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.

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.

Determination of detection sensitivity for cerebral microbleeds using susceptibility-weighted imaging.

Cerebral microbleeds (CMBs) are small brain hemorrhages caused by the break down or structural abnormalities of small vessels of the brain. Owing to the paramagnetic properties of blood degradation products, CMBs can be detected in vivo using susceptibility-weighted imaging (SWI). SWI can be used not only to detect iron changes and CMBs, but also to differentiate them from calcifications, both of which may be important MR-based biomarkers for neurodegenerative diseases. Moreover, SWI can be used to quantify the iron in CMBs. SWI and gradient echo (GE) imaging are the two most common methods for the detection of iron deposition and CMBs. This study provides a comprehensive analysis of the number of voxels detected in the presence of a CMB on GE magnitude, phase and SWI composite images as a function of resolution, signal-to-noise ratio (SNR), TE, field strength and susceptibility using in silico experiments. Susceptibility maps were used to quantify the bias in the effective susceptibility value and to determine the optimal TE for CMB quantification. We observed a non-linear trend with susceptibility for CMB detection from the magnitude images, but a linear trend with susceptibility for CMB detection from the phase and SWI composite images. The optimal TE values for CMB quantification were found to be 3 ms at 7 T, 7 ms at 3 T and 14 ms at 1.5 T for a CMB of one voxel in diameter with an SNR of 20: 1. The simulations of signal loss and detectability were used to generate theoretical formulae for predictions. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Susceptibility and size quantification of small human veins from an MRI method.

Recently a method called CISSCO (Complex Image Summation around a Spherical or a Cylindrical Object) was introduced for accurately quantifying the susceptibility and the radius of any narrow cylindrical object at any orientation using a typical two-echo gradient echo sequence. This work further optimizes the method for quantifying oxygen saturation in small cerebral veins in the human brain. The revised method is first validated through numerical simulations and then applied to data from phantom and human brain. The effect of phase high pass filtering on the quantified parameters is studied and procedures for mitigating its adverse effects are suggested. Uncertainty of each measurement is estimated from the error propagation method. It is shown that the revised method allows for accurate quantification of both the vessel size and its oxygen saturation even in the case of a low SNR (signal to noise ratio) in the vein. The results are self consistent across different veins within a given subject with a variation of less than 6%. Finally, imaging parameters and some procedures are suggested for accurate susceptibility and radius quantifications of small human veins.

An improved method for susceptibility and radius quantification of cylindrical objects from MRI.

A new method is developed to measure the magnetic susceptibilities and radii of small cylinder-like objects at arbitrary orientations accurately. This method for most biological substances only requires a standard gradient echo sequence with one or two echo times, depending on the orientation of an object relative to the main magnetic field. For objects oriented at the magic angle, however, this method is not applicable. As a byproduct of this method, the cross-sectional area as well as signals inside and outside the object can be determined. The uncertainty of each measurement is estimated from the error propagation method. Partial volume, dephasing, and phase aliasing effects are naturally included in the equations of this method. A number of simulations, phantom, and pilot in-vivo human studies are carried out to validate the theory. When the maximal phase value at the boundary of a given cylindrical object is larger than 3 radians, and the phase inside the object is more than 1 radian, the susceptibility can be accurately quantified within 15%. The radius of the object can be determined to subpixel accuracy. This is the case when the signal-to-noise ratio inside the object is about 6:1 or higher and the radius of the object is about one pixel or larger. These conditions are realistic when considering medullary and pial veins for example.

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.

Improved MR venography using quantitative susceptibility-weighted imaging.

PURPOSE: To remove the geometry dependence of phase-based susceptibility weighting masks in susceptibility-weighted imaging (SWI) and to improve the visualization of the veins and microbleeds. MATERIALS AND METHODS: True SWI (tSWI) was generated using susceptibility-based masks. Simulations were used to evaluate the influence of the characteristic parameters defining the mask. In vivo data from three healthy adult human volunteers were used to compare the contrast-to-noise-ratios (CNRs) of the right septal vein and the left internal cerebral vein as measured from both tSWI and SWI data. A traumatic brain injury (TBI) patient dataset was used to illustrate qualitatively the proper visualization of microbleeds using tSWI. RESULTS: Compared with conventional SWI, tSWI improved the CNR of the two selected veins by a factor of greater than three for datasets with isotropic resolution and greater than 30% for datasets with anisotropic resolution. Veins with different orientations can be properly enhanced in tSWI. Furthermore, the blooming artifact due to the strong dipolar phase of microbleeds in conventional SWI was reduced in tSWI for the TBI case. CONCLUSION: The use of tSWI overcomes the geometric limitations of using phase and provides better visualization of the venous system, especially for data collected with isotropic resolution.

Measuring iron in the brain using quantitative susceptibility mapping and X-ray fluorescence imaging.

Measuring iron content in the brain has important implications for a number of neurodegenerative diseases. Quantitative susceptibility mapping (QSM), derived from magnetic resonance images, has been used to measure total iron content in vivo and in post mortem brain. In this paper, we show how magnetic susceptibility from QSM correlates with total iron content measured by X-ray fluorescence (XRF) imaging and by inductively coupled plasma mass spectrometry (ICPMS). The relationship between susceptibility and ferritin iron was estimated at 1.10±0.08 ppb susceptibility per µg iron/g wet tissue, similar to that of iron in fixed (frozen/thawed) cadaveric brain and previously published data from unfixed brains. We conclude that magnetic susceptibility can provide a direct and reliable quantitative measurement of iron content and that it can be used clinically at least in regions with high iron content.

Quantitative susceptibility mapping of small objects using volume constraints.

Microbleeds have been implicated to play a role in many neurovascular and neurodegenerative diseases. The diameter of each microbleed has been used previously as a possible quantitative measure for grading microbleeds. We propose that magnetic susceptibility provides a new quantitative measure of extravasated blood. Recently, a Fourier-based method has been used that allows susceptibility quantification from phase images for any arbitrarily shaped structures. However, when very small objects, such as microbleeds, are considered, the accuracy of this susceptibility mapping method still remains to be evaluated. In this article, air bubbles and glass beads are taken as microbleed surrogates to evaluate the quantitative accuracy of the susceptibility mapping method. We show that when an object occupies only a few voxels, an estimate of the true volume of the object is necessary for accurate susceptibility quantification. Remnant errors in the quantified susceptibilities and their sources are evaluated. We show that quantifying magnetic moment, rather than the susceptibility of these small structures, may be a better and more robust alternative.

Quantifying effective magnetic moments of narrow cylindrical objects in MRI.

A new procedure for accurately measuring effective magnetic moments of long cylinders is presented. Partial volume, dephasing and phase aliasing effects are naturally included and overcome in our approach. Images from a typical gradient echo sequence at one single echo time are usually sufficient to quantify the effective magnetic moment of a cylindrical-like object. Only pixels in the neighborhood of the object are needed. Our approach can accurately quantify the magnetic moments and distinguish subpixel changes of cross sections between cylindrical objects. Uncertainties of our procedure are studied through the error propagation method. Images acquired with different parameters are used to test the robustness of our method. Alternate approaches and their limitations to extract magnet moments of objects with different orientations are also discussed. Our method has the potential to be applied to any long object whose cross section is close to a disk.

Removing background phase variations in susceptibility-weighted imaging using a fast, forward-field calculation.

PURPOSE: To estimate magnetic field variations induced from air-tissue interface geometry and remove their effects from susceptibility-weighted imaging (SWI) data. MATERIALS AND METHODS: A Fourier transform-based field estimation method is used to calculate the field deviation arising from air-tissue interface geometry. This is accomplished by manually drawing or automatically detecting the sinuses, the mastoid cavity, and the head geometry. The difference in susceptibility, Deltachi, between brain tissue and air spaces is then calculated using a residual-phase minimization approach. SWI data are corrected by subtracting the predicted phase from the original phase images. Resultant phase images are then used to perform the SWI postprocessing. RESULTS: Significant improvement in the postprocessed SWI data is demonstrated, most notably in the frontal and midbrain regions and to a lesser extent at the boundary of the brain. Specifically, there is much less dropout of signal after phase correction near air-tissue interfaces, making it possible to see vessels and structures that were often incorrectly removed by the conventional SWI postprocessing. CONCLUSION: The Fourier transform-based field estimation method is a powerful 3D background phase removal method for improving SWI images, providing clearer images of the forebrain and the midbrain regions.

Limitations of calculating field distributions and magnetic susceptibilities in MRI using a Fourier based method.

A discrete Fourier based method for calculating field distributions and local magnetic susceptibility in MRI is carefully studied. Simulations suggest that the method based on discrete Green's functions in both 2D and 3D spaces has less error than the method based on continuous Green's functions. The 2D field calculations require the correction of the 'Lorentz disk', which is similar to the Lorentz sphere term in the 3D case. A standard least-squares fit is proposed for the extraction of susceptibility for a single object from MR images. Simulations and a phantom study confirm both the discrete method and the feasibility of the least-squares fit approach. Finding accurate susceptibility values of local structures in the brain from MR images may be possible with this approach in the future.

Quantifying magnetic nanoparticles in non-steady flow by MRI.

OBJECTIVE: This work compares the measured R*2 of magnetic nanoparticles to their corresponding theoretical values in both gel phantoms and dynamic water flows on the basis of the static dephasing theory. MATERIALS AND METHODS: The magnetic moment of a nanoparticle solution was measured by a magnetometer. The R*2 of the nanoparticle solution doped in a gel phantom was measured at both 1.5 and 4.7 T. A total of 12 non-steady state flow experiments with different nanoparticle concentrations were conducted. The R*2 at each time point was measured. RESULTS: The theoretical R*2 on the basis of the magnetization of nanoparticles measured by the magnetometer agree within 11% of MRI measurements in the gel phantom study, a significant improvement from previous work. In dynamic flow experiments, the total R*2 calculated from each experiment agrees within 15% of the theoretical R*2 for 10 of the 12 cases. The MRI phase values are also reasonably predicted by the theory. The diffusion effect does not seem to contribute significantly. CONCLUSIONS: Under certain situations with known R*2, the static dephasing theory can be used to quantify the susceptibility or concentration of nanoparticles in either a static or dynamic flow environment at a given time point. This approach may be applied to in vivo studies.

A complex sum method of quantifying susceptibilities in cylindrical objects: the first step toward quantitative diagnosis of small objects in MRI.

A complex sum method of quantifying the magnetic susceptibility of a long, narrow cylinder embedded in a uniform medium has been developed. The radius of the cylinder can be as small as one pixel. The susceptibility inside the object is extracted from the magnetic resonance complex images, using two concentric circles around the axis of the cylinder. The numerical simulations of this complex sum method are in good agreement with the phantom studies. Specifically, the method was tested with a susceptibility difference of -9 ppm to mimic air/tissue interface in the human body at 1.5 T with an echo time of 5 ms. Phantom studies using an air-filled cylinder in a solidified gel have shown that the susceptibility of the gel cannot be determined by the usual least-squares-fit method but can be determined by the complex sum method to within 5-10% of the expected value.

Biocompatibilities of sapphire and borosilicate glass as cortical neuroprostheses.

The in vivo biocompatibility of pure sapphire and borosilicate glass (BSG) implanted onto the cerebral cortex was studied via magnetic resonance imaging (MRI) and histopathology. Each implant was embedded onto the cortical surface of an adult rat brain for a total of 28 days. Rats underwent surgery with and without implants, and rats with purposely damaged cortical implant sites were also studied. Each animal was imaged via MRI before surgery as well as 10 and 28 days after the surgery. Histopathological results of animals were obtained on the 28th day to determine the specific effect on neurons. Despite the fact that sapphire has been widely used in a variety of medical implants, both MRI and histopathological results indicate that pure sapphire is not biocompatible with the cerebral cortex. On the contrary, BSG implants appear to be biocompatible with the cortical surface.

Active-passive gradient shielding for MRI acoustic noise reduction.

An important source of MRI acoustic noise-magnet cryostat warm-bore vibrations caused by eddy-current-induced forces-can be mitigated by a passive metal shield mounted on the outside of a vibration-isolated, vacuum-enclosed shielded gradient set. Finite-element (FE) calculations for a z-gradient indicate that a 2-mm-thick Cu layer wrapped on the gradient assembly can decrease mechanical power deposition in the warm bore and reduce warm-bore acoustic noise production by about 25 dB. Eliminating the conducting warm bore and other magnet parts as significant acoustic noise sources could lead to the development of truly quiet, fully functioning MRI systems with noise levels below 70 dB.