Intervention-based multidimensional phase unwrapping using recursive orthogonal referring

A predictor-corrector phase unwrapping algorithm for temporally undersampled gradient-echo MRI

PURPOSE

To develop a method for unwrapping temporally undersampled and nonlinear gradient recalled echo (GRE) phase.

THEORY AND METHODS

Temporal unwrapping is performed as a sequential one step prediction of the echo phase, followed by a correction to the nearest integer wrap-count. A spatio-temporal extension of the 1D predictor corrector unwrapping (PCU) algorithm improves the prediction accuracy, and thereby maintains spatial continuity. The proposed method is evaluated using numerical phantom, physical phantom, and in vivo brain data at both 3 T and 9.4 T. The unwrapping performance is compared with the state-of-the-art temporal and spatial unwrapping algorithms, and the spatio-temporal iterative virtual-echo based Nyquist sampled (iVENyS) algorithm.

RESULTS

Simulation results showed significant reduction in unwrapping errors at higher echoes compared with the state-of-the-art algorithms. Similar to the iVENyS algorithm, the PCU algorithm was able to generate spatially smooth phase images for in vivo data acquired at 3 T and 9.4 T, bypassing the use of additional spatial unwrapping step. A key advantage over iVENyS algorithm is the superior performance of PCU algorithm at higher echoes.

CONCLUSION

PCU algorithm serves as a robust phase unwrapping method for temporally undersampled and nonlinear GRE phase, particularly in the presence of high field gradients.

Effective magnetic susceptibility of 3D-printed porous metal scaffolds

PURPOSE

3D-printed porous metal scaffolds are a promising emerging technology in orthopedic implant design. Compared to solid metal implants, porous metal implants have lower magnetic susceptibility values, which have a direct impact on imaging time and image quality. The purpose of this study is to determine the relationship between porosity and effective susceptibility through quantitative estimates informed by comparing coregistered scanned and simulated field maps.

METHODS

Five porous scaffold cylinders were designed and 3D-printed in titanium alloy (Ti-6Al-4V) with nominal porosities ranging from 60% to 90% using a cellular sheet-based gyroid design. The effective susceptibility of each cylinder was estimated by comparing acquired B₀ field maps against simulations of a solid cylinder of varying assigned magnetic susceptibility, where the orientation and volume of interest of the simulations was informed by a custom alignment phantom.

RESULTS

Magnitude images and field maps showed obvious decreases in artifact size and field inhomogeneity with increasing porosity. The effective susceptibility was found to be linearly correlated with porosity (R²  = 0.9993). The extrapolated 100% porous (no metal) magnetic susceptibility was -9.9 ppm, closely matching the expected value of pure water (-9 ppm), indicating a reliable estimation of susceptibility.

CONCLUSION

Effective susceptibility of porous metal scaffolds is linearly correlated with porosity. Highly porous implants have sufficiently low effective susceptibilities to be more amenable to routine imaging with MRI.

Multi-echo gradient-recalled-echo phase unwrapping using a Nyquist sampled virtual echo train in the presence of high-field gradients

PURPOSE

To develop a spatio-temporal approach to accurately unwrap multi-echo gradient-recalled echo phase in the presence of high-field gradients.

THEORY AND METHODS

Using the virtual echo-based Nyquist sampled (VENyS) algorithm, the temporal unwrapping procedure is modified by introduction of one or more virtual echoes between the first lower and the immediate higher echo, so as to reinstate the Nyquist condition at locations with high-field gradients. An iterative extension of the VENyS algorithm maintains spatial continuity by adjusting the phase rotations to make the neighborhood phase differences less than π. The algorithm is evaluated using simulated data, Gadolinium contrast-doped phantom, and in vivo brain, abdomen, and chest data sets acquired at 3 T and 9.4 T. The unwrapping performance is compared with the standard temporal unwrapping algorithm used in the morphology-enabled dipole inversion-QSM pipeline as a benchmark for validation.

RESULTS

Quantitative evaluation using numerical phantom showed significant reduction in unwrapping errors in regions of large field gradients, and the unwrapped phase revealed an exact match with the linear concentration profile of vials in a gadolinium contrast-doped phantom data acquired at 9.4 T. Without the need for additional spatial unwrapping, the iterative VENyS algorithm was able to generate spatially continuous phase images. Application to in vivo data resulted in better unwrapping performance, especially in regions with large susceptibility changes such as the air/tissue interface.

CONCLUSION

The iterative VENyS algorithm serves as a robust unwrapping method for multi-echo gradient-recalled echo phase in the presence of high-field gradients.

Phantom Validation of DCE-MRI Magnitude and Phase-Based Vascular Input Function Measurements

Accurate, patient-specific measurement of arterial input functions (AIF) may improve model-based analysis of vascular permeability. This study investigated factors affecting AIF measurements from magnetic resonance imaging (MRI) magnitude (AIF_MAGN) and phase (AIF_PHA) signals, and compared them against computed tomography (CT) (AIF_CT), under controlled conditions relevant to clinical protocols using a multimodality flow phantom. The flow phantom was applied at flip angles of 20° and 30°, flow rates (3-7.5 mL/s), and peak bolus concentrations (0.5-10 mM), for in-plane and through-plane flow. Spatial 3D-FLASH signal and variable flip angle T1 profiles were measured to investigate in-flow and radiofrequency-related biases, and magnitude- and phase-derived Gd-DTPA concentrations were compared. MRI AIF performance was tested against AIF_CT via Pearson correlation analysis. AIF_MAGN was sensitive to imaging orientation, spatial location, flip angle, and flow rate, and it grossly underestimated AIF_CT peak concentrations. Conversion to Gd-DTPA concentration using T1 taken at the same orientation and flow rate as the dynamic contrast-enhanced acquisition improved AIF_MAGN accuracy; yet, AIF_MAGN metrics remained variable and significantly reduced from AIF_CT at concentrations above 2.5 mM. AIF_PHA performed equivalently within 1 mM to AIF_CT across all tested conditions. AIF_PHA, but not AIF_MAGN, reported equivalent measurements to AIF_CT across the range of tested conditions. AIF_PHA showed superior robustness.

Seed prioritized unwrapping (SPUN) for MR phase imaging

BACKGROUND

Region-growing-based phase unwrapping methods have the potential for lossless phase aliasing removal, but generally suffer from unwrapping error propagation associated with discontinuous phase and/or long calculation times. The tradeoff point between robustness and efficiency of phase unwrapping methods in the region-growing category requires improvement.

PURPOSE

To demonstrate an accurate, robust, and efficient region-growing phase unwrapping method for MR phase imaging applications.

STUDY TYPE

Prospective. SUBJECTS, PHANTOM: normal human subjects (10) / brain surgery patients (2) / water phantoms / computer simulation.

FIELD STRENGTH/SEQUENCE

3 T/gradient echo sequences (2D and 3D).

ASSESSMENT

A seed prioritized unwrapping (SPUN) method was developed based on single-region growing, prioritizing only a portion (eg, 100 seeds or 1% seeds) of available seed voxels based on continuity quality during each region-growing iteration. Computer simulation, phantom, and in vivo brain and pelvis scans were performed. The error rates, seed percentages, and calculation times were recorded and reported. SPUN unwrapped phase images were visually evaluated and compared with Laplacian unwrapped results.

STATISTICAL TESTS

Monte Carlo simulation was performed on a 3D dipole phase model with a signal-to-noise ratio (SNR) of 1-9 dB, to obtain the mean and standard deviation of calculation error rates and calculation times.

RESULTS

Simulation revealed a very robust unwrapping performance of SPUN, reaching an error rate of <0.4% even with SNR as low as 1 dB. For all in vivo data, SPUN was able to robustly unwrap the phase images of modest SNR and complex morphology with visually minimal errors and fast calculation speed (eg, <4 min for 368 × 312 × 128 data) when using a proper seed priority number, eg, N_sp = 1 or 10 voxels for 2D and N_sp = 1% for 3D data.

DATA CONCLUSION

SPUN offers very robust and fast region-growing-based phase unwrapping, and does not require any tissue masking or segmentation, nor poses a limitation over imaging parameters.

LEVEL OF EVIDENCE

3 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019;50:62-70.

Cyclic Continuous Max-Flow: A Third Paradigm in Generating Local Phase Shift Maps in MRI

Sensitivity to phase deviations in MRI forms the basis of a variety of techniques, including magnetic susceptibility weighted imaging and chemical shift imaging. Current phase processing techniques fall into two families: those which process the complex image data with magnitude and phase coupled, and phase unwrapping-based techniques that first linearize the phase topology across the image. However, issues, such as low signal and the existence of phase poles, can lead both methods to experience error. Cyclic continuous max-flow (CCMF) phase processing uses primal-dual-variational optimization over a cylindrical manifold, which represent the inherent topology of phase images, increasing its robustness to these issues. CCMF represents a third distinct paradigm in phase processing, being the only technique equipped with the inherent topology of phase. CCMF is robust and efficient with at least comparable accuracy as the prior paradigms.

Method of B0 mapping with magnitude-based correction for bipolar two-point Dixon cardiac MRI

PURPOSE

The conventional two-point (2pt) Dixon technique explicitly estimates B0 map by performing phase unwrapping. When signal loss, phase singularity, artifacts, or spatially isolated regions corrupt the measured phase images, this unwrapping-based technique will face difficulty. This work aims to improve the reliability of B0 mapping by performing unwrapping error correction.

METHOD

To detect the unwrapping-caused phase errors, we determined a magnitude-based fat/water mask and used it as reference to identify pixels being mismatched by the phase-based mask, which was derived from the B0-corrected phase term of the Hermitian product between echoes. Then, we corrected the afore-determined phase error on a region-by-region basis. We tested the developed method with nine patients' data, and the results were compared with a well-established region-growing technique.

RESULTS

By adding the step to correct unwrapping-caused error, we improved the robustness of B0 mapping, resulting in better fat-water separation when compared with the conventional 2pt and the phasor-based region-growing techniques.

CONCLUSION

We showed the feasibility of B0 mapping with bipolar 2pt human cardiac data. The software is freely available to the scientific community. Magn Reson Med 78:1862-1869, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

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.

Field inhomogeneity correction using partial differential phases in magnetic resonance imaging

Correction of an inhomogeneous magnetic field is proposed using partial differential phases in magnetic resonance imaging. Estimation of the inhomogeneous magnetic field from a measured phase is not an easy task due to phase wrapping and chemical-dependent phase shifts. Using the proposed partial differential phase technique, such problems are resolved. The proposed technique uses most of the 3D pixel data regardless of chemical compounds for the estimation of the inhomogeneous magnetic field. A large number of partial difference data compared to the number of expansion terms for the model of inhomogeneous magnetic field provides a very stable estimation, robust to noise. The technique is applicable to in vivo shimming, water-fat imaging, eddy current compensation, and most phase-related measurements and imaging. The efficacy of the proposed technique is demonstrated with in vivo water-fat imaging.

Method for B0 off-resonance mapping by non-iterative correction of phase-errors (B0-NICE)

PURPOSE

To develop and evaluate a multiecho phase-unwrapping-based B0 mapping method.

METHODS

The proposed method estimates a B0 map by Non-Iterative Correction of phase-Errors (B0-NICE). The B0-NICE method generates an initial B0 map from a "pseudo in-phase" data set by introducing a bias frequency shift to the multipeak fat model, followed by correcting the phase errors using both phase and magnitude information. The performance of the B0-NICE method was evaluated with all data cases from the 2012 ISMRM Challenge.

RESULTS

The B0 field estimates from B0-NICE were compared with those generated by GlObally Optimal Surface Estimation (GOOSE). In the presence of large B0 inhomogeneity, the B0-NICE method was able to generate more realistic B0 maps from multiecho data, compared with GOOSE. Accurate estimation of fat-fraction (FF) map was also achieved using the proposed algorithm.

CONCLUSION

The primary finding of the present study is that accurate FF and B0 maps are achievable if magnitude data is processed independently and used to correct phase errors existing in B0 maps generated by phase unwrapping. The B0-NICE software is freely available to the scientific community.