Dependence of the frequency distribution around a sphere on the voxel orientation.

Microscopically small magnetic field inhomogeneities within an external static magnetic field cause a free induction decay in magnetic resonance imaging that generally exhibits two transverse components that are usually summarized to a complex entity. The Fourier transform of the complex-valued free induction decay is the purely real and positive-valued frequency distribution which allows an easy interpretation of the underlying dephasing mechanism. Typically, the frequency distribution inside a cubic voxel as caused by a spherical magnetic field inhomogeneity is determined by a histogram technique in terms of subdivision of the whole voxel into smaller subvoxels. A faster and more accurate computation is achieved by analytical expressions for the frequency distribution that are derived in this work. In contrast to the usually assumed simplified case of a spherical voxel, we also consider the tilt angles of the cubic voxel to the external magnetic field. The typical asymmetric form of the frequency distribution is reproduced and analyzed for the more realistic case of a cubic voxel. We observe a splitting of frequency distribution peaks for increasing tilt of the cubic voxel against the direction of the external magnetic field in analogy to the case for dephasing around cylindrical, vessel-like objects inside cubic voxels. These results are of value, e.g., for the analysis of susceptibility-weighted images or in quantitative susceptibility imaging since the reconstruction of these images is performed in cubic-shaped voxels.

Gibbs point field model quantifies disorder in microvasculature of U87-glioblastoma.

Microvascular proliferation in glioblastoma multiforme is a biological key mechanism to facilitate tumor growth and infiltration and a main target for treatment interventions. The vascular architecture can be obtained by Single Plane Illumination Microscopy (SPIM) to evaluate vascular heterogeneity in tumorous tissue. We make use of the Gibbs point field model to quantify the order of regularity in capillary distributions found in the U87 glioblastoma model in a murine model and to compare tumorous and healthy brain tissue. A single model parameter Γ was assigned that is linked to tissue-specific vascular topology through Monte-Carlo simulations. Distributions of the model parameter Γ differ significantly between glioblastoma tissue with mean 〈ΓG〉=2.1±0.4, as compared to healthy brain tissue with mean 〈ΓH〉=4.9±0.4, suggesting that the average Γ-value allows for tissue differentiation. These results may be used for diagnostic magnetic resonance imaging, where it has been shown recently that Γ is linked to tissue-inherent relaxation parameters.

Susceptibility based multiparametric quantification of liver disease: Non-invasive evaluation of steatosis and iron overload.

PURPOSE: To evaluate if single-voxel MR spectroscopy (MRS) of iron and fat correlates with biopsy results of hepatic steatosis and iron overload, and to compare MR-measurements with room-temperature susceptometer (RTS), ultrasound, controlled attenuation parameter (CAP) and serum ferritin. MATERIAL AND METHODS: In this prospective study, a set of 42 patients out of 47 screened patients with several chronic liver diseases underwent MRI-examination at 1.5 T including R2-measurements by single-voxel high-speed T2-corrected multiecho spectroscopy, additional liver biopsy, abdominal ultrasound, CAP, and RTS. Routine blood and serum parameters were determined, including ferritin. Atomic absorption spectroscopy (AAS) and histologically confirmed extent of hepatic steatosis from liver biopsy were used as reference standard. For correlation of R2, RTS, CAP, ferritin, and ultrasound with results of AAS and histologically determined fat fraction of liver biopsy specimen, Spearman's and Pearson's correlation as well as receiver operating characteristics curve (ROC) analysis with cut-off values determined by maximizing Youden index was used. RESULTS: MRS iron assessment correlated best with AAS, with a Pearson correlation coefficient of 0.715 (p < 0.001), followed by RTS 0.520 (p < 0.001), and serum ferritin 0.213 (p = 0.088, not significant). MRS fat quantification correlated best with the histological confirmed extent of steatosis hepatis with a Spearman correlation coefficient of 0.836 (p < 0.001), followed by CAP 0.604 (p < 0.001) and sonographically diagnosed steatosis 0.358 (p = 0.013). CONCLUSION: MRS by T2-corrected multiecho single-voxel spectroscopy correlated best with histological results of hepatic fat and iron content compared to RTS, CAP, abdominal ultrasound, and ferritin. Non-invasive methods to assess hepatic fat and iron are of clinical interest for follow-up examinations of patients with chronic liver diseases, where repeated biopsy is not indicated.

Vessel architecture imaging using multiband gradient-echo/spin-echo EPI.

OBJECTIVES: To apply the MB (multiband) excitation and blipped-CAIPI (blipped-controlled aliasing in parallel imaging) techniques in a spin and gradient-echo (SAGE) EPI sequence to improve the slice coverage for vessel architecture imaging (VAI). MATERIALS AND METHODS: Both MB excitation and blipped-CAIPI with in-plane parallel imaging were incorporated into a gradient-echo (GE)/spin-echo (SE) EPI sequence for simultaneous tracking of the dynamic MR signal changes in both GE and SE contrasts after the injection of contrast agent. MB and singleband (SB) excitation were compared using a 20-channel head coil at 3 Tesla, and high-resolution MB VAI could be performed in 32 glioma patients. RESULTS: Whole-brain covered high resolution VAI can be achieved after applying multiband excitation with a factor of 2 and in-plane parallel imaging with a factor of 3. The quality of the images resulting from MB acceleration was comparable to those from the SB method: images were reconstructed without any loss of spatial resolution or severe distortions. In addition, MB and SB signal-to-noise ratios (SNR) were similar. A relative low g-factor induced from the MB acceleration method was achieved after using a blipped-CAIPI technique (1.35 for GE and 1.33 for SE imaging). Performing quantitative VAI, we found that, among all VAI parametric maps, microvessel type indicator (MTI), distance map (I) and vascular-induced bolus peak-time shift (VIPS) were highly correlated. Likewise, VAI parametric maps of slope, slope length and short axis were highly correlated. CONCLUSIONS: Multiband accelerated SAGE successfully doubles the number of readout slices in the same measurement time when compared to conventional readout sequences. The corresponding VAI parametric maps provide insights into the complexity and heterogeneity of vascular changes in glioma.

Improved compressed sensing reconstruction for [Formula: see text]F magnetic resonance imaging.

OBJECTIVE: In magnetic resonance imaging (MRI), compressed sensing (CS) enables the reconstruction of undersampled sparse data sets. Thus, partial acquisition of the underlying k-space data is sufficient, which significantly reduces measurement time. While 19F MRI data sets are spatially sparse, they often suffer from low SNR. This can lead to artifacts in CS reconstructions that reduce the image quality. We present a method to improve the image quality of undersampled, reconstructed CS data sets. MATERIALS AND METHODS: Two resampling strategies in combination with CS reconstructions are presented. Numerical simulations are performed for low-SNR spatially sparse data obtained from 19F chemical-shift imaging measurements. Different parameter settings for undersampling factors and SNR values are tested and the error is quantified in terms of the root-mean-square error. RESULTS: An improvement in overall image quality compared to conventional CS reconstructions was observed for both strategies. Specifically spike artifacts in the background were suppressed, while the changes in signal pixels remained small. DISCUSSION: The proposed methods improve the quality of CS reconstructions. Furthermore, because resampling is applied during post-processing, no additional measurement time is required. This allows easy incorporation into existing protocols and application to already measured data.

Voxel-size dependent quantitative susceptibility mapping of blood vessel networks: A simulation study.

Quantitative susceptibility mapping provides a measure for the local susceptibility within a voxel in magnetic resonance imaging (MRI). So far, theoretical and numerical studies focus on the assumption of a constant susceptibility inside each MR voxel. For blood vessel networks, however, susceptibility differences between blood and surrounding tissue occur on a much smaller length scale than the typical voxel size in routine MRI. In this work, the dependency of the quantitative susceptibility value on vessel size and voxel size is analyzed.

Dual-contrast pCASL using simultaneous gradient-echo/spin-echo multiband EPI.

A 2D gradient-echo EPI is commonly employed for arterial spin labeling (ASL) readout to achieve fast whole brain coverage measurements. However, such a readout suffers from susceptibility artifacts induced by magnetic field inhomogeneities. To reduce these susceptibility effects, single-shot spin-echo EPI was proposed to be used for acquisitions in continuous ASL (CASL). To minimize functional and physiological variations, a gradient-echo (GE)/spin-echo (SE) dual-echo EPI readout of the CASL sequence is needed for a comparison between GE- and SE-based determination of cerebral blood flow (CBF). In this study, we employed a simultaneous GE/SE multiband EPI as the readout of a pseudo-CASL (pCASL) sequence. Motor cortex activations derived from a finger-tapping task and functional networks from resting state fMRI were compared for both GE and SE contrasts. Direct comparison of SE and GE contrasts revealed that GE ASL provides an improved sensitivity of functional activity in finger-tapping and in resting-state imaging. SE ASL, on the other hand, suffered less from susceptibility artifacts induced by magnetic field inhomogeneities and pulsatile flow artifacts.

Microstructural Analysis of Peripheral Lung Tissue through CPMG Inter-Echo Time R2 Dispersion.

Since changes in lung microstructure are important indicators for (early stage) lung pathology, there is a need for quantifiable information of diagnostically challenging cases in a clinical setting, e.g. to evaluate early emphysematous changes in peripheral lung tissue. Considering alveoli as spherical air-spaces surrounded by a thin film of lung tissue allows deriving an expression for Carr-Purcell-Meiboom-Gill transverse relaxation rates R2 with a dependence on inter-echo time, local air-tissue volume fraction, diffusion coefficient and alveolar diameter, within a weak field approximation. The model relaxation rate exhibits the same hyperbolic tangent dependency as seen in the Luz-Meiboom model and limiting cases agree with Brooks et al. and Jensen et al. In addition, the model is tested against experimental data for passively deflated rat lungs: the resulting mean alveolar radius of RA = 31.46 ± 13.15 µm is very close to the literature value (∼34 µm). Also, modeled radii obtained from relaxometer measurements of ageing hydrogel foam (that mimics peripheral lung tissue) are in good agreement with those obtained from µCT images of the same foam (mean relative error: 0.06 ± 0.01). The model's ability to determine the alveolar radius and/or air volume fraction will be useful in quantifying peripheral lung microstructure.

Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions.

The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros [Formula: see text] and [Formula: see text] are considered in the complex plane for real as well as complex values of the index [Formula: see text] and approximations for the exceptional zero [Formula: see text] are obtained. A numerical scheme based on the discretization of the two-dimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.

Diffusion-mediated dephasing in the dipole field around a single spherical magnetic object.

In this work, the time evolution of the free induction decay caused by the local dipole field of a spherical magnetic perturber is analyzed. The complicated treatment of the diffusion process is replaced by the strong-collision-approximation that allows a determination of the free induction decay in dependence of the underlying microscopic tissue parameters such as diffusion coefficient, sphere radius and susceptibility difference. The interplay between susceptibility- and diffusion-mediated effects yields several dephasing regimes of which, so far, only the classical regimes of motional narrowing and static dephasing for dominant and negligible diffusion, respectively, were extensively examined. Due to the asymmetric form of the dipole field for spherical objects, the free induction decay exhibits a complex component in contradiction to the cylindrical case, where the symmetric local dipole field only causes a purely real induction decay. Knowledge of the shape of the corresponding frequency distribution is necessary for the evaluation of more sophisticated pulse sequences and a detailed understanding of the off-resonance distribution allows improved quantification of transverse relaxation.