Estimation of pressure gradients in pulsatile flow from magnetic resonance acceleration measurements

Four-dimensional flow cardiovascular magnetic resonance aortic cross-sectional pressure changes and their associations with flow patterns in health and ascending thoracic aortic aneurysm

BACKGROUND

Ascending thoracic aortic aneurysm (ATAA) is a silent and threatening dilation of the ascending aorta (AscAo). Maximal aortic diameter which is currently used for ATAA patients management and surgery planning has been shown to inadequately characterize risk of dissection in a large proportion of patients. Our aim was to propose a comprehensive quantitative evaluation of aortic morphology and pressure-flow-wall associations from four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) data in healthy aging and in patients with ATAA.

METHODS

We studied 17 ATAA patients (64.7 ± 14.3 years, 5 females) along with 17 age- and sex-matched healthy controls (59.7 ± 13.3 years, 5 females) and 13 younger healthy subjects (33.5 ± 11.1 years, 4 females). All subjects underwent a CMR exam, including 4D flow and three-dimensional anatomical images of the aorta. This latter dataset was used for aortic morphology measurements, including AscAo maximal diameter (iDMAX) and volume, indexed to body surface area. 4D flow MRI data were used to estimate 1) cross-sectional local AscAo spatial (∆PS) and temporal (∆PT) pressure changes as well as the distance (∆DPS) and time duration (∆TPT) between local pressure peaks, 2) AscAo maximal wall shear stress (WSSMAX) at peak systole, and 3) AscAo flow vorticity amplitude (VMAX), duration (VFWHM), and eccentricity (VECC).

RESULTS

Consistency of flow and pressure indices was demonstrated through their significant associations with AscAo iDMAX (WSSMAX:r = -0.49, p < 0.001; VECC:r = -0.29, p = 0.045; VFWHM:r = 0.48, p < 0.001; ∆DPS:r = 0.37, p = 0.010; ∆TPT:r = -0.52, p < 0.001) and indexed volume (WSSMAX:r = -0.63, VECC:r = -0.51, VFWHM:r = 0.53, ∆DPS:r = 0.54, ∆TPT:r = -0.63, p < 0.001 for all). Intra-AscAo cross-sectional pressure difference, ∆PS, was significantly and positively associated with both VMAX (r = 0.55, p = 0.002) and WSSMAX (r = 0.59, p < 0.001) in the 30 healthy subjects (48.3 ± 18.0 years). Associations remained significant after adjustment for iDMAX, age, and systolic blood pressure. Superimposition of ATAA patients to normal aging trends between ∆PS and WSSMAX as well as VMAX allowed identifying patients with substantially high pressure differences concomitant with AscAo dilation.

CONCLUSION

Local variations in pressures within ascending aortic cross-sections derived from 4D flow MRI were associated with flow changes, as quantified by vorticity, and with stress exerted by blood on the aortic wall, as quantified by wall shear stress. Such flow-wall and pressure interactions might help for the identification of at-risk patients.

Phase-contrast acceleration mapping with synchronized encoding

PURPOSE

To develop a phase-contrast (PC) -based method for direct and unbiased quantification of the acceleration vector field by synchronization of the spatial and acceleration encoding time points. The proposed method explicitly aims at in-vitro applications, requiring high measurement accuracy, as well as the validation of clinically relevant acceleration-encoded sequences.

METHODS

A velocity-encoded sequence with synchronized encoding (SYNC SPI) was modified to allow direct acceleration mapping by replacing the bipolar encoding gradients with tripolar gradient waveforms. The proposed method was validated in two in-vitro flow cases: a rotation and a stenosis phantom. The thereby obtained velocity and acceleration vector fields were quantitatively compared to those acquired with conventional PC methods, as well as to theoretical data.

RESULTS

The rotation phantom study revealed a systematic bias of the conventional PC acceleration mapping method that resulted in an average pixel-wise relative angle between the measured and theoretical vector field of (7.8 ± 3.2)°, which was reduced to (-0.4 ± 2.7)° for the proposed SYNC SPI method. Furthermore, flow features in the stenosis phantom were displaced by up to 10 mm in the conventional PC data compared with the acceleration-encoded SYNC SPI data.

CONCLUSIONS

This work successfully demonstrates a highly accurate method for direct acceleration mapping. It thus complements the existing velocity-encoded SYNC SPI method to enable the direct and unbiased quantification of both the velocity and acceleration vector field for in vitro studies. Hence, this method can be used for the validation of conventional acceleration-encoded PC methods applicable in-vivo.

Noninvasive measurement of pressure gradient across a coronary stenosis using phase contrast (PC)-MRI: A feasibility study

PURPOSE

To investigate the feasibility of blood pressure difference measurement, ΔP, across the coronary artery using phase contrast (PC)-MRI for potential noninvasive assessment of the functional significance of coronary artery stenosis.

METHODS

Three-directional velocities in the coronary arteries acquired using 2D-PC-MRI were used with the Navier-Stokes equations to derive ΔP. Repeat phantom studies were performed to assess the reproducibility of flow velocity and ΔP. ΔP derived using PC-MRI (ΔP_MR ) and that obtained using pressure transducer (ΔP_PT ) were compared. Reproducibility of coronary flow velocity was assessed in healthy controls (n = 11). Patients with suspected coronary artery disease (n = 6) were studied to evaluate the feasibility of ΔP_MR measurement across a coronary stenosis.

RESULTS

Phantom: Good overall reproducibility of flow velocity and ΔP measurements and excellent correlation (ΔP_MR vs ΔP_PT ) was observed: intraclass correlation (ICC) of 0.95(V_z ), 0.72(V_x ), 0.73(V_y ), and 0.87(ΔP_MR ) and R²  = 0.94, respectively. Human: Good reproducibility of coronary flow velocity was observed: ICC of 0.94/0.95(V_z ), 0.76/0.74(V_x ), and 0.80/0.77(V_y ) at cardiac phase 1/2. Significant (p = 0.025) increase in ΔP_MR was observed in patients (6.40 ± 4.43 mmHg) versus controls (0.70 ± 0.57 mmHg).

CONCLUSION

ΔP_MR in the coronary arteries is feasible. Upon further validation using the invasive measure, ΔP_MR has the potential for noninvasive assessment of coronary artery stenosis. Magn Reson Med 77:529-537, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Noninvasive estimation of 2-D pressure gradients in steady flow using ultrasound

A noninvasive method for estimating 2-D pressure gradients from ultrasound vector velocity data is presented. It relies on vector velocity fields acquired using the transverse oscillation method during steady flow conditions. The pressure gradients are calculated from the velocity fields using the Navier-Stokes equations. Scans of a carotid bifurcation phantom with a 70% constriction are performed using a linear transducer connected to a scanner. The performance of the estimator is evaluated by comparing its results to those of a computational fluid dynamics model of the carotid bifurcation phantom. The geometry of the model is determined from magnetic resonance imaging. The presented study is conducted assuming steady flow using velocity data acquired at 18 frames per second. The proposed method shows pressure gradients at the constricted region from -8 kPa/m to 9 kPa/m, with a maximum bias of -7% for the axial component and -8% for the lateral component. The relative standard deviation of the estimator is 5% (axial component) and 30% (lateral component) when studying the pressure gradient across the constriction using 3 velocity frames per pressure estimate. The study shows that 2-D pressure gradients can be achieved noninvasively using ultrasound data in a constant flow environment.

Geometry is a major determinant of flow reversal in proximal aorta

The aim of this study is to quantify aortic backward flow (BF) using phase-contrast cardiovascular magnetic resonance (PC-CMR) and to study its associations with age, indexes of arterial stiffness, and geometry. Although PC-CMR blood flow studies showed a simultaneous presence of BF and forward flow (FF) in the ascending aorta (AA), the relationship between aortic flows and aging as well as arterial stiffness and geometry in healthy volunteers has never been reported. We studied 96 healthy subjects [47 women, 39 ± 15 yr old (19–79 yr)]. Aortic stiffness [arch pulse wave velocity (PWVAO), AA distensibility], geometry (AA diameter and arch length), and parameters related to AA BF and FF (volumes, peaks, and onset times) were estimated from CMR. Applanation tonometry carotid-femoral pulse-wave velocity (PWVCF), carotid augmentation index, and time to return of the reflected pressure wave were assessed. Whereas FF parameters remained unchanged, BF onset time shortened significantly ( R2 = 0.18, P < 0.0001) and BF volume and BF-to-FF peaks ratio increased significantly ( R2 = 0.38 and R2 = 0.44, respectively, P < 0.0001) with aging. These two latter BF indexes were also related to stiffness indexes (PWVCF, R2 > 0.30; PWVAO, R2 > 0.24; and distensibility, R2 > 0.20, P < 0.001), augmentation index ( R2 > 0.20, P < 0.001), and aortic geometry (AA diameter, R2 > 0.58; and arch length, R2 > 0.31, P < 0.001). In multivariate analysis, aortic diameter was the strongest independent correlate of BF beyond age effect. In conclusion, AA BF estimated using PC-CMR increased significantly in terms of magnitude and volume and appeared earlier with aging and was mostly determined by aortic geometry. Thus BF indexes could be relevant markers of subclinical arterial wall alterations.

CT and MRI of pulmonary valvular abnormalities

Pulmonary valve disease constitutes a wide spectrum of conditions. Traditionally, echocardiography has been the technique of choice for the evaluation of pulmonary and other valvular disease. However, with advances in technology, computed tomography (CT) and magnetic resonance imaging (MRI) are playing increasingly important roles in the evaluation of these disorders. In this article, we review the normal appearance of the pulmonary valve and then illustrate various variants and pathological entities of the pulmonary valve.

In vivo noninvasive 4D pressure difference mapping in the human aorta: phantom comparison and application in healthy volunteers and patients

In this work, we present a systematic phantom comparison and clinical application of noninvasive pressure difference mapping in the human aorta based on time-resolved 3D phase contrast data. Relative pressure differences were calculated based on integration and iterative refinement of pressure gradients derived from MR-based three-directional velocity vector fields (flow-sensitive 4D MRI with spatial/temporal resolution ∼ 2.1 mm(3)/40 ms) using the Navier-Stokes equation. After in vitro study using a stenosis phantom, time-resolved 3D pressure gradients were systematically evaluated in the thoracic aorta in a group of 12 healthy subjects and 6 patients after repair for aortic coarctation. Results from the phantom study showed good agreement with expected values and standard methods (Bernoulli). Data of healthy subjects showed good intersubject consistency and good agreement with the literature. In patients, pressure waveforms showed elevated peak values. Pressure gradients across the stenosis were compared with reference measurements from Doppler ultrasound. The MRI findings demonstrated a significant correlation (r = 0.96, P < 0.05) but moderate underestimation (14.7% ± 15.5%) compared with ultrasound when the maximum pressure difference for all possible paths connecting proximal and distal locations of the stenosis were used. This study demonstrates the potential of the applied approach to derive additional quantitative information such as pressure gradients from time-resolved 3D phase contrast MRI.

Impact of image spatial, temporal, and velocity resolutions on cardiovascular indices derived from color-Doppler echocardiography

Quantitative processing of color-Doppler echocardiographic images has substantially improved noninvasive assessment of cardiac physiology. Many indices are computed from the velocity fields derived either from color-Doppler tissue imaging (DTI), such as acceleration, strain and strain-rate, or from blood-flow color-Doppler, such as intracardiac pressure gradients (ICPG). All of these indices are dependent on the finite resolution of the ultrasound scanner. Therefore, we developed an image-dependent method for assessing the influence of temporal, spatial, and velocity resolutions, on cardiovascular parameters derived from velocity images. In order to focus our study on the spatial, temporal, and velocity resolutions of the digital image, we did not consider the effect of other sources of noise such as the interaction between ultrasound and tissue. A simple first-order Taylor's expansion was used to establish the functional relationship between the acquired image velocity and the calculated cardiac index. Resolutions were studied on: (a) myocardial acceleration, strain, and strain-rate from DTI, and (b) ICPG from blood-flow color-Doppler. The performance of Taylor's-based error bounds (TBEB) was demonstrated on simulated models and illustrated on clinical images. Velocity and temporal resolution were highly relevant for the accuracy of DTI-derived parameters and ICPGs. TBEB allow to assess the effects of ideal digital image resolution on quantitative cardiovascular indices derived from velocity measurements obtained by cardiac imaging techniques.

BEM performance in calculation of pressure distribution in spline based segmented medical images

Conventional methods for non-invasively estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. This study evaluates the advantages of using integral form of governing equations. The concepts provided with the Boundary Element Method (BEM) together with the boundary based image segmentation tools are used to develop a fast calculation algorithm. Boundary based segmentation provides facility for BEM with domain pixel extraction, boundary meshing, wall normal vector calculation and accurate calculation of boundary element length. The integral form of governing equation reviewed in detail. Both the differential and integral based formulations are evaluated using mathematical test flow image.

Magnetic resonance imaging assessment of myocardial elastic modulus and viscosity using displacement imaging and phase-contrast velocity mapping

Approximately half of patients experiencing congestive heart failure present with a normal left ventricular ejection fraction. Perturbations in material properties affecting ventricular pressure/volume relationships likely play an important role in the "stiff heart syndrome" yet noninvasive tools permitting the accurate assessment of myocardial elasticity are extremely limited. We developed an MRI-based technique to examine regional left ventricular stress/strain relationships by incorporating displacement-encoding with stimulated-echoes (DENSE) and phase-contrast (PC) velocity mapping and compared regional elastic moduli (EM) and viscous delay time constants (VDTCs) (N=10) with immediate postmortem direct strain gauge measurements (N=8) and global chamber compliance (literature) in normal dogs. EMs by MRI were significantly greater in papillary muscle columns when compared with lateral wall and septal locations by MRI (7.59+/-1.65 versus 3.40+/-0.87 versus 2.55+/-0.93 kPa, P<0.0001) and were in agreement with direct strain gauge measurements (3.78+/-0.93 and 2.96+/-0.88 kPa for the lateral wall and the septum, P=ns for both versus MRI). MRI-determined VDTCs were similar in the three regions (VDTC=-1.15+/-12.37 versus 3.04+/-7.25 versus 4.17+/-5.76 ms, P=ns) and did not differ from lateral and septal wall strain gauge assessment (VDTC=3.09+/-0.40 and 4.57+/-1.86 ms, P=ns for both versus MRI). Viscoelastic measurements obtained in six normal volunteers demonstrated the feasibility of this technique in humans. Noninvasive, regional assessment of myocardial stiffness using DENSE and PC velocity mapping techniques is accurate in a canine model and feasible in humans.

Fast measurement of intracardiac pressure differences with 2D breath-hold phase-contrast MRI

Intracardiovascular blood pressure differences can be derived from velocity images acquired with phase-contrast (PC) MRI by evaluating the Navier-Stokes equations. Pressure differences within a slice of interest can be calculated using only the in-plane velocity components from that slice. This rapid exam is proposed as an alternative to the lengthy 3D velocity imaging exams. Despite their good spatial coverage, the 3D exams are prone to artifacts and errors from respiratory motion and insufficient temporal resolution, and are unattractive in the clinical setting due to their excessive scan times (>10 min of free breathing). The proposed single-slice approach requires only one or two breath-holds of acquisition time, and the velocity data can be processed for the calculation of pressure differences online with immediate feedback. The impact of reducing the pressure difference calculation to two dimensions is quantified by comparison with 3D data sets for the case of blood flow within the cardiac chambers. The calculated pressure differences are validated using high-fidelity pressure transducers both in a pulsatile flow phantom and in vivo in a dog model. There was excellent agreement between the transducer and PC-MRI results in all of the studies.

Pulse-wave velocity measured in one heartbeat using MR tagging

A noninvasive method for measuring the aortic pulse-wave velocity (PWV) in a single heartbeat is introduced. The method sinusoidally tags a column of blood within the vessel, and rapidly acquires a series of 1D projections of the tags as they move (in practice, 64 projections at 4-ms intervals). From these projections, the relative motion of blood at different positions along the vessel is measured. The PWV is obtained by fitting a mathematical model of blood flow to the tag trajectories. Tests of this method in a pulsatile flow phantom are presented using latex and polyurethane tubes. The PWV measured in these tubes was (mean +/- standard deviation) 4.4 +/- 0.5 m/s and 2.3 +/- 0.2 m/s, respectively. The distensibility of each tube was calculated from the PWV (latex = (7 +/- 2) 10(-3) mm Hg(-1), poly. = (25 +/- 4) 10(-3)mmHg(-1)) and found to agree within error with distensibility measurements based on the change of tube area with pressure (latex = (6.3 +/- 0.3) 10(-3)mmHg(-1), poly. = (27 +/- 1) 10(-3) mmHg(-1)). To test its feasibility, the PWV measurement was applied to four normal volunteers. The measured PWV values were 3.9 +/- 0.8 m/s, 3.6 +/- 0.9 m/s, 3.9 +/- 0.5 m/s, and 5.3 +/- 0.8 m/s. By acquiring an independent PWV measurement each heartbeat, errors introduced by arrhythmia and trigger variability appear to be avoided with this method.