Phase gradient mapping as an aid in the analysis of object-induced and system-related phase perturbations in MRI

A Single-Scan, Rapid Whole-Brain Protocol for Quantitative Water Content Mapping With Neurobiological Implications

Water concentration is tightly regulated in the healthy human brain and changes only slightly with age and gender in healthy subjects. Consequently, changes in water content are important for the characterization of disease. MRI can be used to measure changes in brain water content, but as these changes are usually in the low percentage range, highly accurate and precise methods are required for detection. The method proposed here is based on a long-TR (10 s) multiple-echo gradient-echo measurement with an acquisition time of 7:21 min. Using such a long TR ensures that there is no T₁ weighting, meaning that the image intensity at zero echo time is only proportional to the water content, the transmit field, and to the receive field. The receive and transmit corrections, which are increasingly large at higher field strengths and for highly segmented coil arrays, are multiplicative and can be approached heuristically using a bias field correction. The method was tested on 21 healthy volunteers at 3T field strength. Calibration using cerebral-spinal fluid values (~100% water content) resulted in mean values and standard deviations of the water content distribution in white matter and gray matter of 69.1% (1.7%) and 83.7% (1.2%), respectively. Measured distributions were coil-independent, as seen by using either a 12-channel receiver coil or a 32-channel receiver coil. In a test-retest investigation using 12 scans on one volunteer, the variation in the mean value of water content for different tissue types was ~0.3% and the mean voxel variability was ~1%. Robustness against reduced SNR was assessed by comparing results for 5 additional volunteers at 1.5T and 3T. Furthermore, water content distribution in gray matter is investigated and regional contrast reported for the first time. Clinical applicability is illustrated with data from one stroke patient and one brain tumor patient. It is anticipated that this fast, stable, easy-to-use, high-quality mapping method will facilitate routine quantitative MR imaging of water content.

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.

Tracking and Quantification of Magnetically Labeled Stem Cells using Magnetic Resonance Imaging

Stem cell based therapies have critical impacts on treatments and cures of diseases such as neurodegenerative or cardiovascular disease. In vivo tracking of stem cells labeled with magnetic contrast agents is of particular interest and importance as it allows for monitoring of the cells' bio-distribution, viability, and physiological responses. Herein, recent advances are introduced in tracking and quantification of super-paramagnetic iron oxide (SPIO) nanoparticles-labeled cells with magnetic resonance imaging, a noninvasive approach that can longitudinally monitor transplanted cells. This is followed by recent translational research on human stem cells that are dual-labeled with green fluorescence protein (GFP) and SPIO nanoparticles, then transplanted and tracked in a chicken embryo model. Cell labeling efficiency, viability, and cell differentiation are also presented.

Quantification of susceptibility change at high-concentrated SPIO-labeled target by characteristic phase gradient recognition

Phase map cross-correlation detection and quantification may produce highlighted signal at superparamagnetic iron oxide nanoparticles, and distinguish them from other hypointensities. The method may quantify susceptibility change by performing least squares analysis between a theoretically generated magnetic field template and an experimentally scanned phase image. Because characteristic phase recognition requires the removal of phase wrap and phase background, additional steps of phase unwrapping and filtering may increase the chance of computing error and enlarge the inconsistence among algorithms. To solve problem, phase gradient cross-correlation and quantification method is developed by recognizing characteristic phase gradient pattern instead of phase image because phase gradient operation inherently includes unwrapping and filtering functions. However, few studies have mentioned the detectable limit of currently used phase gradient calculation algorithms. The limit may lead to an underestimation of large magnetic susceptibility change caused by high-concentrated iron accumulation. In this study, mathematical derivation points out the value of maximum detectable phase gradient calculated by differential chain algorithm in both spatial and Fourier domain. To break through the limit, a modified quantification method is proposed by using unwrapped forward differentiation for phase gradient generation. The method enlarges the detectable range of phase gradient measurement and avoids the underestimation of magnetic susceptibility. Simulation and phantom experiments were used to quantitatively compare different methods. In vivo application performs MRI scanning on nude mice implanted by iron-labeled human cancer cells. Results validate the limit of detectable phase gradient and the consequent susceptibility underestimation. Results also demonstrate the advantage of unwrapped forward differentiation compared with differential chain algorithms for susceptibility quantification at high-concentrated iron accumulation.

Detecting breast microcalcifications with high-field MRI

The aim of this study was to detect microcalcifications in human whole breast specimens using high-field MRI. Four mastectomy specimens, obtained with approval of the institutional review board, were subjected to gradient-echo MRI acquisitions on a high-field MR scanner. The phase derivative was used to detect microcalcifications. The echo time and imaging resolution were varied to study the sensitivity of the proposed method. Computed tomography images of the mastectomy specimens and prior acquired mammography images were used to validate the results. A template matching algorithm was designed to detect microcalcifications automatically. The three spatial derivatives of the signal phase surrounding a field-perturbing object allowed three-dimensional localization, as well as the discrimination of diamagnetic field-perturbing objects, such as calcifications, and paramagnetic field-perturbing structures, e.g. blood. A longer echo time enabled smaller disturbances to be detected, but also resulted in shading as a result of other field-disturbing materials. A higher imaging resolution increased the detection sensitivity. Microcalcifications in a linear branching configuration that spanned over 8 mm in length were detected. After manual correction, the automatic detection tool identified up to 18 microcalcifications within the samples, which was in close agreement with the number of microcalcifications found on previously acquired in vivo mammography images. Microcalcifications can be detected by MRI in human whole breast specimens by the application of phase derivative imaging.

In vivo quantification of SPIO nanoparticles for cell labeling based on MR phase gradient images

Along with the development of modern imaging technologies, contrast agents play increasingly important roles in both clinical applications and scientific research. Super-paramagnetic iron oxide (SPIO) nanoparticles, a negative contrast agent, have been extensively used in magnetic resonance imaging (MRI), such as in vivo labeling and tracking of cells. However, there still remain many challenges, such as in vivo quantification of SPIO nanoparticles. In this work, an MR phase gradient-based method was proposed to quantify the SPIO nanoparticles. As a calibration, a phantom experiment using known concentrations (10, 25, 50, 100, 150 and 250 µg/ml) of SPIO was first conducted to verify the proposed quantification method. In a following in vivo experiment, C6 glioma cells labeled with SPIO nanoparticles were implanted into flanks of four mice, which were scanned 1-3 days post-injection for in vivo quantification of SPIO concentration. The results showed that the concentration of SPIO nanoparticles could be determined in both phantom and in vivo experiments using the developed MR phase gradients approach.

MR measurement of alloy magnetic susceptibility: towards developing tissue-susceptibility matched metals

Magnetic resonance imaging (MRI) can be used to relate structure to function mapped with high-temporal resolution electrophysiological recordings using metal electrodes. Additionally, MRI may be used to guide the placement of electrodes or conductive cannula in the brain. However, the magnetic susceptibility mismatch between implanted metals and surrounding brain tissue can severely distort MR images and spectra, particularly in high magnetic fields. In this study, we present a modified MR method of characterizing the magnetic susceptibility of materials that can be used to develop biocompatible, metal alloys that match the susceptibility of host tissue in order to eliminate MR distortions proximal to the implant. This method was applied at 4.7T and 11.1T to measure the susceptibility of a model solid-solution alloy of Cu and Sn, which is inexpensive but not biocompatible. MR-derived relative susceptibility values of four different compositions of Cu-Sn alloy deviated by less than 3.1% from SQUID magnetometry absolute susceptibility measurements performed up to 7T. These results demonstrate that the magnetic susceptibility varies linearly with atomic percentage in these solid-solution alloys, but are not simply the weighted average of Cu and Sn magnetic susceptibilities. Therefore susceptibility measurements are necessary when developing susceptibility-matched, solid-solution alloys for the elimination of susceptibility artifacts in MR. This MR method does not require any specialized equipment and is free of geometrical constraints, such as sample shape requirements associated with SQUID magnetometry, so the method can be used at all stages of fabrication to guide the development of a susceptibility matched, biocompatible device.

Selective depiction of susceptibility transitions using Laplace-filtered phase maps

In this work, we aim to demonstrate the ability of Laplace-filtered three-dimensional (3D) phase maps to selectively depict the susceptibility transitions in an object. To realize this goal, it is first shown that both the Laplace derivative of the z component of the static magnetic field in an object and the Laplacian of the corresponding phase distribution may be expected to be zero in regions of constant or linearly varying susceptibility and to be nonzero when there is an abrupt change in susceptibility, for instance, at a single point, a ridge, an interface, an edge or a boundary. Next, a method is presented by which the Laplace derivative of a 3D phase map can be directly extracted from the complex data, without the need for phase unwrapping or subtraction of a reference image. The validity of this approach and of the theory behind it is subsequently demonstrated by simulations and phantom experiments with exactly known susceptibility distributions. Finally, the potential of the Laplace derivative analysis is illustrated by simulations with a Shepp-Logan digital brain phantom and experiments with a gel phantom containing positive and negative focal susceptibility deviations.

Derivative encoding for parallel magnetic resonance imaging

PURPOSE

To introduce a linear shift-invariant relationship between the partial derivatives of k space signals acquired using multichannel receive coils and to demonstrate that k space derivatives can be used for image unwrapping.

METHODS

Fourier transform of k space derivatives contains information on the spatial origins of aliased pixels; therefore, images can be reconstructed by k space derivatives. Fully sampled phantom and brain images acquired at 3 T using a standard eight channel receive coil were used to validate the k space derivatives theorem by unwrapping aliased images.

RESULTS

Derivative encoding leads to new methods for parallel imaging reconstruction in both k space and image domains. Noise amplification in sensitivity encoding image reconstruction, which is considered to produce the optimal SNR, can be further reduced using k space derivative encoding without making any assumptions on the characteristics of the images to be reconstructed.

CONCLUSIONS

This work demonstrated that the partial derivative of the k space signal acquired from one coil with respect to one direction can be expressed as a sum of partial derivatives of signals from multiple coils with respect to the perpendicular k space direction(s). This relationship between the partial derivatives of k space signals is linear and shift-invariant in the Cartesian coordinate system.

Automated detection and characterization of SPIO-labeled cells and capsules using magnetic field perturbations

Understanding how individual cells behave inside living systems will help enable new diagnostic tools and cellular therapies. Superparamagnetic iron oxide particles can be used to label cells and theranostic capsules for noninvasive tracking using MRI. Contrast changes from superparamagnetic iron oxide are often subtle relative to intrinsic sources of contrast, presenting a detection challenge. Here, we describe a versatile postprocessing method, called Phase map cross-correlation Detection and Quantification (PDQ), that automatically identifies localized deposits of superparamagnetic iron oxide, estimating their volume magnetic susceptibility and magnetic moment. To demonstrate applicability, PDQ was used to detect and characterize superparamagnetic iron oxide-labeled magnetocapsules implanted in porcine liver and suspended in agarose gel. PDQ was also applied to mouse brains infiltrated by MPIO-labeled macrophages following traumatic brain injury; longitudinal, in vivo studies tracked individual MPIO clusters over 3 days, and tracked clusters were corroborated in ex vivo brain scans. Additionally, we applied PDQ to rat hearts infiltrated by MPIO-labeled macrophages in a transplant model of organ rejection. PDQ magnetic measurements were signal-to-noise ratio invariant for images with signal-to-noise ratio > 11. PDQ can be used with conventional gradient-echo pulse sequences, requiring no extra scan time. The method is useful for visualizing biodistribution of cells and theranostic magnetocapsules and for measuring their relative iron content.

Positive contrast technique for the detection and quantification of superparamagnetic iron oxide nanoparticles in MRI

In vivo detection and quantification of cells labeled with superparamagnetic iron oxide (SPIO) nanoparticles has been attracting increasing attention. In particular, positive contrast methods, such as susceptibility gradient mapping (SGM) and phase gradient mapping (PGM), have been proposed for the improved detection of SPIO nanoparticles. In this study, a different implementation of the PGM method is introduced; it calculates the phase gradient in the image space using a fast Fourier transform without the need for phase unwrapping. We first compared positive contrast generation between the PGM and SGM methods, which estimates the susceptibility gradient in k space through echo shift measurements. Next, PGM was applied to quantify SPIO concentrations by fitting the resulting phase gradient maps to those of a theoretical model. MR experiments were conducted using a 3-T magnet scanner to acquire two datasets: the first was acquired from a gelatin phantom with three SPIO-doped vials of different concentrations, and the second was obtained in vivo from a nude rat with SPIO-labeled C6 glioma cells implanted in the flanks. The sensitivity of the PGM and SGM methods was compared using various factors, including different SPIO concentrations, TEs and signal-to-noise ratios. Based on the theoretical model of an infinite cylinder, the results demonstrated that, without loss of spatial resolution, the PGM method presents positive contrast maps with a higher sensitivity than SGM at medium and low SPIO concentrations, whereas SGM is more sensitive than PGM at longer TEs. The quantification of SPIO concentrations using the phantom dataset was also reported. On the basis of the same infinite cylinder model, it was shown that the PGM method provides an accurate estimation of SPIO concentration.

Quantification of SPIO nanoparticles in vivo using the finite perturber method

The susceptibility gradients generated by super-paramagnetic iron oxide (SPIO) nanoparticles make them an ideal contrast agent in magnetic resonance imaging. Traditional quantification methods for SPIO nanoparticle-based contrast agents rely on either mapping T₂* values within a region or by modeling the magnetic field inhomogeneities generated by the contrast agent. In this study, a new model-based SPIO quantification method is introduced. The proposed method models magnetic field inhomogeneities by approximating regions containing SPIOs as ensembles of magnetic dipoles, referred to as the finite perturber method. The proposed method was verified using data acquired from a phantom and in vivo mouse models. The phantom consisted of an agar solution with four embedded vials, each vial containing known but different concentrations of SPIO nanoparticles. Gaussian noise was also added to the phantom data to test performance of the proposed method. The in vivo dataset was acquired using five mice, each of which was subcutaneously implanted in the flanks with 1 × 10(5) labeled and 1 × 10(6) unlabeled C6 glioma cells. For the phantom data set, the proposed algorithm was generate accurate estimations of the concentration of SPIOs. For the in vivo dataset, the method was able to give estimations of the concentration within SPIO-labeled tumors that are reasonably close to the known concentration.

Multi-parametric neuroimaging reproducibility: a 3-T resource study

Modern MRI image processing methods have yielded quantitative, morphometric, functional, and structural assessments of the human brain. These analyses typically exploit carefully optimized protocols for specific imaging targets. Algorithm investigators have several excellent public data resources to use to test, develop, and optimize their methods. Recently, there has been an increasing focus on combining MRI protocols in multi-parametric studies. Notably, these have included innovative approaches for fusing connectivity inferences with functional and/or anatomical characterizations. Yet, validation of the reproducibility of these interesting and novel methods has been severely hampered by the limited availability of appropriate multi-parametric data. We present an imaging protocol optimized to include state-of-the-art assessment of brain function, structure, micro-architecture, and quantitative parameters within a clinically feasible 60-min protocol on a 3-T MRI scanner. We present scan-rescan reproducibility of these imaging contrasts based on 21 healthy volunteers (11 M/10 F, 22-61 years old). The cortical gray matter, cortical white matter, ventricular cerebrospinal fluid, thalamus, putamen, caudate, cerebellar gray matter, cerebellar white matter, and brainstem were identified with mean volume-wise reproducibility of 3.5%. We tabulate the mean intensity, variability, and reproducibility of each contrast in a region of interest approach, which is essential for prospective study planning and retrospective power analysis considerations. Anatomy was highly consistent on structural acquisition (~1-5% variability), while variation on diffusion and several other quantitative scans was higher (~<10%). Some sequences are particularly variable in specific structures (ASL exhibited variation of 28% in the cerebral white matter) or in thin structures (quantitative T2 varied by up to 73% in the caudate) due, in large part, to variability in automated ROI placement. The richness of the joint distribution of intensities across imaging methods can be best assessed within the context of a particular analysis approach as opposed to a summary table. As such, all imaging data and analysis routines have been made publicly and freely available. This effort provides the neuroimaging community with a resource for optimization of algorithms that exploit the diversity of modern MRI modalities. Additionally, it establishes a baseline for continuing development and optimization of multi-parametric imaging protocols.

Recursive approach to the moment-based phase unwrapping method

The moment-based phase unwrapping algorithm approximates the phase map as a product of Gegenbauer polynomials, but the weight function for the Gegenbauer polynomials generates artificial singularities along the edge of the phase map. A method is presented to remove the singularities inherent to the moment-based phase unwrapping algorithm by approximating the phase map as a product of two one-dimensional Legendre polynomials and applying a recursive property of derivatives of Legendre polynomials. The proposed phase unwrapping algorithm is tested on simulated and experimental data sets. The results are then compared to those of PRELUDE 2D, a widely used phase unwrapping algorithm, and a Chebyshev-polynomial-based phase unwrapping algorithm. It was found that the proposed phase unwrapping algorithm provides results that are comparable to those obtained by using PRELUDE 2D and the Chebyshev phase unwrapping algorithm.

Quantification of SPIO nanoparticles using phase gradient mapping

A new method is developed to quantify the concentration of super-paramagnetic iron oxide (SPIO) contrast agent using magnetic resonance imaging (MRI). The proposed method utilizes a positive contrast method, known as phase gradient mapping (PGM), to find the gradient of the field map. Then the concentration is calculated by fitting the gradient of the field map to the gradient of an ideal geometric model. The proposed method was compared to relaxivity-based SPIO quantification method and was applied to calculate the concentration of SPIO contrast agent for MRI experiments performed on a phantom with known concentrations. The results obtained from the proposed method accord well with the true concentrations.