Diffusion-direction-dependent imaging: a novel MRI approach for peripheral nerve imaging

A novel magnetic resonance imaging approach, called diffusion-direction-dependent imaging (DDI), is introduced. Due to inherent anisotropic diffusion properties, peripheral nerves can be visualized on diffusion tensor imaging (DTI). The largest signal attenuation on DTI correlates with the direction of a nerve fiber, and the least signal attenuation correlates with the direction perpendicular to the nerve fiber. Since low signal-to-noise ratio is a concern in peripheral nerve DTI, we explored a new approach focusing on the perpendicular diffusion direction. A 36-gradient diffusion direction scheme was used. A mean expected curve specific for peripheral nerves was calculated based on the sciatic nerve and its division into the common peroneal nerve and the tibial nerve in three healthy volunteers. By a simple postprocessing method, a comparison of the mean expected curve and the measured curve was made voxel by voxel, and the sciatic nerve and its division were reconstructed, excluding other tissues. More studies are needed to investigate whether other postprocessing methods or other diffusion direction schemes are more suited for peripheral nerve imaging with DDI. Further studies may also be of interest to investigate whether DDI can be a complementary method to conventional T(1)-weighted and T(2)-weighted sequences in the imaging of peripheral nerve pathology or even in the visualization of other tissues, possibly with different diffusion direction schemes.     

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.     

Brain tissue classification based on DTI using an improved Fuzzy C-means algorithm with spatial constraints

We present an effective method for brain tissue classification based on diffusion tensor imaging (DTI) data. The method accounts for two main DTI segmentation obstacles: random noise and magnetic field inhomogeneities. In the proposed method, DTI parametric maps were used to resolve intensity inhomogeneities of brain tissue segmentation because they could provide complementary information for tissues and define accurate tissue maps. An improved fuzzy c-means with spatial constraints proposal was used to enhance the noise and artifact robustness of DTI segmentation. Fuzzy c-means clustering with spatial constraints (FCM_S) could effectively segment images corrupted by noise, outliers, and other imaging artifacts. Its effectiveness contributes not only to the introduction of fuzziness for belongingness of each pixel but also to the exploitation of spatial contextual information. We proposed an improved FCM_S applied on DTI parametric maps, which explores the mean and covariance of the feature spatial information for automated segmentation of DTI. The experiments on synthetic images and real-world datasets showed that our proposed algorithms, especially with new spatial constraints, were more effective.     

Novel multisection design of anisotropic diffusion phantoms

Diffusion-weighted magnetic resonance imaging provides access to fiber pathways and structural integrity in fibrous tissues such as white matter in the brain. In order to enable better access to the sensitivity of the diffusion indices to the underlying microstructure, it is important to develop artificial model systems that exhibit a well-known structure, on the one hand, but benefit from a reduced complexity on the other hand. In this work, we developed a novel multisection diffusion phantom made of polyethylene fibers tightly wound on an acrylic support. The phantom exhibits three regions with different geometrical configuration of fibers: a region with fibers crossing at right angles, a region with parallel fibers and homogeneous density, and, finally, a region with parallel fibers but with a gradient of fiber density along the axis of symmetry. This gives rise to a gradual change of the degree of anisotropy within the same phantom. In this way, the need to construct several phantoms with different fiber densities is avoided, and one can access different fractional anisotropies in the same experiment under the same physical conditions. The properties of the developed phantom are demonstrated by means of diffusion tensor imaging and diffusion kurtosis imaging. The measurements were performed using a diffusion-weighted spin-echo and a diffusion-weighted stimulated-echo pulse sequence programmed in-house. The influence of the fiber density packing on the diffusion parameters was analyzed. We also demonstrate how the novel phantom can be used for the validation of high angular resolution diffusion imaging data analysis.     

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.     

Dependence of the fractional anisotropy in cervical spine from the number of diffusion gradients,repeated acquisition and voxel size

The aim of this study is to investigate the consequences of using different gradient schemes, number of repeated measurements and voxel size on the fractional anisotropy (FA) value in a diffusion tensor imaging (DTI) sequence on the cervical tract of the spinal cord. Twenty healthy volunteers underwent a total of 86 DTI axial acquisitions performed by using different voxel size and number of diffusion gradient directions (NDGDs). Three different diffusion gradient schemes were applied, named 6, 15 and 32 according to the NDGD. Furthermore, some acquisitions were repeated to investigate the effects of image averaging on FA value.     

Comparative analysis of single-channel direction finding algorithms for automotive applications at 2400 MHz in a complex reflecting environment

This paper presents an amplitude-based single-channel direction finding system for automotive applications and compares its performance against two different phase-based single-channel direction finding algorithms in a complex reflecting environment (parking garage) at 2400 MHz. All three direction finding algorithms utilize a multi-element receiving antenna array placed at two locations on a vehicle. The received complex electric fields at each antenna element within the receiving antenna array are used as inputs to the three direction finding algorithms, resulting in a direction of arrival estimate. The results from this research provide insightful information on the performance of various direction finding algorithms as a function of complex reflecting environment, transmitter height, receiving antenna array location, number of receiving antenna elements and pass rate acceptance criteria.     

Statistical physics of inference: thresholds and algorithms

Many questions of fundamental interest in today's science can be formulated as inference problems: some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. The connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which, formulated as an inference problem, we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic.     

A statistical framework for the classification of tensor morphologies in diffusion tensor images

Tractography algorithms for diffusion tensor (DT) images consecutively connect directions of maximal diffusion across neighboring DTs in order to reconstruct the 3-dimensional trajectories of white matter tracts in vivo in the human brain. The performance of these algorithms, however, is strongly influenced by the amount of noise in the images and by the presence of degenerate tensors-- i.e., tensors in which the direction of maximal diffusion is poorly defined. We propose a simple procedure for the classification of tensor morphologies that uses test statistics based on invariant measures of DTs, such as fractional anisotropy, while accounting for the effects of noise on tensor estimates. Examining DT images from seven human subjects, we demonstrate that this procedure validly classifies DTs at each voxel into standard types (nondegenerate DTs, as well as degenerate oblate, prolate or isotropic DTs), and we provide preliminary estimates for the prevalence and spatial distribution of degenerate tensors in these brains. We also show that the P values for test statistics are more sensitive tools for classifying tensor morphologies than are invariant measures of anisotropy alone.     

Angular smoothing and spatial diffusion from the Feynman path integral representation of radiative transfer

The propagation kernel for time dependent radiative transfer is represented by a Feynman path integral (FPI). The FPI is approximately evaluated in the spatial-Fourier domain. Spatial diffusion is exhibited in the kernel when the approximations lead to a Gaussian dependence on the Fourier domain wave vector. The approximations provide an explicit expression for the diffusion matrix. They also provide an asymptotic criterion for the self-consistency of the diffusion approximation. The criterion is weakly violated in the limit of large numbers of scattering lengths. Additional expansion of higher-order terms may resolve whether this weak violation is significant.     

Glaucoma classification based on visual pathway analysis using diffusion tensor imaging

Most of the existing methods for diagnosing glaucoma analyze the eye with a main focus on the retina, despite the transsynaptic nature of the fiber degeneration caused by glaucoma. Thus, they ignore a significant part of the visual system represented by the visual pathway in the brain. The advances in neuroimaging, especially diffusion tensor imaging (DTI), enable the identification and characterization of white matter fibers. In this work, we propose a system based on DTI analysis of the visual pathway fibers in the optic radiation for detecting and discriminating different glaucoma entities. The optic radiation is identified semi-automatically. DTI provides information about the fiber orientation as well as a set of derived parameters describing the degree of diffusion anisotropy and diffusivity. Features for each DTI derived measure are extracted from a specified region of interest on the optic radiation. The features are grouped into three sets: Histogram, co-occurrence matrices, and Laws features. For feature selection, the features are ranked using a support vector machine classifier. The highest ranked features are used for classification. A support vector machine classifier is used for classification in a 10-fold cross validation setup. The system is applied to three age-matched subjects’ categories containing 27 healthy, 39 primary open angle glaucoma (POAG), and 18 normal tension glaucoma (NTG) subjects. The discrimination accuracy between healthy and glaucoma (POAG and NTG) subjects is 94.1% with an area under the ROC of 0.97. Classification accuracy of 92.4% is obtained for the normal and the POAG groups while it increased to 100% in case of healthy and NTG groups. In addition, the system could differentiate between glaucoma types (POAG and NTG) with an accuracy of 98.3%. A complementary analysis was performed to estimate the selection bias in the obtained accuracy. The bias ranged from 10% to 20% depending on the group pair under consideration. The classification results indicate the high performance of the system compared to retina-based glaucoma detection systems. The proposed approach utilizes visual pathway analysis rather than the conventional eye analysis which presents a new trend in glaucoma detection. Analyzing the entire visual system could provide significant information that can improve the glaucoma examination flow and treatment.     

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.     

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.     

Geometrically constrained two-tensor model for crossing tracts in DWI

MR diffusion tensor imaging (DTI) of the brain and spine provides a unique tool for both visualizing directionality and assessing intactness of white matter fiber tracts in vivo. At the spatial resolution of clinical MRI, much of primate white matter is composed of interdigitating fibers. Analyses based on an assumed single diffusion tensor per voxel yield important information about the average diffusion in the voxel but fail to reveal structure in the presence of crossing tracts. Until today, all clinical scans assume only one tensor, causing potential serious errors in tractography. Since high angular resolution imaging remains, so far, untenable for routine clinical use, a method is proposed whereby the single-tensor field is augmented with additional information gleaned from standard clinical DTI. The method effectively resolves two distinct tract directions within voxels, in which only two tracts are assumed to exist. The underlying constrained two-tensor model is fitted in two stages, utilizing the information present in the single-tensor fit. As a result, the necessary MRI time can be drastically reduced when compared with other approaches, enabling widespread clinical use. Upon evaluation in simulations and application to in vivo human brain DTI data, the method appears to be robust and practical and, if correctly applied, could elucidate tract directions at critical points of uncertainty.     

Effects of random subject rotation on optimised diffusion gradient sampling schemes in diffusion tensor MRI

The choice of the number (N) and orientation of diffusion sampling gradients required to measure accurately the water diffusion tensor remains contentious. Monte Carlo studies have suggested that between 20 and 30 uniformly distributed sampling orientations are required to provide robust estimates of water diffusions parameters. These simulations have not, however, taken into account what effect random subject motion, specifically rotation, might have on optimised gradient schemes, a problem which is especially relevant to clinical diffusion tensor MRI (DT-MRI). Here this question is investigated using Monte Carlo simulations of icosahedral sampling schemes and in vivo data. These polyhedra-based schemes, which have the advantage that large N can be created from optimised subsets of smaller N, appear to be ideal for the study of restless subjects since if scanning needs to be prematurely terminated it should be possible to identify a subset of images that have been acquired with a near optimised sampling scheme. The simulations and in vivo data show that as N increases, the rotational variance of fractional anisotropy (FA) estimates becomes progressively less dependent on the magnitude of subject rotation (), while higher FA values are progressively underestimated as increases. These data indicate that for large subject rotations the B-matrix should be recalculated to provide accurate diffusion anisotropy information.     

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.     

Magnetic field anisotropy based MR tractography

Non-invasive measurements of structural orientation provide unique information regarding the connectivity and functionality of fiber materials. In the present study, we use a capillary model to demonstrate that the direction of fiber structure can be obtained from susceptibility-induced magnetic field anisotropy. The interference pattern between internal and external magnetic field gradients carries the signature of the underlying anisotropic structure and can be measured by MRI-based water diffusion measurements. Through both numerical simulation and experiments, we found that this technique can determine the capillary orientation within 3°. Therefore, susceptibility-induced magnetic field anisotropy may be useful for an alternative tractography method when diffusion anisotropy is small at higher magnetic field strength without the need to rotate the subject inside the scanner.     

Discreteness inducing coexistence

Consider two species that diffuse through space. Consider further that they differ only in initial densities and, possibly, in diffusion constants. Otherwise they are identical. What happens if they compete with each other in the same environment? What is the influence of the discrete nature of the interactions on the final destination? And what are the influence of diffusion and additive fluctuations corresponding to random migration and immigration of individuals? This paper aims to answer these questions for a particular competition model that incorporates intra and interspecific competition between the species. Based on mean field theory, the model has a stationary state dependent on the initial density conditions. We investigate how this initial density dependence is affected by the presence of demographic multiplicative noise and additive noise in space and time. There are three main conclusions: (1) Additive noise favors denser populations at the expense of the less dense, ratifying the competitive exclusion principle. (2) Demographic noise, on the other hand, favors less dense populations at the expense of the denser ones, inducing equal densities at the quasi-stationary state, violating the aforementioned principle. (3) The slower species always suffers the more deleterious effects of statistical fluctuations in a homogeneous medium.