Time-varying myocardial stress and systolic pressure-stress relationship: role in myocardial-arterial coupling in hypertension.

BACKGROUND: Myocardial afterload depends on left ventricular (LV) cavity size, pressure, and wall thickness, all of which change markedly throughout ejection. We assessed the relationship between instantaneous ejection-phase pressure and myocardial stress and the effect of arterial wave reflections on myocardial stress in hypertensive and normotensive adults. METHODS AND RESULTS: We studied 42 untreated hypertensive, 42 treated hypertensive, and 42 normotensive adults with normal LV ejection fraction. Time-resolved central pressure, flow, and LV geometry were measured with carotid tonometry, Doppler, and speckle-tracking echocardiography for computation of arterial load and time-varying circumferential and longitudinal myocardial stress. In all 3 groups, peak myocardial stress typically occurred in early systole (within the first 100 milliseconds of ejection), followed by a marked midsystolic shift in the pressure-stress relationship, which favored lower late systolic stress values (P<0.001) relative to pressure. The mean magnitude of this midsystolic shift was quantitatively important in all 3 groups (circumferential stress, 144 to 148 kdynes/cm(2)) and was independently predicted by a higher LV ejection fraction and ratio of LV end-diastolic cavity to wall volume. Time of peak myocardial stress independently correlated with time of the first systolic but not with time of the second systolic central pressure peak. CONCLUSIONS: Peak myocardial stress occurs in early systole, before important contributions of reflected waves to central pressure. In the presence of normal LV ejection fraction, a midsystolic shift in the pressure-stress relationship protects cardiomyocytes against excessive late systolic stress (despite pressure augmentation associated with wave reflections), a coupling mechanism that may be altered in various disease states.

Arterial pulsatile hemodynamic load induced by isometric exercise strongly predicts left ventricular mass in hypertension.

Although resting hemodynamic load has been extensively investigated as a determinant of left ventricular (LV) hypertrophy, little is known about the relationship between provoked hemodynamic load and the risk of LV hypertrophy. We studied central pressure-flow relations among 40 hypertensive and 19 normotensive adults using carotid applanation tonometry and Doppler echocardiography at rest and during a 40% maximal voluntary forearm contraction (handgrip) maneuver. Carotid-femoral pulse wave velocity (CF-PWV) was measured at rest. Hypertensive subjects demonstrated various abnormalities in resting and induced pulsatile load. Isometric exercise significantly increased systemic vascular resistance, aortic characteristic impedance (Zc), induced earlier wave reflections, increased augmentation index, and decreased total arterial compliance (TAC; all P < or = 0.01). In hypertensive subjects, CF-PWV was the strongest resting predictor of LV mass index (LVMI) and remained an independent predictor after adjustment for age, gender, systemic vascular resistance, reflection magnitude, aortic Zc, and TAC (beta = 2.52 m/s; P < 0.0001). Age, sex, CF-PWV, and resting hemodynamic indexes explained 48% of the interindividual variability in LVMI. In stepwise regression, TAC (beta = -17.85; P < 0.0001) during handgrip, Zc during handgrip (beta = -150; P < 0.0001), and the change in the timing of wave reflections during handgrip (beta = -0.63; P = 0.03) were independent predictors of LVMI. A model that included indexes of provoked hemodynamic load explained 68% of the interindividual variability in LVMI. Hemodynamic load provoked by isometric exercise strongly predicts LVMI in hypertension. The magnitude of this association is far greater than for resting hemodynamic load, suggesting that provoked testing captures important arterial properties that are not apparent at rest and is advantageous to assess dynamic arterial load in hypertension.

A simulation environment for validating ultrasonic blood flow and vessel wall imaging based on fluid-structure interaction simulations: ultrasonic assessment of arterial distension and wall shear rate.

PURPOSE: Ultrasound (US) is a commonly used vascular imaging tool when screening for patients at high cardiovascular risk. However, current blood flow and vessel wall imaging methods are hampered by several limitations. When optimizing and developing new ultrasound modalities, proper validation is required before clinical implementation. Therefore, the authors present a simulation environment integrating ultrasound and fluid-structure interaction (FSI) simulations, allowing construction of synthetic ultrasound images based on physiologically realistic behavior of an artery. To demonstrate the potential of the model for vascular ultrasound research, the authors studied clinically relevant imaging modalities of arterial function related to both vessel wall deformation and arterial hemodynamics: Arterial distension (related to arterial stiffness) and wall shear rate (related to the development of atherosclerosis) imaging. METHODS: An in-house code ("TANGO") was developed to strongly couple the flow solver FLUENT and structural solver ABAQUS using an interface quasi-Newton technique. FIELD II was used to model realistic transducer and scan settings. The input to the FSI-US model is a scatterer phantom on which the US waves reflect, with the scatterer displacement derived from the FSI flow and displacement fields. The authors applied the simulation tool to a 3D straight tube, representative of the common carotid artery (length: 5 cm; and inner and outer radius: 3 and 4 mm). A mass flow inlet boundary condition, based on flow measured in a healthy subject, was applied. A downstream pressure condition, based on a noninvasively measured pressure waveform, was chosen and scaled to simulate three different degrees of arterial distension (1%, 4%, and 9%). The RF data from the FSI-US coupling were further processed for arterial wall and flow imaging. Using an available wall tracking algorithm, arterial distensibility was assessed. Using an autocorrelation estimator, blood velocity and shear rate were obtained along a scanline. RESULTS: The authors obtained a very good agreement between the flow and the distension as obtained from the FSI-US model and the reference FSI values. The wall application showed a high sensitivity of distension measurements to the measurement location, previously reported based on in vivo data. Interestingly, the model indicated that strong reflections between tissue transitions can potentially cloud a correct measurement. The flow imaging application demonstrated that maximum shear rate was underestimated for a relevant simulation setup. Moreover, given the difficulty of measuring near-wall velocities with ultrasound, maximal shear rate was obtained at a distance from the wall [0.812 mm for the anterior and 0.689 mm for the posterior side (9% distension case)]. However, ultrasound shear rates correlated well with the FSI ground truth for all distension degrees, suggesting that correction of the severe underestimation by ultrasound might be feasible in certain flow conditions. CONCLUSIONS: The authors demonstrated a simulation environment to validate and develop ultrasonic vascular imaging. An elaborate technique to integrate FSI and FIELD II ultrasound simulations was presented. This multiphysics simulation tool was applied to two imaging applications where distensible ultrasound phantoms are indispensable: Wall distension and shear rate measurement. Results showed that the method to couple fluid-structure interaction and ultrasound simulations provides realistic RF signals from the tissue and the blood pool.

Atherosclerotic carotid bifurcation phantoms with stenotic soft inclusions for ultrasound flow and vessel wall elastography imaging.

As the complexity of ultrasound signal processing algorithms increases, it becomes more difficult to demonstrate their added value and thus robust validation strategies are required. We propose a method of manufacturing ultrasonic vascular phantoms mimicking an atheromatous plaque in an internal carotid artery bifurcation for applications in flow imaging and elastography. During the fabrication process, a soft inclusion mimicking a stenotic lipid pool was embedded within the vascular wall. Mechanical testing measured Young's moduli of the vascular wall and soft inclusion at 342 ± 25 kPa and 17 ± 3 kPa, respectively. B-mode, color Doppler, power Doppler, shear wave elastography, and strain elastography images of the different phantoms were produced to show the validity of the fabrication process. Because of their realistic geometries and mechanical properties, those phantoms may become advantageous for fluid-structure experimental modeling and validation of new ultrasound-based imaging technologies.

Effect of an abdominal aortic aneurysm on wave reflection in the aorta.

Despite extensive attention to abdominal aortic aneurysm (AAA) in the biomedical engineering community, its effect on aortic hemodynamics and arterial wave reflection has not been addressed before. We used experimental and numerical methods, relying on a realistic AAA geometry constructed from patient computer tomography scans (CT-scans), to study this issue. Pressure and flow waves were measured and simulated before and after AAA repair, and wave reflections were analyzed using linear wave separation and wave intensity analysis. With AAA, pronounced reflections were present in the pressure and flow waveforms. The reflection coefficient measured experimentally in the upper aorta was negative with AAA (-0.10) versus 0.47 without AAA. Wave intensity analysis confirmed the presence of a backward expansion wave caused by sudden expansion of the aorta; this was absent without AAA. These results were confirmed using a 1-D numerical model. A parameter study using this model demonstrated that dominant factors are diameter and compliance of the aneurysm, with larger diameters and more compliant AAA generating more negative reflections. Finally, a preliminary noninvasive study in three patients before and after AAA repair demonstrated that AAA-repair increased the reflection coefficient. In conclusion, the presence of AAA significantly alters wave reflection and hemodynamics in the aorta, with apparently measurable effects in humans.

An in silico framework to analyze the anisotropic shear wave mechanics in cardiac shear wave elastography.

Shear wave elastography (SWE) is a potential tool to non-invasively assess cardiac muscle stiffness. This study focused on the effect of the orthotropic material properties and mechanical loading on the performance of cardiac SWE, as it is known that these factors contribute to complex 3D anisotropic shear wave propagation. To investigate the specific impact of these complexities, we constructed a finite element model with an orthotropic material law subjected to different uniaxial stretches to simulate SWE in the stressed cardiac wall. Group and phase speed were analyzed in function of tissue thickness and virtual probe rotation angle. Tissue stretching increased the group and phase speed of the simulated shear wave, especially in the direction of the muscle fiber. As the model provided access to the true fiber orientation and material properties, we assessed the accuracy of two fiber orientation extraction methods based on SWE. We found a higher accuracy (but lower robustness) when extracting fiber orientations based on the location of maximal shear wave speed instead of the angle of the major axis of the ellipsoidal group speed surface. Both methods had a comparable performance for the center region of the cardiac wall, and performed less well towards the edges. Lastly, we also assessed the (theoretical) impact of pathology on shear wave physics and characterization in the model. It was found that SWE was able to detect changes in fiber orientation and material characteristics, potentially associated with cardiac pathologies such as myocardial fibrosis. Furthermore, the model showed clearly altered shear wave patterns for the fibrotic myocardium compared to the healthy myocardium, which forms an initial but promising outcome of this modeling study.

Assessment of methodologies to calculate intraventricular pressure differences in computational models and patients.

Intraventricular pressure differences (IVPDs) govern left ventricular (LV) efficient filling and are a significant determinant of LV diastolic function. Our primary aim is to assess the performance of available methods (color M-mode (CMM) and 1D/2D MRI-based methods) to determine IVPDs from intracardiac flow measurements. Performance of three methods to calculate IVPDs was first investigated via an LV computational fluid dynamics (CFD) model. CFD velocity data were derived along a modifiable scan line, mimicking ultrasound/MRI acquisition of 1D (IVPDCMM/IVPD1D MRI) and 2D (IVPD2D MRI) velocity-based IVPD information. CFD pressure data (IVPDCFD) was used as a ground truth. Methods were also compared in a small cohort (n = 13) of patients with heart failure with preserved ejection fraction (HFpEF). In silico data showed a better performance of the IVPD2D MRI approach: RMSE values for a well-aligned scan line were 0.2550 mmHg (IVPD1D MRI), 0.0798 mmHg (IVPD2D MRI), and 0.2633 mmHg (IVPDCMM). In vivo data exhibited moderate correlation between techniques. Considerable differences found may be attributable to different timing of measurements and/or integration path. CFD modeling demonstrated an advantage using 2D velocity information to compute IVPDs, and therefore, a 2D MRI-based method should be favored. However, further studies are needed to support the clinical significance of MRI-based computation of IVPDs over CMM.

Wall Shear Rate Measurement: Validation of a New Method Through Multiphysics Simulations.

Wall shear stress is known to affect the vessel endothelial function and to be related to important pathologies like the development of atherosclerosis. It is defined as the product of the blood viscosity by the blood velocity gradient at the wall position, i.e., the wall shear rate (WSR). The WSR measurement is particularly challenging in important cardiovascular sites, like the carotid bifurcation, because of the related complex flow configurations characterized by high spatial and temporal gradients, wall movement, and clutter noise. Moreover, accuracy of any method for WSR measurement can be effectively tested only if reliable gold standard WSR values, considering all the aforementioned disturbing effects, are available. Unfortunately, these requirements are difficult to achieve in a physical phantom, so that the accuracy test of the novel WSR measurement methods was so far limited to straight pipes and/or similar idealistic configurations. In this paper, we propose a new method for WSR measurement and its validation based on a mathematical model of the carotid bifurcation, which, exploiting fluid-structure simulations, is capable of reproducing realistic flow configuration, wall movement, and clutter noise. In particular, the profile near the wall, not directly measurable because affected by clutter, is estimated through a power-law fitting and compared with the gold standard provided by the model. In this condition, the WSR measurements featured an accuracy of ±20 %. A preliminary test on a volunteer confirmed the feasibility of the WSR method for in vivo application.

Investigating Shear Wave Physics in a Generic Pediatric Left Ventricular Model via In Vitro Experiments and Finite Element Simulations.

Shear wave elastography (SWE) is a potentially valuable tool to noninvasively assess ventricular function in children with cardiac disorders, which could help in the early detection of abnormalities in muscle characteristics. Initial experiments demonstrated the potential of this technique in measuring ventricular stiffness; however, its performance remains to be validated as complicated shear wave (SW) propagation characteristics are expected to arise due to the complex non-homogenous structure of the myocardium. In this work, we investigated the (i) accuracy of different shear modulus estimation techniques (time-of-flight (TOF) method and phase velocity analysis) across myocardial thickness and (ii) effect of the ventricular geometry, surroundings, acoustic loading, and material viscoelasticity on SW physics. A generic pediatric (10-15-year old) left ventricular model was studied numerically and experimentally. For the SWE experiments, a polyvinylalcohol replicate of the cardiac geometry was fabricated and SW acquisitions were performed on different ventricular areas using varying probe orientations. Additionally, the phantom's stiffness was obtained via mechanical tests. The results of the SWE experiments revealed the following trends for stiffness estimation across the phantom's thickness: a slight stiffness overestimation for phase speed analysis and a clear stiffness underestimation for the TOF method for all acquisitions. The computational model provided valuable 3-D insights in the physical factors influencing SW patterns, especially the surroundings (water), interface force, and viscoelasticity. In conclusion, this paper presents a validation study of two commonly used shear modulus estimators for different ventricular locations and the essential role of SW modeling in understanding SW physics in the pediatric myocardium.

Grading of mitral regurgitation based on intensity analysis of the continuous wave Doppler signal.

OBJECTIVES: Echocardiographic methods are used to quantify mitral regurgitation (MR) severity; however, their applicability, accuracy and reproducibility have been debated. We aimed to develop and validate a novel custom-made transthoracic echocardiographic method for grading MR severity based on average pixel intensity (API) analysis of the continuous wave (CW) Doppler envelope. METHODS: MR was assessed in 290 patients using API, colour Doppler imaging, vena contracta width (VCW) and proximal iso-velocity surface area (PISA) method. For the validation of the API method, a pulsatile in vitro cardiac phantom was used. RESULTS: Indices of MR severity, such as left ventricular and atrial dimension, pulmonary arterial pressure, significantly cosegregate with API severity (p≤0.002). The API method showed a linear correlation with colour Doppler (r=0.79), VCW (r=0.68), PISA-effective regurgitant orifice area (r=0.72) and PISA-regurgitant volume (r=0.67); p<0.001 for all. The API was significantly more applicable than VCW (95% vs 75% of all patients; p<0.001) and PISA-based methods (65%; p<0.001). Additionally, the API showed a stronger intraobserver and interobserver agreement compared with other methods. Finally, in the in vitro validation, API values showed a strong linear correlation with increasing regurgitant volumes (r=0.81; p<0.001). CONCLUSIONS: We showed the clinical feasibility and in vitro validation of a novel digital quantitative echocardiographic method to grade MR severity. This method is more applicable and has less interobserver and intraobserver variability compared with current quantitative methods.

Pitfalls of Doppler Measurements for Arterial Blood Flow Quantification in Small Animal Research: A Study Based on Virtual Ultrasound Imaging.

High-resolution Doppler is a popular tool for evaluating cardiovascular physiology in mutant mice, though its 1-D nature and spectral broadening processes complicate interpretation of the measurement. Hence, it is crucial for pre-clinical researchers to know how error sources in Doppler assessments reveal themselves in the murine arterial system. Therefore, we performed virtual Doppler experiments in a computer model of an aneurysmatic murine aorta with full control of the imaging and insonified fluid dynamics. We observed significant variability in Doppler performance and derived vascular indices depending on the interrogated flow, operator settings and signal processing. In particular, we found that (i) Doppler spectra in the upper aortic branches and celiac artery exhibited more broadening because of complex out-of-beam flow paths; (ii) mean frequency tracking outperforms tracking of the outer envelope, but is sensitive to errors in angle correction; and (iii) imaging depths deviating much from the elevation focus suffer from decreased spectral quality.

An Extended Least Squares Method for Aliasing-Resistant Vector Velocity Estimation.

An extended least squares method for robust, angle-independent 2-D vector velocity estimation using plane-wave ultrasound imaging is presented. The method utilizes a combination of least squares regression of Doppler autocorrelation estimates and block matching to obtain aliasing-resistant vector velocity estimates. It is shown that the aliasing resistance of the technique may be predicted using a single parameter, which is dependent on the selected transmit and receive steering angles. This parameter can therefore be used to design the aliasing-resistant transmit-receive setups. Furthermore, it is demonstrated that careful design of the transmit-receive steering pattern is more effective than increasing the number of Doppler measurements to obtain robust vector velocity estimates, especially in the presence of higher order aliasing. The accuracy and robustness of the method are investigated using the realistic simulations of blood flow in the carotid artery bifurcation, with velocities up to five times the Nyquist limit. Normalized root-mean-square (rms) errors are used to assess the performance of the technique. At -5 dB channel data blood SNR, rms errors in the vertical and horizontal velocity components were approximately 5% and 15% of the maximum absolute velocity, respectively. Finally, the in vivo feasibility of the technique is shown by imaging the carotid arteries of healthy volunteers.

Assessing the Performance of Ultrafast Vector Flow Imaging in the Neonatal Heart via Multiphysics Modeling and In Vitro Experiments.

Ultrafast vector flow imaging would benefit newborn patients with congenital heart disorders, but still requires thorough validation before translation to clinical practice. This paper investigates 2-D speckle tracking (ST) of intraventricular blood flow in neonates when transmitting diverging waves at ultrafast frame rate. Computational and in vitro studies enabled us to quantify the performance and identify artifacts related to the flow and the imaging sequence. First, synthetic ultrasound images of a neonate's left ventricular flow pattern were obtained with the ultrasound simulator Field II by propagating point scatterers according to 3-D intraventricular flow fields obtained with computational fluid dynamics (CFD). Noncompounded diverging waves (opening angle of 60°) were transmitted at a pulse repetition frequency of 9 kHz. ST of the B-mode data provided 2-D flow estimates at 180 Hz, which were compared with the CFD flow field. We demonstrated that the diastolic inflow jet showed a strong bias in the lateral velocity estimates at the edges of the jet, as confirmed by additional in vitro tests on a jet flow phantom. Furthermore, ST performance was highly dependent on the cardiac phase with low flows (<5 cm/s), high spatial flow gradients, and out-of-plane flow as deteriorating factors. Despite the observed artifacts, a good overall performance of 2-D ST was obtained with a median magnitude underestimation and angular deviation of, respectively, 28% and 13.5° during systole and 16% and 10.5° during diastole.

2-D Versus 3-D Cross-Correlation-Based Radial and Circumferential Strain Estimation Using Multiplane 2-D Ultrafast Ultrasound in a 3-D Atherosclerotic Carotid Artery Model.

Three-dimensional (3-D) strain estimation might improve the detection and localization of high strain regions in the carotid artery (CA) for identification of vulnerable plaques. This paper compares 2-D versus 3-D displacement estimation in terms of radial and circumferential strain using simulated ultrasound (US) images of a patient-specific 3-D atherosclerotic CA model at the bifurcation embedded in surrounding tissue generated with ABAQUS software. Global longitudinal motion was superimposed to the model based on the literature data. A Philips L11-3 linear array transducer was simulated, which transmitted plane waves at three alternating angles at a pulse repetition rate of 10 kHz. Interframe (IF) radio-frequency US data were simulated in Field II for 191 equally spaced longitudinal positions of the internal CA. Accumulated radial and circumferential displacements were estimated using tracking of the IF displacements estimated by a two-step normalized cross-correlation method and displacement compounding. Least-squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2-D and 3-D methods was compared by calculating the root-mean-squared error of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3-D displacement estimation for the entire cardiac cycle. The 3-D technique clearly outperformed the 2-D technique in phases with high IF longitudinal motion. In fact, the large IF longitudinal motion rendered it impossible to accurately track the tissue and cumulate strains over the entire cardiac cycle with the 2-D technique.

Assessment of shear stress related parameters in the carotid bifurcation using mouse-specific FSI simulations.

The ApoE(-)(/)(-) mouse is a common small animal model to study atherosclerosis, an inflammatory disease of the large and medium sized arteries such as the carotid artery. It is generally accepted that the wall shear stress, induced by the blood flow, plays a key role in the onset of this disease. Wall shear stress, however, is difficult to derive from direct in vivo measurements, particularly in mice. In this study, we integrated in vivo imaging (micro-Computed Tomography-µCT and ultrasound) and fluid-structure interaction (FSI) modeling for the mouse-specific assessment of carotid hemodynamics and wall shear stress. Results were provided for 8 carotid bifurcations of 4 ApoE(-)(/)(-) mice. We demonstrated that accounting for the carotid elasticity leads to more realistic flow waveforms over the complete domain of the model due to volume buffering capacity in systole. The 8 simulated cases showed fairly consistent spatial distribution maps of time-averaged wall shear stress (TAWSS) and relative residence time (RRT). Zones with reduced TAWSS and elevated RRT, potential indicators of atherosclerosis-prone regions, were located mainly at the outer sinus of the external carotid artery. In contrast to human carotid hemodynamics, no flow recirculation could be observed in the carotid bifurcation region.

Performance comparison of ultrasound-based methods to assess aortic diameter and stiffness in normal and aneurysmal mice.

OBJECTIVE: Several ultrasound-based methods are currently used to assess aortic diameter, circumferential strain and stiffness in mice, but none of them is flawless and a gold standard is lacking. We aimed to assess the validity and sensitivity of these methods in control animals and animals developing dissecting abdominal aortic aneurysm. METHODS AND RESULTS: We first compared systolic and diastolic diameters as well as local circumferential strains obtained in 47 Angiotensin II-infused ApoE(-/-) mice with three different techniques (BMode, short axis MMode, long axis MMode), at two different abdominal aortic locations (supraceliac and paravisceral), and at three different time points of abdominal aneurysm formation (baseline, 14 days and 28 days). We found that short axis BMode was preferred to assess diameters, but should be avoided for strains. Short axis MMode gave good results for diameters but high standard deviations for strains. Long axis MMode should be avoided for diameters, and was comparable to short axis MMode for strains. We then compared pulse wave velocity measurements using global, ultrasound-based transit time or regional, pressure-based transit time in 10 control and 20 angiotensin II-infused, anti-TGF-Beta injected C57BL/6 mice. Both transit-time methods poorly correlated and were not able to detect a significant difference in PWV between controls and aneurysms. However, a combination of invasive pressure and MMode diameter, based on radio-frequency data, detected a highly significant difference in local aortic stiffness between controls and aneurysms, with low standard deviation. CONCLUSIONS: In small animal ultrasound the short axis view is preferred over the long axis view to measure aortic diameters, local methods are preferred over transit-time methods to measure aortic stiffness, invasive pressure-diameter data are preferred over non-invasive strains to measure local aortic stiffness, and the use of radiofrequency data improves the accuracy of diameter, strain as well as stiffness measurements.

A versatile and experimentally validated finite element model to assess the accuracy of shear wave elastography in a bounded viscoelastic medium.

The feasibility of shear wave elastography (SWE) in arteries for cardiovascular risk assessment remains to be investigated as the artery's thin wall and intricate material properties induce complex shear wave (SW) propagation phenomena. To better understand the SW physics in bounded media, we proposed an in vitro validated finite element model capable of simulating SW propagation, with full flexibility at the level of the tissue's geometry, material properties, and acoustic radiation force. This computer model was presented in a relatively basic set-up, a homogeneous slab of gelatin-agar material (4.35 mm thick), allowing validation of the numerical settings according to actual SWE measurements. The resulting tissue velocity waveforms and SW propagation speed matched well with the measurement: 4.46 m/s (simulation) versus 4.63 ± 0.07 m/s (experiment). Further, we identified the impact of geometrical and material parameters on the SW propagation characteristics. As expected, phantom thickness was a determining factor of dispersion. Adding viscoelasticity to the model augmented the estimated wave speed to 4.58 m/s, an even better match with the experimental determined value. This study demonstrated that finite element modeling can be a powerful tool to gain insight into SWE mechanics and will in future work be advanced to more clinically relevant settings.

Wave reflection leads to over- and underestimation of local wave speed by the PU- and QA-loop methods: theoretical basis and solution to the problem.

Single-point methods such as the PU- and QA-loop methods are used to estimate local pulse wave velocity (PWVPU and PWVQA) in arteries from a combination of pressure (P), flow (Q), velocity (U) or cross-sectional area (A) waveforms. Available data indicate that the PU-loop method tends to overestimate PWV, while the QA-loop method tends to underestimate. Wave reflection has been suggested as a factor playing a role in the agreement between different methods. In this work, we first provide a theoretical basis to (i) demonstrate the interference of wave reflection with the PU-loop method for both solitary sinusoidal waves as well as physiological waveforms; (ii) develop an operator-independent method to correct for the presence of reflections. Fluid-structure interaction simulations in a tube and carotid artery model with known mechanical properties confirm the theory. For the carotid artery model, PWVPU severely overestimates PWV, while PWVQA underestimates PWV. Correction (leading to an estimate termed PWV1-5) seems to eliminate the impact of reflections. Finally, methods are applied in vivo. Compared to PWVPU and PWVQA, PWV1-5 leads to significantly better correlations of carotid PWV with PWV derived from carotid distensibility based on the Bramwell-Hill equation (with r(2) improving from about 0.25 to 0.91). We conclude that neither the PU-loop nor the QA-loop method provides reliable estimates of local PWV in settings where wave reflections are present-even when the PU- or QA-loops show a linear segment. They offer no alternative for the Bramwell-Hill based approach and their application should therefore be discouraged, especially for the carotid artery, although caution is probably warranted in general.

Comparison of non-invasive methods for measurement of local pulse wave velocity using FSI-simulations and in vivo data.

In the search for better predictors of cardiovascular events, pulse wave velocity (PWV) has gained considerable interest. We compared three single-location methods to locally estimate PWV based on simultaneous measurements of pressure (P), velocity (U) or arterial diameter (D): the PU, ln(D)U and QA-method. First, the performance of these methods was analyzed using 3D fluid-structure interaction simulations (FSI) in a tube and patient-specific carotid artery. We demonstrated that the outcome was dependent on whether the methods were tested in the ideal conditions of a 3D axisymmetrical and reflection-free tube or in the more realistic setup of a carotid artery. The three single-location PWV methods performed similarly in the tube (4.29 m/s for PU, 4.44 m/s for ln(D)U and 4.38 m/s for QA) while the carotid data showed that the PU-method dramatically overestimates PWV (9.16 m/s), and the ln(D)U and QA-method underestimate (3.86 and 3.84 m/s, respectively). The erroneously high wavespeeds from the PU-method were attributed to wave reflections, which was confirmed by measurements in 37 healthy adults. This in vivo study showed similar discrepancies between the 3 single-location techniques as present in the carotid simulations, with the difference between the PU- and ln(D)U-method related to the magnitude of wave reflection.

Simultaneous quantification of flow and tissue velocities based on multi-angle plane wave imaging.

A quantitative angle-independent 2-D modality for flow and tissue imaging based on multi-angle plane wave acquisition was evaluated. Simulations of realistic flow in a carotid artery bifurcation were used to assess the accuracy of the vector Doppler (VD) technique. Reduction in root mean square deviation from 27 cm/s to 6 cm/s and 7 cm/s to 2 cm/s was found for the lateral (vx) and axial (vz) velocity components, respectively, when the ensemble size was increased from 8 to 50. Simulations of a Couette flow phantom (vmax = 2.7 cm/s) gave promising results for imaging of slowly moving tissue, with root mean square deviation of 4.4 mm/s and 1.6 mm/s for the x- and z-components, respectively. A packet acquisition scheme providing both B-mode and vector Doppler RF data was implemented on a research scanner, and beamforming and further post-processing was done offline. In vivo results of healthy volunteers were in accordance with simulations and gave promising results for flow and tissue vector velocity imaging. The technique was also tested in patients with carotid artery disease. Using the high ensemble vector Doppler technique, blood flow through stenoses and secondary flow patterns were better visualized than in ordinary color Doppler. Additionally, the full velocity spectrum could be obtained retrospectively for arbitrary points in the image.