Jan Sijbers

Investigating the Prevalence of Complex Fiber Configurations in White Matter Tissue with Diffusion Magnetic Resonance Imaging

It has long been recognized that the diffusion tensor model is inappropriate to characterize complex fiber architecture, causing tensor‐derived measures such as the primary eigenvector and fractional anisotropy to be unreliable or misleading in these regions. There is however still debate about the impact of this problem in practice. A recent study using a Bayesian automatic relevance detection (ARD) multicompartment model suggested that a third of white matter (WM) voxels contain crossing fibers, a value that, whilst already significant, is likely to be an underestimate. The aim of this study is to provide more robust estimates of the proportion of affected voxels, the number of fiber orientations within each WM voxel, and the impact on tensor‐derived analyses, using large, high‐quality diffusion‐weighted data sets, with reconstruction parameters optimized specifically for this task. Two reconstruction algorithms were used: constrained spherical deconvolution (CSD), and the ARD method used in the previous study. We estimate the proportion of WM voxels containing crossing fibers to be ∼90% (using CSD) and 63% (using ARD). Both these values are much higher than previously reported, strongly suggesting that the diffusion tensor model is inadequate in the vast majority of WM regions. This has serious implications for downstream processing applications that depend on this model, particularly tractography, and the interpretation of anisotropy and radial/axial diffusivity measures. Hum Brain Mapp 34:2747–2766, 2013.

Maximum-likelihood estimation of Rician distribution parameters

The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximum-likelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signal-to-noise ratio (SNR) and to yield physical relevant results for low SNR.

Probabilistic fiber tracking using the residual bootstrap with constrained spherical deconvolution.

Constrained spherical deconvolution (CSD) is a new technique that, based on high‐angular resolution diffusion imaging (HARDI) MR data, estimates the orientation of multiple intravoxel fiber populations within regions of complex white matter architecture, thereby overcoming the limitations of the widely used diffusion tensor imaging (DTI) technique. One of its main applications is fiber tractography. The noisy nature of diffusion‐weighted (DW) images, however, affects the estimated orientations and the resulting fiber trajectories will be subject to uncertainty. The impact of noise can be large, especially for HARDI measurements, which employ relatively high b‐values. To quantify the effects of noise on fiber trajectories, probabilistic tractography was introduced, which considers multiple possible pathways emanating from one seed point, taking into account the uncertainty of local fiber orientations. In this work, a probabilistic tractography algorithm is presented based on CSD and the residual bootstrap. CSD, which provides accurate and precise estimates of multiple fiber orientations, is used to extract the local fiber orientations. The residual bootstrap is used to estimate fiber tract probability within a clinical time frame, without prior assumptions about the form of uncertainty in the data. By means of Monte Carlo simulations, the performance of the CSD fiber pathway uncertainty estimator is measured in terms of accuracy and precision. In addition, the performance of the proposed method is compared to state‐of‐the‐art DTI residual bootstrap tractography and to an existing probabilistic CSD tractography algorithm using clinical DW data. Hum Brain Mapp, 2011.

Estimation of the Noise in Magnitude MR Images

Magnitude magnetic resonance data are Rician distributed. In this note a new method is proposed to estimate the image noise variance for this type of data distribution. The method is based on a double image acquisition, thereby exploiting the knowledge of the Rice distribution moments.

Maximum Likelihood Estimation of Signal Amplitude and Noise Variance From MR Data

In MRI, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian‐distributed noise. After applying an inverse Fourier transform, the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets. This article addresses the question whether it is better to use complex valued data or magnitude data for the estimation of these parameters using the maximum likelihood method. As a performance criterion, the mean‐squared error (MSE) is used. Magn Reson Med 51:586–594, 2004.

3D imaging of nanomaterials by discrete tomography

The field of discrete tomography focuses on the reconstruction of samples that consist of only a few different materials. Ideally, a three-dimensional (3D) reconstruction of such a sample should contain only one grey level for each of the compositions in the sample. By exploiting this property in the reconstruction algorithm, either the quality of the reconstruction can be improved significantly, or the number of required projection images can be reduced. The discrete reconstruction typically contains fewer artifacts and does not have to be segmented, as it already contains one grey level for each composition. Recently, a new algorithm, called discrete algebraic reconstruction technique (DART), has been proposed that can be used effectively on experimental electron tomography datasets. In this paper, we propose discrete tomography as a general reconstruction method for electron tomography in materials science. We describe the basic principles of DART and show that it can be applied successfully to three different types of samples, consisting of embedded ErSi(2) nanocrystals, a carbon nanotube grown from a catalyst particle and a single gold nanoparticle, respectively.

Gliomas: Diffusion Kurtosis MR Imaging in Grading

PURPOSE To assess the diagnostic accuracy of diffusion kurtosis magnetic resonance imaging parameters in grading gliomas. MATERIALS AND METHODS The institutional review board approved this prospective study, and informed consent was obtained from all patients. Diffusion parameters-mean diffusivity (MD), fractional anisotropy (FA), mean kurtosis, and radial and axial kurtosis-were compared in the solid parts of 17 high-grade gliomas and 11 low-grade gliomas (P<.05 significance level, Mann-Whitney-Wilcoxon test, Bonferroni correction). MD, FA, mean kurtosis, radial kurtosis, and axial kurtosis in solid tumors were also normalized to the corresponding values in contralateral normal-appearing white matter (NAWM) and the contralateral posterior limb of the internal capsule (PLIC) after age correction and were compared among tumor grades. RESULTS Mean, radial, and axial kurtosis were significantly higher in high-grade gliomas than in low-grade gliomas (P = .02, P = .015, and P = .01, respectively). FA and MD did not significantly differ between glioma grades. All values, except for axial kurtosis, that were normalized to the values in the contralateral NAWM were significantly different between high-grade and low-grade gliomas (mean kurtosis, P = .02; radial kurtosis, P = .03; FA, P = .025; and MD, P = .03). When values were normalized to those in the contralateral PLIC, none of the considered parameters showed significant differences between high-grade and low-grade gliomas. The highest sensitivity and specificity for discriminating between high-grade and low-grade gliomas were found for mean kurtosis (71% and 82%, respectively) and mean kurtosis normalized to the value in the contralateral NAWM (100% and 73%, respectively). Optimal thresholds for mean kurtosis and mean kurtosis normalized to the value in the contralateral NAWM for differentiating high-grade from low-grade gliomas were 0.52 and 0.51, respectively. CONCLUSION There were significant differences in kurtosis parameters between high-grade and low-grade gliomas; hence, better separation was achieved with these parameters than with conventional diffusion imaging parameters.

DART: A Practical Reconstruction Algorithm for Discrete Tomography

In this paper, we present an iterative reconstruction algorithm for discrete tomography, called discrete algebraic reconstruction technique (DART). DART can be applied if the scanned object is known to consist of only a few different compositions, each corresponding to a constant gray value in the reconstruction. Prior knowledge of the gray values for each of the compositions is exploited to steer the current reconstruction towards a reconstruction that contains only these gray values. Based on experiments with both simulated CT data and experimental μCT data, it is shown that DART is capable of computing more accurate reconstructions from a small number of projection images, or from a small angular range, than alternative methods. It is also shown that DART can deal effectively with noisy projection data and that the algorithm is robust with respect to errors in the estimation of the gray values.

Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs)

Iterative reconstruction algorithms are becoming increasingly important in electron tomography of biological samples. These algorithms, however, impose major computational demands. Parallelization must be employed to maintain acceptable running times. Graphics Processing Units (GPUs) have been demonstrated to be highly cost-effective for carrying out these computations with a high degree of parallelism. In a recent paper by Xu et al. (2010), a GPU implementation strategy was presented that obtains a speedup of an order of magnitude over a previously proposed GPU-based electron tomography implementation. In this technical note, we demonstrate that by making alternative design decisions in the GPU implementation, an additional speedup can be obtained, again of an order of magnitude. By carefully considering memory access locality when dividing the workload among blocks of threads, the GPUs cache is used more efficiently, making more effective use of the available memory bandwidth.

Watershed-based segmentation of 3D MR data for volume quantization

The aim of this work is the development of a semiautomatic segmentation technique for efficient and accurate volume quantization of Magnetic Resonance (MR) data. The proposed technique uses a 3D variant of Vincent and Soilles immersion-based watershed algorithm that is applied to the gradient magnitude of the MR data and that produces small volume primitives. The known drawback of the watershed algorithm, oversegmentation, is strongly reduced by a priori application of a 3D adaptive anisotropic diffusion filter to the MR data. Furthermore, oversegmentation is a posteriori reduced by properly merging small volume primitives that have similar gray level distributions. The outcome of the proceeding image processing steps is presented to the user for manual segmentation. Through selection of volume primitives, the user quickly segments of first slice, which contains the object of interest. Afterwards, the subsequent slices are automatically segmented by extrapolation. Segmentation results are contingently manually corrected. The proposed segmentation technique is tested on phantom objects, where segmentation errors less than 2% are observed. In addition, the technique is demonstrated on 3D MR data of the mouse head from which the cerebellum is extracted. Volumes of the mouse cerebellum and the mouse brains in toto are calculated.