B-Tensor: Brain Connectome Tensor Factorization for Alzheimer's Disease

AD is the highly severe part of the dementia spectrum and impairs cognitive abilities of individuals, bringing economic, societal and psychological burdens beyond the diseased. A promising approach in AD research is the analysis of structural and functional brain connectomes, i.e., sNETs and fNETs, respectively. We propose to use tensor representation (B-tensor) of uni-modal and multi-modal brain connectomes to define a low-dimensional space via tensor factorization. We show on a cohort of 47 subjects, spanning the spectrum of dementia, that diagnosis with an accuracy of 77% to 100% is achievable in a 5D connectome space using different structural and functional connectome constructions in a uni-modal and multi-modal fashion. We further show that multi-modal tensor factorization improves the results suggesting complementary information in structure and function. A neurological assessment of the connectivity patterns identified largely agrees with prior knowledge, yet also suggests new associations that may play a role in the disease progress.

Central nervous system metastatic epithelial ovarian cancer. Clinical parameters and prognostic factors: a multicenter study of Anatolian Society of Medical Oncology

Central nervous system (CNS) metastasis is a rare event in the course of late stage epithelial ovarian cancer (EOC); however its incidence is increasing in parallel with prolonged survival of patients.

OBJECTIVE

The authors assessed the clinical parameters and potential prognostic features in patients with CNS metastatic disease.

MATERIALS AND METHODS

Clinical data of the 33 patients from the participating centers were retrospectively collected and analyzed. Median age at the time of CNS metastasis was 57 years. Median time from the diagnosis of primary EOC until CNS metastatic disease was 22 months. Nearly half (45.5%) of the patients had single CNS metastatic lesions and all patients in the study group except two received radiotherapy as palliative treatment. Median overall survival (OS) from the time of CNS metastasis was 15 months (0-66). At univariate analysis only number of brain metastatic lesions (p = 0.001) and presence of extracranial disease (p = 0.004) were strongly associated with OS whereas multimodal treatment, size of metastatic lesions, platinum sensitivity, age, grade, and disease stage at presentation were not. Development of CNS metastasis carries a poor prognosis, however patients with single metastatic lesions and only intracranial metastatic disease can have prolonged survival after appropriate palliative management of their disease.

Measurement tensors in diffusion MRI: generalizing the concept of diffusion encoding

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

Sparse and optimal acquisition design for diffusion MRI and beyond

PURPOSE

Diffusion magnetic resonance imaging (MRI) in combination with functional MRI promises a whole new vista for scientists to investigate noninvasively the structural and functional connectivity of the human brain-the human connectome, which had heretofore been out of reach. As with other imaging modalities, diffusion MRI data are inherently noisy and its acquisition time-consuming. Further, a faithful representation of the human connectome that can serve as a predictive model requires a robust and accurate data-analytic pipeline. The focus of this paper is on one of the key segments of this pipeline-in particular, the development of a sparse and optimal acquisition (SOA) design for diffusion MRI multiple-shell acquisition and beyond.

METHODS

The authors propose a novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and a novel and effective semistochastic and moderately greedy combinatorial search strategy with simulated annealing to locate the optimum design or configuration. The goal of the optimality criteria is threefold: first, to maximize uniformity of the diffusion measurements in each shell, which is equivalent to maximal incoherence in angular measurements; second, to maximize coverage of the diffusion measurements around each radial line to achieve maximal incoherence in radial measurements for multiple-shell acquisition; and finally, to ensure maximum uniformity of diffusion measurement directions in the limiting case when all the shells are coincidental as in the case of a single-shell acquisition. The approach taken in evaluating the stability of various acquisition designs is based on the condition number and the A-optimal measure of the design matrix.

RESULTS

Even though the number of distinct configurations for a given set of diffusion gradient directions is very large in general-e.g., in the order of 10(232) for a set of 144 diffusion gradient directions, the proposed search strategy was found to be effective in finding the optimum configuration. It was found that the square design is the most robust (i.e., with stable condition numbers and A-optimal measures under varying experimental conditions) among many other possible designs of the same sample size. Under the same performance evaluation, the square design was found to be more robust than the widely used sampling schemes similar to that of 3D radial MRI and of diffusion spectrum imaging (DSI).

CONCLUSIONS

A novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and an effective search strategy for finding the best configuration have been developed. The results are very promising, interesting, and practical for diffusion MRI acquisitions.

NMR characterization of general compartment size distributions

The influence of molecular diffusion on the nuclear magnetic resonance (NMR) signal can be exploited to estimate compartment size distributions in heterogeneous specimens. Theoretical relationships between the NMR signal intensity at long diffusion times and the moments of a general distribution of isolated pores with characteristic shapes (planar, cylindrical or spherical) are established. A numerical method based on expressing a general diffusion-attenuated NMR signal profile in a series of complete orthogonal basis functions is introduced and subsequently employed to estimate the moments of the compartment size distribution. The results on simulated and real data obtained from controlled water-filled microcapillaries demonstrate the power of the approach to create contrast based not only on the mean of the compartment size but also its variance. The technique can be employed to address a variety of problems such as characterizing distributions of droplet sizes in emulsions and of apparent axon diameters in nerve fascicles.

Noninvasive bipolar double-pulsed-field-gradient NMR reveals signatures for pore size and shape in polydisperse, randomly oriented, inhomogeneous porous media

Noninvasive characterization of pore size and shape in opaque porous media is a formidable challenge. NMR diffusion-diffraction patterns were found to be exceptionally useful for obtaining such morphological features, but only when pores are monodisperse and coherently placed. When locally anisotropic pores are randomly oriented, conventional diffusion NMR methods fail. Here, we present a simple, direct, and general approach to obtain both compartment size and shape even in such settings and even when pores are characterized by internal field gradients. Using controlled porous media, we show that the bipolar-double-pulsed-field-gradient (bp-d-PFG) methodology yields diffusion-diffraction patterns from which pore size can be directly obtained. Moreover, we show that pore shape, which cannot be obtained by conventional methods, can be directly inferred from the modulation of the signal in angular bp-d-PFG experiments. This new methodology significantly broadens the types of porous media that can be studied using noninvasive diffusion-diffraction NMR.

Noninvasive bipolar double-pulsed-field-gradient NMR reveals signatures for pore size and shape in polydisperse, randomly oriented, inhomogeneous porous media

Noninvasive characterization of pore size and shape in opaque porous media is a formidable challenge. NMR diffusion-diffraction patterns were found to be exceptionally useful for obtaining such morphological features, but only when pores are monodisperse and coherently placed. When locally anisotropic pores are randomly oriented, conventional diffusion NMR methods fail. Here, we present a simple, direct, and general approach to obtain both compartment size and shape even in such settings and even when pores are characterized by internal field gradients. Using controlled porous media, we show that the bipolar-double-pulsed-field-gradient (bp-d-PFG) methodology yields diffusion-diffraction patterns from which pore size can be directly obtained. Moreover, we show that pore shape, which cannot be obtained by conventional methods, can be directly inferred from the modulation of the signal in angular bp-d-PFG experiments. This new methodology significantly broadens the types of porous media that can be studied using noninvasive diffusion-diffraction NMR.

Detecting diffusion-diffraction patterns in size distribution phantoms using double-pulsed field gradient NMR: Theory and experiments

NMR observable nuclei undergoing restricted diffusion within confining pores are important reporters for microstructural features of porous media including, inter-alia, biological tissues, emulsions and rocks. Diffusion NMR, and especially the single-pulsed field gradient (s-PFG) methodology, is one of the most important noninvasive tools for studying such opaque samples, enabling extraction of important microstructural information from diffusion-diffraction phenomena. However, when the pores are not monodisperse and are characterized by a size distribution, the diffusion-diffraction patterns disappear from the signal decay, and the relevant microstructural information is mostly lost. A recent theoretical study predicted that the diffusion-diffraction patterns in double-PFG (d-PFG) experiments have unique characteristics, such as zero-crossings, that make them more robust with respect to size distributions. In this study, we theoretically compared the signal decay arising from diffusion in isolated cylindrical pores characterized by lognormal size distributions in both s-PFG and d-PFG methodologies using a recently presented general framework for treating diffusion in NMR experiments. We showed the gradual loss of diffusion-diffraction patterns in broadening size distributions in s-PFG and the robustness of the zero-crossings in d-PFG even for very large standard deviations of the size distribution. We then performed s-PFG and d-PFG experiments on well-controlled size distribution phantoms in which the ground-truth is well-known a priori. We showed that the microstructural information, as manifested in the diffusion-diffraction patterns, is lost in the s-PFG experiments, whereas in d-PFG experiments the zero-crossings of the signal persist from which relevant microstructural information can be extracted. This study provides a proof of concept that d-PFG may be useful in obtaining important microstructural features in samples characterized by size distributions.

A multivariate hypothesis testing framework for tissue clustering and classification of DTI data

The primary aim of this work is to propose and investigate the effectiveness of a novel unsupervised tissue clustering and classification algorithm for diffusion tensor MRI (DTI) data. The proposed algorithm utilizes information about the degree of homogeneity of the distribution of diffusion tensors within voxels. We adapt frameworks proposed by Hext and Snedecor, where the null hypothesis of diffusion tensors belonging to the same distribution is assessed by an F-test. Tissue type is classified according to one of the four possible diffusion models, the assignment of which is determined by a parsimonious model selection framework based on Schwarz Criterion. Both numerical phantoms and diffusion-weighted imaging (DWI) data obtained from excised rat and pig spinal cords are used to test and validate these tissue clustering and classification approaches. The unsupervised clustering method effectively identifies distinct regions of interest (ROIs) in phantoms and real experimental DTI data.

Probabilistic Identification and Estimation of Noise (PIESNO): a self-consistent approach and its applications in MRI

Data analysis in MRI usually entails a series of processing procedures. One of these procedures is noise assessment, which in the context of this work, includes both the identification of noise-only pixels and the estimation of noise variance (standard deviation). Although noise assessment is critical to many MRI processing techniques, the identification of noise-only pixels has received less attention than has the estimation of noise variance. The main objectives of this paper are, therefore, to demonstrate (a) that the identification of noise-only pixels has an important role to play in the analysis of MRI data, (b) that the identification of noise-only pixels and the estimation of noise variance can be combined into a coherent framework, and (c) that this framework can be made self-consistent. To this end, we propose a novel iterative approach to simultaneously identify noise-only pixels and estimate the noise standard deviation from these identified pixels in a commonly used data structure in MRI. Experimental and simulated data were used to investigate the feasibility, the accuracy and the stability of the proposed technique.

Compartment shape anisotropy (CSA) revealed by double pulsed field gradient MR

The multiple scattering extensions of the pulsed field gradient (PFG) experiments can be used to characterize restriction-induced anisotropy at different length scales. In double-PFG acquisitions that involve two pairs of diffusion gradient pulses, the dependence of the MR signal attenuation on the angle between the two gradients is a signature of restriction that can be observed even at low gradient strengths. In this article, a comprehensive theoretical treatment of the double-PFG observation of restricted diffusion is presented. In the first part of the article, the problem is treated for arbitrarily shaped pores under idealized experimental conditions, comprising infinitesimally narrow gradient pulses with long separation times and long or vanishing mixing times. New insights are obtained when the treatment is applied to simple pore shapes of spheres, ellipsoids, and capped cylinders. The capped cylinder geometry is considered in the second part of the article where the solution for a double-PFG experiment with arbitrary experimental parameters is introduced. Although compartment shape anisotropy (CSA) is emphasized here, the findings of this article can be used in gleaning the volume, eccentricity, and orientation distribution function associated with ensembles of anisotropic compartments using double-PFG acquisitions with arbitrary experimental parameters.

Measuring small compartmental dimensions with low-q angular double-PGSE NMR: The effect of experimental parameters on signal decay

In confined geometries, the MR signal attenuation obtained from single pulsed gradient spin echo (s-PGSE) experiments reflects the dimension of the compartment, and in some cases, its geometry. However, to measure compartment size, high q-values must be applied, requiring high gradient strengths and/or long pulse durations and diffusion times. The angular double PGSE (d-PGSE) experiment has been proposed as a means to extract dimensions of confined geometries using low q-values. In one realization of the d-PGSE experiment, the first gradient pair is fixed along the x-axis, and the orientation of the second gradient pair is varied in the X-Y plane. Such a measurement is sensitive to microscopic anisotropy induced by the boundaries of the restricting compartment, and allows extraction of the compartment dimension. In this study, we have juxtaposed angular d-PGSE experiments and simulations to extract sizes from well-characterized NMR phantoms consisting of water filled microcapillaries. We are able to accurately extract sizes of small compartments (5mum) using the angular d-PGSE experiment even when the short gradient pulse (SGP) approximation is violated and over a range of mixing and diffusion times. We conclude that the angular d-PGSE experiment may fill an important niche in characterizing compartment sizes in which restricted diffusion occurs.

A signal transformational framework for breaking the noise floor and its applications in MRI

A long-standing problem in magnetic resonance imaging (MRI) is the noise-induced bias in the magnitude signals. This problem is particularly pressing in diffusion MRI at high diffusion-weighting. In this paper, we present a three-stage scheme to solve this problem by transforming noisy nonCentral Chi signals to noisy Gaussian signals. A special case of nonCentral Chi distribution is the Rician distribution. In general, the Gaussian-distributed signals are of interest rather than the Gaussian-derived (e.g., Rayleigh, Rician, and nonCentral Chi) signals because the Gaussian-distributed signals are generally more amenable to statistical treatment through the principle of least squares. Monte Carlo simulations were used to validate the statistical properties of the proposed framework. This scheme opens up the possibility of investigating the low signal regime (or high diffusion-weighting regime in the case of diffusion MRI) that contains potentially important information about biophysical processes and structures of the brain.

A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments

Based on a description introduced by Robertson, Grebenkov recently introduced a powerful formalism to represent the diffusion-attenuated NMR signal for simple pore geometries such as slabs, cylinders, and spheres analytically. In this work, we extend this multiple correlation function formalism by allowing for possible variations in the direction of the magnetic field gradient waveform. This extension is necessary, for example, to incorporate the effects of imaging gradients in diffusion-weighted NMR imaging scans and in characterizing anisotropy at different length scales via double pulsed field gradient (PFG) experiments. In cylindrical and spherical pores, respectively, two- and three-dimensional vector operators are employed whose form is deduced from Grebenkov's results via elementary operator algebra for the case of cylinders and the Wigner-Eckart theorem for the case of spheres. The theory was validated by comparison with known findings and with experimental double-PFG data obtained from water-filled microcapillaries.

Microscopic anisotropy revealed by NMR double pulsed field gradient experiments with arbitrary timing parameters

We consider a general double pulsed field gradient experiment with arbitrary experimental parameters and calculate an exact expression for the NMR signal attenuation from restricted geometries, which is valid at long wavelengths, i.e., when the product of the gyromagnetic ratio of the spins, the pulsed gradients' duration, and their magnitude is small compared to the reciprocal of the pore size. It is possible to observe microscopic anisotropy within the pore space induced by the boundaries of the pore, which can be used to differentiate restricted from free or multicompartmental diffusion and to estimate a characteristic pore dimension in the former case. Explicit solutions for diffusion taking place between parallel plates as well as in cylindrical and spherical pores are provided. In coherently packed cylindrical pores, it is possible to measure simultaneously the cylinders' orientation and diameter using small gradient strengths. The presence of orientational heterogeneity of cylinders is addressed, and a scheme for differentiating microscopic from ensemble anisotropy is proposed.

Anisotropy induced by macroscopic boundaries: surface-normal mapping using diffusion-weighted imaging

In MRI, macroscopic boundaries lead to a diffusion-related increase in signal intensity near them--an effect commonly referred to as edge-enhancement. In diffusion-weighted imaging protocols where the signal attenuation due to diffusion results predominantly from the application of magnetic field gradients, edge-enhancement will depend on the orientation of these diffusion gradients. The resulting diffusion anisotropy can be exploited to map the direction normal to the macroscopic boundary. Simulations suggest that the hypothesized anisotropy may be within observable limits even when the voxel contains no boundary itself--hence, the name remote-anisotropy. Moreover, for certain experimental parameters there may be significant phase cancellations within the voxel that may lead to an edge detraction effect. When this is avoided, the eigenvector corresponding to the smallest eigenvalue of the diffusion tensor obtained from diffusion-tensor imaging can be used to create surface-normal maps conveniently. Experiments performed on simple geometric constructs as well as real tissue demonstrate the feasibility of using the edge-enhancement mechanism to map orientations orthogonal to macroscopic surfaces, which may be used to assess the integrity of tissue and organ boundaries noninvasively.

Characterization of anomalous diffusion from mr signal may be a new probe to tissue microstructure

Observation of translational self-diffusion of water molecules using magnetic resonance (MR) techniques has proven to be a powerful means to probe tissue microstructure. The collected MR signal depends on experimentally controllable parameters as well as the descriptors of tissue geometry. In order to obtain the latter, one needs to employ accurate models to characterize the dependence of the signal on the varied experimental parameters. In this work, a simple model describing diffusion in disordered media and fractal spaces is shown to describe the diffusion-time dependence of the diffusion attenuated MR signal obtained from biological specimens successfully. The model enables one to quantify the evolution of the average water displacement probabilities in terms of two exponents--dw and ds. The experiments performed on excised human neural tissue samples and human red blood cell ghosts indicate that these two parameters are sensitive to tissue microstructure. Therefore, it may be possible to use the proposed scheme to generate novel contrast mechanism for classifying and segmenting tissue.

Parsimonious model selection for tissue segmentation and classification applications: a study using simulated and experimental DTI data

One aim of this work is to investigate the feasibility of using a hierarchy of models to describe diffusion tensor magnetic resonance (MR) data in fixed tissue. Parsimonious model selection criteria are used to choose among different models of diffusion within tissue. Using this information, we assess whether we can perform simultaneous tissue segmentation and classification. Both numerical phantoms and diffusion weighted imaging (DWI) data obtained from excised pig spinal cord are used to test and validate this model selection framework. Three hierarchical approaches are used for parsimonious model selection: the Schwarz criterion (SC), the F-test t-test (F- t), proposed by Hext, and the F-test F-test (F-F), adapted from Snedecor. The F - t approach is more robust than the others for selecting between isotropic and general anisotropic (full tensor) models. However, due to its high sensitivity to the variance estimate and bias in sorting eigenvalues, the F-F and SC are preferred for segmenting models with transverse isotropy (cylindrical symmetry). Additionally, the SC method is easier to implement than the F - t and F - F methods and has better performance. As such, this approach can be efficiently used for evaluating large MRI data sets. In addition, the proposed voxel-by-voxel segmentation framework is not susceptible to artifacts caused by the inhomogeneity of the variance in neighboring voxels with different degrees of anisotropy, which might contaminate segmentation results obtained with the techniques based on voxel averaging.

Three-dimensional analytical magnetic resonance imaging phantom in the Fourier domain

This work presents a basic framework for constructing a 3D analytical MRI phantom in the Fourier domain. In the image domain the phantom is modeled after the work of Kak and Roberts on a 3D version of the famous Shepp-Logan head phantom. This phantom consists of several ellipsoids of different sizes, orientations, locations, and signal intensities (or gray levels). It will be shown that the k-space signal derived from the phantom can be analytically expressed. As a consequence, it enables one to bypass the need for interpolation in the Fourier domain when testing image-reconstruction algorithms. More importantly, the proposed framework can serve as a benchmark for contrasting and comparing different image-reconstruction techniques in 3D MRI with a non-Cartesian k-space trajectory. The proposed framework can also be adapted for 3D MRI simulation studies in which the MRI parameters of interest may be introduced to the signal intensity from the ellipsoid.

MR diffusion - "diffraction" phenomenon in multi-pulse-field-gradient experiments

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Simulations to calculate signal values from arbitrary gradient waveforms are performed for diffusion in restricted geometries using a matrix operator formalism. The simulations suggest that the differences in the characteristics of the attenuation curves are expected to make it possible to measure smaller pore sizes, to improve the accuracy of pore size measurements and potentially to distinguish different pore shapes using the N-PFG technique. Moreover, when an even number of PFG pairs is used, it is possible to observe the diffraction pattern at shorter diffusion times and measure an approximation to the average pore size even when the sample contains pores with a broad distribution of sizes.

Diffusion tensor microscopy indicates the cytoarchitectural basis for diffusion anisotropy in the human hippocampus

BACKGROUND AND PURPOSE

Observing changes to water diffusivity and fractional anisotropy (FA) for particular hippocampal regions may improve the sensitivity and specificity of diffusion tensor MR imaging for hippocampal pathologies like Alzheimer disease and mesial temporal sclerosis. As a first step toward this goal, this study characterized the cytoarchitectural features underlying diffusion anisotropy in human hippocampus autopsy specimens at 60-microm in-plane resolution.

MATERIALS AND METHODS

Eight-millimeter coronal segments of the hippocampal body were dissected from 5 autopsy specimens (mean = 55.6 +/- 6.2 years of age) with short postmortem intervals to fixation (21.2 +/- 5.7 hours) and no histologic evidence of neuropathology. Diffusion tensor microscopy data were collected from hippocampal specimens by using a 14.1T magnet with a protocol that included 21 unique diffusion gradient orientations (diffusion time = 17 ms, b = 1250 s/mm(2)). The resulting images were used to determine the mean diffusivity, FA, and principal fiber orientation for manually segmented hippocampal regions that included the stratum oriens, stratum radiatum, stratum pyramidale (CA1 and CA3), stratum lacunosum-molecular, hilus, molecular layer, granule cell layer, fimbria, and subiculum.

RESULTS

Diffusion-weighted images had high signal-to-noise ratios (31.1 +/- 13.0) and delineated hippocampal anatomy well. Water diffusivity ranged from 1.21 +/- 0.22 x 10(-4) mm(2)/s in the fimbria to 3.48 +/- 0.72 x 10(-4) mm(2)/s in granule cells (analysis of variance, P<.001). Color fiber-orientation maps indicated the underlying microstructures responsible for diffusion anisotropy in the hippocampal lamina.

CONCLUSION

Diffusion tensor microscopy provided novel microstructural information about the different lamina of the human hippocampus. These ex vivo data obtained at high-magnetic-field strengths can be used to study injury-specific diffusion changes to susceptible hippocampal regions and may lead to more specific MR imaging surrogate markers for Alzheimer disease or epilepsy.

A CONTINUOUS MIXTURE OF TENSORS MODEL FOR DIFFUSION-WEIGHTED MR SIGNAL RECONSTRUCTION

Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecular diffusion through tissue in vivo. In this paper, we present a novel statistical model which describes the diffusion-attenuated MR signal by the Laplace transform of a probability distribution over symmetric positive definite matrices. Using this new model, we analytically derive a Rigaut-type asymptotic fractal law for the MR signal decay which has been phenomenologically used before. We also develop an efficient scheme for reconstructing the multiple fiber bundles from the DW-MRI measurements. Experimental results on both synthetic and real data sets are presented to show the robustness and accuracy of the proposed algorithms.

Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal

This report introduces a novel method to characterize the diffusion-time dependence of the diffusion-weighted magnetic resonance (MR) signal in biological tissues. The approach utilizes the theory of diffusion in disordered media where two parameters, the random walk dimension and the spectral dimension, describe the evolution of the average propagators obtained from q-space MR experiments. These parameters were estimated, using several schemes, on diffusion MR spectroscopy data obtained from human red blood cell ghosts and nervous tissue autopsy samples. The experiments demonstrated that water diffusion in human tissue is anomalous, where the mean-square displacements vary slower than linearly with diffusion time. These observations are consistent with a fractal microstructure for human tissues. Differences observed between healthy human nervous tissue and glioblastoma samples suggest that the proposed methodology may provide a novel, clinically useful form of diffusion MR contrast.

Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT)

This article describes an accurate and fast method for fiber orientation mapping using multidirectional diffusion-weighted magnetic resonance (MR) data. This novel approach utilizes the Fourier transform relationship between the water displacement probabilities and diffusion-attenuated MR signal expressed in spherical coordinates. The radial part of the Fourier integral is evaluated analytically under the assumption that MR signal attenuates exponentially. The values of the resulting functions are evaluated at a fixed distance away from the origin. The spherical harmonic transform of these functions yields the Laplace series coefficients of the probabilities on a sphere of fixed radius. Alternatively, probability values can be computed nonparametrically using Legendre polynomials. Orientation maps calculated from excised rat nervous tissue data demonstrate this technique's ability to accurately resolve crossing fibers in anatomical regions such as the optic chiasm. This proposed methodology has a trivial extension to multiexponential diffusion-weighted signal decay. The developed methods will improve the reliability of tractography schemes and may make it possible to correctly identify the neural connections between functionally connected regions of the nervous system.

Structural insights from high-resolution diffusion tensor imaging and tractography of the isolated rat hippocampus

The hippocampus is a critical structure for learning and memory formation injured by diverse neuropathologies such as epilepsy or Alzheimer's disease. Recently, clinical investigations have attempted to use diffusion tensor MRI as a more specific surrogate marker for hippocampal damage. To first better understand the tissue architecture of healthy hippocampal regions, this study characterized 10 rat hippocampi with diffusion tensor imaging (DTI) at 50-microm in-plane image resolution using a 14.1-T magnet. Chemical fixation of the dissected and straightened rat hippocampus provided a simple, effective way to reduce partial volume effects when segmenting hippocampal regions and improved mean signal-to-noise per unit time (e.g. 50.6+/-4.4 at b=1250 s/mm2 in 27 min). Contrary to previous reports that water diffusion is homogeneous throughout the nervous system, statistically different mean diffusivities were observed (e.g. 0.238+/-0.054 and 0.318+/-0.084 microm2/ms for the molecular and granule cell layers respectively) (ANOVA, P<0.05). Different hippocampal subregions had lower fractional anisotropy than uniformly fibrous structures like corpus callosum because of their complex architecture. DTI-derived color fiber orientation maps and tractography demonstrated most components of the trisynaptic intrahippocampal pathway (e.g. orientations in stratum lacunosum-moleculare were dominated by perforant and Schaffer fibers) and also permitted some assessment of connectivity in the rat hippocampus.

Fast orientation mapping from HARDI

This paper introduces a new, accurate and fast method for fiber orientation mapping using high angular resolution diffusion imaging (HARDI) data. The approach utilizes the Fourier relationship between the water displacement probabilities and diffusion attenuated magnetic resonance (MR) signal expressed in spherical coordinates. The Laplace series coefficients of the water displacement probabilities are evaluated at a fixed distance away from the origin. The computations take under one minute for most three-dimensional datasets. We present orientation maps computed from excised rat optic chiasm, brain and spinal cord images. The developed method will improve the reliability of tractography schemes and make it possible to correctly identify the neural connections between functionally connected regions of the nervous system.

Generalized scalar measures for diffusion MRI using trace, variance, and entropy

This paper details the derivation of rotationally invariant scalar measures from higher-rank diffusion tensors (DTs) and functions defined on a unit sphere. This was accomplished with the use of an expression that generalizes the evaluation of the trace operator to tensors of arbitrary rank, and even to functions whose domains are the unit sphere. It is shown that the mean diffusivity is invariant to the selection of tensor rank for the model used. However, this rank invariance does not apply to the anisotropy measures. Therefore, a variance-based, general anisotropy measure is proposed. Also an information theoretical parametrization of anisotropy is introduced that is frequently more consistent with the meaning attributed to anisotropy. We accomplished this by associating anisotropy with the amount of orientational information present in the data, regardless of the imaging technique used. Using a simplified model of fibrous tissue, we simulated anisotropy values with varying orientational complexity and tensor models. Simulations suggested that a lower-rank tensor model may produce artificially low anisotropy values in voxels with complex structure. This was confirmed with a spin-echo experiment performed on an excised rat brain.

Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging

A new method for mapping diffusivity profiles in tissue is presented. The Bloch-Torrey equation is modified to include a diffusion term with an arbitrary rank Cartesian tensor. This equation is solved to give the expression for the generalized Stejskal-Tanner formula quantifying diffusive attenuation in complicated geometries. This makes it possible to calculate the components of higher-rank tensors without using the computationally-difficult spherical harmonic transform. General theoretical relations between the diffusion tensor (DT) components measured by traditional (rank-2) DT imaging (DTI) and 3D distribution of diffusivities, as measured by high angular resolution diffusion imaging (HARDI) methods, are derived. Also, the spherical tensor components from HARDI are related to the rank-2 DT. The relationships between higher- and lower-rank Cartesian DTs are also presented. The inadequacy of the traditional rank-2 tensor model is demonstrated with simulations, and the method is applied to excised rat brain data collected in a spin-echo HARDI experiment.

Acute lymphoblastic leukaemia presenting with arthritis in an adult patient

The earliest manifestations of leukaemia often include rheumatic signs and symptoms. Arthritis is a well recognised complication of leukaemia in children, but acute and chronic leukaemia may also cause arthritis in adults. Leukaemic arthritis may occur at any time during the course of leukaemia and may be the presenting manifestation. It should therefore be considered in the differential diagnosis of both childhood and adult rheumatic disease. We present an adult patient presenting with arthritis due to acute leukaemia.