Alias subtraction more efficient than conventional zero-padding in the Fourier-based calculation of the susceptibility induced perturbation of the magnetic field in MR

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.

Rapid calculation of static magnetic field perturbation generated by magnetized objects in arbitrary orientations

PURPOSE

Most previous work on the calculation of susceptibility-induced static magnetic field (B₀ ) inhomogeneity has considered strictly unidirectional magnetic fields. Here, we present the theory and implementation of a computational method to rapidly calculate static magnetic field vectors produced by an arbitrary distribution of voxelated magnetization vectors.

THEORY AND METHODS

Two existing B₀ calculation methods were systematically extended to include arbitrary orientations of the magnetization and the magnetic field; they are (1) Fourier-domain convolution with k-space-discretized (KD) dipolar field, and (2) generalized susceptibility voxel convolution (gSVC). The methods were tested on an analytical ellipsoid model and a tilted human head model, as well as against experimentally measured B₀ fields induced by a stainless-steel implant located in an inhomogeneous region of a clinical 3T MRI magnet.

RESULTS

Both methods were capable of correctly calculating B₀ fields inside a magnetized ellipsoid in all tested orientations. The KD method generally required a larger grid and longer computation time to achieve accuracy comparable to gSVC. Measured B₀ fields due to the implant showed a good match with the gSVC-calculated fields that accounted for the spatial variation of the applied magnetic field including the radial components.

CONCLUSION

Our method can provide a reliable and efficient computational tool to calculate B₀ perturbation by magnetized objects under a variety of circumstances, including those with inhomogeneous magnetizing fields, anisotropic susceptibility, and a rotated coordinate system.

Silicon Carbide and MRI: Towards Developing a MRI Safe Neural Interface

An essential method to investigate neuromodulation effects of an invasive neural interface (INI) is magnetic resonance imaging (MRI). Presently, MRI imaging of patients with neural implants is highly restricted in high field MRI (e.g., 3 T and higher) due to patient safety concerns. This results in lower resolution MRI images and, consequently, degrades the efficacy of MRI imaging for diagnostic purposes in these patients. Cubic silicon carbide (3C-SiC) is a biocompatible wide-band-gap semiconductor with a high thermal conductivity and magnetic susceptibility compatible with brain tissue. It also has modifiable electrical conductivity through doping level control. These properties can improve the MRI compliance of 3C-SiC INIs, specifically in high field MRI scanning. In this work, the MRI compliance of epitaxial SiC films grown on various Si wafers, used to implement a monolithic neural implant (all-SiC), was studied. Via finite element method (FEM) and Fourier-based simulations, the specific absorption rate (SAR), induced heating, and image artifacts caused by the portion of the implant within a brain tissue phantom located in a 7 T small animal MRI machine were estimated and measured. The specific goal was to compare implant materials; thus, the effect of leads outside the tissue was not considered. The results of the simulations were validated via phantom experiments in the same 7 T MRI system. The simulation and experimental results revealed that free-standing 3C-SiC films had little to no image artifacts compared to silicon and platinum reference materials inside the MRI at 7 T. In addition, FEM simulations predicted an ~30% SAR reduction for 3C-SiC compared to Pt. These initial simulations and experiments indicate an all-SiC INI may effectively reduce MRI induced heating and image artifacts in high field MRI. In order to evaluate the MRI safety of a closed-loop, fully functional all-SiC INI as per ISO/TS 10974:2018 standard, additional research and development is being conducted and will be reported at a later date.

Tumor-site specific geometric distortions in high field integrated magnetic resonance linear accelerator radiotherapy

Magnetic resonance imaging (MRI) has exquisite soft-tissue contrast and is the foundation for image guided radiotherapy (IGRT) with integrated magnetic resonance linacs. However, MRI suffers from geometrical distortions. In this study the MRI system- and patient-induced geometric distortion at four different tumor-sites was investigated: adrenal gland (7 patients), liver (4 patients), pancreas (6 patients), prostate (20 patients). Maximum level of total distortion within the gross-tumor-volume (GTV) was 0.96 mm with no significant difference between abdominal patients (adrenal gland, liver, pancreas) and pelvic patients (prostate). Total tumor-site specific distortion depended on location in the field-of-view and increased with the distance to MRI iso-center.

Correction of motion-induced susceptibility artifacts and B0 drift during proton resonance frequency shift-based MR thermometry in the pelvis with background field removal methods

Purpose

The linear change of the water proton resonance frequency shift (PRFS) with temperature is used to monitor temperature change based on the temporal difference of image phase. Here, the effect of motion‐induced susceptibility artifacts on the phase difference was studied in the context of mild radio frequency hyperthermia in the pelvis.

Methods

First, the respiratory‐induced field variations were disentangled from digestive gas motion in the pelvis. The projection onto dipole fields (PDF) as well as the Laplacian boundary value (LBV) algorithm were applied on the phase difference data to eliminate motion‐induced susceptibility artifacts. Both background field removal (BFR) algorithms were studied using simulations of susceptibility artifacts, a phantom heating experiment, and volunteer and patient heating data.

Results

Respiratory‐induced field variations were negligible in the presence of the filled water bolus. Even though LBV and PDF showed comparable results for most data, LBV seemed more robust in our data sets. Some data sets suggested that PDF tends to overestimate the background field, thus removing phase attributed to temperature. The BFR methods even corrected for susceptibility variations induced by a subvoxel displacement of the phantom. The method yielded successful artifact correction in 2 out of 4 patient treatment data sets during the entire treatment duration of mild RF heating of cervical cancer. The heating pattern corresponded well with temperature probe data.

Conclusion

The application of background field removal methods in PRFS‐based MR thermometry has great potential in various heating applications and body regions to reduce motion‐induced susceptibility artifacts that originate outside the region of interest, while conserving temperature‐induced PRFS. In addition, BFR automatically removes up to a first‐order spatial B₀ drift.

MRI artifact simulation for clinically relevant MRI sequences for guidance of prostate HDR brachytherapy

For the purpose of magnetic resonance imaging (MRI) guidance of prostate high-dose-rate (HDR) brachytherapy, this paper presents a study on the potential of clinically relevant MRI sequences to facilitate tracking or localization of brachytherapy devices (HDR source/titanium needle), and which could simultaneously be used to visualize the anatomy. The tracking or localization involves simulation of the MRI artifact in combination with a template matching algorithm. Simulations of the MRI artifacts induced by an HDR brachytherapy source and a titanium needle were implemented for four types of sequences: spoiled gradient echo, spin echo, balanced steady-state free precession (bSSFP) and bSSFP with spectral attenuated inversion recovery (SPAIR) fat suppression. A phantom study was conducted in which mentioned sequences (in 2D) as well as the volumetric MRI sequences of the current clinical scan protocol were applied to obtain the induced MRI artifacts for an HDR source and a titanium needle. Localization of the objects was performed by a phase correlation based template matching algorithm. The simulated images demonstrated high correspondences with the acquired MR images, and allowed localization of the objects. A comparison between the object positions obtained for all applied MRI sequences showed deviations (from the average position) of 0.2-0.3 mm, proving that all MRI sequences were suitable for localization of the objects, irrespective of their 2D or volumetric nature. This study demonstrated that the MRI artifact induced by an HDR source or a titanium needle could be simulated for the four investigated types of MRI sequences (spoiled gradient echo, spin echo, bSSFP and bSSFP-SPAIR), valuable for real-time object localization in clinical practice. This leads to more flexibility in the choice of MRI sequences for guidance of HDR brachytherapy, as they are suitable for both object localization and anatomy visualization.

Reducing distortions in echo-planar breast imaging at ultrahigh field with high-resolution off-resonance maps

PURPOSE

DWI is a promising modality in breast MRI, but its clinical acceptance is slow. Analysis of DWI is hampered by geometric distortion artifacts, which are caused by off-resonant spins in combination with the low phase-encoding bandwidth of the EPI sequence used. Existing correction methods assume smooth off-resonance fields, which we show to be invalid in the human breast, where high discontinuities arise at tissue interfaces.

METHODS

We developed a distortion correction method that incorporates high-resolution off-resonance maps to better solve for severe distortions at tissue interfaces. The method was evaluated quantitatively both ex vivo in a porcine tissue phantom and in vivo in 5 healthy volunteers. The added value of high-resolution off-resonance maps was tested using a Wilcoxon signed rank test comparing the quantitative results obtained with a low-resolution off-resonance map with those obtained with a high-resolution map.

RESULTS

Distortion correction using low-resolution off-resonance maps corrected most of the distortions, as expected. Still, all quantitative comparison metrics showed increased conformity between the corrected EPI images and a high-bandwidth reference scan for both the ex vivo and in vivo experiments. All metrics showed a significant improvement when a high-resolution off-resonance map was used (P < 0.05), in particular at tissue boundaries.

CONCLUSION

The use of off-resonance maps of a resolution higher than EPI scans significantly improves upon existing distortion correction techniques, specifically by superior correction at glandular tissue boundaries.

isoPhasor: a generic and precise marker visualization, localization, and quantification method based on phase saddles in 3D MR imaging

PURPOSE

To derive a generic approach for accurate localization and characterization of susceptibility markers in MRI, compatible with many common types of pulse sequences, sampling trajectories, and acceleration methods.

THEORY AND METHODS

A susceptibility marker's dipolar phase evolution creates 3 saddles in the phase gradient of the spatial encoding, for each sampled data point in k-space. The signal originating from these saddles can be focused at the location of the marker to create positive contrast. The required phase shift can be calculated from the scan parameters and the marker properties, providing a marker detection algorithm generic for different scan types. The method was validated numerically and experimentally for a broad range of spherical susceptibility markers (0.3 < radius < 1.6 mm, 10 < |∆χ| < 3300 ppm), under various conditions.

RESULTS

For all numerical and experimental phantoms, the average localization error was below one third of the voxel size, whereas the average error in magnetic strength quantification was 7%. The experiments included different pulse sequences (gradient echo, spin echo [SE], and free induction decay scans), sampling strategies (Cartesian, radial), and acceleration methods (echo planar imaging EPI, turbo SE).

CONCLUSION

Spherical markers can be identified from their phase saddles, enabling clear visualization, precise localization, and accurate quantification of their magnetic strength, in a wide range of clinically relevant pulse sequences and sampling strategies.

MR-based source localization for MR-guided HDR brachytherapy

For the purpose of MR-guided high-dose-rate (HDR) brachytherapy, a method for real-time localization of an HDR brachytherapy source was developed, which requires high spatial and temporal resolutions. MR-based localization of an HDR source serves two main aims. First, it enables real-time treatment verification by determination of the HDR source positions during treatment. Second, when using a dummy source, MR-based source localization provides an automatic detection of the source dwell positions after catheter insertion, allowing elimination of the catheter reconstruction procedure. Localization of the HDR source was conducted by simulation of the MR artifacts, followed by a phase correlation localization algorithm applied to the MR images and the simulated images, to determine the position of the HDR source in the MR images. To increase the temporal resolution of the MR acquisition, the spatial resolution was decreased, and a subpixel localization operation was introduced. Furthermore, parallel imaging (sensitivity encoding) was applied to further decrease the MR scan time. The localization method was validated by a comparison with CT, and the accuracy and precision were investigated. The results demonstrated that the described method could be used to determine the HDR source position with a high accuracy (0.4-0.6 mm) and a high precision (⩽0.1 mm), at high temporal resolutions (0.15-1.2 s per slice). This would enable real-time treatment verification as well as an automatic detection of the source dwell positions.

Rapid, theoretically artifact-free calculation of static magnetic field induced by voxelated susceptibility distribution in an arbitrary volume of interest

PURPOSE

To demonstrate a computationally efficient and theoretically artifact-free method to calculate static field (B₀ ) inhomogeneity in a volume of interest induced by an arbitrary voxelated susceptibility distribution.

METHODS

Our method computes B₀ by circular convolution between a zero-filled susceptibility matrix and a shifted, voxel-integrated dipolar field kernel on a grid of size N_S +N_T - 1 in each dimension, where N_S and N_T are the sizes of the susceptibility source and B₀ target grids, respectively. The computational resource requirement is independent of source-target separation. The method, called generalized susceptibility voxel convolution, is demonstrated on three susceptibility models: an ellipsoid, MR-compatible screws, and a dynamic human heartbeat model.

RESULTS

B₀ in an ellipsoid calculated by generalized susceptibility voxel convolution matched an analytical solution nearly exactly. The method also calculated screw-induced B₀ in agreement with experimental data. Dynamic simulation demonstrated its computational efficiency for repeated B₀ calculations on time-varying susceptibility. On the contrary, conventional and alias-subtracted k-space-discretized Fourier convolution methods showed nonnegligible aliasing and Gibbs ringing artifacts in the tested models.

CONCLUSION

Generalized susceptibility voxel convolution can be a fast and reliable way to compute susceptibility-induced B₀ when the susceptibility source is not colocated with the B₀ target volume of interest, as in modeling B₀ variations from motion and foreign objects.

Challenges in MR-only seed localization for postimplant dosimetry in permanent prostate brachytherapy

PURPOSE

An MR-only postimplant dosimetry workflow for low dose rate (LDR) brachytherapy could reduce patient burden, improve accuracy, and improve cost efficiency. However, localization of brachytherapy seeds on MRI scans remains a major challenge for this type of workflow. In this study, we propose and validate an MR-only seed localization method and identify remaining challenges.

METHODS AND MATERIALS

The localization method was based on template matching of simulations of complex-valued imaging artifacts around metal brachytherapy seeds. The method was applied to MRI scans of 25 prostate cancer patients who underwent LDR brachytherapy and for whom postimplant dosimetry was performed after 4 weeks. The seed locations found with the MR-only method were validated against the seed locations found on CT. The circumstances in which detection errors were made were classified to gain an insight in the nature of the errors.

RESULTS

A total of 1490 of 1557 (96%) seeds were correctly detected, while 67 false-positive errors were made. The correctly detected seed locations had a high spatial accuracy with an average error of 0.8 mm compared with CT. A majority of the false positives occurred near other seeds. Most false negatives were found in either stranded configurations without spacers or near other seeds.

CONCLUSIONS

The low detection error rate and high localization accuracy obtained by the complex-valued template matching approach are promising for future clinical application of MR-only dosimetry. The most important remaining challenge is robustness with regard to configurations of multiple seeds in close vicinity, such as in strands of seeds without spacers. This issue could potentially be resolved by simulating specific configurations of multiple seeds or by constraining the treatment planning to avoid these configurations, which could make the proposed method competitive with CT-based seed localization.

Fast Fourier-based simulation of off-resonance artifacts in steady-state gradient echo MRI applied to metal object localization

PURPOSE

To accelerate simulation of off-resonance artifacts in steady-state gradient echo MRI by using fast Fourier transforms and demonstrate its applicability to metal object localization.

THEORY AND METHODS

By exploiting the repetitive nature of steady-state pulse sequences it is possible to use fast Fourier transforms to calculate the MR signal. Based on this principle, a method for fast simulation of off-resonance artifacts was designed. The method was validated against Bloch simulations and MRI scans. Its clinical relevance was demonstrated by employing it for template matching-based metal object localization, as applied to a titanium cylinder, an oxidized zirconium knee implant, and gold fiducials.

RESULTS

The fast simulations were accurate compared with actual MRI scans of the objects. The differences between the fast simulations and Bloch simulations were minor, while the acceleration scaled linearly with the number of phase-encoding lines. The object localization method accurately localized the various metal objects.

CONCLUSION

The proposed simulation methodology provided accurate 3D simulations of off-resonance artifacts with a lower computational complexity than Bloch simulations. The speed of the simulations opens up possibilities in image reconstructions involving off-resonance phenomena that were previously infeasible due to computational limitations, as demonstrated for metal object localization. Magn Reson Med 78:2035-2041, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Metallic implant geometry and susceptibility estimation using multispectral B0 field maps

PURPOSE

To estimate the susceptibility and the geometry of metallic implants from multispectral imaging (MSI) information, to separate the metal implant region from the surrounding signal loss region.

THEORY AND METHODS

The susceptibility map of signal-void regions is estimated from MSI B₀ field maps using total variation (TV) regularized inversion. Voxels with susceptibility estimates above a predetermined threshold are identified as metal. The accuracy of the estimated susceptibility and implant geometry was evaluated in simulations, phantom, and in vivo experiments.

RESULTS

The proposed method provided more accurate susceptibility estimation compared with a previous method without TV regularization, in both simulations and phantom experiments. In the phantom experiment where the actual implant was 40% of the signal-void region, the mean estimated susceptibility was close to the susceptibility in literature, and the precision and recall of the estimated geometry was 85% and 93%. In vivo studies in subjects with hip implants also demonstrated that the proposed method can distinguish implants from surrounding low-signal tissues, such as cortical bone.

CONCLUSION

The proposed method can improve the delineation of metallic implant geometry by distinguishing metal voxels from artificial signal voids and low-signal tissues by estimating the susceptibility maps. Magn Reson Med 77:2402-2413, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Multistage Background Field Removal (MUBAFIRE)-Compensating for B0 Distortions at Ultra-High Field

The investigation of tissue magnetic susceptibility and the resultant magnetic field offers a new avenue for quantitative tissue characterisation by MRI. One crucial step in mining the phase and field data for relevant tissue information is the correction of externally induced field shifts. This article outlines a multistep approach comprising several methodologies for background field removal. The virtues of B₀ long-range variation detection and compensation of more localised external disturbances are unified in a sequential filter chain. The algorithm is tested by means of a numerical Monte Carlo simulation model and applied to in vivo measurements at 3T and 9.4T as well as to a fixed brain tissue measurement at 9.4T. Further, a comparison to conventional filter types has been undertaken.

Influence of water and fat heterogeneity on fat-referenced MR thermometry

PURPOSE

To investigate the effect of the aqueous and fatty tissue magnetic susceptibility distribution on absolute and relative temperature measurements as obtained directly from the water/fat (w/f) frequency difference.

METHODS

Absolute thermometry was investigated using spherical phantoms filled with pork and margarine, which were scanned in three orthogonal orientations. To evaluate relative fat referencing, multigradient echo scans were acquired before and after heating pork tissue via high-intensity focused ultrasound (HIFU). Simulations were performed to estimate the errors that can be expected in human breast tissue.

RESULTS

The sphere experiment showed susceptibility-related errors of 8.4 °C and 0.2 °C for pork and margarine, respectively. For relative fat referencing measurements, fat showed pronounced phase changes of opposite polarity to aqueous tissue. The apparent mean temperature for a numerical breast model assumed to be 37 °C was 47.2 ± 21.6 °C. Simulations of relative fat referencing for a HIFU sonication (ΔT = 29.7 °C) yielded a maximum temperature error of 6.6 °C compared with 2.5 °C without fat referencing.

CONCLUSION

Variations in the observed frequency difference between water and fat are largely due to variations in the w/f spatial distribution. This effect may lead to considerable errors in absolute MR thermometry. Additionally, fat referencing may exacerbate rather than correct for proton resonance frequency shift-temperature measurement errors.

Characterizing the limits of MRI near metallic prostheses

PURPOSE

To characterize the fundamental limits of MRI near metallic implants on RF excitation, frequency encoding, and chemical shift-encoding water-fat separation.

METHODS

Multicomponent three-dimensional (3D) digital models of a total hip and a total knee replacement were used to construct material-specific susceptibility maps. The fundamental limits and spatial relationship of imaging near metallic prostheses were investigated as a function of distance from the prosthetic surface by calculating 3D field map perturbations using a well-validated k-space based dipole kernel.

RESULTS

Regions limited by the bandwidth of RF excitation overlap substantially with those fundamentally limited by frequency encoding. Rapid breakdown of water-fat separation occurs once the intravoxel off-resonance exceeds ∼6 ppm over a full range of fat fractions (0%-100%) and SNR (5-100).

CONCLUSION

Current 3D multispectral imaging methods would not benefit greatly from exciting spins beyond ±12 kHz despite the presence of signal that lies outside of this range from tissue directly adjacent to the metallic implants. Methods such as phase encoding in all three spatial dimensions are necessary to spatially resolve spins beyond an excitation bandwidth of ±12 kHz. The approach described in this study provides a benchmark for the capabilities of current imaging techniques to guide development of new MRI methods for imaging near metal.

Correction of proton resonance frequency shift MR-thermometry errors caused by heat-induced magnetic susceptibility changes during high intensity focused ultrasound ablations in tissues containing fat

PURPOSE

In this study, we aim to demonstrate the sensitivity of proton resonance frequency shift (PRFS) -based thermometry to heat-induced magnetic susceptibility changes and to present and evaluate a model-based correction procedure.

THEORY AND METHODS

To demonstrate the expected temperature effect, field disturbances during high intensity focused ultrasound sonications were monitored in breast fat samples with a three-dimensional (3D) gradient echo sequence. To evaluate the correction procedure, the interface of tissue-mimicking ethylene glycol gel and fat was sonicated. During sonication, the temperature was monitored with a 2D dual flip angle multi-echo gradient echo sequence, allowing for PRFS-based relative and referenced temperature measurements in the gel and T1 -based temperature measurements in fat. The PRFS-based measurement in the gel was corrected by minimizing the discrepancy between the observed 2D temperature profile and the profile predicted by a 3D thermal model.

RESULTS

The HIFU sonications of breast fat resulted in a magnetic field disturbance which completely disappeared after cooling. For the correction method, the 5th to 95th percentile interval of the PRFS-thermometry error in the gel decreased from 3.8°C before correction to 2.0-2.3°C after correction.

CONCLUSION

This study has shown the effects of magnetic susceptibility changes induced by heating of breast fatty tissue samples. The resultant errors can be reduced by the use of a model-based correction procedure.