems more sensitive in response to an arterial stenosis than resistance change. Additional information on arterial resistance could be obtained using end-diastolic ratios, resistive indices, and potentially end-systolic notch velocity measurements.

[Research Progress on Vector Flow Imaging of Cardiac Ultrasound].

Echocardiogram is vital for the diagnosis of cardiac disease. The heart has complex hemodynamics requiring an advanced ultrasound imaging mode. Cardiac ultrasound vector flow imaging is capable of measuring the actual magnitude and direction of the blood flow velocity, obtaining the quantitative parameters of hemodynamics, and then providing more information for clinical research and diagnosis. This study mainly reviewed several different vector flow imaging techniques for cardiac flow and presented the implementation difficulties, and proposed a diverging wave based high frame rate cardiac ultrasound vector flow imaging. The study discussed the limitation of current ultrasound technology used in the cardiac flow measurement, analyzed and demonstrated the specific reasons for these implementation difficulties and the potential future development.

[Calculation and Comparison of the Resistance Index Based on Vector Velocities and Correction Method Studies].

Resistance Index (RI) is one of the indicators for ultrasound evaluation of hemodynamic changes. The purpose of this study is to evaluate the reliability of V Flow, which is a new ultrasound examination, when calculating this index. Data were collected from six positions of the bilateral common carotid artery (CCA) at the beginning, middle, and end of 10 healthy volunteers. The result shows that the RI error between V Flow and PW is about 12%. After angle correction for PW results both the relative error and its variance is reduced. Based on V Flow, users can directly obtain the actual flow velocity without manually correcting the angle. In addition to RI, blood flow velocity angle at different times can be compared to more intuitively to understand the hemodynamic details.

Wall Shear Stress Measurements Based on Ultrasound Vector Flow Imaging: Theoretical Studies and Clinical Examples.

Wall shear stress (WSS) is considered as a key factor for atherosclerosis development. Previous WSS research based on pulsed wave Doppler (PWD) showed limitations in complex flows. To improve accuracy for nonlaminar flow, a commercial ultrasound vector flow imaging (UVFI)-based WSS calculation is proposed. Errors for PWD are presented theoretically when flow is not laminar. Based on this, simulations of WSS calculations between PWD and UVFI were set up for different turbulent flows. Our simulations show that UVFI has obviously better performance than PWD in WSS calculations. Wall shear stress results in different flow conditions at carotid bifurcations are described.

[Quantitative Ultrasound Measurements of Blood Flow Velocity and Turbulence].

The paper described the hemodynamics of blood flow based on fluid mechanics and its corresponding formulas, and revealed the limitation of blood flow velocity measurement for non-laminar flow when using the conventional pulse wave Doppler. The paper demonstrated the calculation of turbulence for blood flow based on velocity directions and quantified the turbulence according to the presented formulas. Two methods were introduced and the simulated results were analyzed. An example using real data based on ultrasound vector flow imaging for calculating the turbulence of blood flow was presented in the end.

Vector flow imaging techniques: An innovative ultrasonographic technique for the study of blood flow.

Doppler ultrasonography is routinely used to identify abnormal blood flow. Nevertheless, conventional Doppler can be used to determine only the axial component of blood flow velocity and is angle dependent. A new method of multidimensional angle-independent estimation of flow velocity, called Vector Flow Imaging (VFI), has been proposed. It quantitatively evaluates the true velocity vector's amplitude and direction at any location into a vessel and displays a more intuitive depiction of the flow movements. High frame rate VFI, based on plane wave imaging, allows a detailed dynamic visualization of complex flow by showing even transient events, otherwise undetectable. © 2017 Wiley Periodicals, Inc. J Clin Ultrasound 45:582-588, 2017.

Evaluation of Turbulence Index and Flow Pattern for Atherosclerotic Carotid Stenosis: A High-Frame-Rate Vector Flow Imaging Study.

OBJECTIVE: The emerging high-frame-rate vector flow imaging provides a new way of hemodynamic evaluation for complex blood flow. This study was aimed at exploring quantitatively the characteristics of complex flow with turbulence (Tur) index and analyzing flow patterns in atherosclerotic internal carotid artery stenosis (ICAS) using high-frame-rate vector flow imaging. METHODS: This study prospectively included 60 patients with ICAS. Tur values in different segments of stenosis and cardiac phases were compared. Spearman correlation analysis was performed between clinical plaque characteristics with turbulence grading by ln(Tur). Three complex flow patterns were qualitatively drawn on vector flow mode, and the rates of detection of flow patterns in different stenosis groups and ulceration groups were compared. RESULTS: Highly disordered blood flow was observed in the stenotic (Tur [M, QR] = 12.5%, 21.5%) and distal segment (15.4%, 27.2%), particularly during systole (21.0%, 30.7%, 33.3%, 38.7%, p < 0.05). Spearman correlation analysis revealed that stenosis rate was correlated with turbulence grading in the stenotic (ρ = 0.65, p < 0.05) and distal segment (ρ = 0.79, p < 0.05), and ulcer formation was correlated with turbulence grading in the stenotic segment (ρ = 0.58, p < 0.05). The overall rate of detection of three flow patterns was higher in the severe stenosis group (22/22) versus the mild to moderate stenosis group (21/38) (p < 0.001) and in the ulcer group (21/23) versus the non-ulcer group (23/37) (p < 0.001). CONCLUSION: High-frame-rate vector flow imaging was helpful in assessing the severity and characteristics of flow turbulence. Lumen geometric factors could affect flow turbulence and blood flow patterns around the plaque. This would provide important hemodynamic information for the detection of high-risk plaque.

Velocity vector comparison between vector flow imaging and computational fluid dynamics in the carotid bifurcation.

It has been largely documented that local hemodynamic conditions, characterized by low and oscillating wall shear stresses, play a key role in the initiation and progression of vascular atherosclerotic lesions. Thus, investigation of the flow field in the carotid bifurcation can lead to early identification of vulnerable plaques. In this scenario, the development of novel non-invasive imaging tools that can be used in routine clinical practice to identify disturbed and recirculating blood flow becomes crucial. In this context, Vector Flow Imaging is becoming a relevant tool as it provides an angle independent assessment of blood flow velocity and multidimensional flow vector visualization. The purpose of the present study was to validate, in several locations of the carotid bifurcation, the high-frame rate vector flow imaging (HiFR-VFI) technique by comparing with computational fluid dynamic simulations (CFD). In all eight carotid bifurcations, HiFR-VFI accurately detected regions of laminar flow as well as recirculation and unsteady flow areas. An accurate and statistically significant agreement was observed between velocity vectors obtained by HiFR-VFI and those computed by CFD, both for vector magnitude (R = 0.85) and direction (R = 0.74). Our study demonstrated that HiFR-VFI is a valid technique for rapid and advanced visual representation of velocity field in large arteries. Thus, it has a great potential in research-based clinical practice for the identification of flow recirculation, low and oscillating velocity gradients near vessel wall. The use of HiFR-VFI may provide a great improvement in the investigation of the role of local hemodynamics in vascular pathologies, as well in the assessment of the effect of pharmacological treatments.

Detection of Abnormal Wall Shear Stress and Oscillatory Shear Index via Ultrasound Vector Flow Imaging as Possible Indicators for Arteriovenous Fistula Stenosis in Hemodialysis.

OBJECTIVE: The arteriovenous fistula (AVF) is an essential vascular access for hemodialysis patients. AVF stenosis may occur at sites with abnormal wall shear stress (WSS) and oscillatory shear index (OSI), which are caused by the complex flow in the AVF. At present, an effective method for rapid determination of the WSS and OSI of the AVF is lacking. The objective of this study was to apply an ultrasound-based method for determination of the WSS and OSI to explore the risk sites of the AVF. METHODS: In this study, the ultrasound vector flow imaging technique V Flow was applied to measure the WSS and OSI at four different regions of the AVF to detect and analyze the risk sites: (i) anastomosis region, (ii) curved region, (iii) proximal vein and (iv) distal vein. Twenty-one patients were included in this study. The relative residence time was calculated based on the measured WSS and OSI. RESULTS: The curved region had the lowest WSS; the anastomosis region had a significantly higher OSI (p < 0.05) compared with the venous regions, and the curved region had a significantly higher RRT (p < 0.05) compared with the proximal vein region. CONCLUSION: V Flow is a feasible tool for studying WSS variations in AVF. The possible risk site in the AVF may be located in the anastomosis and curved regions, where the latter could present a higher risk for AVF stenosis.

Feasibility study of combining wall shear stress and elastography to assess the vascular status of carotid artery.

INTRODUCTION: At present, early detection of the potential risk of atherosclerosis and prevention is of great significance to reduce the occurrence of stroke. AIM: This study aims to explore the value of combining the wall shear stress measured by ultrasound vector flow imaging technique and sound touch elastography of common carotid artery in normal adults using the Mindray Resona 7 ultrasound system. METHODS: Forty volunteers (mean age 39.5 y, 23 females, 17 males) were divided into four groups according to their age. All volunteers underwent ultrasound carotid artery examination, and the values of wall shear stress and elasticity on the posterior wall of the common carotid artery were measured using advanced imaging functions, vector flow imaging technique, and sound touch elastography. RESULTS: Different cut-off values of wall shear stress were used to investigate the significance between two groups with corresponding sound touch elastography values. It can be seen that the statistical difference could be found when the mean wall shear stress was larger than 1.5 Pa approximately (statistical significance was defined when P < 0.05), and the sound touch elastography value was positively correlated with the wall shear stress value. CONCLUSION: This study reveals that the combination of wall shear stress and sound touch elastography is an effective and feasible method for assessing carotid artery health. When the mean wall shear stress value is over 1.5 Pa, the corresponding sound touch elastography value increases significantly. The risk of atherosclerosis increases with the stiffness of blood vessel walls.

Corrigendum: Quantitative evaluation of post-stenotic blood flow disturbance in canine femoral artery stenosis model: An early experience with vector flow imaging.

[This corrects the article DOI: 10.3389/fcvm.2022.829825.].

Quantitative Evaluation of Post-stenotic Blood Flow Disturbance in Canine Femoral Artery Stenosis Model: An Early Experience With Vector Flow Imaging.

Objective: To investigate the value of Vector Flow Imaging (V Flow) in the assessment of post-stenotic turbulence in the canine arterial stenosis model. Materials and Methods: Canine femoral artery stenosis models were established using ameroid constrictors in 12 beagle dogs. 50% and then 70% femoral artery stenoses were confirmed by selective femoral artery angiography. V Flow was used to measure femoral artery flow turbulence index (Tur) preoperatively as a baseline. After establishing of a 50% and then 70% stenoses, the Tur indices were recorded in the femoral artery at 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 mm distal to the stenosis. Results: Baseline Tur indices of normal canine femoral arteries were <1% in 11 of 12 cases (91.7%). Distal to a 50% stenosis, the Tur index (>1%) was recorded in 83.3-100% cases between 1 and 9 mm, 41.7-58.3% between 11 and 17 mm, and 16.7% at 19 mm. For a 70% stenosis, the Tur index (>1%) occurred in 81.8-100% cases between 1 and 17 mm distal to the stenosis, and 63.6% at 19 mm. The Tur index peaked around 7 mm or 2.3 times of the initial vessel diameter (3 mm) downstream for a 50% stenosis and 11 mm or 3.7 times of vessel diameter downstream for a 70% stenosis. Conclusion: V Flow with Tur index measurement adds quantitative information of post-stenotic turbulence when assessing an arterial stenosis with ultrasound. Tur index of 1% seems a useful threshold for assessment of flow turbulence in this small sample study. Further studies with larger sample size are needed to evaluate the value of V Flow in clinical applications.

Quantitative Blood Flow Measurements in the Common Carotid Artery: A Comparative Study of High-Frame-Rate Ultrasound Vector Flow Imaging, Pulsed Wave Doppler, and Phase Contrast Magnetic Resonance Imaging.

V Flow is commercially developed by high-frame-rate ultrasound vector flow imaging. Compared to conventional color Doppler, V Flow is angle-independent and is capable of measuring both the magnitude and the direction of blood flow velocities. This paper aims to investigate the differences between V Flow and pulsed wave Doppler (PW) relative to phase contrast magnetic resonance imaging (PC-MRI), for the quantitative measurements of blood flow in common carotid arteries (CCA) and, consequently, to evaluate the accuracy of the new technique, V Flow. Sixty-four CCAs were measured using V Flow, PW, and PC-MRI. The maximum velocities, time-averaged mean (TAMEAN) velocities, and volume flow were measured using different imaging technologies. The mean error with standard deviation (Std), the median of absolute errors, and the r-values between V Flow and PC-MRI results for the maximum velocity, the TAMEAN velocity, and the volume flow measurements are {9.40% ± 14.91%; 11.84%; 0.84}, {21.52% ± 14.46%; 19.28%; 0.86}, and {-2.80% ± 14.01%; 10.38%; 0.7}, respectively, and are {53.44% ± 29.68%; 49.79%; 0.74}, {27.83% ± 31.60%; 23.83; 0.71}, and {21.01% ± 29.64%; 25.48%; 0.34}, respectively, for those between PW and PC-MRI. The boxplot, linear regression and Bland-Altman plots were performed for each comparison, which illustrated that the results measured via V Flow rather than via PW agreed more closely with those measured via PC-MRI.

Investigation on the differences of hemodynamics in normal common carotid, subclavian, and common femoral arteries using the vector flow technique.

Objectives: To investigate the feasibility of the vector flow imaging (V Flow) technique to measure peripheral arterial hemodynamic parameters, including wall shear stress (WSS) and turbulence index (Tur) in healthy adults, and compare the results in different arteries. Materials and methods: Fifty-two healthy adult volunteers were recruited in this study. The maximum and mean values of WSS, and the Tur values at early-systole, mid-systole, late-systole, and early diastole for total 156 normal peripheral arteries [common carotid arteries (CCA), subclavian arteries (SCA), and common femoral arteries (CFA)] were assessed using the V Flow technique. Results: The mean WSS values for CCA, SCA, and CFA were (1.66 ± 0.68) Pa, (0.62 ± 0.30) Pa, and (0.56 ± 0.27) Pa, respectively. The mean Tur values for CCA, SCA, and CFA were (0.46 ± 1.09%), (20.7 ± 9.06%), and (24.63 ± 17.66%), respectively. The CCA and SCA, as well as the CCA and CFA, showed statistically significant differences in the mean WSS and the mean Tur (P < 0.01). The mean Tur values had a negative correlation with the mean WSS; the correlation coefficient between log(Tur) and WSS is -0.69 (P < 0.05). Conclusion: V Flow technique is a simple, practical, and feasible quantitative imaging approach for assessing WSS and Tur in peripheral arteries. It has the potential to be a useful tool for evaluating atherosclerotic plaques in peripheral arteries. The results provide a new quantitative foundation for future investigations into diverse arterial hemodynamic parameters.

A framework for simulating ultrasound imaging based on first order nonlinear pressure-velocity relations.

An ultrasound imaging framework modeled with the first order nonlinear pressure-velocity relations (NPVR) and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA) with a RMS error of 3% at the focal point for a 2D field, and Field II with RMS errors of 0.8% and 1.5% at the electronic and the elevation focuses for 3D fields, respectively. The accuracy for the NPVR based nonlinear propagation is investigated by comparing with the Abersim simulation for pulsed fields and with the nonlinear ASA for monochromatic fields. The RMS errors of the nonlinear pulses calculated by the NPVR and Abersim are respectively 2.4%, 7.4%, 17.6% and 36.6% corresponding to initial pressure amplitudes of 50kPa, 200kPa, 500kPa and 1MPa at the transducer. By increasing the sampling frequency for the strong nonlinearity, the RMS error for 1MPa initial pressure amplitude is reduced from 36.6% to 27.3%.