Comparison of different methods for combining phase-contrast images obtained with multiple coils

Coil combination using linear deconvolution in k-space for phase imaging

Background

The combination of multi-channel data is a critical step for the imaging of phase and susceptibility contrast in magnetic resonance imaging (MRI). Magnitude-weighted phase combination methods often produce noise and aliasing artifacts in the magnitude images at accelerated imaging sceneries. To address this issue, an optimal coil combination method through deconvolution in k-space is proposed in this paper.

Methods

The proposed method firstly employs the sum-of-squares and phase aligning method to yield a complex reference coil image which is then used to calculate the coil sensitivity and its Fourier transform. Then, the coil k-space combining weights is computed, taking into account the truncated frequency data of coil sensitivity and the acquired k-space data. Finally, combining the coil k-space data with the acquired weights generates the k-space data of proton distribution, with which both phase and magnitude information can be obtained straightforwardly. Both phantom and in vivo imaging experiments were conducted to evaluate the performance of the proposed method.

Results

Compared with magnitude-weighted method and MCPC-C, the proposed method can alleviate the phase cancellation in coil combination, resulting in a less wrapped phase.

Conclusions

The proposed method provides an effective and efficient approach to combine multiple coil image in parallel MRI reconstruction, and has potential to benefit routine clinical practice in the future.

Noise estimation for the velocity in MRI phase-contrast

The purpose of this study is to estimate the precision or statistical variability of the velocity measurements computed from MRI phase-contrast. From the analytical probability density function (PDF) of the phase in the signal we obtain the PDF of the velocity by means of an auto-convolution. This PDF allows the estimation of the precision of the velocity, important for the correct interpretation of the many parameters that are based on it. We show that for high Signal-to-Noise Ratio (SNR) voxels, the distribution is well approximated by a Gaussian distribution. On the other hand, this is not true for lower SNR voxels, where the distribution adopts a form in between the Gaussian and the uniform distributions. This was confirmed empirically. Also, knowing the PDF on a coil by coil basis it is possible to combine the data from multiple coils in an optimal way. We showed that the optimal combination reduces the resulting global variability of the velocity, in comparison with the commonly used Weighted Mean or with a SENSE reconstruction with R = 1.

Overview of quantitative susceptibility mapping

Magnetic susceptibility describes the magnetizability of a material to an applied magnetic field and represents an important parameter in the field of MRI. With the recently introduced method of quantitative susceptibility mapping (QSM) and its conceptual extension to susceptibility tensor imaging (STI), the non-invasive assessment of this important physical quantity has become possible with MRI. Both methods solve the ill-posed inverse problem to determine the magnetic susceptibility from local magnetic fields. Whilst QSM allows the extraction of the spatial distribution of the bulk magnetic susceptibility from a single measurement, STI enables the quantification of magnetic susceptibility anisotropy, but requires multiple measurements with different orientations of the object relative to the main static magnetic field. In this review, we briefly recapitulate the fundamental theoretical foundation of QSM and STI, as well as computational strategies for the characterization of magnetic susceptibility with MRI phase data. In the second part, we provide an overview of current methodological and clinical applications of QSM with a focus on brain imaging. Copyright © 2016 John Wiley & Sons, Ltd.

Combining phase images from array coils using a short echo time reference scan (COMPOSER)

PURPOSE

To develop a simple method for combining phase images from multichannel coils that does not require a reference coil and does not entail phase unwrapping, fitting or iterative procedures.

THEORY AND METHODS

At very short echo time, the phase measured with each coil of an array approximates to the phase offset to which the image from that coil is subject. Subtracting this information from the phase of the scan of interest matches the phases from the coils, allowing them to be combined. The effectiveness of this approach is quantified in the brain, calf and breast with coils of diverse designs.

RESULTS

The quality of phase matching between coil elements was close to 100% with all coils assessed even in regions of low signal. This method of phase combination was similar in effectiveness to the Roemer method (which needs a reference coil) and was superior to the rival reference-coil-free approaches tested.

CONCLUSION

The proposed approach-COMbining Phase data using a Short Echo-time Reference scan (COMPOSER)-is a simple and effective approach to reconstructing phase images from multichannel coils. It requires little additional scan time, is compatible with parallel imaging and is applicable to all coils, independent of configuration. Magn Reson Med 77:318-327, 2017. © 2015 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Foundations of MRI phase imaging and processing for Quantitative Susceptibility Mapping (QSM)

Quantitative Susceptibility Mapping (QSM) is a novel MRI based technique that relies on estimates of the magnetic field distribution in the tissue under examination. Several sophisticated data processing steps are required to extract the magnetic field distribution from raw MRI phase measurements. The objective of this review article is to provide a general overview and to discuss several underlying assumptions and limitations of the pre-processing steps that need to be applied to MRI phase data before the final field-to-source inversion can be performed. Beginning with the fundamental relation between MRI signal and tissue magnetic susceptibility this review covers the reconstruction of magnetic field maps from multi-channel phase images, background field correction, and provides an overview of state of the art QSM solution strategies.

Quantitative susceptibility mapping (QSM): Decoding MRI data for a tissue magnetic biomarker

In MRI, the main magnetic field polarizes the electron cloud of a molecule, generating a chemical shift for observer protons within the molecule and a magnetic susceptibility inhomogeneity field for observer protons outside the molecule. The number of water protons surrounding a molecule for detecting its magnetic susceptibility is vastly greater than the number of protons within the molecule for detecting its chemical shift. However, the study of tissue magnetic susceptibility has been hindered by poor molecular specificities of hitherto used methods based on MRI signal phase and T2* contrast, which depend convolutedly on surrounding susceptibility sources. Deconvolution of the MRI signal phase can determine tissue susceptibility but is challenged by the lack of MRI signal in the background and by the zeroes in the dipole kernel. Recently, physically meaningful regularizations, including the Bayesian approach, have been developed to enable accurate quantitative susceptibility mapping (QSM) for studying iron distribution, metabolic oxygen consumption, blood degradation, calcification, demyelination, and other pathophysiological susceptibility changes, as well as contrast agent biodistribution in MRI. This paper attempts to summarize the basic physical concepts and essential algorithmic steps in QSM, to describe clinical and technical issues under active development, and to provide references, codes, and testing data for readers interested in QSM.

Phase reconstruction from multiple coil data using a virtual reference coil

PURPOSE

This study develops a method to obtain optimal estimates of absolute magnetization phase from multiple-coil MRI data.

THEORY AND METHODS

The element-specific phases of a multi-element receiver coil array are accounted for by using the phase of a real or virtual reference coil that is sensitive over the entire imaged volume. The virtual-reference coil is generated as a weighted combination of measurements from all receiver coils. The phase-corrected multiple coil complex images are combined using the inverse covariance matrix. These methods are tested on images of an agar phantom, an in vivo breast, and an anesthetized rabbit obtained using combinations of four, nine, and three receiver channels, respectively.

RESULTS

The four- and three-channel acquisitions require formation of a virtual-reference receiver coil while one channel of the nine-channel receive array has a sensitivity profile covering the entire imaged volume. Referencing to a real or virtual coil gives receiver phases that are essentially identical except for the individual receiver channel noise. The resulting combined images, which account for receiver channel noise covariance, show the expected reduction in phase variance.

CONCLUSION

The proposed virtual reference coil method determines a phase distribution for each coil from which an optimal phase map can be obtained.

Highly accelerated cardiac cine phase-contrast MRI using an undersampled radial acquisition and temporally constrained reconstruction

PURPOSE

To evaluate a method to enable single-slice or multiple-slice cine phase contrast (cine-PC) acquisition during a single breath-hold using a highly sparsified radial acquisition ordering and temporally constrained image reconstruction with a spatially varying temporal constraint.

MATERIALS AND METHODS

Simulated and in vivo cine-PC datasets of the proximal ascending aorta were obtained at different acceleration factors using a view projection acquisition order optimized for temporally constrained reconstruction (TCR). Reconstruction of the sparse cine-PC data performed with TCR was compared to reconstructions using zero-filled regridding and temporal interpolation.

RESULTS

TCR resulted in more accurate velocity measurements than regridding or temporal interpolation. In one dataset, TCR of undersampled in vivo data (16 views per cardiac phase) resulted in a peak systolic velocity within 3.3% of the value measured by Doppler ultrasound while shortening the scan time to 13 seconds. High temporal-resolution undersampled TCR was also compared lower temporal-resolution, more highly sampled, regridding in three normal volunteers.

CONCLUSION

TCR proved to be an effective method for reconstructing undersampled radial PC data. Although TCR utilizes a temporal constraint, temporal blurring was minimized by using appropriate constraint weights in addition to a spatially varying temporal constraint. TCR allowed for the acquisition time to be reduced to the duration of a breath-hold, while still resulting in accurate velocity measurements.

Probabilistic 4D blood flow tracking and uncertainty estimation

Phase-Contrast (PC) MRI utilizes signal phase shifts resulting from moving spins to measure tissue motion and blood flow. Time-resolved 4D vector fields representing the motion or flow can be derived from the acquired PC MRI images. In cardiovascular PC MRI applications, visualization techniques such as vector glyphs, streamlines, and particle traces are commonly employed for depicting the blood flow. Whereas these techniques indeed provide useful diagnostic information, uncertainty due to noise in the PC-MRI measurements is ignored, which may lend the results a false sense of precision. In this work, the statistical properties of PC MRI flow measurements are investigated and a probabilistic flow tracking method based on sequential Monte Carlo sampling is devised to calculate flow uncertainty maps. The theoretical derivations are validated using simulated data and a number of real PC MRI data sets of the aorta and carotid arteries are used to demonstrate the flow uncertainty mapping technique.

Real-time MR thermometry for monitoring HIFU ablations of the liver

A high-resolution and high-speed pulse sequence is presented for monitoring high-intensity focused ultrasound ablations in the liver in the presence of motion. The sequence utilizes polynomial-order phase saturation bands to perform outer volume suppression, followed by spatial-spectral excitation and three readout segmented echo-planar imaging interleaves. Images are processed with referenceless thermometry to create temperature-rise images every frame. The sequence and reconstruction were implemented in RTHawk and used to image stationary and moving sonications in a polyacrylamide gel phantom (62.4 acoustic W, 50 sec, 550 kHz). Temperature-rise images were compared between moving and stationary experiments. Heating spots and corresponding temperature-rise plots matched very well. The stationary sonication had a temperature standard deviation of 0.15 degrees C compared to values of 0.28 degrees C and 0.43 degrees C measured for two manually moved sonications at different velocities. Moving the phantom (while not heating) with respect to the transducer did not cause false temperature rises, despite susceptibility changes. The system was tested on nonheated livers of five normal volunteers. The mean temperature rise was -0.05 degrees C, with a standard deviation of 1.48 degrees C. This standard deviation is acceptable for monitoring high-intensity focused ultrasound ablations, suggesting real-time imaging of moving high-intensity focused ultrasound sonications can be clinically possible.

Optimal phase difference reconstruction: comparison of two methods

The present study compares the performance of the weighted mean (WM) and sensitivity encoding (SENSE) methods for reconstructing phase difference images over a large range of signal-to-noise ratio (SNR). It is found that the WM algorithm is suboptimal, compared to the SENSE method at low SNR. Numerical simulations, phantom and in vivo results are presented.

Optimization of sensitivity encoding with arbitrary k-space trajectories

Sensitivity encoding (SENSE) is a magnetic resonance technique that unifies gradient and receive coil encoding. SENSE reconstructs the image by solving a large, ill-conditioned inverse problem, which generally requires regularization and preconditioning. The present study suggests a simple heuristic for determining the regularization parameter. Also discussed are the use of density weighting and intensity correction as preconditioners and the role that coil sensitivity estimation has in regularization. A modification to the intensity correction is proposed for use with a phase constraint.