Strategically Acquired Gradient Echo (STAGE) Imaging, part IV: Constrained Reconstruction of White Noise (CROWN) Processing as a Means to Improve Signal-to-Noise in STAGE Imaging at 3 Tesla.

Increasing the signal-to-noise ratio (SNR) has always been of critical importance for magnetic resonance imaging. Although increasing field strength provides a linear increase in SNR, it is more and more costly as field strength increases. Therefore, there is a major effort today to use signal processing methods to improve SNR since it is more efficient and economical. There are a variety of methods to improve SNR such as averaging the data at the expense of imaging time, or collecting the data with a lower resolution, all of these methods, including imaging processing methods, usually come at the expense of loss of image detail or image blurring. Therefore, we developed a new mathematical approach called CROWN (Constrained Reconstruction of White Noise) to enhance SNR without loss of structural detail and without affecting scanning time. In this study, we introduced and tested the concept behind CROWN specifically for STAGE (strategically acquired gradient echo) imaging. The concept itself is presented first, followed by simulations to demonstrate its theoretical effectiveness. Then the SNR improvement on proton spin density (PSD) and R2⁎ maps was investigated using brain STAGE data acquired from 10 healthy controls (HCs) and 10 patients with Parkinson's disease (PD). For the PSD and R2* maps, the SNR and CNR between white matter and gray matter were improved by a factor of 1.87 ± 0.50 and 1.72 ± 0.88, respectively. The white matter hyperintensity lesions in PD patients were more clearly defined after CROWN processing. Using these improved maps, simulated images for any repeat time, echo time or flip angle can be created with improved SNR. The potential applications of this technology are to trade off the increased SNR for higher resolution images and/or faster imaging.

Distributions of discrete spherical particles with a constant susceptibility can lead to echo time dependent phase shifts which deviate from theories.

PURPOSE: When an object contains a distribution of discrete magnetic inclusions with a constant susceptibility, the MRI signal inside the object may no longer be determined analytically by assuming that the object is uniform or magnetic inclusions are completely random. Through simulations and experiments with spherical particles inside cylinders, this work is to study the signal behavior in the static dephasing regime. METHODS: MRI complex images of long cylinders containing spherical particles with different arrangements were simulated and compared to similar experimental phantom data. All experiments were designed for the static dephasing regime so that diffusion was neglected. RESULTS: Several factors can lead to different phase shifts over echo time. These include numbers of particles per image voxel, particle arrangements, and Gibbs ringing effects. Purely random arrangements of particles in simulations can agree with a revised theoretical formula at short echo times, but quasi-random arrangements of particles do not agree with the theory. In addition, close to half of experimental results show deviations from the theory and the quasi-random arrangements of particles can explain those experimental results. Simulated R2' values are about the same for different cylinder orientations but increase when random particle arrangement is restricted toward lattice. Nonetheless, as expected, phase distributions outside and far away from each cylinder are independent of any factor affecting phase inside and behave as if they are from a cylinder with a uniform bulk susceptibility. CONCLUSION: Phase over echo time inside an object containing discrete spheres can be nonlinear and deviate from current theories in the static dephasing regime. Phase outside the object can be used to accurately determine its magnetic moment and bulk susceptibility without a priori knowledge of the spherical particle distribution inside the object. These results can be extended to the subcortical gray matter and suggest that in vivo susceptibility quantification will need to be re-thought.

Removing unwanted background phase with a reference phantom for applications in susceptibility quantification.

PURPOSE: A method of removing the background phase with a reference phantom but without overcorrecting the induced phase from objects of interest is proposed. Several factors during the imaging procedure and post-processing are investigated for their accuracies. METHODS: A method using a reference phantom to remove eddy currents as well as using the least squares fit to quantify susceptibility and to remove the background phase is proposed. Phase induced from simulated spheroids was fitted and compared to their true magnetic moments, an important concept for the proposed method. A cylindrical phantom and its simulation, a phantom with straws filled with Gd-DTPA, and a simulated head model were used to study systematic errors due to some confounding factors. The feasibility for in vivo applications was demonstrated from an actual human head. Susceptibility and remaining phase after removing the background phase were measured in all cases. RESULTS: Simulations show that magnetic moments of various spheroids and phantoms can be accurately quantified from images, regardless of the partial volume effect. All measured susceptibility values are within ±0.16 ppm of -9.4 ppm for agarose and 0.05 ppm of 1 ppm for Gd-DTPA. Most residual phase is within ±0.1 rad from the phantom center. Susceptibilities close to -9.4 ppm are also obtained for the simulated and actual head. Correspondingly, the remaining phase has a mean value less than two standard deviations. CONCLUSION: The proposed method from phantom studies can reliably remove the background phase without overcorrections. The in vivo example demonstrates the feasibility of the method.

A study of MRI gradient echo signals from discrete magnetic particles with considerations of several parameters in simulations.

Modeling MRI signal behaviors in the presence of discrete magnetic particles is important, as magnetic particles appear in nanoparticle labeled cells, contrast agents, and other biological forms of iron. Currently, many models that take into account the discrete particle nature in a system have been used to predict magnitude signal decays in the form of R2* or R2' from one single voxel. Little work has been done for predicting phase signals. In addition, most calculations of phase signals rely on the assumption that a system containing discrete particles behaves as a continuous medium. In this work, numerical simulations are used to investigate MRI magnitude and phase signals from discrete particles, without diffusion effects. Factors such as particle size, number density, susceptibility, volume fraction, particle arrangements for their randomness, and field of view have been considered in simulations. The results are compared to either a ground truth model, theoretical work based on continuous mediums, or previous literature. Suitable parameters used to model particles in several voxels that lead to acceptable magnetic field distributions around particle surfaces and accurate MR signals are identified. The phase values as a function of echo time from a central voxel filled by particles can be significantly different from those of a continuous cubic medium. However, a completely random distribution of particles can lead to an R2' value which agrees with the prediction from the static dephasing theory. A sphere with a radius of at least 4 grid points used in simulations is found to be acceptable to generate MR signals equivalent from a larger sphere. Increasing number of particles with a fixed volume fraction in simulations reduces the resulting variance in the phase behavior, and converges to almost the same phase value for different particle numbers at each echo time. The variance of phase values is also reduced when increasing the number of particles in a fixed voxel. These results indicate that MRI signals from voxels containing discrete particles, even with a sufficient number of particles per voxel, cannot be properly modeled by a continuous medium with an equivalent susceptibility value in the voxel.

Quantifications of in vivo labeled stem cells based on measurements of magnetic moments.

Cells labeled by super paramagnetic iron-oxide (SPIO) nanoparticles are more easily seen in gradient echo MR images, but it has not been shown that the amount of nanoparticles or the number of cells can be directly quantified from MR images. This work utilizes a previously developed and improved Complex Image Summation around a Spherical or Cylindrical Object (CISSCO) method to quantify the magnetic moments of several clusters of SPIO nanoparticle labeled cells from archived rat brain images. With the knowledge of mass magnetization of the cell labeling agent and cell iron uptake, the number of cells in each nanoparticle cluster can be determined. Using a high pass filter with a reasonable size has little effect on each measured magnetic moment from the CISSCO method. These procedures and quantitative results may help improve the efficacy of cell-based treatments in vivo.

A quantitative study of susceptibility and additional frequency shift of three common materials in MRI.

PURPOSE: This work quantifies magnetic susceptibilities and additional frequency shifts derived from different samples. METHODS: Twenty samples inside long straws were imaged with a multiecho susceptibility weighted imaging and analyzed with two approaches for comparisons. One approach applied our complex image summation around a spherical or cylindrical object method to phase distributions outside straws. The other approach utilized phase values inside each straw from two orientations. Both methods quantified susceptibilities of each sample at each echo time. The R2* value of each sample was measured too. Uncertainty of each measurement was also estimated. RESULTS: Quantified susceptibilities from complex image summation around a spherical or cylindrical object are consistent within uncertainties between different echo times. However, this is not the case for the other method. Nonetheless, most quantified susceptibilities are consistent between these two methods. Phase values due to additional frequency shifts in some of ferritin and nanoparticle samples have been identified. Only R2* values quantified from low concentration nanoparticle samples agree with the predictions from the static dephasing theory. CONCLUSION: This work suggests that using the sample sizes and phase values only outside samples can correctly quantify the susceptibilities of those samples. With the presence of a possible additional frequency shift inside a material, it will not be suitable to obtain susceptibility maps without taking that into account. Magn Reson Med 76:1263-1269, 2016. © 2015 Wiley Periodicals, Inc.

Magnetic moment quantifications of small spherical objects in MRI.

PURPOSE: The purpose of this work is to develop a method for accurately quantifying effective magnetic moments of spherical-like small objects from magnetic resonance imaging (MRI). A standard 3D gradient echo sequence with only one echo time is intended for our approach to measure the effective magnetic moment of a given object of interest. METHODS: Our method sums over complex MR signals around the object and equates those sums to equations derived from the magnetostatic theory. With those equations, our method is able to determine the center of the object with subpixel precision. By rewriting those equations, the effective magnetic moment of the object becomes the only unknown to be solved. Each quantified effective magnetic moment has an uncertainty that is derived from the error propagation method. If the volume of the object can be measured from spin echo images, the susceptibility difference between the object and its surrounding can be further quantified from the effective magnetic moment. Numerical simulations, a variety of glass beads in phantom studies with different MR imaging parameters from a 1.5T machine, and measurements from a SQUID (superconducting quantum interference device) based magnetometer have been conducted to test the robustness of our method. RESULTS: Quantified effective magnetic moments and susceptibility differences from different imaging parameters and methods all agree with each other within two standard deviations of estimated uncertainties. CONCLUSION: An MRI method is developed to accurately quantify the effective magnetic moment of a given small object of interest. Most results are accurate within 10% of true values, and roughly half of the total results are accurate within 5% of true values using very reasonable imaging parameters. Our method is minimally affected by the partial volume, dephasing, and phase aliasing effects. Our next goal is to apply this method to in vivo studies.

Quantifying errors in flow measurement using phase contrast magnetic resonance imaging: comparison of several boundary detection methods.

Quantifying flow from phase-contrast MRI (PC-MRI) data requires that the vessels of interest be segmented. The estimate of the vessel area will dictate the type and magnitude of the error sources that affect the flow measurement. These sources of errors are well understood, and mathematical expressions have been derived for them in previous work. However, these expressions contain many parameters that render them difficult to use for making practical error estimates. In this work, some realistic assumptions were made that allow for the simplification of such expressions in order to make them more useful. These simplified expressions were then used to numerically simulate the effect of segmentation accuracy and provide some criteria that if met, would keep errors in flow quantification below 10% or 5%. Four different segmentation methods were used on simulated and phantom MRA data to verify the theoretical results. Numerical simulations showed that including partial volumed edge pixels in vessel segmentation provides less error than missing them. This was verified with MRA simulations, as the best performing segmentation method generally included such pixels. Further, it was found that to obtain a flow error of less than 10% (5%), the vessel should be at least 4 (5) pixels in diameter, have an SNR of at least 10:1 and have a peak velocity to saturation cut-off velocity ratio of at least 5:3.

Cerebrospinal fluid flow dynamics in multiple sclerosis patients through phase contrast magnetic resonance imaging.

We studied cerebrospinal fluid (CSF) flow dynamics at the cervical level in association with internal jugular veins (IJV) flow for 92 patients with multiple sclerosis (MS). Phase contrast magnetic resonance imaging was used to quantify flow of the CSF and major vessels (including the IJV and the carotid arteries) at the C2-C3 level in the neck. Contrast enhanced MR angiography and time-of-flight MR venography were used to subdivide MS patients into stenotic (ST) and non-stenotic (NST) populations. We evaluated: IJV flow normalized by arterial flow; CSF peaks; CSF outflow duration and its onset from systole. We tested if these variables were statistically different among different MS phenotypes and between ST and NST MS patients. The delay between the beginning of beginning of systole and the CSF outflow was higher in ST compared to NST MS. Less IJV flow was observed in ST vs NST MS. None of the measures was different between the different MS phenotypes. These results suggest that alterations of IJV morphology affect both IJV flow and CSF flow timing but not CSF flow amplitude.