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.

A comparison of phase unwrapping methods in velocity-encoded MRI for aortic flows

PURPOSE

The phase of a MRI signal is used to encode the velocity of blood flow. Phase unwrapping artifacts may appear when aiming to improve the velocity-to-noise ratio (VNR) of the measured velocity field. This study aims to compare various unwrapping algorithms on ground-truth synthetic data generated using computational fluid dynamics (CFD) simulations.

METHODS

We compare four different phase unwrapping algorithms on two different synthetic datasets of four-dimensional flow MRI and 26 datasets of 2D PC-MRI acquisitions including the ascending and descending aorta. The synthetic datasets are constructed using CFD simulations of an aorta with a coarctation, with different levels of spatiotemporal resolutions and noise. The error of the unwrapped images was assessed by comparison against the ground truth velocity field in the synthetic data and dual-VENC reconstructions in the in vivo data.

RESULTS

Using the unwrapping algorithms, we were able to remove aliased voxels in the data almost entirely, reducing the L2-error compared to the ground truth by 50%-80%. Results indicated that the best choice of algorithm depend on the spatiotemporal resolution and noise level of the dataset. Temporal unwrapping is most successful with a high temporal and low spatial resolution (δ t = 30 $$ \delta t=30 $$  ms,h = 2 . 5 $$ h=2.5 $$  mm), reducing the L2-error by 70%-85%, while Laplacian unwrapping performs better with a lower temporal or better spatial resolution (δ t = 60 $$ \delta t=60 $$ ms,h = 1 . 5 $$ h=1.5 $$ mm), especially for signal-to-noise ratio (SNR) 12 as opposed to SNR 15, with an error reduction of 55%-85% compared to the 50%-75% achieved by the Temporal method. The differences in performance between the methods are statistically significant.

CONCLUSIONS

The temporal method and spatiotemporal Laplacian method provide the best results, with the spatiotemporal Laplacian being more robust. However, single-V enc $$ {V}_{\mathrm{enc}} $$ methods only situationally and not generally reach the performance of dual-V enc $$ {V}_{\mathrm{enc}} $$ unwrapping methods.

Advances in machine learning applications for cardiovascular 4D flow MRI

Four-dimensional flow magnetic resonance imaging (MRI) has evolved as a non-invasive imaging technique to visualize and quantify blood flow in the heart and vessels. Hemodynamic parameters derived from 4D flow MRI, such as net flow and peak velocities, but also kinetic energy, turbulent kinetic energy, viscous energy loss, and wall shear stress have shown to be of diagnostic relevance for cardiovascular diseases. 4D flow MRI, however, has several limitations. Its long acquisition times and its limited spatio-temporal resolutions lead to inaccuracies in velocity measurements in small and low-flow vessels and near the vessel wall. Additionally, 4D flow MRI requires long post-processing times, since inaccuracies due to the measurement process need to be corrected for and parameter quantification requires 2D and 3D contour drawing. Several machine learning (ML) techniques have been proposed to overcome these limitations. Existing scan acceleration methods have been extended using ML for image reconstruction and ML based super-resolution methods have been used to assimilate high-resolution computational fluid dynamic simulations and 4D flow MRI, which leads to more realistic velocity results. ML efforts have also focused on the automation of other post-processing steps, by learning phase corrections and anti-aliasing. To automate contour drawing and 3D segmentation, networks such as the U-Net have been widely applied. This review summarizes the latest ML advances in 4D flow MRI with a focus on technical aspects and applications. It is divided into the current status of fast and accurate 4D flow MRI data generation, ML based post-processing tools for phase correction and vessel delineation and the statistical evaluation of blood flow.

High quality of an absolute phase reconstruction for coherent digital holography with an enhanced anti-speckle deep neural unwrapping network

It is always a challenge how to overcome speckle noise interference in the phase reconstruction for coherent digital holography (CDH) and its application, as this issue has not been solved well so far. In this paper, we are proposing an enhanced anti-speckle deep neural unwrapping network (E-ASDNUN) approach to achieve high quality of absolute phase reconstruction for CDH. The method designs a special network-based noise filter and embeds it into a deep neural unwrapping network to enhance anti-noise capacity in the image feature recognition and extraction process. The numerical simulation and experimental test on the phase unwrapping reconstruction and the image quality evaluation under the noise circumstances show that the E-ASDNUN approach is very effective against the speckle noise in realizing the high quality of absolute phase reconstruction. Meanwhile, it also demonstrates much better robustness than the typical U-net neural network and the traditional phase unwrapping algorithms in reconstructing high wrapping densities and high noise levels of phase images. The E-ASDNUN approach is also examined and confirmed by measuring the same phase object using a commercial white light interferometry as a reference. The result is perfectly consistent with that obtained by the E-ASDNUN approach.

Deep learning-based velocity antialiasing of 4D-flow MRI

Purpose

To develop a convolutional neural network (CNN) for the robust and fast correction of velocity aliasing in 4D‐flow MRI.

Methods

This study included 667 adult subjects with aortic 4D‐flow MRI data with existing velocity aliasing (n = 362) and no velocity aliasing (n = 305). Additionally, 10 controls received back‐to‐back 4D‐flow scans with systemically varied velocity‐encoding sensitivity (vencs) at 60, 100, and 175 cm/s. The no‐aliasing data sets were used to simulate velocity aliasing by reducing the venc to 40%–70% of the original, alongside a ground truth locating all aliased voxels (153 training, 152 testing). The 152 simulated and 362 existing aliasing data sets were used for testing and compared with a conventional velocity antialiasing algorithm. Dice scores were calculated to quantify CNN performance. For controls, the venc 175‐cm/s scans were used as the ground truth and compared with the CNN‐corrected venc 60 and 100 cm/s data sets

Results

The CNN required 176 ± 30 s to perform compared with 162 ± 14 s for the conventional algorithm. The CNN showed excellent performance for the simulated data compared with the conventional algorithm (median range of Dice scores CNN: [0.89–0.99], conventional algorithm: [0.84–0.94], p < 0.001, across all simulated vencs) and detected more aliased voxels in existing velocity aliasing data sets (median detected CNN: 159 voxels [31–605], conventional algorithm: 65 [7–417], p < 0.001). For controls, the CNN showed Dice scores of 0.98 [0.95–0.99] and 0.96 [0.87–0.99] for venc = 60 cm/s and 100 cm/s, respectively, while flow comparisons showed moderate‐excellent agreement.

Conclusion

Deep learning enabled fast and robust velocity anti‐aliasing in 4D‐flow MRI.

Velocity vector reconstruction for real-time phase-contrast MRI with radial Maxwell correction

PURPOSE

To develop an auto-calibrated image reconstruction for highly accelerated multi-directional phase-contrast (PC) MRI that compensates for (1) reconstruction instabilities occurring for phase differences near ± π and (2) phase errors by concomitant magnetic fields that differ for individual radial spokes.

THEORY AND METHODS

A model-based image reconstruction for real-time PC MRI based on nonlinear inversion is extended to multi-directional flow by exploiting multiple flow-encodings for the estimation of velocity vectors. An initial smoothing constraint during iterative optimization is introduced to resolve the ambiguity of the solution space by penalizing phase wraps. Maxwell terms are considered as part of the signal model on a line-by-line basis to address phase errors by concomitant magnetic fields. The reconstruction methods are evaluated using simulated data and cross-sectional imaging of a rotating-disc, as well as in vivo for the aortic arch and cervical spinal canal at 3T.

RESULTS

Real-time three-directional velocity mapping in the aortic arch is achieved at 1.8 × 1.8 × 6 mm³ spatial and 60 ms temporal resolution. Artificial phase wraps are avoided in all cases using the smoothness constraint. Inter-spoke differences of concomitant magnetic fields are effectively compensated for by the model-based image reconstruction with integrated radial Maxwell correction.

CONCLUSION

Velocity vector reconstructions based on nonlinear inversion allow for high degrees of radial data undersampling paving the way for multi-directional PC MRI in real time. Whether a spoke-wise treatment of Maxwell terms is required or a computationally cheaper frame-wise approach depends on the individual application.

Fast and accurate phase-unwrapping algorithm based on the transport of intensity equation

The phase information of a complex field is routinely obtained using coherent measurement techniques as, e.g., interferometry or holography. The obtained measurement result is subject to a 2π ambiguity and is often referred to as wrapped phase. Phase-unwrapping algorithms (PUAs) are commonly employed to remove this ambiguity and, hence, obtain the absolute phase. However, implementing PUAs can be computationally intensive, and the accuracy of those algorithms may be low. Recently, the transport of intensity equation (TIE) has been proposed as a simple and practical alternative for obtaining the absolute phase map. Nevertheless, an efficient implementation of this technique has not yet been made. In this work, we propose an accurate solution for the TIE-based PUA that does not require the use of wave-propagation techniques, as previously reported TIE-based approaches. The proposed method calculates directly the axial derivative of the intensity from the wrapped phase when considering the correct propagation method. This is done in order to bypass the time-consuming wave-propagation techniques employed in similar methods. The analytical evaluation of this parameter allows obtaining an accurate solution when unwrapping the phase map with low computational effort. This work further introduces the use of the iterative TIE-PUA that, in a few steps, improves significantly the accuracy of the final absolute phase map, even in the presence of noise or aliasing of the wrapped data. The high accuracy and utility of the developed TIE-PUA technique is proven by both numerical simulations and experiments for various objects.

Susceptibility-weighted imaging using inter-echo-variance channel combination for improved contrast at 7 tesla

PURPOSE

To implement and optimize a new approach for susceptibility-weighted image (SWI) generation from multi-echo multi-channel image data and compare its performance against optimized traditional SWI pipelines.

MATERIALS AND METHODS

Five healthy volunteers were imaged at 7 Tesla. The inter-echo-variance (IEV) channel combination, which uses the variance of the local frequency shift at multiple echo times as a weighting factor during channel combination, was used to calculate multi-echo local phase shift maps. Linear phase masks were combined with the magnitude to generate IEV-SWI. The performance of the IEV-SWI pipeline was compared with that of two accepted SWI pipelines-channel combination followed by (i) Homodyne filtering (HPH-SWI) and (ii) unwrapping and high-pass filtering (SVD-SWI). The filtering steps of each pipeline were optimized. Contrast-to-noise ratio was used as the comparison metric. Qualitative assessment of artifact and vessel conspicuity was performed and processing time of pipelines was evaluated.

RESULTS

The optimized IEV-SWI pipeline (σ = 7 mm) resulted in continuous vessel visibility throughout the brain. IEV-SWI had significantly higher contrast compared with HPH-SWI and SVD-SWI (P < 0.001, Friedman nonparametric test). Residual background fields and phase wraps in HPH-SWI and SVD-SWI corrupted the vessel signal and/or generated vessel-mimicking artifact. Optimized implementation of the IEV-SWI pipeline processed a six-echo 16-channel dataset in under 10 min.

CONCLUSION

IEV-SWI benefits from channel-by-channel processing of phase data and results in high contrast images with an optimal balance between contrast and background noise removal, thereby presenting evidence of importance of the order in which postprocessing techniques are applied for multi-channel SWI generation.

LEVEL OF EVIDENCE

2 J. Magn. Reson. Imaging 2017;45:1113-1124.

Spatiotemporal three-dimensional phase unwrapping in digital speckle pattern interferometry

We propose a hybrid spatiotemporal three-dimensional phase unwrapping algorithm for use in digital speckle pattern interferometry (DSPI). The feature of the proposed algorithm is the integration of one-dimensional temporal and two-dimensional spatial phase unwrapping algorithms. By demodulating the phase on a single reference point or multiple reference points using temporal phase unwrapping and on each separated phase map region using spatial phase unwrapping, the DSPI with the spatiotemporal three-dimensional phase unwrapping algorithm can realize the measurement of dynamic absolute displacements and the determination of abrupt phase changes which are usually caused by object discontinuities. We demonstrate that the presented algorithm can overcome the drawbacks of the traditional spatial and temporal phase unwrapping algorithms.