Dynamic range extension of cine velocity measurements using motion-registered spatiotemporal phase unwrapping

Unwrapping phase contrast MRI by iterative graph cuts

PURPOSE

To develop and evaluate a phase unwrapping method for cine phase contrast MRI based on graph cuts.

METHODS

A proposed Iterative Graph Cuts method was evaluated in 10 cardiac patients with two-dimensional flow quantification which was repeated at low venc settings to provoke wrapping. The images were also unwrapped by a path-following method (ROMEO), and a Laplacian-based method (LP). Net flow was quantified using semi-automatic vessel segmentation. High venc images were also wrapped retrospectively to asses the residual amount of wrapped voxels.

RESULTS

The absolute net flow error after unwrapping at venc = 100 cm/s was 1.8 mL, which was 0.83 mL smaller than for LP. The repeatability error at high venc without unwrapping was 2.5 mL. The error at venc = 50 cm/s was 7.5 mL, which was 8.2 mL smaller than for ROMEO and 5.7 mL smaller than for LP. For retrospectively wrapped images with synthetic venc of 100/50/25 cm/s, the residual amount of wrapped voxels was 0.00/0.12/0.79%, which was 0.09/0.26/8.0 percentage points smaller than for LP. With synthetic venc of 25 cm/s, omitting magnitude information resulted in 3.2 percentage points more wrapped voxels, and only spatial/temporal unwrapping resulted in 4.6/21 percentage points more wrapped voxels compared to spatiotemporal unwrapping.

CONCLUSION

Iterative Graph Cuts enables unwrapping of cine phase contrast MRI with very small errors, except for at extreme blood velocities, with equal or better performance compared to ROMEO and LP. The use of magnitude information and spatiotemporal unwrapping is recommended.

Flow inefficiencies in non-obstructive HCM revealed by kinetic energy and hemodynamic forces on 4D-flow CMR

Aims

Patients with non-obstructive hypertrophic cardiomyopathy (HCM) exhibit myocardial changes which may cause flow inefficiencies not detectable on echocardiogram. We investigated whether left ventricular (LV) kinetic energy (KE) and hemodynamic forces (HDF) on 4D-flow cardiovascular magnetic resonance (CMR) can provide more sensitive measures of flow in non-obstructive HCM.

Methods and results

Ninety participants (70 with non-obstructive HCM and 20 healthy controls) underwent 4D-flow CMR. Patients were categorized as phenotype positive (P+) based on maximum wall thickness (MWT) ≥ 15 mm or ≥13 mm for familial HCM, or pre-hypertrophic sarcomeric variant carriers (P-). LV KE and HDF were computed from 4D-flow CMR. Stroke work was computed using a previously validated non-invasive method. P+ and P- patients and controls had comparable diastolic velocities and LV outflow gradients on echocardiography, LV ejection fraction, and stroke volume on CMR. P+ patients had greater stroke work than P- patients, higher systolic KE compared with controls (5.8 vs. 4.1 mJ, P = 0.0009), and higher late diastolic KE relative to P- patients and controls (2.6 vs. 1.4 vs. 1.9 mJ, P < 0.0001, respectively). MWT was associated with systolic KE (r = 0.5, P < 0.0001) and diastolic KE (r = 0.4, P = 0.005), which also correlated with stroke work. Systolic HDF ratio was increased in P+ patients compared with controls (1.0 vs. 0.8, P = 0.03) and correlated with MWT (r = 0.3, P = 0.004). Diastolic HDF was similar between groups. Sarcomeric variant status was not associated with KE or HDF.

Conclusion

Despite normal flow velocities on echocardiography, patients with non-obstructive HCM exhibited greater stroke work, systolic KE and HDF ratio, and late diastolic KE relative to controls. 4D-flow CMR provides more sensitive measures of haemodynamic inefficiencies in HCM, holding promise for clinical trials of novel therapies and clinical surveillance of non-obstructive HCM.

MR Elastography With Optimization-Based Phase Unwrapping and Traveling Wave Expansion-Based Neural Network (TWENN)

Magnetic Resonance Elastography (MRE) can characterize biomechanical properties of soft tissue for disease diagnosis and treatment planning. However, complicated wavefields acquired from MRE coupled with noise pose challenges for accurate displacement extraction and modulus estimation. Using optimization-based displacement extraction and Traveling Wave Expansion-based Neural Network (TWENN) modulus estimation, we propose a new pipeline for processing MRE images. An objective function with Dual Data Consistency (Dual-DC) has been used to ensure accurate phase unwrapping and displacement extraction. For the estimation of complex wavenumbers, a complex-valued neural network with displacement covariance as an input has been developed. A model of traveling wave expansion is used to generate training datasets for the network with varying levels of noise. The complex shear modulus map is obtained through fusion of multifrequency and multidirectional data. Validation using brain and liver simulation images demonstrates the practical value of the proposed pipeline, which can estimate the biomechanical properties with minimal root-mean-square errors when compared to state-of-the-art methods. Applications of the proposed method for processing MRE images of phantom, brain, and liver reveal clear anatomical features, robustness to noise, and good generalizability of the pipeline.

Comparison of Improved Unidirectional Dual Velocity-Encoding MRI Methods

BACKGROUND

In phase-contrast (PC) MRI, several dual velocity encoding methods have been proposed to robustly increase velocity-to-noise ratio (VNR), including a standard dual-VENC (SDV), an optimal dual-VENC (ODV), and bi- and triconditional methods.

PURPOSE

To develop a correction method for the ODV approach and to perform a comparison between methods.

STUDY TYPE

Case-control study.

POPULATION

Twenty-six volunteers.

FIELD STRENGTH/SEQUENCE

1.5 T phase-contrast MRI with VENCs of 50, 75, and 150 cm/second.

ASSESSMENT

Since we acquired single-VENC protocols, we used the background phase from high-VENC (VENC_H ) to reconstruct the low-VENC (VENC_L ) phase. We implemented and compared the unwrapping methods for different noise levels and also developed a correction of the ODV method.

STATISTICAL TESTS

Shapiro-Wilk's normality test, two-way analysis of variance with homogeneity of variances was performed using Levene's test, and the significance level was adjusted by Tukey's multiple post hoc analysis with Bonferroni (P < 0.05).

RESULTS

Statistical analysis revealed no extreme outliers, normally distributed residuals, and homogeneous variances. We found statistically significant interaction between noise levels and the unwrapping methods. This implies that the number of non-unwrapped pixels increased with the noise level. We found that for β = VENC_L /VENC_H  = 1/2, unwrapping methods were more robust to noise. The post hoc test showed a significant difference between the ODV corrected and the other methods, offering the best results regarding the number of unwrapped pixels.

DATA CONCLUSIONS

All methods performed similarly without noise, but the ODV corrected method was more robust to noise at the price of a higher computational time.

LEVEL OF EVIDENCE

4 TECHNICAL EFFICACY STAGE: 1.

Increased biventricular hemodynamic forces in precapillary pulmonary hypertension

Precapillary pulmonary hypertension (PHprecap) is a condition with elevated pulmonary vascular pressure and resistance. Patients have a poor prognosis and understanding the underlying pathophysiological mechanisms is crucial to guide and improve treatment. Ventricular hemodynamic forces (HDF) are a potential early marker of cardiac dysfunction, which may improve evaluation of treatment effect. Therefore, we aimed to investigate if HDF differ in patients with PHprecap compared to healthy controls. Patients with PHprecap (n = 20) and age- and sex-matched healthy controls (n = 12) underwent cardiac magnetic resonance imaging including 4D flow. Biventricular HDF were computed in three spatial directions throughout the cardiac cycle using the Navier-Stokes equations. Biventricular HDF (N) indexed to stroke volume (l) were larger in patients than controls in all three directions. Data is presented as median N/l for patients vs controls. In the RV, systolic HDF diaphragm-outflow tract were 2.1 vs 1.4 (p = 0.003), and septum-free wall 0.64 vs 0.42 (p = 0.007). Diastolic RV HDF apex-base were 1.4 vs 0.87 (p < 0.0001), diaphragm-outflow tract 0.80 vs 0.47 (p = 0.005), and septum-free wall 0.60 vs 0.38 (p = 0.003). In the LV, systolic HDF apex-base were 2.1 vs 1.5 (p = 0.005), and lateral wall-septum 1.5 vs 1.2 (p = 0.02). Diastolic LV HDF apex-base were 1.6 vs 1.2 (p = 0.008), and inferior-anterior 0.46 vs 0.24 (p = 0.02). Hemodynamic force analysis conveys information of pathological cardiac pumping mechanisms complementary to more established volumetric and functional parameters in precapillary pulmonary hypertension. The right ventricle compensates for the increased afterload in part by augmenting transverse forces, and left ventricular hemodynamic abnormalities are mainly a result of underfilling rather than intrinsic ventricular dysfunction.

Comparison of axial and sagittal spinal cord motion measurements in degenerative cervical myelopathy

BACKGROUND AND PURPOSE

The timing of decision-making for a surgical intervention in patients with mild degenerative cervical myelopathy (DCM) is challenging. Spinal cord motion phase contrast MRI (PC-MRI) measurements can reveal the extent of dynamic mechanical strain on the spinal cord to potentially identify high-risk patients. This study aims to determine the comparability of axial and sagittal PC-MRI measurements of spinal cord motion with the prospect of improving the clinical workup.

METHODS

Sixty-four DCM patients underwent a PC-MRI scan assessing spinal cord motion. The agreement of axial and sagittal measurements was determined by means of intraclass correlation coefficients (ICCs) and Bland-Altman analyses.

RESULTS

The comparability of axial and sagittal PC-MRI measurements was good to excellent at all cervical levels (ICCs motion amplitude: .810-.940; p &lt; .001). Significant differences between axial and sagittal amplitude values could be found at segments C3 and C4, while its magnitude was low (C3: 0.07 ± 0.19 cm/second; C4: -0.12 ± 0.30 cm/second). Bland-Altman analysis showed a good agreement between axial and sagittal PC-MRI scans (coefficients of repeatability: minimum -0.23 cm/second at C2; maximum -0.58 cm/second at C4). Subgroup analysis regarding anatomic conditions (stenotic vs. nonstenotic segments) and different velocity encoding (2 vs. 3 cm/second) showed comparable results.

CONCLUSIONS

This study demonstrates good comparability between axial and sagittal spinal cord motion measurements in DCM patients. To this end, axial and sagittal PC-MRI are both accurate and sensitive in detecting pathologic cord motion. Therefore, such measures could identify high-risk patients and improve clinical decision-making (ie, timing of decompression).

Fold-Over Oversampling Effects in the Measurements of Cerebral Cerebrospinal Fluid and Blood Flows with 2D Cine Phase-Contrast MRI

This prospective study investigated the effects of fold-over oversampling on phase-offset background errors with 2D-Cine phase contrast (Cine-PC) magnetic resonance imaging (MRI). It was performed on brain MRI and compared to conventional Full-field of view FOV coverage and it was tested with two different velocity encoding (Venc) values. We chose Venc = 100 mm/s to encode cerebrospinal fluid (CSF) flows in the aqueduct and 600 mm/s to encode blood flow in the carotid artery. Cine-PC was carried out on 10 healthy adult volunteers followed simultaneously by an acquisition on static agar-gel phantom to measure the phase-offset background errors. Pixel-wise correction of both the CSF and the blood flows was calculated through 32 points of the cardiac-cycle. We compared the velocity-to-noise ratio, the section area, the absolute and the corrected velocity (peak; mean and minimum), the net flow, and the stroke volume before and after correction. We performed the statistical T-test to compare Full-FOV and fold-over and Bland–Altman plots to analyze their differences. Our results showed that following phase-offset error correction, the blood stroke-volume was significantly higher with Full-FOV compared to fold-over. We observed a significantly higher CSF mean velocity and net flow values in the fold-over option. Compared to Full-FOV, fold-over provides a significantly larger section area and significantly lower peak velocity-offset in the aqueduct. No significant difference between the two coverages was reported before and after phase-offset in blood flow measurements. In conclusion, fold-over oversampling can be chosen as an alternative to increase spatial resolution and accurate cerebral flow quantification in Cine-PC.

Cardiac magnetic resonance 'virtual catheterization' for the quantification of valvular regurgitations and cardiac shunt

Cardiac magnetic resonance (CMR) is considered the gold-standard noninvasive technique for the quantification of ventricular volumes by cine-imaging and of vascular flows by velocity-encoded phase contrast (VENC). In routine CMR scans, it is common to found clinical conditions, as valve regurgitations and cardiac shunts, producing a volume overload and significant mismatch between the right and left ventricular stroke volumes (RSV and LSV). In the presence of a valve regurgitation, the volume overload involves the respective ventricular chamber, whereas in cardiac shunts, the location of the volume overload depends on the site of the anatomic defect. Moreover, when a cardiac shunt is present, pulmonary and systemic cardiac outputs are different (Qp/Qs < 1 or Qp/Qs > 1), whereas in the presence of valve regurgitation, Qp/Qs = 1. Therefore, by combining the cine-imaging with the VENC technique, it is possible to investigate the cardiac physiology underlying different pathological conditions producing volume overload, and to quantify this overload (the regurgitant volume and/or shunt volume). In this report, we discussed the technical, theoretical and methodological aspects of this sort of 'virtual catheterization' by CMR, providing a simple algorithm to make the correct diagnosis.

Diagnostic Performance of Combined Contrast-Enhanced Magnetic Resonance Angiography and Phase-Contrast Magnetic Resonance Imaging in Suspected Subclavian Steal Syndrome

PURPOSE

The study sought to evaluate the efficacy of magnetic resonance imaging (MRI) in patients with suspected subclavian steal syndrome (SSS) using both contrast-enhanced (CE) MR angiography and phase-contrast (PC) MRI.

METHODS

Fifteen suspected SSSs from 13 patients were evaluated using CE-MR angiography and PC-MRI. Ten patients also received dynamic CE-MR angiography.

RESULTS

All MRI examinations were technically successful. By combining CE-MR angiography with PC-MRI, 10 SSSs were diagnosed in 9 patients. The delay enhancement dynamic technique predicted SSS with a sensitivity, specificity, and accuracy of 57.1%, 100%, and 72.7%, respectively. Without the dynamic technique, affected delay-enhanced arteries were poorly visualized and could be mistaken for occluded vessels. Retrograde vertebral flow by PC-MRI was used to predict ipsilateral SSS with a sensitivity, specificity, and accuracy of 100%, 60%, and 86.7%, respectively. There were 2 false positives including 1 patient with a proximal total occlusion of the affected vertebral artery and another with brachiocephalic steal syndrome rather than SSS. This suggested that retrograde vertebral flow does not always indicate SSS.

CONCLUSIONS

CE-MR angiography combined with PC-MRI is efficacious when evaluating SSS in clinical practice.

Quantitative phase microscopy: automated background leveling techniques and smart temporal phase unwrapping

In order for time-dynamic quantitative phase microscopy to yield meaningful data to scientists, raw phase measurements must be converted to sequential time series that are consistently phase unwrapped with minimal residual background shape. Beyond the initial phase unwrapping, additional steps must be taken to convert the phase to time-meaningful data sequences. This consists of two major operations both outlined in this paper and shown to operate robustly on biological datasets. An automated background leveling procedure is introduced that consistently removes background shape and minimizes mean background phase value fluctuations. By creating a background phase value that is stable over time, the phase values of features of interest can be examined as a function of time to draw biologically meaningful conclusions. Residual differences between sequential frames of data can be present due to inconsistent phase unwrapping, causing localized regions to have phase values at similar object locations inconsistently changed by large values between frames, not corresponding to physical changes in the sample being observed. This is overcome by introducing a new method, referred to as smart temporal unwrapping that temporally unwraps and filters the phase data such that small motion between frames is accounted for and phase data are unwrapped consistently between frames. The combination of these methods results in the creation of phase data that is stable over time by minimizing errors introduced within the processing of the raw data.

Quantitative Phase Microscopy: how to make phase data meaningful

The continued development of hardware and associated image processing techniques for quantitative phase microscopy has allowed superior phase data to be acquired that readily shows dynamic optical volume changes and enables particle tracking. Recent efforts have focused on tying phase data and associated metrics to cell morphology. One challenge in measuring biological objects using interferometrically obtained phase information is achieving consistent phase unwrapping and -dimensions and correct for temporal discrepanices using a temporal unwrapping procedure. The residual background shape due to mean value fluctuations and residual tilts can be removed automatically using a simple object characterization algorithm. Once the phase data are processed consistently, it is then possible to characterize biological samples such as myocytes and myoblasts in terms of their size, texture and optical volume and track those features dynamically. By observing optical volume dynamically it is possible to determine the presence of objects such as vesicles within myoblasts even when they are co-located with other objects. Quantitative phase microscopy provides a label-free mechanism to characterize living cells and their morphology in dynamic environments, however it is critical to connect the measured phase to important biological function for this measurement modality to prove useful to a broader scientific community. In order to do so, results must be highly consistent and require little to no user manipulation to achieve high quality nynerical results that can be combined with other imaging modalities.

MR assessment of regional myocardial mechanics

Regional myocardial function can be measured by several MR techniques including tissue tagging, phase velocity mapping, and more recently, displacement encoding with stimulated echoes (DENSE) and strain encoding (SENC). Each of these techniques was developed separately and has undergone significant change since its original implementation. As a result, in the current literature, the common features and the differences between the techniques and what they measure are often unclear and confusing. This review article delivers an extensively referenced introductory text which clarifies the current methodology from the starting point of the Bloch equations. By doing this in a consistent way for each method, the similarities and differences between them are highlighted. In addition, their capabilities and limitations are discussed, together with their relative advantages and disadvantages. While the focus is on sequence design and development, the principal parameters measured by each technique are also summarized, together with brief results, with the reader being directed to the extensive literature on data processing and clinical applications for more detail.

Cardiovascular magnetic resonance evaluation of aortic stenosis severity using single plane measurement of effective orifice area

BACKGROUND

Transthoracic echocardiography (TTE) is the standard method for the evaluation of the severity of aortic stenosis (AS). Valve effective orifice area (EOA) measured by the continuity equation is one of the most frequently used stenotic indices. However, TTE measurement of aortic valve EOA is not feasible or not reliable in a significant proportion of patients. Cardiovascular magnetic resonance (CMR) has emerged as a non-invasive alternative to evaluate EOA using velocity measurements. The objectives of this study were: 1) to validate a new CMR method using jet shear layer detection (JSLD) based on acoustical source term (AST) concept to estimate the valve EOA; 2) to introduce a simplified JSLD method not requiring vorticity field derivation.

METHODS AND RESULTS

We performed an in vitro study where EOA was measured by CMR in 4 fixed stenoses (EOA = 0.48, 1.00, 1.38 and 2.11 cm²) under the same steady flow conditions (4-20 L/min). The in vivo study included eight (8) healthy subjects and 37 patients with mild to severe AS (0.72 cm² ≤ EOA ≤ 1.71 cm²). All subjects underwent TTE and CMR examinations. EOA was determinated by TTE with the use of continuity equation method (TTE(CONT)). For CMR estimation of EOA, we used 3 methods: 1) Continuity equation (CMR(CONT)); 2) Shear layer detection (CMR(JSLD)), which was computed from the velocity field of a single CMR velocity profile at the peak systolic phase; 3) Single plane velocity truncation (CMR(SPVT)), which is a simplified version of CMR(JSLD) method. There was a good agreement between the EOAs obtained in vitro by the different CMR methods and the EOA predicted from the potential flow theory. In the in vivo study, there was good correlation and concordance between the EOA measured by the TTE(CONT) method versus those measured by each of the CMR methods: CMR(CONT) (r = 0.88), CMR(JSLD) (r = 0.93) and CMR(SPVT) (r = 0.93). The intra- and inter- observer variability of EOA measurements was 5 ± 5% and 9 ± 5% for TTE(CONT), 2 ± 1% and 7 ± 5% for CMR(CONT), 7 ± 5% and 8 ± 7% for CMR(JSLD), 1 ± 2% and 3 ± 2% for CMR(SPVT). When repeating image acquisition, reproducibility of measurements was 10 ± 8% and 12 ± 5% for TTE(CONT), 9 ± 9% and 8 ± 8% for CMR(CONT), 6 ± 5% and 7 ± 4% for CMR(JSLD) and 3 ± 2% and 2 ± 2% for CMR(SPVT).

CONCLUSION

There was an excellent agreement between the EOA estimated by the CMR(JSLD) or CMR(SPVT) methods and: 1) the theoretical EOA in vitro, and 2) the TTE(CONT) EOA in vivo. The CMR(SPVT) method was superior to the TTE and other CMR methods in terms of measurement variability. The novel CMR-based methods proposed in this study may be helpful to corroborate stenosis severity in patients for whom Doppler-echocardiography exam is inconclusive.

Four-dimensional phase contrast MRI with accelerated dual velocity encoding

PURPOSE

To validate a novel approach for accelerated four-dimensional phase contrast MR imaging (4D PC-MRI) with an extended range of velocity sensitivity.

MATERIALS AND METHODS

4D PC-MRI data were acquired with a radially undersampled trajectory (PC-VIPR). A dual V(enc) (dV(enc) ) processing algorithm was implemented to investigate the potential for scan time savings while providing an improved velocity-to-noise ratio. Flow and velocity measurements were compared with a flow pump, conventional 2D PC MR, and single V(enc) 4D PC-MRI in the chest of 10 volunteers.

RESULTS

Phantom measurements showed excellent agreement between accelerated dV(enc) 4D PC-MRI and the pump flow rate (R(2) ≥ 0.97) with a three-fold increase in measured velocity-to-noise ratio (VNR) and a 5% increase in scan time. In volunteers, reasonable agreement was found when combining 100% of data acquired with V(enc) = 80 cm/s and 25% of the high V(enc) data, providing the VNR of a 80 cm/s acquisition with a wider velocity range of 160 cm/s at the expense of a 25% longer scan.

CONCLUSION

Accelerated dual V(enc) 4D PC-MRI was demonstrated in vitro and in vivo. This acquisition scheme is well suited for vascular territories with wide ranges of flow velocities such as congenital heart disease, the hepatic vasculature, and others.

Improved SNR in phase contrast velocimetry with five-point balanced flow encoding

Phase contrast velocimetry can be utilized to measure complex flow for both quantitative and qualitative assessment of vascular hemodynamics. However, phase contrast requires that a maximum measurable velocity be set that balances noise and phase aliasing. To efficiently reduce noise in phase contrast images, several investigators have proposed extended velocity encoding schemes that use extra encodings to unwrap phase aliasing; however, existing techniques can lead to significant increases in echo and scan time, limiting their clinical benefits. In this work, we have developed a novel five-point velocity encoding scheme that efficiently reduces noise with minimal increases in scan and echo time. Investigations were performed in phantoms, demonstrating a 63% increase in velocity-to-noise ratio compared to standard four-point encoding schemes. Aortic velocity measurements were performed in healthy volunteers, showing similar velocity-to-noise ratio improvements. In those volunteers, it was also demonstrated that, without sacrificing accuracy, low-resolution images can be used for the fifth encoding point, reducing the scan time penalty from 25% down to less than 1%.

Extending the dynamic range of phase contrast magnetic resonance velocity imaging using advanced higher-dimensional phase unwrapping algorithms

Phase contrast magnetic resonance velocity imaging is a powerful technique for quantitative in vivo blood flow measurement. Current practice normally involves restricting the sensitivity of the technique so as to avoid the problem of the measured phase being 'wrapped' onto the range -pi to +pi. However, as a result, dynamic range and signal-to-noise ratio are sacrificed. Alternatively, the true phase values can be estimated by a phase unwrapping process which consists of adding integral multiples of 2pi to the measured wrapped phase values. In the presence of noise and data undersampling, the phase unwrapping problem becomes non-trivial. In this paper, we investigate the performance of three different phase unwrapping algorithms when applied to three-dimensional (two spatial axes and one time axis) phase contrast datasets. A simple one-dimensional temporal unwrapping algorithm, a more complex and robust three-dimensional unwrapping algorithm and a novel velocity encoding unwrapping algorithm which involves unwrapping along a fourth dimension (the 'velocity encoding' direction) are discussed, and results from the three are presented and compared. It is shown that compared to the traditional approach, both dynamic range and signal-to-noise ratio can be increased by a factor of up to five times, which demonstrates considerable promise for a possible eventual clinical implementation. The results are also of direct relevance to users of any other technique delivering time-varying two-dimensional phase images, such as dynamic speckle interferometry and synthetic aperture radar.

Bayesian motion recovery framework for myocardial phase-contrast velocity MRI

Detailed assessment of myocardial motion provides a key indicator of ventricular function, enabling the early detection and assessment of a range of cardiac abnormalities. Existing techniques for myocardial contractility analysis are complicated by a combination of factors including resolution, acquisition time, and consistency of quantification results. Phase-contrast velocity MRI is a technique that provides instantaneous, in vivo measurement of tissue velocity on a per-voxel basis. It allows for the direct derivation of contractile indices with minimal post-processing. For this method to be clinically useful, SNR and image artifacts need to be addressed. The purpose of this paper is to present a Maximum a posteriori (MAP) restoration technique for high quality myocardial motion recovery. It employs an accurate noise modeling scheme and a generalized Gaussian Markov random field prior tailored for the myocardial morphology. The quality of the proposed method is evaluated with both simulated myocardial velocity data with known ground truth and in vivo phase-contrast MR velocity acquisitions from a group of normal subjects.

Flow and myocardial interaction: an imaging perspective

Heart failure due to coronary artery disease has considerable morbidity and poor prognosis. An understanding of the underlying mechanics governing myocardial contraction is a prerequisite for interpreting and predicting changes induced by heart disease. Gross changes in contractile behaviour of the myocardium are readily detected with existing techniques. For more subtle changes during early stages of cardiac dysfunction, however, a sensitive method for measuring, as well as a precise criterion for quantifying, normal and impaired myocardial function is required. The purpose of this paper is to outline the role of imaging, particularly cardiovascular magnetic resonance (CMR), for investigating the fundamental relationships between cardiac morphology, function and flow. CMR is emerging as an important clinical tool owing to its safety, versatility and the high-quality images it produces that allow accurate and reproducible quantification of cardiac structure and function. We demonstrate how morphological and functional assessment of the heart can be achieved by CMR and illustrate how blood flow imaging can be used to study flow and structure interaction, particularly for elucidating the underlying haemodynamic significance of directional changes and asymmetries of the cardiac looping. Future outlook on combining imaging with engineering approaches in subject-specific biomechanical simulation is also provided.

Tracking myocardial motion from cine DENSE images using spatiotemporal phase unwrapping and temporal fitting

Displacement encoding with stimulated echoes (DENSE) encodes myocardial tissue displacement into the phase of the MR image. Cine DENSE allows for rapid quantification of myocardial displacement at multiple cardiac phases through the majority of the cardiac cycle. For practical sensitivities to motion, relatively high displacement encoding frequencies are used and phase wrapping typically occurs. In order to obtain absolute measures of displacement, a two-dimensional (2-D) quality-guided phase unwrapping algorithm was adapted to unwrap both spatially and temporally. Both a fully automated algorithm and a faster semi-automated algorithm are proposed. A method for computing the 2-D trajectories of discrete points in the myocardium as they move through the cardiac cycle is introduced. The error in individual displacement measurements is reduced by fitting a time series to sequential displacement measurements along each trajectory. This improvement is in turn reflected in strain maps, which are derived directly from the trajectories. These methods were validated both in vivo and on a rotating phantom. Further measurements were made to optimize the displacement encoding frequency and to estimate the baseline strain noise both on the phantom and in vivo. The fully automated phase unwrapping algorithm was successful for 767 out of 800 images (95.9%), and the semi-automated algorithm was successful for 786 out of 800 images (98.3%). The accuracy of the tracking algorithm for typical cardiac displacements on a rotating phantom is 0.24 +/- 0.15 mm. The optimal displacement encoding frequency is in the region of 0.1 cycles/mm, and, for 2 scans of 17-s duration, the strain noise after temporal fitting was estimated to be 2.5 +/- 3.0% at end-diastole, 3.1 +/- 3.1% at end-systole, and 5.3 +/- 5.0% in mid-diastole. The improvement in intra-myocardial strain measurements due to temporal fitting is apparent in strain histograms, and also in identifying regions of dysfunctional myocardium in studies of patients with infarcts.

Time-Resolved 3-Dimensional Velocity Mapping in the Thoracic Aorta

OBJECTIVE

An analysis of thoracic aortic blood flow in normal subjects and patients with aortic pathologic findings is presented. Various visualization tools were used to analyze blood flow patterns within a single 3-component velocity volumetric acquisition of the entire thoracic aorta

METHODS

Time-resolved, 3-dimensional phase-contrast magnetic resonance imaging (3D CINE PC MRI) was employed to obtain complete spatial and temporal coverage of the entire thoracic aorta combined with spatially registered 3-directional pulsatile blood flow velocities. Three-dimensional visualization tools, including time-resolved velocity vector fields reformatted to arbitrary 2-dimensional cut planes, 3D streamlines, and time-resolved 3D particle traces, were applied in a study with 10 normal volunteers. Results from 4 patient examinations with similar scan prescriptions to those of the volunteer scans are presented to illustrate flow features associated with common pathologic findings in the thoracic aorta.

RESULTS

Previously reported blood flow patterns in the thoracic aorta, including right-handed helical outflow, late systolic retrograde flow, and accelerated passage through the aortic valve plane, were visualized in all volunteers. The effects of thoracic aortic disease on spatial and temporal blood flow patterns are illustrated in clinical cases, including ascending aortic aneurysms, aortic regurgitation, and aortic dissection.

CONCLUSION

Time-resolved 3D velocity mapping was successfully applied in a study of 10 healthy volunteers and 4 patients with documented aortic pathologic findings and has proven to be a reliable tool for analysis and visualization of normal characteristic as well as pathologic flow features within the entire thoracic aorta.

Understanding phase maps in MRI: a new cutline phase unwrapping method

This paper describes phase maps. A review of the phase unwrapping problem is given. Different structures, in particular fringelines, cutlines, and poles, contained within a phase map are described and their origin and behavior investigated. The problem of phase unwrapping can then be addressed with a better understanding of the source of poles or inconsistencies. This understanding, along with some assumptions about what is being encoded in the phase of a magnetic resonance image, are used to derive a new method for phase unwrapping which relies only on the phase map. The method detects cutlines and distinguishes between noise-induced poles and signal undersampling poles based on the length of the fringelines. The method was shown to be robust to noise and successful in unwrapping challenging clinical cases.

Cardiovascular flow measurement with phase-contrast MR imaging: basic facts and implementation

Phase-contrast magnetic resonance (MR) imaging is a well-known but undervalued method of obtaining quantitative information on blood flow. Applications of this technique in cardiovascular MR imaging are expanding. According to the sequences available, phase-contrast measurement can be performed in a breath hold or during normal respiration. Prospective as well as retrospective gating techniques can be used. Common errors in phase-contrast imaging include mismatched encoding velocity, deviation of the imaging plane, inadequate temporal resolution, inadequate spatial resolution, accelerated flow and spatial misregistration, and phase offset errors. Flow measurements are most precise if the imaging plane is perpendicular to the vessel of interest and flow encoding is set to through-plane flow. The sequence should be repeated at least once, with a high encoding velocity used initially. If peak velocity has to be estimated, flow measurement is repeated with an adapted encoding velocity. The overall error of a phase-contrast flow measurement comprises errors during prescription as well as errors that occur during image analysis of the flow data. With phase-contrast imaging, the overall error in flow measurement can be reduced to less than 10%, an acceptable level of error for routine clinical use.

Assessing the accuracy of two-dimensional phase-contrast MRI measurements of complex unsteady flows

Two-dimensional phase-contrast MRI measurements of complex unsteady flows have been assessed for accuracy, together with procedures used to improve the precision of the measurements. Velocity measurements of single harmonic sinusoidal flow in a rigid bypass graft model with a fully three-dimensional geometry were compared to an accurate numerical solution of the Navier-Stokes equations for the same flow. Axial velocity profiles from the MRI were compared with the computational data, and instantaneous root mean square (rms) differences were calculated. Despite the complexity of the flow, with the aid of phase angle dynamic range extension, a spatially and temporally averaged rms error of between 7.8% and 11.5%, with respect to the spatially and temporally averaged velocity, was achieved. Spin saturation primarily and phase dispersion secondarily in complex transient recirculation zones were found to be significant contributors to overall error. Cross flow effects were also investigated but were of lesser significance. The result confirms the suitability of the technique for measuring complex unsteady flows.

Investigating intrinsic myocardial mechanics: the role of MR tagging, velocity phase mapping, and diffusion imaging

Assessment of myocardial mechanics is an integral part of understanding and predicting heart disease. This review covers the two most common magnetic resonance (MR) methods used to measure myocardial motion: myocardial tagging and myocardial velocity mapping. Myocardial tagging has been well established in clinical research, despite its time-consuming postprocessing procedure. Myocardial velocity mapping uses the phase shifts of the spins to encode the velocity into the MR signal. This means that once the myocardial contours have been segmented, the data can be automatically processed to obtain quantitative measurements. Diffusion MR also has found applications in cardiac imaging, with preliminary results of myocardial fiber architecture being obtained recently. These three different MR techniques have provided valuable insights into the assessment of intrinsic cardiac mechanics. J. Magn. Reson. Imaging 2000;12:873-883.

Improved estimation of velocity and flow rate using regularized three-point phase-contrast velocimetry

We improved the three-point phase-contrast method by regularization of MR velocity data after acquisition of a low velocity-to-noise ratio (VNR) velocity image and a high VNR aliased velocity image. The phase unwrapping algorithm is based on the assumed correlation of the velocity of adjacent flow voxels on the low VNR and the unaliased high VNR images. We used Fourier encoding with eight velocity-encoding gradient steps to obtain reference velocity images of the aorta from five subjects (274 images) and compared them with the phase-contrast and three-point phase-contrast images with and without regularization. The VNR of the regularized velocity image was improved by 9.1 dB and the VNR of the three-point phase-contrast velocity image was improved by 0.7 dB with respect to the low first moment velocity image. Corresponding improvements of 9 dB and 3.7 dB were obtained for the estimations of instantaneous flow rate. Magn Reson Med 44:122-128, 2000.

Fluid mechanics of regurgitant jets and calculation of the effective regurgitant orifice in free or complex configurations

The velocity fields of turbulent jets can be described using a single formula which includes two empirical constants: k(core) determining the length of the central core and k(turb) the jet widening. Flow models simulating jet adhesion, confinement and noncircular orifices were studied using laser Doppler anemometer and the modifications of the constants were derived from series of velocity profiles. In circular free jets, k(core) was found equal to 4.1 with a variability of 1.4%. In complex configurations, its variability was equal to 15.2%. For k(turb), the value for free circular jets was of 45.2 with a variability of 6.0% and this variability in complex configurations was significantly higher (30. 1%, p=0.025). The correlation between the actual orifice size and the jet extension was poor (r=0.52). However, the almost constant value of k(core) allowed to define a new algorithm calculating the regurgitant orifice diameter with the use of outlines of the jet image (r=0.89). In conclusion, the fluid mechanics of regurgitant jets is modified in complex configurations but, due to the relative independency of the central core, velocity fields could be used to evaluate the dimensions of the effective regurgitant orifice.

Spatial regularization of flow patterns in magnetic resonance velocity mapping

A technique dedicated to spatial regularization of magnetic resonance (MR) velocity data has been implemented to improve flow image quality. It is assumed that neighboring flow-velocity pixels are partially correlated, although large-velocity discontinuities remain possible. Increasing MR signal magnitude due to the in-flow effect also is used to enhance further reliability of the estimated velocity. By using an eight-step Fourier-encoding approach, 162 "reference" velocity images acquired in the ascending aorta from six healthy volunteers were compared with "raw" and "regularized" images that were computed from only two gradient steps. The mean square error decreased from 0.12 m(2) x s(-2) to 0.06 m(2) x s(-2) (P < 10-9) for velocity pixel values and from 1929 ml(2) x s(-2) to 1336 ml(2) x s(-2) (P < 0.01) for instantaneous flow rates. The regularization of two-step data sets provides the same velocity image quality as that found after using three-step data sets without regularization. The method can be applied to phase-velocity data sets of any MR technique to reduce velocity noise. J. Magn. Reson. Imaging 1999;10:851-860.