Error bounds in diffusion tensor estimation using multiple-coil acquisition systems

We extend the diffusion tensor (DT) signal model for multiple-coil acquisition systems. Considering the sum-of-squares reconstruction method, we compute the Cramér–Rao bound (CRB) assuming the widely accepted noncentral chi distribution. Within this framework, we assess the effect of noise in DT estimation and other measures derived from it, as a function of the number of acquisition coils, as well as other system parameters. We show the applications of CRB in many actual problems related to DT estimation: we compare different gradient field setup schemes proposed in the literature and show how the CRB can be used to choose a convenient one; we show that for fiber-type anisotropy tensors the ellipsoidal area ratio (EAR) can be estimated with less error than other scalar factors such as the fractional anisotropy (FA) or the relative anisotropy (RA), and that for this type of anisotropy tensors, increasing the number of coils is equivalent to increasing the signal-to-noise ratio, i.e., the information of the different coils can be regarded as independent. Also, we present results showing the CRB of several parameters for actual DT-MRI data. We conclude that the CRB is a valuable tool to optimal experiment design in DT-related studies.     

The effect of gradient sampling schemes on diffusion metrics derived from probabilistic analysis and tract-based spatial statistics

Purpose

The purpose was to systematically evaluate the effect of diffusion gradient encoding scheme on estimated fractional anisotropy (FA), mean diffusivity (MD) and the voxel-wise probability of identifying crossing fibers in the brain.

Materials and Methods

Eight healthy volunteers (mean age 26.5±1.3 years, 5 males, 3 females) were imaged using a Spin-Echo Echo-Planar-Imaging sequence acquired with two signal averages [number of signals averaged (NSA)], 127 diffusion directions, and b-values of 750 s/mm² and 1500 s/mm². The number of diffusion gradient directions (N_d) was reduced from the original value whilst maintaining a homogeneous gradient distribution enabling direct comparison of subsampled data sets with N_d=15, 28, 43, 84, 112 and 127. FA and MD maps were generated and analyzed using tract-based spatial statistics. Effect of N_d on estimated FA and MD was tested with voxel-wise statistics in 13 regions of interest. The number of voxels supporting two fiber populations (NV²) at different N_d values was estimated using Bayesian estimation of diffusion parameters.

Results

Low FA values decreased significantly with increasing N_d and with increasing NSA. MD was only marginally sensitive to N_d and NSA. NV₂ increased significantly with N_d but not with NSA. Thus, we conclude that accurate estimation of standard diffusion metrics FA and MD is mainly dependent on the signal-to-noise ratio (SNR), whereas the ability to differentiate multiple fiber populations requires a high diffusion sampling density.     

Localized high-resolution DTI of the human midbrain using single-shot EPI,parallel imaging,and outer-volume suppression at 7 T

Localized high-resolution diffusion tensor images (DTI) from the midbrain were obtained using reduced field-of-view (rFOV) methods combined with SENSE parallel imaging and single-shot echo planar (EPI) acquisitions at 7 T. This combination aimed to diminish sensitivities of DTI to motion, susceptibility variations, and EPI artifacts at ultra-high field. Outer-volume suppression (OVS) was applied in DTI acquisitions at 2- and 1-mm² resolutions, b = 1000 s/mm², and six diffusion directions, resulting in scans of 7- and 14-min durations. Mean apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values were measured in various fiber tract locations at the two resolutions and compared. Geometric distortion and signal-to-noise ratio (SNR) were additionally measured and compared for reduced-FOV and full-FOV DTI scans. Up to an eight-fold data reduction was achieved using DTI-OVS with SENSE at 1 mm², and geometric distortion was halved. The localization of fiber tracts was improved, enabling targeted FA and ADC measurements. Significant differences in diffusion properties were observed between resolutions for a number of regions suggesting that FA values are impacted by partial volume effects even at a 2-mm² resolution. The combined SENSE DTI-OVS approach allows large reductions in DTI data acquisition and provides improved quality for high-resolution diffusion studies of the human brain.     

Fitting of two-tensor models without ad hoc assumptions to detect crossing fibers using clinical DWI data

Analysis of crossing fibers is a challenging topic in recent diffusion-weighted imaging (DWI). Resolving crossing fibers is expected to bring major changes to present tractography results based on the standard tensor model. Model free approaches, like Q-ball or diffusion spectrum imaging, as well as multi-tensor models are used to unfold the different diffusion directions mixed in a voxel of DWI data. Due to its seeming simplicity, the two-tensor model (TTM) is applied frequently to provide two positive-definite tensors and the relative population fraction modeling two crossing fiber branches. However, problems with uniqueness and noise instability are apparent. To stabilize the fit, several of the 13 physical parameters are fixed ad hoc, before fitting the model to the data. Our analysis of the TTM aims at fitting procedures where ad hoc parameters are avoided. Revealing sources of instability, we show that the model's inherent ambiguity can be reduced to one scalar parameter which only influences the fraction and the eigenvalues of the TTM, whereas the diffusion directions are not affected. Based on this, two fitting strategies are proposed: the parsimonious strategy detects the main diffusion directions without extra parameter fixation, to determine the eigenvalues and the population fraction an empirically motivated condition must be added. The expensive strategy determines all 13 physical parameters of the TTM by a fit to DWIs alone; no additional assumption is necessary. Ill-posedness of the model in case of noisy data is cured by denoising of the data and by L-curve regularization combined with global minimization performing a least-squares fit of the full model. By model simulations and real data applications, we demonstrate the feasibility of our fitting strategies and achieve convincing results. Using clinically affordable diffusion acquisition paradigms (encoding numbers: 21, 2*15, 2*21) and b values (b = 500–1500 s/mm²), this methodology can place the TTM parameters involved in crossing fibers on a more empirical basis than fitting procedures with technical assumptions.     

Diffusion tensor parameters and principal eigenvector coherence: Relation to b-value intervals and field strength

Diffusion-weighted MRI images acquired at b-value greater than 1000 s mm^− 2 measure the diffusion of a restricted pool of water molecules. High b-value images are accompanied by a reduction in signal-to-noise ratio (SNR) due to the application of large diffusion gradients. By fitting the diffusion tensor model to data acquired at incremental b-value intervals, we determined the effect of SNR on tensor parameters in normal human brains, in vivo. In addition, we also investigated the impact of field strength on the diffusion tensor model. Data were acquired at 1.5 and 3 T, at b-values 0, 1000, 2000 and 3000 s mm^− 2 in twenty diffusion-sensitised directions. Fractional anisotropy (FA), mean diffusivity (MD) and principal eigenvector coherence (κ) were calculated from diffusion tensors fitted between datasets with b-values 0–1000, 0–2000, 0–3000, 1000–2000 and 2000–3000 s mm^− 2. Field strength and b-value effects on diffusion parameters were analysed in white and grey matter regions of interest. Decreases in FA, κ and MD were found with increasing b-value in white matter. Univariate analysis showed a significant increase in FA with increasing field strength in highly organised white matter. These results suggest there are significant differences in diffusion parameters at 1.5 and 3 T and that the optimal results, in terms of the highest values of FA in white matter, are obtained at 3 T with a maximum b = 1000 s mm^− 2.     

Changes in skeletal muscle diffusion parameters owing to intramyocellular lipid

IntroductionSeveral studies investigated the changes in diffusion of water molecules in skeletal muscle cells of lifestyle-related-disease patients who performed a hybrid training (HYBT) for six months. They reported that the apparent diffusion coefficient (ADC) and all diffusion eigenvalues (λ₁, λ₂, and λ₃) increased after the HYBT, owing to the enlargement of the intramyocellular diffusion space (intracellular space) caused by the muscular hypertrophy.We assumed that the HYBT promoted metabolism of the whole skeletal muscle including lipids, which reduced the amount of intramyocellular lipid (IMCL), and led to a secondary enlargement of the diffusion space in the skeletal muscle cells. However, the IMCL has to be a diffusion limiting factor in order to verify this hypothesis. Until now, there is no report on whether IMCL is a diffusion limiting factor for water molecules.The objective of this study was to examine whether the IMCL is a diffusion limiting factor in skeletal muscle cells.Materials and methodsWe performed a three-dimensional quantification of the IMCL in triceps surae muscles of lifestyle-related-disease patients and healthy volunteers. In addition, we measured the ADC in the volume of interest (VOI), diffusion anisotropy (FA), and diffusion eigenvalues (λ₁, λ₂, and λ₃), and evaluated the correlations between these diffusion parameters and IMCL.ResultsThe results showed that the amount of IMCL was positively and negatively correlated with the FA and λ₃, respectively, in lifestyle-related-disease patients. In addition, there was a weak negative correlation between IMCL and ADC, λ₁, and λ₂. There was no correlation between the amount of IMCL and diffusion parameters of healthy volunteers.DiscussionAbove a certain amount, the IMCL correlates with the diffusion parameters. A higher amount of IMCL leads to smaller diffusion eigenvalues. This result suggested that IMCL possibility of influencing diffusion of water molecules in skeletal muscle cells. However, in order for the influence of IMCL to be reflected in the diffusion eigenvalues, it was needed large amount of IMCL existed, and we thought that the influence was smaller than the influence by the already reported cell membrane.     

Toward an optimal distribution of b values for intravoxel incoherent motion imaging

The intravoxel incoherent motion (IVIM) theory provides a framework for the separation of perfusion and diffusion effects in diffusion-weighted imaging (DWI). To measure the three free IVIM parameters, DWIs with several diffusion weightings b must be acquired. To date, the used b value distributions are chosen heuristically and vary greatly among researchers. In this work, optimal b value distributions for the three parameter fit are determined using Monte-Carlo simulations for the measurement of a low, medium and high IVIM perfusion regime. The first 16 b values of a b value distribution, which was optimized to be appropriate for all three regimes, are {0, 40, 1000, 240, 10, 750, 90, 390, 170, 10, 620, 210, 100, 0, 530 and 970} in units of seconds per square meter. This distribution performed well for all organs and outperformed a distribution frequently used in the literature. In case of limited acquisition time, the b values should be chosen in the given order, but at least 10 b values should be used for current clinical settings. The overall parameter estimation quality depends strongly and nonlinearly on the signal-to-noise ratio (SNR): it is essential that the SNR is considerably higher than a critical SNR. This critical SNR is about 8 for medium and high IVIM perfusion and 50 for the low IVIM perfusion regime. Initial in vivo IVIM measurements were performed in the abdomen and were in keeping with the numerically simulated results.     

Advanced diffusion models in head and neck squamous cell carcinoma patients: Goodness of fit,relationships among diffusion parameters and comparison with dynamic contrast-enhanced perfusion

PurposeWe assessed advanced fitting models of diffusion weighted imaging (DWI) in head/neck squamous cell carcinoma (HNSCC) patients to determine the best goodness of fit and correlations among diffusion parameters. We compared these results with those of dynamic contrast-enhanced (DCE) perfusion parameters.Materials and methodsWe retrospectively evaluated 32 HNSCC patients (12 sinonasal, 20 pharynx/oral cavity). The DWI acquisition used single-shot spin-echo echo-planar imaging (EPI) with 12 b-values (0 − 2000). We calculated 14 DWI parameters using mono-exponential, bi-exponential, and tri-exponential models, stretched exponential model (SEM) and diffusion kurtosis imaging (DKI) models. We compared each model's goodness of fit using the residual sum of squares (RSS), Akaike Information Criterion (AIC) and Bayesian information criterion (BIC) value. We determined the correlation between each pair of DWI parameters and between each DWI parameter and DCE perfusion parameter.ResultsThe tri-exponential fit's RSS, AIC and BIC values were significantly smaller than those for bi-exponential fit. The RSS, AIC and BIC values of the SEM fit and DKI fit were significantly smaller than mono-exponential model. Significant correlations were observed in 30 pairs (sinonasal cavity) and 31 (sinonasal cavity group) among 91 DWI parameter combinations. Significant correlations were also observed in nine pairs (both sinonasal cavity and pharynx/oral cavity group) among 64 DWI/DCE perfusion parameter pairs, in particular, high positive correlations between the tri-exponential model's intermediate diffusion fraction (f₂) and the volume of the extracellular extravascular space per unit volume of tissue (v_e) were observed in both patient groups.ConclusionWe identified several correlations between DWI parameters by advanced fitting models and correlations between DWI and DCE parameters. These will help determine HNSCC patients' detailed tissue structures.     

Development and initial evaluation of 7-T q-ball imaging of the human brain

Diffusion tensor imaging (DTI) noninvasively depicts white matter connectivity in regions where the Gaussian model of diffusion is valid but yields inaccurate results in those where diffusion has a more complex distribution, such as fiber crossings. q-ball imaging (QBI) overcomes this limitation of DTI by more fully characterizing the angular dependence of intravoxel diffusion with larger numbers of diffusion-encoding directional measurements at higher diffusion-weighting factors (b values). However, the former technique results in longer acquisition times and the latter technique results in a lower signal-to-noise ratio (SNR). In this project, we developed specialized 7-T acquisition methods utilizing novel radiofrequency pulses, eight-channel parallel imaging EPI and high-order shimming with a phase-sensitive multichannel B0 field map reconstruction. These methods were applied in initial healthy adult volunteer studies, which demonstrated the feasibility of performing 7-T QBI. Preliminary comparisons of 3 T with 7 T within supratentorial crossing white matter tracts documented a 79.5% SNR increase for b=3000 s/mm2 (P=.0001) and a 38.6% SNR increase for b=6000 s/mm2 (P=.015). With spherical harmonic reconstruction of the q-ball orientation distribution function at b=3000 s/mm2, 7-T QBI allowed for accurate visualization of crossing fiber tracts with fewer diffusion-encoding acquisitions as compared with 3-T QBI. The improvement of 7-T QBI at b factors as high as 6000 s/mm2 resulted in better angular resolution as compared with 3-T QBI for depicting fibers crossing at shallow angles. Although the increased susceptibility effects at 7 T caused problematic distortions near brain-air interfaces at the skull base and posterior fossa, these initial 7-T QBI studies demonstrated excellent quality in much of the supratentorial brain, with significant improvements as compared with 3-T acquisitions in the same individuals.     

On the down-sampling of diffusion MRI data along the angular dimension

BackgroundIt has been established that the diffusion gradient directions in diffusion MRI should be uniformly distributed in 3D spherical space, so that orientation-dependent diffusion properties (e.g., fractional anisotropy or FA) can be properly quantified. Sometimes the acquired data need to be down-sampled along the angular dimension before computing diffusion properties (e.g., to exclude data points corrupted by motion artifact; to harmonize data obtained with different protocols). It is important to quantitatively assess the impact of data down-sampling on measurement of diffusion properties.Materials and methodsHere we report 1) a numerical procedure for down-sampling diffusion MRI (e.g., for data harmonization), and 2) a spatial uniformity index of diffusion directions, aiming to predict the quality of the chosen down-sampling schemes (e.g., from data harmonization; or rejection of motion corrupted data points). We quantitatively evaluated human diffusion MRI data, which were down-sampled from 64 or 60 diffusion gradient directions to 30 directions, in terms of their 1) FA value accuracy (using fully-sampled data as the ground truth), 2) FA fitting residuals, and 3) spatial uniformity indices.ResultsOur experimental data show that the proposed spatial uniformity index is correlated with errors in FA obtained from down-sampled diffusion MRI data. The FA fitting residuals that are typically used to assess diffusion MRI quality are not correlated with either FA errors or spatial uniformity index.ConclusionsThese results suggest that the spatial uniformity index could be more valuable in assessing quality of down-sampled diffusion MRI data, as compared with FA fitting residual measures. We expect that our implemented software procedure should prove valuable for 1) guiding data harmonization for multi-site diffusion MRI studies, and 2) assessing the impact of rejecting motion corrupted data points on the accuracy of diffusion measures.     

The correlation of fractional anisotropy parameters with Ki-67 index,and the clinical implication in grading of non-enhancing gliomas and neuronal-glial tumors

PurposeTo investigate the correlation between the FA parameters and Ki-67 labeling index, and their diagnostic performance in grading supratentorial non-enhancing gliomas and neuronal-glial tumors (GNGT).MethodsThis institutional review board-approved, Health Insurance Portability and Accountability (HIPAA) compliant retrospective study enrolled 35 patients, including 19 with low grade GNGT and 16 with high grade GNGT. The mean FA, maximal FA and mean maximal FA values derived from diffusion tensor imaging were measured. The correlation between the FA parameters and the Ki-67 labeling index was assessed by Spearman rank test. The receiver operating characteristic curve analysis and multivariate logistic regression analysis were performed to detect the optimal imaging parameters in grading GNGT.ResultsThe three FA parameters of low grade GNGT were significantly lower than the high grade GNGT (p < 0.001). The mean FA, maximal FA and mean maximal FA had significant positive correlation with Ki-67 labeling index (p = 0.001, p < 0.001, p < 0.001 respectively). The maximal FA showed a higher sensitivity and specificity in grading of non-enhancing GNGT with specificity of 78.9%, sensitivity of 100.0%, respectively.ConclusionsThe FA parameters correlated with Ki-67 labeling index, and were useful surrogates in preoperative grading supratentorial non-enhancing GNGT.     

In-vivo diffusion MRI protocol optimization for the chimpanzee brain and examination of aging effects on the primate optic nerve at 3T

BackgroundDiffusion MRI (dMRI) data acquisition protocols are well-established on modern high-field clinical scanners for human studies. However, these protocols are not suitable for the chimpanzee (or other large-brained mammals) because of its substantial difference in head geometry and brain volume compared with humans. Therefore, an optimal dMRI data acquisition protocol dedicated to chimpanzee neuroimaging is needed.MethodsA multi-shot (4 segments) double spin-echo echo-planar imaging (MS-EPI) sequence and a single-shot double spin-echo EPI (SS-EPI) sequence were optimized separately for in vivo dMRI data acquisition of chimpanzees using a clinical 3T scanner. Correction for severe susceptibility-induced image distortion and signal drop-off of the chimpanzee brain was performed and evaluated using FSL software. DTI indices in different brain regions and probabilistic tractography were compared. A separate DTI data set from n=34 chimpanzees (13 to 56 years old) was collected using the optimal protocol. Age-related changes in diffusivity indices of optic nerve fibers were evaluated.ResultsThe SS-EPI sequence acquired dMRI data of the chimpanzee brain with approximately doubled the SNR as the MS-EPI sequence given the same scan time. The quality of white matter fiber tracking from the SS-EPI data was much higher than that from MS-EPI data. However, quantitative analysis of DTI indices showed no difference in most ROIs between the SS-EPI and MS-EPI sequences. The progressive evolution of diffusivity indices of optic nerves indicated mild changes in fiber bundles of chimpanzees aged 40 years and above.ConclusionThe single-shot EPI-based acquisition protocol provided better image quality of dMRI for chimpanzee brains and is recommended for in vivo dMRI study or clinical diagnosis of chimpanzees (or other large animals) using a clinical scanner. Also, the tendency of FA decrease or diffusivity increase in the optic nerve of aged chimpanzees was seen but did not show significant age-related changes, suggesting aging may have less impact on optic nerve fiber integrity of chimpanzees, in contrast to previous results for both macaque monkeys and humans.     

Effects of interpolation methods in spatial normalization of diffusion tensor imaging data on group comparison of fractional anisotropy

This study investigated the effects on the measurement of fractional anisotropy (FA) during interpolation of diffusion tensor images in spatial normalization, which is required for voxel-based statistics. Diffusion tensor imaging data were obtained from nine male patients with attention deficit/hyperactivity disorder and nine age-matched control subjects. Regions of interest were selected from the genu of corpus callosum (GCC) and the right anterior corona radiata (RACR), with FA values measured before and after spatial normalization using two interpolation algorithms: linear and rotationally linear. Computer simulations were performed to verify the experimental findings. Between-group difference in FA was observed in the GCC and RACR before spatial normalization (P<.00001). Interpolation reduced the measured FA values significantly (P<.00001 for both algorithms) but did not affect the group difference in the GCC. For the RACR, the between-group difference vanished (P=.968) after linear interpolation but was relatively unaffected by using rotationally linear interpolation (P=.00001). FA histogram analysis and computer simulations confirmed these findings. This work suggests that caution should be exercised in voxel-based group comparisons as spatial normalization may affect the FA value in nonnegligible degrees, particularly in brain areas with predominantly crossing fibers.     

DTI at 7 and 3 T: systematic comparison of SNR and its influence on quantitative metrics

Diffusion tensor imaging (DTI) and advanced related methods such as diffusion spectrum and kurtosis imaging are limited by low signal-to-noise ratio (SNR) at conventional field strengths. DTI at 7 T can provide increased SNR; however, B0 and B1 inhomogeneity and shorter T2? still pose formidable challenges. The purpose of this study was to quantify and compare SNR at 7 and 3 T for different parallel imaging reduction factors, R, and TE, and to evaluate SNRs influences on fractional anisotropy (FA) and apparent diffusion coefficient (ADC). We found that R>4 at 7 T and R≥2 at 3 T were needed to reduce geometric distortions due to B0 inhomogeneity. For these R at 7 T, SNR was 70-90 for b=0 s/mm² and 22-28 for b=1000s/mm² in central brain regions. SNR was lower at 3 T (40 for b=0 s/mm² and 15 for b=1000 s/mm²) and in lateral brain regions at 7 T due to B1 inhomogeneity. FA and ADC did not change with MRI field strength, SENSE factor or TE in the tested range. However, the coefficient of variation for FA increased for SNR <15 and for SNR <10 in ADC, consistent with published theoretical studies. Our study demonstrates that 7 T is advantageous for DTI and lays the groundwork for further development. Foremost, future work should further address challenges with B0 and B1 inhomogeneity to take full advantage for the increased SNR at 7 T.     

Minimum SNR and acquisition for bias-free estimation of fractional anisotropy in diffusion tensor imaging - a comparison of two analytical techniques and field strengths

Although it is known that low signal-to-noise ratio (SNR) can affect tensor metrics, few studies reporting disease or treatment effects on fractional anisotropy (FA) report SNR; the implicit assumption is that SNR is adequate. However, the level at which low SNR causes bias in FA may vary with tissue FA, field strength and analytical methodology. We determined the SNR thresholds at 1.5 T vs. 3 T in regions of white matter (WM) with different FA and compared FA derived using manual region-of-interest (ROI) analysis to tract-based spatial statistics (TBSS), an operator-independent whole-brain analysis tool. Using ROI analysis, SNR thresholds on our hardware-software magnetic resonance platforms were 25 at 1.5 T and 20 at 3 T in the callosal genu (CG), 40 at 1.5 and 3 T in the anterior corona radiata (ACR), and 50 at 1.5 T and 70 at 3 T in the putamen (PUT). Using TBSS, SNR thresholds were 20 at 1.5 T and 3 T in the CG, and 35 at 1.5 T and 40 at 3 T in the ACR. Below these thresholds, the mean FA increased logarithmically, and the standard deviations widened. Achieving bias-free SNR in the PUT required at least nine acquisitions at 1.5 T and six acquisitions at 3 T. In the CG and ACR, bias-free SNR was achieved with at least three acquisitions at 1.5 T and one acquisition at 3 T. Using diffusion tensor imaging (DTI) to study regions of low FA, e.g., basal ganglia, cerebral cortex, and WM in the abnormal brain, SNR should be documented. SNR thresholds below which FA is biased varied with the analytical technique, inherent tissue FA and field strength. Studies using DTI to study WM injury should document that bias-free SNR has been achieved in the region of the brain being studied as part of quality control.     

White matter maturation in the brains of Long Evans shaker myelin mutant rats by ex-vivo QSI and DTI

The brains of Long Evans shaker (les) rats, a model of dysmyelination, and their age- matched controls were studied by ex-vivo q-space diffusion imaging (QSI) and diffusion tensor imaging (DTI). The QSI and DTI indices were computed from the same acquisition. The les and the control brains were studied at different stages of maturation and disease progression. The mean displacement, the probability for zero displacement and kurtosis were computed from QSI data while the fractional anisotropy (FA) and the eigenvalues were computed from DTI. It was found that all QSI indices detect the les pathology, at all stages of maturation, while only some of the DTI indices could detect the les pathology. The QSI mean displacement was larger in the les group as compared with their age-matched controls while the probability for zero displacement and the kurtosis were both lower all indicating higher degree of restriction in the control brains. Since all the DTI eigenvalues were higher in the les brains as compared to controls, the less efficient DTI measure for discerning the les pathology was found to be the FA. Clearly, the most sensitive DTI parameter to the les pathology is λ₃, i.e. the minimal diffusivity. Since the QSI and DTI data were obtained from the same acquisition, despite the somewhat higher SNR of the QSI data compared to the DTI data, it seems that the higher diagnostic capacity of the QSI data in this experimental model of dysmyelination, originates mainly from the higher diffusing weighting of the QSI data.     

水下宽带源方位估计的克拉美-罗界研究

推导了水下宽带源方位估计的克拉美-罗界(CRB)解析式。它揭示了宽带CRB的特点和影响方位估计性能的因素:(1)单源的宽带CRB可分为两部分:与阵列相关的部分包括阵列结构、目标方位及基阵参考点等因素;与信号相关的部分包括信号频率二阶矩及信噪比等。(2)相互独立的两个目标源,每个源的CRB与单源时相应目标源得到的结果相等。(3)两个相关源之间的夹角大于一个波束宽度时,每个源的CRB与单源结果也很接近。(4)由于信源数估计错误,单源误以为是双源,将使CRB值趋于无穷大。仿真结果验证了理论分析的正确性。因此,宽带CRB除给出宽带方位估计算法的最佳估计性能外,还能从方位估计的角度,为宽带阵列及信号波形设计等提供有益的指导。      

Empirical consideration of the effects of acquisition parameters and analysis model on clinically feasible q-ball imaging

Q-ball imaging (QBI) is a popular high angular resolution diffusion imaging (HARDI) technique used to study brain architecture in vivo. Simulation and phantom-based studies suggest that QBI results are affected by the b-value, the number of diffusion weighting directions, and the signal-to-noise ratio (SNR). However, optimal acquisition schemes for QBI in clinical settings are largely undetermined given empirical (observed) imaging considerations. In this study, we acquire a HARDI dataset at five b-values with 11 repetitions on a single subject to investigate the effects of acquisition scheme and subsequent analysis models on the accuracy and precision of measures of tissue composition and fiber orientation derived from clinically feasible QBI at 3 T. Clinical feasibility entails short scan protocols - less than 5 minutes in the current study - resulting in lower SNR, lower b-values, and fewer diffusion directions than are typical in most QBI protocols with research applications, where time constraints are less prevalent. In agreement with previous studies, we find that the b-value and number of diffusion directions impact the magnitude and variation of QBI indices in both white matter and gray matter regions; however, QBI indices are most heavily dependent on the maximum order of the spherical harmonic (SH) series used to represent the diffusion orientation distribution function (ODF). Specifically, to ensure numerical stability and reduce the occurrence of false peaks and inflated anisotropy, we recommend oversampling by at least 8–12 more diffusion directions than the number of estimated coefficients for a given SH order. In addition, in an equal scan time comparison of QBI accuracy, we find that increasing the directional resolution of the HARDI dataset is preferable to repeating observations; however, our results indicate that as few as 32 directions at a low b-value (1000 s/mm²) captures most of the angular information in the q-ball ODF. Our findings provide guidance for determining an optimal acquisition scheme for QBI in the low SNR and low scan time regime, and suggest that care must be taken when choosing the basis functions used to represent the QBI ODF.     

Improved performance of prostate DCE-MRI using a 32-coil vs. 12-coil receiver array

PurposeTo assess whether acquisition with 32 receiver coils rather than the vendor-recommended 12 coils provides significantly improved performance in 3D dynamic contrast-enhanced MRI (DCE-MRI) of the prostate.MaterialsThe study was approved by the institutional review board and was compliant with HIPAA. 50 consecutive male patients in whom prostate MRI was clinically indicated were prospectively imaged in March 2015 with an accelerated DCE-MRI sequence in which image reconstruction was performed using 12 and 32 coil elements. The two reconstructions were compared quantitatively and qualitatively. The first was done using signal-to-noise ratio (SNR) and g-factor analysis to assess sensitivity to acceleration. The second was done using a five-point scale by two experienced radiologists using criteria of perceived SNR, artifact, sharpness, and overall preference. Significance was assessed with the Wilcoxon signed rank test. Extension to T2-weighted spin-echo and diffusion sequences was assessed in phantom studies.ResultsReconstruction using 32 vs. 12 coil elements provided improved performance in DCE-MRI based on intrinsic SNR (18% higher) and g-factor statistics (14% higher), with a median 32% higher overall SNR within the prostate volume over all subjects. Reconstruction using 32 coils was qualitatively rated significantly improved (p < 0.001) vs. 12 coils on the basis of perceived SNR and radiologist preference and equivalent for sharpness and artifact. Phantom studies suggested the improvement in intrinsic SNR could extend to T2-weighted spin-echo and diffusion sequences.ConclusionsReconstruction of 3D accelerated DCE-MRI studies of the prostate using 32 independent receiver coils provides improved overall performance vs. using 12 coils.     

Rapid microscopic fractional anisotropy imaging via an optimized linear regression formulation

Water diffusion anisotropy in the human brain is affected by disease, trauma, and development. Microscopic fractional anisotropy (μFA) is a diffusion MRI (dMRI) metric that can quantify water diffusion anisotropy independent of neuron fiber orientation dispersion. However, there are several different techniques to estimate μFA and few have demonstrated full brain imaging capabilities within clinically viable scan times and resolutions. Here, we present an optimized spherical tensor encoding (STE) technique to acquire μFA directly from the 2nd order cumulant expansion of the powder averaged dMRI signal obtained from direct linear regression (i.e. diffusion kurtosis) which requires fewer powder-averaged signals than other STE fitting techniques and can be rapidly computed. We found that the optimal dMRI parameters for white matter μFA imaging were a maximum b-value of 2000 s/mm² and a ratio of STE to LTE tensor encoded acquisitions of 1.7 for our system specifications. We then compared two implementations of the direct regression approach to the well-established gamma model in 4 healthy volunteers on a 3 Tesla system. One implementation used mean diffusivity (D) obtained from a 2nd order fit of the cumulant expansion, while the other used a linear estimation of D from the low b-values. Both implementations of the direct regression approach showed strong linear correlations with the gamma model (ρ = 0.97 and ρ = 0.90) but mean biases of −0.11 and − 0.02 relative to the gamma model were also observed, respectively. All three μFA measurements showed good test-retest reliability (ρ ≥ 0.79 and bias = 0). To demonstrate the potential scan time advantage of the direct approach, 2 mm isotropic resolution μFA was demonstrated over a 10 cm slab using a subsampled data set with fewer powder-averaged signals that would correspond to a 3.3-min scan. Accordingly, our results introduce an optimization procedure that has enabled nearly full brain μFA in only several minutes.