A Comparison Study of Vector Velocity, Spectral Doppler and Magnetic Resonance of Blood Flow in the Common Carotid Artery

Carotid Doppler ultrasound for non-invasive haemodynamic monitoring: a narrative review

Objective.Accurate haemodynamic monitoring is the cornerstone in the management of critically ill patients. It guides the optimization of tissue and organ perfusion in order to prevent multiple organ failure. In the past decades, carotid Doppler ultrasound (CDU) has been explored as a non-invasive alternative for long-established invasive haemodynamic monitoring techniques. Considering the large heterogeneity in reported studies, we conducted a review of the literature to clarify the current status of CDU as a haemodynamic monitoring tool.Approach.In this article, firstly an overview is given of the equipment and workflow required to perform a CDU exam in clinical practice, the limitations and technical challenges potentially faced by the CDU sonographer, and the cerebrovascular mechanisms that may influence CDU measurement outcomes. The following chapter describes alternative techniques for non-invasive haemodynamic monitoring, detailing advantages and limitations compared to CDU. Next, a comprehensive review of the literature regarding the use of CDU for haemodynamic monitoring is presented. Furthermore, feasibility aspects, training requirements and technical developments of CDU are addressed.Main results.Based on the outcomes of these studies, we assess the applicability of CDU-derived parameters within three clinical domains (cardiac output, volume status, and fluid responsiveness), and amongst different patient groups. Finally, recommendations are provided to improve the quality and standardization of future research and clinical practice in this field.Significance.Although CDU is not yet interchangeable with invasive 'gold standard' cardiac output monitoring, the present work shows that certain CDU-derived parameters prove promising in the context of functional haemodynamic monitoring.

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.

Novel Method for Fetal and Maternal Heart Rate Measurements Using 2-D Ultrasound Color Doppler Flow Images

Fetal heart rate (FHR) and maternal heart rate (MHR) are important indicators of fetal well-being during pregnancy. A common method in clinical examination is to estimate the FHR using the Doppler shift of echoes from umbilical artery blood flow based on an ultrasound pulsed-wave (PW) Doppler technique. Similarly, a sampling gate can be located at the maternal blood flow to measure MHR using PW Doppler. Ultrasound color Doppler flow imaging (CDFI) is one of the most commonly used imaging modes for clinical fetal examinations. Color coding is employed to display the blood flow velocity and direction in color grades according to the Doppler shift. Continuous CDF images contain dynamic changes characteristics of the blood flow. The periodic characteristics can be used to obtain heart rate information. Therefore, here we propose a novel method to measure FHR and MHR simultaneously using CDF images. The proposed method calculates the histogram of color similarity of CDF images to initially extract the periodic characteristics of the CDF image sequence. The histogram of color similarity function is then processed by a bandpass filter and autocorrelation operation to reduce noise and enhance periodicity. Finally, peak detection is performed on the processed signal to obtain the period and estimate the heart rate. The proposed method can measure the FHR and MHR in parallel after selecting two regions containing the umbilical artery and maternal blood flow, respectively. Thus, the method has high computational efficiency. The proposed method was evaluated on a Doppler flow phantom and clinical CDF images and then compared with the PW Doppler method. The correlation analysis and Bland-Altman plots reveal that the proposed method agrees well with the PW Doppler. It is a sanity check method for real-time clinical FHR and MHR measurements.

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.

Transthoracic Vector Flow Imaging in Pediatric Patients with Valvular Stenosis - A Proof of Concept Study

Purpose Continuous wave Doppler ultrasound is routinely used to detect cardiac valve stenoses. Vector flow imaging (VFI) is an angle-independent real-time ultrasound method that can quantify flow complexity. We aimed to evaluate if quantification of flow complexity could reliably assess valvular stenosis in pediatric patients.

Materials and Methods Nine pediatric patients with echocardiographically confirmed valvular stenosis were included in the study. VFI and Doppler measurements were compared with transvalvular peak-to-peak pressure differences derived from invasive endovascular catheterization.

Results Vector concentration correlated with the catheter measurements before intervention after exclusion of one outlier (r=−0.83, p=0.01), whereas the Doppler method did not (r=0.49, p=0.22). The change in vector concentration after intervention correlated strongly with the change in the measured catheter pressure difference (r=−0.86, p=0.003), while Doppler showed a tendency for a moderate correlation (r=0.63, p=0.07).

Conclusion Transthoracic flow complexity quantification calculated from VFI data is feasible and may be useful for assessing valvular stenosis severity in pediatric patients.

Comparison of algorithms for estimating blood flow velocities in cerebral arteries based on the transport information of contrast agent: An in silico study

While many algorithms have been proposed to estimate blood flow velocities based on the transport information of contrast agent acquired by digital subtraction angiography (DSA), most relevant studies focused on a single vessel, leaving a question open as to whether the algorithms would be suitable for estimating blood flow velocities in arterial systems with complex topological structures. In this study, a one-dimensional (1-D) modeling method was developed to simulate the transport of contrast agent in cerebral arterial networks with various anatomical variations or having occlusive disease, thereby generating an in silico database for examining the accuracies of some typical algorithms (i.e., time-of-center of gravity (TCG), shifted least-squares (SLS), and cross correlation (CC) algorithms) that estimate blood flow velocity based on the concentration-time curves (CTCs) of contrast agent. The results showed that the TCG algorithm had the best performance in estimating blood flow velocities in most cerebral arteries, with the accuracy being only mildly affected by anatomical variations of the cerebral arterial network. Nevertheless, the presence of a stenosis of moderate to high severity in the internal carotid artery could considerably impair the accuracy of the TCG algorithm in estimating blood flow velocities in some cerebral arteries where the transport of contrast agent was disturbed by strong collateral flows. In summary, the study suggests that the TCG algorithm may offer a promising means for estimating blood flow velocities based on CTCs of contrast agent monitored in cerebral arteries, provided that the shapes of CTCs are not highly distorted by collateral flows.

Highlights of the development in ultrasound during the last 70 years: A historical review

This review looks at highlights of the development in ultrasound, ranging from interventional ultrasound and Doppler to the newest techniques like contrast-enhanced ultrasound and elastography, and gives reference to some of the valuable articles in Acta Radiologica. Ultrasound equipment is now available in any size and for any purpose, ranging from handheld devices to high-end devices, and the scientific societies include ultrasound professionals of all disciplines publishing guidelines and recommendations. Interventional ultrasound is expanding the field of use of ultrasound-guided interventions into nearly all specialties of medicine, from ultrasound guidance in minimally invasive robotic procedures to simple ultrasound-guided punctures performed by general practitioners. Each medical specialty is urged to define minimum requirements for equipment, education, training, and maintenance of skills, also for medical students. The clinical application of contrast-enhanced ultrasound and elastography is a topic often seen in current research settings.

Common Carotid Artery Volume Flow: A Comparison Study between Ultrasound Vector Flow Imaging and Phase Contrast Magnetic Resonance Imaging

Volume flow estimation in the common carotid artery (CCA) can assess the absolute hemodynamic effect of a carotid stenosis. The aim of this study was to compare a commercial vector flow imaging (VFI) setup against the reference method magnetic resonance phase contrast angiography (MRA) for volume flow estimation in the CCA. Ten healthy volunteers were scanned with VFI and MRA over the CCA. VFI had an improved precision of 19.2% compared to MRA of 31.9% (p = 0.061). VFI estimated significantly lower volume flow than MRA (mean difference: 63.2 mL/min, p = 0.017), whilst the correlation between VFI and MRA was strong (R² = 0.81, p < 0.0001). A Bland–Altman plot indicated a systematic bias. After bias correction, the percentage error was reduced from 41.0% to 25.2%. This study indicated that a VFI setup for volume flow estimation is precise and strongly correlated to MRA volume flow estimation, and after correcting for the systematic bias, VFI and MRA become interchangeable.

Translation of Simultaneous Vessel Wall Motion and Vectorial Blood Flow Imaging in Healthy and Diseased Carotids to the Clinic: A Pilot Study

This study aims to investigate the clinical feasibility of simultaneous extraction of vessel wall motion and vectorial blood flow at high frame rates for both extraction of clinical markers and visual inspection. If available in the clinic, such a technique would allow a better estimation of plaque vulnerability and improved evaluation of the overall arterial health of patients. In this study, both healthy volunteers and patients were recruited and scanned using a planewave acquisition scheme that provided a data set of 43 carotid recordings in total. The vessel wall motion was extracted based on the complex autocorrelation of the signals received, while the vector flow was extracted using the transverse oscillation technique. Wall motion and vector flow were extracted at high frame rates, which allowed for a visual appreciation of tissue movement and blood flow simultaneously. Several clinical markers were extracted, and visual inspections of the wall motion and flow were conducted. From all the potential markers, young healthy volunteers had smaller artery diameter (7.72 mm) compared with diseased patients (9.56 mm) ( p -value ≤ 0.001), 66% of diseased patients had backflow compared with less than 10% for the other patients ( p -value ≤ 0.05), a carotid with a pulse wave velocity extracted from the wall velocity greater than 7 m/s was always a diseased vessel, and the peak wall shear rate decreased as the risk increases. Based on both the pathological markers and the visual inspection of tissue motion and vector flow, we conclude that the clinical feasibility of this approach is demonstrated. Larger and more disease-specific studies using such an approach will lead to better understanding and evaluation of vessels, which can translate to future use in the clinic.

Flow Complexity Estimation in Dysfunctional Arteriovenous Dialysis Fistulas using Vector Flow Imaging

Non-invasive assessment is preferred for monitoring arteriovenous dialysis fistulas (AVFs). Vector concentration assesses flow complexity, which may correlate with stenosis severity. We determined whether vector concentration could assess stenosis severity in dysfunctional AVFs. Vector concentration was estimated in four stenotic phantoms at different pulse repetition frequencies. Spectral Doppler peak velocity and vector concentration were measured in 12 patients with dysfunctional AVFs. Additionally, 5 patients underwent digital subtraction angiography (DSA). In phantoms, vector concentration exhibited an inverse relationship with stenosis severity and was less affected by aliasing in severe stenoses. In nine stenoses of 5 patients undergoing DSA, vector concentration correlated strongly with stenosis severity (first stenosis: r = -0.73, p = 0.04; other stenoses; r = -0.69, p = 0.02) and mid-stenotic diameter (first stenosis: r = 0.87, p = 0.006; other stenoses: r = 0.70, p = 0.02) as opposed to peak velocities (p > 0.05). Vector concentration is less affected by aliasing in severe stenoses and correlates with DSA in patients with dysfunctional AVF.

Subspace-Based Blood Power Spectral Capon Combined with Wiener Postfilter to Provide a High-Quality Velocity Waveform with Low Mathematical Complexity

In Doppler analysis, the power spectral density (PSD), which accounts for the axial velocity distribution of the blood scatterers, is estimated. The conventional spectral estimator is Welch's method, which suffers from frequency leakage at small observation window length. The performance of adaptive techniques such as blood power Capon (BPC) has been promising at the cost of higher computation complexity. Reducing the computational complexity while retaining the benefits of BPC would be necessary for real-time implementation. The purpose of the work described here was to investigate whether it is possible to decrease the computation load in BPC and still obtain acceptable results. The computation complexity in BPC is owing primarily to the matrix inversion required for computing the PSD estimate. We here propose the subspace blood power Capon technique, which employs a data covariance matrix with reduced number of rows in estimation of the weight vector. In maximum velocity estimation in the spectra, the signal noise slope intersection envelop estimator that makes use of the integrated power spectrum is employed. The evaluations are made based on both simulated and in vivo data. The results indicate that it is possible to reduce the order of complexity to almost 12.25% at the cost of 2.31% and 2.24% increases in the relative standard deviation and relative bias of the estimates. Moreover, the Wiener post-filter as a post-weighting factor, which will be multiplied by the final weight vector of the spectral estimator, estimates the power of the desired signal and the power of the interference plus noise to improve the contrast. The proposed estimator has exhibited a promising performance at beam-to-flow angles of 45°, 60° and 75°. Furthermore, the robust performance of the proposed estimator against variation in the flow rate is also documented.

Carotid Stenosis Assessment with Vector Concentration before and after Stenting

Digital subtraction angiography (DSA) is considered the reference method for the assessment of carotid artery stenosis; however, the procedure is invasive and accompanied by ionizing radiation. Velocity estimation with duplex ultrasound (DUS) is widely used for carotid artery stenosis assessment since no radiation or intravenous contrast is required; however, the method is angle-dependent. Vector concentration (VC) is a parameter for flow complexity assessment derived from the angle independent ultrasound method vector flow imaging (VFI), and VC has shown to correlate strongly with stenosis degree. The aim of this study was to compare VC estimates and DUS estimated peak-systolic (PSV) and end-diastolic velocities (EDV) for carotid artery stenosis patients, with the stenosis degree obtained with DSA. Eleven patients with symptomatic carotid artery stenosis were examined with DUS, VFI, and DSA before and after stent treatment. Compared to DSA, VC showed a strong correlation (r = -0.79, p < 0.001), while PSV (r = 0.68, p = 0.002) and EDV (r = 0.51, p = 0.048) obtained with DUS showed a moderate correlation. VFI using VC calculations may be a useful ultrasound method for carotid artery stenosis and stent patency assessment.

Vector Flow Imaging of the Ascending Aorta in Patients with Tricuspid and Bicuspid Aortic Valve Stenosis Treated with Biological and Mechanical Implants

Aortic valve stenosis (AS) is treated with biological prostheses (BPs) and mechanical prostheses (MPs). Vector flow imaging (VFI), an angle-independent ultrasound method, can quantify flow complexity (vector concentration (VC)) and secondary rotation (SR). Ten patients (mean age: 70.7 y) with tricuspid AS scheduled for BPs, 10 patients (mean age: 56.2 y) with bicuspid AS scheduled for MPs and 10 patients (mean age: 63.9 y) with normal aortic valves were scanned intra-operatively on the ascending aorta with VFI and conventional spectral Doppler. Bicuspid AS (peak systolic velocity (PSV): 380.9 cm/s, SR: 16.7 Hz, VC: 0.21) had more complex flow (p < 0.02) than tricuspid AS (PSV: 346.1 cm/s, SR: 17.1 Hz, VC: 0.33). Both groups had more complex and faster flow (p < 0.0001) than normal aortic valve patients (PSV: 124.0 cm/s, SR: 4.3 Hz, VC: 0.79). VC (r = 0.87) and SR (r = 0.89) correlated to PSV. After surgery, flow parameters changed (p < 0.0001) for patients with MPs (PSV: 250.4 cm/s, SR: 9.8 Hz, VC: 0.54) and BPs (PSV: 232.4 cm/s, SR: 12.5 Hz, VC: 0.61), with MPs having slower SR (p < 0.01). None of the implants had normal flow (p < 0.0001). In conclusion, VFI can provide new flow parameters for AS and implant assessment.

Ultrasound vector projectile imaging for detection of altered carotid bifurcation hemodynamics during reductions in cardiac output

PURPOSE

Complex blood flow is commonly observed in the carotid bifurcation, although the factors that regulate these patterns beyond arterial geometry are unknown. The emergence of high-frame-rate ultrasound vector flow imaging allows for noninvasive, time-resolved analysis of complex hemodynamic behavior in humans, and it can potentially help researchers understand which physiological stressors can alter carotid bifurcation hemodynamics in vivo. Here, we seek to pursue the first use of vector projectile imaging (VPI), a dynamic form of vector flow imaging, to analyze the regulation of carotid bifurcation hemodynamics during experimental reductions in cardiac output induced via a physiological stressor called lower body negative pressure (LBNP).

METHODS

Seven healthy adults (age: 27 ± 4 yr, 4 men) underwent LBNP at -45 mmHg to simulate a postural hemodynamic response in a controlled environment. Using a research-grade, high-frame-rate ultrasound platform, vector flow estimation in each subject's right carotid bifurcation was performed through a multi-angle plane wave imaging (two transmission angles of 10° and -10°) formulation, and VPI cineloops were generated at a frame rate of 750 fps. Vector concentration was quantified by the resultant blood velocity vector angles within a region of interest; lower concentration indicated greater flow dispersion. Discrete concentration values during peak and late systole were compared across different segments of the carotid artery bifurcation before, and during, LBNP.

RESULTS

Vector projectile imaging revealed that external and internal carotid arteries exhibited regional hemodynamic changes during LBNP, which acted to reduce both the subject's cardiac output (Δ - 1.2 ± 0.5 L/min, -19%; P < 0.01) and peak carotid blood velocity (Δ - 6.30 ± 8.27 cm/s, -7%; P = 0.05). In these carotid artery branches, the vector concentration time trace before and during LBNP were observed to be different. The impact of LBNP on flow complexity in the two carotid artery branches showed variations between subjects.

CONCLUSIONS

Using VPI, intuitive visualization of complex hemodynamic changes can be obtained in healthy humans subjected to LBNP. This imaging tool has potential for further applications in vascular physiology to identify and quantify complex hemodynamic features in humans during different physiological stressor tests that regulate hemodynamics.

In Vivo Blood Velocity Vector Imaging Using Adaptive Velocity Compounding in the Carotid Artery Bifurcation

Visualization and quantification of blood flow are considered important for early detection of atherosclerosis and patient-specific diagnosis and intervention. As conventional Doppler imaging is limited to 1-D velocity estimates, 2-D and 3-D techniques are being developed. We introduce an adaptive velocity compounding technique that estimates the 2-D velocity vector field using predominantly axial displacements estimated by speckle tracking from dual-angle plane wave acquisitions. Straight-vessel experiments with a 7.8-MHz linear array transducer connected to a Verasonics Vantage ultrasound system revealed that the technique performed with a maximum velocity magnitude bias and angle bias of -3.7% (2.8% standard deviation) and -0.16° (0.41° standard deviation), respectively. In vivo, complex flow patterns were visualized in two healthy and three diseased carotid arteries and quantified using a vector complexity measure that increased with increasing wall irregularity. This measure could potentially be a relevant clinical parameter which might aid in early detection of atherosclerosis.

Vector Flow Imaging Compared with Digital Subtraction Angiography for Stenosis Assessment in the Superficial Femoral Artery - A Study of Vector Concentration, Velocity Ratio and Stenosis Degree Percentage

Purpose

Stenosis of the superficial femoral artery (SFA) induces complex blood flow with increased velocities. Disease assessment is performed with Doppler ultrasound and digital subtraction angiography (DSA), but Doppler ultrasound is limited by angle dependency and DSA by ionizing radiation. An alternative is the vector flow imaging method based on transverse oscillation (TO), an angle-independent vector velocity technique using ultrasound. In this study, flow complexity and velocity measured with TO were compared with DSA for the assessment of stenosis in the SFA.

Materials and Methods

The vector concentration, a measure of flow complexity, and the velocity ratio obtained from the stenosis and a disease-free adjacent vessel segment, were estimated with TO in 11 patients with a total of 16 stenoses of the SFA. TO data were compared with the corresponding stenosis degree percentage obtained with DSA.

Results

The correlation between the vector concentration and DSA was very strong (R=0.93; p<0.001; 95% confidence interval (CI): 0.81-0.98), while only moderate for velocity ratio and DSA (R=0.50; p<0.07; 95% CI: 0.00-0.80). The correlation coefficients that were found were significantly different (p<0.005) without overlapping CI.

Conclusion

The study indicated that flow changes in the SFA induced by stenosis can be quantified with TO, and that stenosis grading may be improved by estimation of flow complexity instead of velocity ratio. TO is a potential diagnostic tool for the assessment of atherosclerosis and peripheral arterial disease.

Real-Time Transthoracic Vector Flow Imaging of the Heart in Pediatric Patients

In children with congenital heart defects, Doppler ultrasound is the standard, bedside imaging modality. However, precise characterization of blood flow is challenging due to angle-dependent and one-dimensional velocity estimation. Contrast agent free Vector Flow Imaging is a new ultrasound technology that enables angle-independent visualization of the detailed flow field. Two piglets, one with normal cardiac anatomy and one with congenital heart disease comprised of valvular pulmonary stenosis, a dilated main pulmonary artery, and an incomplete atrioventricular canal defect, were imaged transthoracically and epicardially using a BK Ultrasound bk5000 with built-in vector flow imaging and a 5MHz linear probe. Subsequently, two children, one with normal cardiac anatomy and one with congenital heart disease comprised of aortic valve stenosis and coarctation of the aorta were imaged transthoracically. Transthoracic two-dimensional echocardiography and vector flow imaging were readily performed in both animals and were limited only by the geometry of the porcine thorax. In addition, transthoracic vector flow imaging was successfully performed in both children, and abnormal flow secondary to cardiac anomalies was visible. Adequate penetration was obtained to a depth of 6.5 cm. Our group has previously demonstrated for the first time that transthoracic vector flow imaging echocardiography is feasible and practicable in pediatric-sized patients, and this paper describes examples of these concepts and in-depth comparisons with traditional imaging modalities. This paper demonstrates that commercially available vector flow imaging technology can be utilized in pediatric cardiac applications as a bedside transthoracic imaging modality, providing advanced detail of blood flow patterns within the cardiac chambers, across valves, and in the great arteries.

Non-Invasive Assessment of Intravascular Pressure Gradients: A Review of Current and Proposed Novel Methods

Invasive catheterization is associated with a low risk of serious complications. However, although it is the gold standard for measuring pressure gradients, it induces changes to blood flow and requires significant resources. Therefore, non-invasive alternatives are urgently needed. Pressure gradients are routinely estimated non-invasively in clinical settings using ultrasound and calculated with the simplified Bernoulli equation, a method with several limitations. A PubMed literature search on validation of non-invasive techniques was conducted, and studies were included if non-invasively estimated pressure gradients were compared with invasively measured pressure gradients in vivo. Pressure gradients were mainly estimated from velocities obtained with Doppler ultrasound or magnetic resonance imaging. Most studies used the simplified Bernoulli equation, but more recent studies have employed the expanded Bernoulli and Navier⁻Stokes equations. Overall, the studies reported good correlation between non-invasive estimation of pressure gradients and catheterization. Despite having strong correlations, several studies reported the non-invasive techniques to either overestimate or underestimate the invasive measurements, thus questioning the accuracy of the non-invasive methods. In conclusion, more advanced imaging techniques may be needed to overcome the shortcomings of current methods.