The SIMRI project: a versatile and interactive MRI simulator

This paper gives an overview of SIMRI, a new 3D MRI simulator based on the Bloch equation. This simulator proposes an efficient management of the T2* effect, and in a unique simulator integrates most of the simulation features that are offered in different simulators. It takes into account the main static field value and enables realistic simulations of the chemical shift artifact, including off-resonance phenomena. It also simulates the artifacts linked to the static field inhomogeneity like those induced by susceptibility variation within an object. It is implemented in the C language and the MRI sequence programming is done using high level C functions with a simple programming interface. To manage large simulations, the magnetization kernel is implemented in a parallelized way that enables simulation on PC grid architecture. Furthermore, this simulator includes a 1D interactive interface for pedagogic purpose illustrating the magnetization vector motion as well as the MRI contrasts.     

Choice of soft pulse shapes for signal excitation in chemical shift selective imaging

The choice of soft pulse shapes for chemical shift selective excitation in chemical shift imaging is discussed. In the presence of inhomogeneities in the static magnetic field resulting from susceptibility anomalies, it is important to optimise pulse bandshape and frequency offset as well as bandwidth, in order to minimize artefacts arising from excitation of unwanted resonances. A comparison of the use of Gaussian and sinc shaped excitation pulses in the chemical shift micro-imaging of grapes serves to illustrate some of the effects that may be observed.     

Improvement of spectral resolution by spectroscopic imaging

We propose to use three-dimensional spectroscopic imaging (SI) to increase the spectral resolution for biological samples for which strong susceptibility effects (or poor magnetic homogeneity) cause significant line broadening. Due to susceptibility effects (or poor field homogeneity) the SI voxel spectra even from a uniform sample are shifted with respect to each other and much less broadened than the total sample spectrum. Realignment of the spectra from individual voxels prior to their coaddition produces a total-volume spectrum with significantly narrower lines.     

MRI phase offset correction method impacts quantitative susceptibility mapping

Individual channel ultra-high field (7T) phase images have to be phase offset corrected prior to the mapping of magnetic susceptibility of tissue. Whilst numerous methods have been proposed for gradient recalled echo MRI phase offset correction, it remains unclear how they affect quantitative magnetic susceptibility values derived from phase images. Methods already proposed either employ a single or multiple echo time MRI data. In terms of the latter, offsets can be derived using an ultra-short echo time acquisition, or by estimating the offset based on two echo points with the assumption of linear phase evolution with echo time. Our evaluation involved 32 channel multi-echo time 7T GRE (Gradient Recalled Echo) and ultra-short echo time PETRA (Pointwise Encoding Time Reduction with Radial Acquisition) MRI data collected for a susceptibility phantom and three human brains. The combined phase images generated using four established offset correction methods (two single and two multiple echo time) were analysed, followed by an assessment of quantitative susceptibility values obtained for a phantom and human brains. The effectiveness of each method in removing the offsets was shown to reduce with increased echo time, decreased signal intensity and reduced overlap in coil sensitivity profiles. Quantitative susceptibility values and how they change with echo time were found to be method specific. Phase offset correction methods based on single echo time data have a tendency to produce more accurate and less noisy quantitative susceptibility maps in comparison with methods employing multiple echo time data.     

A post-processing method for correction and enhancement of chemical shift images

Chemical shift imaging (CSI) relies on a strong and homogeneous main field. Field homogeneity ensures adequate coherence between the precessions of individual spins within each voxel. Variation of field strength between different voxels causes geometric distortion and intensity variation in chemical shift images, resulting in errors when analyzing the spatial distribution of specific chemical compounds. A post-processing method, based on detection of the spectral peak of water and baseline subtraction with Lorentzian functions, was developed in this study to automatically correct spectra offsets caused by field inhomogeneity, thus enhancing the contrast of the chemical shift images. Because this method does not require prior field plot information, it offers advantages over existing correction methods. Furthermore, the method significantly reduces geometric distortion and enhances signals of chemical compounds even when the water suppression protocol was applied during the CSI data acquisition. The experimental results of the water and glucose phantoms showed a considerable reduction of artifacts in the spectroscopic images when this post-processing method was employed. The significance of this method was also demonstrated by an analysis of the spatial distributions of sugar and water contents in ripe and unripe bananas.     

Shift of the proton NMR field in aqueous solutions of paramagnetic ions

In the paper there is discussed the proton NMR field shift in aqueous solutions of transition metal ions, which has to be taken into account in exact measurements of the static magnetic field. Using the results of Luz's and Shulman's measurements (1965) the empirical expression for the field shift is evaluated, which is a function of the sample shape, of the concentration and the susceptibility of paramagnetic ions in the solution. It is shown that in exact field measurements the diamagnetic part of the susceptibility of the solution cannot be neglected and that one may eliminate the field shift by a suitable choice of the paramagnetic-ions concentration in transversely magnetized cylindrical samples.     

Correction of local B0 shifts in 3D EPSI of the human brain at 4 T

High-spatial-resolution acquisition (HR) was previously proposed for 3D echo-planar spectroscopic imaging (EPSI) in combination with a high-spatial-resolution water reference EPSI data set to minimize inhomogeneous spectral line broadening, allowing for local frequency shift (B(0) shift) correction in human brain metabolite maps at 1.5 T (Ebel A et al., Magn. Reson. Imaging 21:113-120, 2003). At a higher magnetic field strength, B(0), increased field inhomogeneities typically lead to increased line broadening. Additionally, increased susceptibility variations render shimming of the main magnetic field over the whole head more difficult. This study addressed the question whether local B(0)-shift correction still helps limit line broadening in whole-brain 3D EPSI at higher magnetic fields. The combination of HR and local B(0)-shift correction to limit line broadening was evaluated at 4 T. Similar to the results at 1.5 T, the approach provided a high yield of voxels with good spectral quality for 3D EPSI, resulting in improved brain coverage.     

Quantitative evaluation of optimal imaging parameters for single-cell detection in MRI using simulation

Super-paramagnetic iron oxide (SPIO) nanoparticles are actively investigated to enhance disease detection through molecular imaging using magnetic resonance imaging (MRI). Detection of the cells labeled by SPIO depends on the MRI protocols and pulse sequence parameters that can be optimized. To evaluate the sensitivity and specificity of the image acquisition methods and to obtain optimal imaging parameters for single-cell detection, we further developed an MRI simulator. The simulator models an object (tissue) at a microscopic level to evaluate effects of spatial distribution and concentration of nanoparticles on the resulting image. In this study, the simulator was used to evaluate and compare imaging of the labeled cells by the gradient-echo (GE), true-FISP [fast imaging employing steady-state acquisition (FIESTA)] and echo-planar imaging (EPI) pulse sequences. Effects of the imaging and object parameters, such as field strength, imaging protocol and pulse sequence parameters, imaging resolution, cell iron load, position of SPIO within the voxel and cell division within the voxel, were investigated in the work. The results suggest that true-FISP has the highest sensitivity for single-cell detection by MRI.     

Radiofrequency magnetic field gradient echoes have reduced sensitivity to susceptibility gradients

The amplitudes of gradient-echoes produced using static field gradients are sensitive to diffusion of tissue water during the echo evolution time. Gradient-echoes have been used to produce MR images in which image intensity is proportional to the self-diffusion coefficient of water. However, such measurements are subject to error due to the presence of background magnetic field gradients caused by variations in local magnetic susceptibility. These local gradients add to the applied gradients. The use of radiofrequency (RF) gradients to produce gradient-echoes may avoid this problem. The RF magnetic field is orthogonal to the offset field produced by local magnetic susceptibility gradients. Thus, the effect of the local gradients on RF gradient-echo amplitude is small if the RF field is strong enough to minimize resonance offset effects. The effects of susceptibility gradients can be further reduced by storing magnetization longitudinally during the echo evolution period. A water phantom was used to evaluate the effects of background gradients on the amplitudes of RF gradient-echoes. A surface coil was used to produce an RF gradient of between 1.3 and 1.6 gauss/cm. Gradient-echoes were detected with and without a 0.16 gauss/cm static magnetic field gradient applied along the same direction as the RF gradient. The background static field gradient had no significant effect on the decay of RF gradient-echo amplitude as a function of echo evolution time. In contrast, the effect of the background gradient on echoes produced using a 1.6 gauss/cm static field gradient is calculated to be significant. This analysis suggests that RF gradient-echoes can produce MR images in which signal intensity is a function of the self-diffusion coefficient of water, but is not significantly affected by background gradients.     

Extreme gravitational lensing in vicinity of Schwarzschild-de Sitter black holes

We have developed a realistic, fully general relativistic computer code to simulate optical projection in a strong, spherically symmetric gravitational field. The standard theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole is extended to black hole spacetimes with a repulsive cosmological constant, i.e, Schwarzschild-de Sitterspacetimes. Influence of the cosmological constant is investigated for static observers and observers radially free-falling from the static radius. Simulations include effects of the gravitational lensing, multiple images, Doppler and gravitational frequency shift, as well as the intensity amplification. The code generates images of the sky for the static observer and a movie simulations of the changing sky for the radially free-falling observer. Techniques of parallel programming are applied to get a high performance and a fast run of the BHC simulation code.      

定量磁化率成像多回波相位拟合算法研究

定量磁化率成像(quantitative susceptibility mapping,QSM)技术大多采用多回波梯度回波序列采集相位数据,经加权最小二乘法(weighted linear least-square,WLS)拟合得到局部磁场分布.对于组织磁化率分布不均匀的区域,尤其是颅底部位,常规WLS算法拟合得到的局部磁场误差较大,导致相应部位磁化率分布图信噪比较低.针对常规WLS算法的这一不足,该文提出了一种截断WLS算法.对两种算法拟合得到的磁化率分布图对比研究发现,截断WLS算法可有效提高颅底部位定量磁化率分布图的图像质量,使其噪声明显下降.     

Spectral resolution enhancement by chemical shift imaging

Three-dimensional chemical shift imaging (3D CSI) with appropriate data postprocessing can be used as a tool to improve spectral resolution in samples where large susceptibility differences and limited shim capabilities prevent good sample shimming. Data postprocessing is reduced to the realignment of individual 3D voxel spectra. As a result, the line broadening due to the field inhomogeneity over the sample's volume is reduced to the broadening by inhomogeneity within individual voxels. We compared this method with the resolution enhancement by window multiplication. We demonstrated, theoretically and experimentally, that in the presence of large, lower-order gradients, 3D CSI achieves better resolution enhancement with smaller sensitivity losses. An application of the method to a simple biological system is presented as well.     

Magnetic resonance sounding: Enhanced modeling of a phase shift

Magnetic resonance sounding (MRS) is a geophysical method for noninvasive groundwater investigation. A wire loop on the surface is energized by a pulse of oscillating current. After the pulse is cut off, the free induction decay signal from groundwater is measured with the same loop. The Larmor frequency depends on the Earth’s magnetic field and varies between 800 and 2800 Hz around the world. Available mathematical models assume that the geomagnetic field is constant and the pulse frequency is equal to the Larmor frequency. These assumptions allow calculation of the phase shift of the signal caused by only the electrical conductivity of the subsurface. However, the existing models are simplified. The Earth’s magnetic field may be locally modified by rocks and often is not homogeneous over the volume investigated by MRS. It may also vary in time. A nonconstant geomagnetic field is changing the Larmor frequency at 1 to 5 Hz during one sounding, whilst the pulse frequency is set in the beginning of the sounding. Under these conditions, the assumption of zero frequency offset between the pulse frequency and the Larmor frequency is often unsound. The nonzero frequency offset causes a phase shift in the MRS signal comparable with the shift caused by electrically conductive rocks. For increasing the accuracy of phase shift modeling, and enhanced mathematical model in which the frequency offset is taken into account has been developed. With the enhanced model, the phase of the MRS signal can be calculated with better accuracy. Field measurements reveal a good correlation between experimental and theoretical signals.     

Field strength influences on gradient recalled echo MRI signal compartment frequency shifts

Different trends of echo time dependent gradient recalled echo MRI signals in different brain regions have been attributed to signal compartments in image voxels. It remains unclear how variations in gradient recalled echo MRI signals change as a function of MRI field strength, and how data processing may impact signal compartment parameters. We used two popular quantitative susceptibility mapping methods of processing raw phase images (Laplacian and path-based unwrapping with V-SHARP) and expressed values in the form of induced frequency shifts (in Hz) in six specific brain regions at 3T and 7T. We found the frequency shift curves to vary with echo time, and a good overlap between 3T and 7T mean frequency shift curves was present. However, the amount of variation across participants was greater at 3T, and we were able to obtain better compartment model fits of the signal at 7T. We also found the temporal trends in the signal and compartment frequency shifts to change with the method used to process images. The inter-participant averaged trends were consistent between 3T and 7T for each quantitative susceptibility pipeline. However, signal compartment frequency shifts generated using different pipelines may not be comparable.     

Wavelet Encoding Spectroscopic Imaging in Small FOV Regime: Comparison to Chemical Shift Imaging at 3?Tesla

We have recently proposed a new magnetic resonance spectroscopic imaging (MRSI) technique called wavelet encoding spectroscopic imaging (WE-SI), and described its implementation on a clinical 1.5?T scanner. This technique is proposed as an alternative to chemical shift imaging (CSI), to decrease acquisition time, and voxel contamination. The proposed method is implemented here on a clinical 3?T scanner. Phantom and in vivo studies are chosen to validate the technique at higher field, as well as to fully explore the usefulness of this technique, and find its niche of application in the chain of existing MRSI techniques. In wavelet encoding, a set of dilated and translated wavelets are used to span a localized space by dividing it into a set of sub-spaces with pre-determined sizes and locations. Due to their simple shapes, Haar wavelets are chosen. They are represented in the modified PRESS sequence by the selective excitation and refocusing radio-frequency (RF) pulses. The wavelets dilation and translation are achieved by changing the strength of the localization gradients and frequency shift of the RF pulses, respectively. Data acquisition time is reduced using the minimum recovery time when successive MR signals from adjacent sub-spaces are collected. The results obtained at 3?T confirm those obtained at 1.5?T, and demonstrate that despite the low signal-to-noise ratio, the proposed WE-SI provides accurate results and reduces both voxel contamination and acquisition time as compared to CSI. This applies especially in the small field-of-view regime where only a small number of voxels is required.     

Theory of microwave absorption by the spin-1/2 Heisenberg-Ising magnet

We analyze the problem of microwave absorption by the Heisenberg-Ising magnet in terms of shifted moments of the imaginary part of the dynamical susceptibility. When both the Zeeman field and the wave vector of the incident microwave are parallel to the anisotropy axis, the first four moments determine the shift of the resonance frequency and the linewidth in a situation where the frequency is varied for fixed Zeeman field. For the one-dimensional model we can calculate the moments exactly. This provides exact data for the resonance shift and the linewidth at arbitrary temperatures and magnetic fields. In current ESR experiments the Zeeman field is varied for fixed frequency. We show how in this situation the moments give perturbative results for the resonance shift and for the integrated intensity at small anisotropy as well as an explicit formula connecting the linewidth with the anisotropy parameter in the high-temperature limit.     

Quantification of trabecular structure in the distal femur using magnetic resonance phase imaging

A new approach for quantifying trabecular bone tissue using the phase images of a simple gradient-echo sequence is presented. The proposed method is based on the hypothesis that the differences in susceptibility between bone and bone marrow cause magnetic field (i.e., precession phase) variations between the image voxels. Phase images of the distal femur were obtained in vivo and characterised with the use of the phase variance. Computer simulations and experimental results indicate that the distribution of the phases varies with echo time and image resolution, as expected. Keeping these fixed, however, the phase variance is found to strongly reflect variations in trabecular structure.     

Fluctuation limitations on the voxel minimal size at laser nanopolymerization

Laser (or two-photon) nanopolymerization is an effective way of producing 3D polymeric submicron structures. The mainstream in developing this technology is improvement of the spatial resolution of nano-objects. Fluctuation-induced inhomogeneities are studied as the main physical reason limiting the spatial resolution of polymeric structures obtained by nanopolymerization. Typically, complex polymeric structures have the form of a raster composed of many elements, voxels, about 100 nm across. Monte Carlo simulation of a spherically symmetric polymeric voxel is carried out. It is shown that, when the voxel size becomes less than critical, the position and size of a voxel vary from realization to realization (become irreproducible). This effect is attributed to the disappearance of the voxel??s core??part of a voxel that has macroscopic properties. Irreproducible formation of the single voxels may lead to distortions of the fine features of complex microstructures and, hence, to a deterioration of the spatial resolution. Estimates are made of the minimal size of voxels that can be reproducibly produced in real laser experiments.     

Effects of spin fluctuations on the paramagnetic susceptibility and metamagnetic transition in UPt3

The paramagnetic susceptibility for UPt₃ is calculated in the static gaussian statistics of spin fluctuations by using a realistic itinerant electron model. The magnetic field dependence of the magnetisation is also calculated and it is shown that the metamagnetic transition occurs at about 140 T.     

Functional magnetic resonance imaging with intermolecular multiple-quantum coherences

For the first time, we demonstrate here functional magnetic resonance imaging (fMRI) using intermolecular multiple-quantum coherences (iMQCs). iMQCs are normally not observed in liquid-state NMR because dipolar interactions between spins average to zero. If the magnetic isotropy of the sample is broken through the use of magnetic field gradients, dipolar couplings can reappear, and hence iMQCs can be observed. Conventional (BOLD) fMRI measures susceptibility variations averaged over each voxel. In the experiment performed here, the sensitivity of iMQCs to frequency variations over mesoscopic and well-defined distances is exploited. We show that iMQC contrast is qualitatively and quantitatively different from BOLD contrast in a visual stimulation task. While the number of activated pixels is smaller in iMQC contrast, the intensity change in some pixels exceeds that of BOLD contrast severalfold.