How accurately can the diffusion profiles indicate multiple fiber orientations? A study on general fiber crossings in diffusion MRI

The q-space imaging techniques and high angular resolution diffusion (HARD) imaging have shown promise to identify intravoxel multiple fibers. The measured orientation distribution function (ODF) and apparent diffusion coefficient (ADC) profiles can be used to identify the orientations of the actual intravoxel fibers. The present study aims to examine the accuracy of these profile-based orientation methods by comparing the angular deviations between the estimated local maxima of the profiles and the real fiber orientation for a fiber crossing simulated with various intersection angles under different b values in diffusion-weighted MRI experiments. Both noisy and noise-free environments were investigated. The diffusion spectrum imaging (DSI), q-ball imaging (QBI), and HARD techniques were used to generate ODF and ADC profiles. To provide a better comparison between ODF and ADC techniques, the phase-corrected angular deviations were also presented for the ADC method based on a circular spectrum mapping method. The results indicate that systematic angular deviations exist between the actual fiber orientations and the corresponding local maxima of either the ADC or ODF profiles. All methods are apt to underestimation of acute intersection and overestimation of obtuse intersection angle. For a typical slow-exchange fiber crossing, the ODF methods have a non-deviation zone around the 90 degrees intersection. Before the phase-correction, the deviation of ADC profiles approaches a peak at the 90 degrees intersection, while after the correction the ADC deviations are significantly reduced. When the b factor is larger than 1000 s/mm2, the ODF methods have smaller angular deviations than the ADC methods for the intersections close to 90 degrees . QBI method demonstrates a slight yet consistent advantage over the DSI method under the same conditions. In the noisy environment, the mean value of the deviation angles shows a high consistency with the corresponding deviation in the nose-free condition.     

Anisotropic Phantoms for Quantitative Diffusion Tensor Imaging and Fiber-Tracking Validation

Different fiber materials (hemp, linen, viscose rayon, polyamide and dyneema twine) were tested for their suitability as fiber phantoms for diffusion tensor imaging (DTI) calibration on clinical magnetic resonance imaging systems with common diffusion-weighted echo planar imaging sequences. Additionally, the potential for fiber tracking validation of these fiber phantoms was investigated. For phantom manufacturing the fibers were wound up into a bundle of parallel fibers enwrapped by plastic ribbon. The most homogenously distributed fractional anisotropy (FA) values (0.63 ± 0.10) were determined in the dyneema and polyamide (0.3 ± 0.1) fiber phantom. FA values in the viscose, linen and hemp bundles were at high variations (about 0.2 ± 0.10). The dispersion of the direction of the principal eigenvector in the polyamide and dyneema phantom was less than 7°, for the other fiber phantoms it was over 30°. Thus, the presented results may indicate that polyamide- and dyneema-based fiber phantoms provide the opportunity for verification and validation of DTI sequences on clinical scanner. Additionally, they can be applicable for testing the accuracy of fiber tracking algorithms. A strong parallel alignment of the fibers with a constant compression grade of the fiber bundles could be achieved by machine-made production. This could also provide highly reproducible diffusion properties within the anisotropic fiber phantoms. Authors' address: Kamil A. Il'yasov, Physics Department, Kazan State University, Kremlevskaya ulitsa 18, Kazan 420008, Russian Federation     

Diffusion tensor fiber tractography of the olfactory tract

Magnetic resonance diffusion tensor imaging with fiber tracking is used for 3-dimensional visualization of the nervous system. Peripheral nerves and all cranial nerves, except for the olfactory tract, have previously been visualized. The olfactory tracts are difficult to depict with diffusion-weighted imaging due to the high sensitivity to susceptibility artifacts at the base of the skull. Here we report an optimized single-shot diffusion-weighted echo planar imaging sequence that can visualize the olfactory tracts with fiber tracking. Five healthy individuals were examined, and the olfactory tracts could be fiber tracked with the diffusion-weighted sequence. For comparison and as a negative control, an anosmic patient was examined. No olfactory tracts were visualized on T2-weighted nor diffusion-weighted fiber tracking images. Measuring diffusion in the olfactory tracts promise to facilitate the identification of different hyposmic and anosmic conditions.     

Variational multiple-tensor fitting of fiber-ambiguous diffusion-weighted magnetic resonance imaging voxels

Partial volume effects are often experienced in diffusion-weighted MRI of biologic tissue. This is when the signal attenuation reflects a mixture of diffusion processes, originating from different tissue compartments, residing in the same voxel. Decomposing the mixture requires elaborated models that account for multiple compartments, yet the fitting problem for those models is usually ill posed. We suggest a novel approach for stabilizing the fitting problem of the multiple-tensors model by a variational framework that adds biologically oriented assumption of neighborhood alignments. The framework is designed to address fiber ambiguity caused by a number of neuronal fiber compartments residing in the same voxel. The method requires diffusion data acquired by common, clinically feasible MRI sequences, and is able to derive familiar tensor quantities for each compartment. Neighborhood alignment is performed by adding piece-wise smooth regularization constraints to an energy function. Minimization with the gradient descent method produces a set of diffusion-reaction partial differential equations that describe a tensor-preserving flow towards a best approximation of the data while maintaining the constraints. We analyze fiber compartment separation capabilities on a synthetic model of crossing fibers and on brain areas known to have crossing fibers. We compare the results with diffusion tensor imaging analysis and discuss applications for the framework.     

Simulation and experimental verification of the diffusion in an anisotropic fiber phantom

Diffusion weighted magnetic resonance imaging enables the visualization of fibrous tissues such as brain white matter. The validation of this non-invasive technique requires phantoms with a well-known structure and diffusion behavior. This paper presents anisotropic diffusion phantoms consisting of parallel fibers. The diffusion properties of the fiber phantoms are measured using diffusion weighted magnetic resonance imaging and bulk NMR measurements. To enable quantitative evaluation of the measurements, the diffusion in the interstitial space between fibers is modeled using Monte Carlo simulations of random walkers. The time-dependent apparent diffusion coefficient and kurtosis, quantifying the deviation from a Gaussian diffusion profile, are simulated in 3D geometries of parallel fibers with varying packing geometries and packing densities. The simulated diffusion coefficients are compared to the theory of diffusion in porous media, showing a good agreement. Based on the correspondence between simulations and experimental measurements, the fiber phantoms are shown to be useful for the quantitative validation of diffusion imaging on clinical MRI-scanners.     

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.     

Evaluation of diffusion models of fiber tracts using diffusion tensor magnetic resonance imaging

Modeling of water diffusion in white matter is useful for revealing microstructure of the brain tissue and hence diagnosis and evaluation of white matter diseases. Researchers have modeled diffusion in white matter using mathematical and mechanical analysis at the cellular level. However, less work has been devoted to evaluate these models using macroscopic real data such as diffusion tensor magnetic resonance imaging (DTMRI) data. DTMRI is a noninvasive tool for evaluating white matter microstructure by measuring random motion of water molecules referred to as diffusion. It reflects directional information of microscopic structures such as fibers. Thus, it is applicable for evaluation and modification of mathematical models of white matter. Nevertheless, a realistic relation between a fiber model and imaging data does not exist. This work opens a promising avenue for relating DTMRI data to microstructural parameters of white matter. First, we propose a strategy for relating DTMRI and fiber model parameters to evaluate mathematical models in light of real data. The proposed strategy is then applied to evaluate and extend an existing model of white matter based on clinically available DTMRI data. Next, the proposed strategy is used to estimate microstructural characteristics of fiber tracts. We illustrate this approach through its application to approximation of myelin sheath thickness and fraction of volume occupied by fibers. Using sufficiently small imaging voxels, the proposed approach is capable of estimating model parameters with desirable precision.     

On the effects of dephasing due to local gradients in diffusion tensor imaging experiments: relevance for diffusion tensor imaging fiber phantoms

The effect of susceptibility differences between fluid and fibers on the properties of DTI fiber phantoms was investigated. Thereto, machine-made, easily producible and inexpensive DTI fiber phantoms were constructed by winding polyamide fibers of 15 microm diameter around a circular acrylic glass spindle. The achieved fractional anisotropy was 0.78+/-0.02. It is shown by phantom measurements and Monte Carlo simulations that the transversal relaxation time T(2) strongly depends on the angle between the fibers and the B(0) field if the susceptibilities of the fibers and fluid are not identical. In the phantoms, the measured T(2) time at 3 T decreased by 60% for fibers running perpendicular to B(0). Monte Carlo simulations confirmed this result and revealed that the exact relaxation time depends strongly on the exact packing of the fibers. In the phantoms, the measured diffusion was independent of fiber orientation. Monte Carlo simulations revealed that the measured diffusion strongly depends on the exact fiber packing and that field strength and -orientation dependencies of measured diffusion may be minimal for hexagonal packing while the diffusion can be underestimated by more than 50% for cubic packing at 3 T. To overcome these effects, the susceptibilities of fibers and fluid were matched using an aqueous sodium chloride solution (83 g NaCl per kilogram of water). This enables an orientation independent and reliable use of DTI phantoms for evaluation purposes.     

Globally optimized fiber tracking and hierarchical clustering -- a unified framework

Structural connectivity between cortical regions of the human brain can be characterized noninvasively with diffusion tensor imaging (DTI)-based fiber tractography. In this paper, a novel fiber tractography technique, globally optimized fiber tracking and hierarchical fiber clustering, is presented. The proposed technique uses k-means clustering in conjunction with modified Hubert statistic to partition fiber pathways, which are evaluated with simultaneous consideration of consistency with underlying DTI data and smoothness of fiber courses in the sense of global optimality, into individual anatomically coherent fiber bundles. In each resulting bundle, fibers are sampled, perturbed and clustered iteratively to approach the optimal solution. The global optimality allows the proposed technique to resist local image artifacts and to possess inherent capabilities of handling complex fiber structures and tracking fibers between gray matter regions. The embedded hierarchical clustering allows multiple fiber bundles between a pair of seed regions to be naturally reconstructed and partitioned. The integration of globally optimized tracking and hierarchical clustering greatly benefits applications of DTI-based fiber tractography to clinical studies, particularly to studies of structure-function relations of the complex neural network of the human. Experiments with synthetic and in vivo human DTI data have demonstrated the effectiveness of the proposed technique in tracking complex fiber structures, thus proving its significant advantages over traditionally used streamline fiber tractography.     

Regularization of bending and crossing white matter fibers in MRI Q-ball fields

In diffusion magnetic resonance imaging with high-angular-resolution diffusion imaging, a set of techniques has become available that allows better acquisition and representation of multidirectional diffusion profiles, e.g., in voxels with crossing, branching and kissing fibers. The poor spatial resolution and low signal-to-noise ratio of the data, particularly when acquired under clinical conditions, prevent tractography algorithms from reliably reconstructing complex white matter structures. With cone-beam regularization, an intervoxel smoothing approach has been described, which, in this article, is refined and adapted to fibers with subvoxel bending. By introducing the concept of asymmetric orientation distribution functions (aODFs), we are able to sharpen diffusion profiles of bending fibers and estimate subvoxel curvature. We also propose a deterministic fiber-tracking algorithm that exploits the enhanced resolution of aODFs. The approach is evaluated quantitatively and compared with state-of-the-art noise-suppression techniques in a study with a biological diffusion phantom. Moreover, we present results from an in vivo study in which we demonstrate the method's ability to optimize tractography of bending fiber pathways of optic radiation.     

Manifestation and post hoc correction of gradient cross-term artifacts in DTI

Cross-terms between imaging and diffusion gradients, unaccounted for during tensor calculations, can lead to erroneous estimation of diffusivity and fractional anisotropy (FA) in regions of isotropic and anisotropic diffusion. Cross-term of magnitude 136.8±1.6 s/mm(2), artificially introduced in the slice-encode direction, caused an increase in FA in isotropic phantom from 0.0546±0.0001 to 0.0996±0.0001, while the change in chimpanzee brain depended on the orientation of the white matter (WM). Mean diffusivity (MD) remained unchanged in isotropic phantom, but increased by ～20% in the WM due to cross-terms. A bias was observed in the principal eigenvectors in both phantom and chimpanzee brain, resulting in significant increase in midline crossing fibers along the bias than perpendicular to it in tractography in chimpanzee brain. Post hoc correction of these artifacts was achieved by estimating the cross-term factors using calibration scans on an isotropic phantom and modifying the b-matrix before tensor calculation. Upon correction, the FA and MD values closely resembled the values obtained from sequence without cross-terms, and the bias in principal eigenvectors was eliminated. Customized sequences involving large b-values, high-resolution imaging, or long diffusion or echo times should therefore be evaluated and any residual cross-terms corrected before implementation.     

Intermolecular double quantum coherences (iDQc) and diffusion-weighted imaging (DWI) imaging of the human brain at 1.5 T

To study the sensitivity of intermolecular double quantum coherences (iDQc) imaging contrast to brain microstructure and brain anisotropy, we investigated the iDQC contrast between differently structured areas of the brain according to the strength and the direction of the applied correlation gradient. Thus diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) maps have been obtained. This procedure, which consists of analyzing both iDQc and DWI images at different gradient strength and gradient direction, could be a promising tool for clinical brain investigations performed with higher than 1.5 T magnetic fields.     

Transfer characteristics of arterial pulsatile force in regional intracranial tissue using dynamic diffusion MRI: A phantom study

Introduction

To clarify the mechanism underlying apparent diffusion coefficient (ADC) changes in regional intracranial tissue during the cardiac cycle, we investigated relationships among ADC changes, volume loading, and intracranial pressure using a hemodialyzer phantom in magnetic resonance imaging (MRI).

Materials and Methods

The hemodialyzer phantom consisted of hollow fibers (HF), the external space of HFs (ES), and a gateway of dialysis solution, filled with syrup solution and air. The high-volume and low-volume loadings were periodically applied to HFs by a to-and-fro flow pump, and syrup solution was permitted to enter or leave HFs during the volume loading cycles. ADC maps at each volume loading phase were obtained using ECG-triggered single-shot diffusion echo-planar imaging. Dynamic phase contrast MRI was also used to measure volume loading to the phantom. We compared the ADC changes, volume loading, and intracranial pressure in the phantom during the cardiac cycle.

Results

ADC changes synchronized significantly with absolute volumetric flow rate change. The maximum ADC change was higher in high-volume loading cycles than in low-volume loading cycles. Results showed that the water molecules in ES fluctuated according to the force transferred from HF to ES. ADC changes were dependent upon the volumetric flow rate during the cardiac cycle.

Conclusions

Our original phantom allowed us to clarify the mechanism underlying water fluctuations in intracranial tissues. Measurement of maximum changes in ADC is an effective method to define the transfer characteristics of the arterial pulsatile force in regional intracranial tissue.     

Repeatability of echo-planar-based diffusion measurements of the human prostate at 3 T

Echo-planar-based diffusion-weighted imaging (DWI) of the prostate is increasingly being suggested as a viable technique, complementing information derived from conventional magnetic resonance imaging methods for use in tissue discrimination. DWI has also been suggested as a potentially useful tool in the assessment of tumor response to treatment. In this study, the repeatability of apparent diffusion coefficient (ADC) values obtained from both DWI and diffusion tensor imaging (DTI) has been assessed as a precursor to determining the magnitude of treatment-induced changes required for reliable detection. The repeatability values of DWI and DTI were found to be similar, with ADC values repeatable to within 35% or less over a short time period of a few minutes and a longer time period of a month. Fractional anisotropy measurements were found to be less repeatable (between 26% and 71%), and any changes duly recorded in longitudinal studies must therefore be treated with a degree of caution.     

Measurement of diffusion coefficients using a quick echo split NMR imaging technique

A new method for the ultrafast generation of diffusion-weighted images is reported. The technique combines a quick echo split NMR imaging sequence with the principle of Stejskal and Tanner. It allows to determine the diffusion constant with nearly the same accuracy as the conventional spin-echo technique, requiring only a fraction of the time. The determined values for water doped with 1 g Cu(NO₃)₂ per liter of H₂O and pure acetone were D_water = (1.95 ± 0.02) × 10⁻⁹ m²/s and D_acetone = (4.05 ± 0.02) × 10⁻⁹ m²/s at 18.5°C. They are in good agreement both with literature and our own reference measurements using a diffusion-weighted spin-echo sequence. In addition, the temperature dependence of D_water was measured in the range of 18.5–45.9°C and a good correspondence with reported data was found.     

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.     

Earlier detection of tumor treatment response using magnetic resonance diffusion imaging with oscillating gradients

An improved method for detecting early changes in tumors in response to treatment, based on a modification of diffusion-weighted magnetic resonance imaging, has been demonstrated in an animal model. Early detection of therapeutic response in tumors is important both clinically and in pre-clinical assessments of novel treatments. Noninvasive imaging methods that can detect and assess tumor response early in the course of treatment, and before frank changes in tumor morphology are evident, are of considerable interest as potential biomarkers of treatment efficacy. Diffusion-weighted magnetic resonance imaging is sensitive to changes in water diffusion rates in tissues that result from structural variations in the local cellular environment, but conventional methods mainly reflect changes in tissue cellularity and do not convey information specific to microstructural variations at sub-cellular scales. We implemented a modified imaging technique using oscillating gradients of the magnetic field for evaluating water diffusion rates over very short spatial scales that are more specific for detecting changes in intracellular structure that may precede changes in cellularity. Results from a study of orthotopic 9L gliomas in rat brains indicate that this method can detect changes as early as 24 h following treatment with 1,3-bis(2-chloroethyl)-1-nitrosourea, when conventional approaches do not find significant effects. These studies suggest that diffusion imaging using oscillating gradients may be used to obtain an earlier indication of treatment efficacy than previous magnetic resonance imaging methods.     

Quantitative characterization of tissue microstructure with temporal diffusion spectroscopy

The signals recorded by diffusion-weighted magnetic resonance imaging (DWI) are dependent on the micro-structural properties of biological tissues, so it is possible to obtain quantitative structural information non-invasively from such measurements. Oscillating gradient spin echo (OGSE) methods have the ability to probe the behavior of water diffusion over different time scales and the potential to detect variations in intracellular structure. To assist in the interpretation of OGSE data, analytical expressions have been derived for diffusion-weighted signals with OGSE methods for restricted diffusion in some typical structures, including parallel planes, cylinders and spheres, using the theory of temporal diffusion spectroscopy. These analytical predictions have been confirmed with computer simulations. These expressions suggest how OGSE signals from biological tissues should be analyzed to characterize tissue microstructure, including how to estimate cell nuclear sizes. This approach provides a model to interpret diffusion data obtained from OGSE measurements that can be used for applications such as monitoring tumor response to treatment in vivo.     

Complimentary aspects of diffusion imaging and fMRI: II. Elucidating contributions to the fMRI signal with diffusion sensitization

Tissue water molecules reside in different biophysical compartments. For example, water molecules in the vasculature reside for variable periods of time within arteries, arterioles, capillaries, venuoles and veins, and may be within blood cells or blood plasma. Water molecules outside of the vasculature, in the extravascular space, reside, for a time, either within cells or within the interstitial space between cells. Within these different compartments, different types of microscopic motion that water molecules may experience have been identified and discussed. These range from Brownian diffusion to more coherent flow over the time scales relevant to functional magnetic resonance imaging (fMRI) experiments, on the order of several 10s of milliseconds. How these different types of motion are reflected in magnetic resonance imaging (MRI) methods developed for "diffusion" imaging studies has been an ongoing and active area of research. Here we briefly review the ideas that have developed regarding these motions within the context of modern "diffusion" imaging techniques and, in particular, how they have been accessed in attempts to further our understanding of the various contributions to the fMRI signal changes sought in studies of human brain activation.     

A quantitative comparison of two methods to correct eddy current-induced distortions in DT-MRI

Eddy current-induced geometric distortions of single-shot, diffusion-weighted, echo-planar (DW-EP) images are a major confounding factor to the accurate determination of water diffusion parameters in diffusion tensor MRI (DT-MRI). Previously, it has been suggested that these geometric distortions can be removed from brain DW-EP images using affine transformations determined from phantom calibration experiments using iterative cross-correlation (ICC). Since this approach was first described, a number of image-based registration methods have become available that can also correct eddy current-induced distortions in DW-EP images. However, as yet no study has investigated whether separate eddy current calibration or image-based registration provides the most accurate way of removing these artefacts from DT-MRI data. Here we compare how ICC phantom calibration and affine FLIRT (http://www.fmrib.ox.ac.uk), a popular image-based multi-modal registration method that can correct both eddy current-induced distortions and bulk subject motion, perform when registering DW-EP images acquired with different slice thicknesses (2.8 and 5 mm) and b-values (1000 and 3000 s/mm(2)). With the use of consistency testing, it was found that ICC was a more robust algorithm for correcting eddy current-induced distortions than affine FLIRT, especially at high b-value and small slice thickness. In addition, principal component analysis demonstrated that the combination of ICC phantom calibration (to remove eddy current-induced distortions) with rigid body FLIRT (to remove bulk subject motion) provided a more accurate registration of DT-MRI data than that achieved by affine FLIRT.