Multidimensional MRI Core Publications

Ning L, Setsompop K, Westin C-F, Rathi Y. New Insights about Time-varying Diffusivity and its Estimation from Diffusion MRI. Magn Reson Med. 2017;78 (2) :763-74.Abstract

PURPOSE: Characterizing the relation between the applied gradient sequences and the measured diffusion MRI signal is important for estimating the time-dependent diffusivity, which provides important information about the microscopic tissue structure. THEORY AND METHODS: In this article, we extend the classical theory of Stepišnik for measuring time-dependent diffusivity under the Gaussian phase approximation. In particular, we derive three novel expressions which represent the diffusion MRI signal in terms of the mean-squared displacement, the instantaneous diffusivity, and the velocity autocorrelation function. We present the explicit signal expressions for the case of single diffusion encoding and oscillating gradient spin-echo sequences. Additionally, we also propose three different models to represent time-varying diffusivity and test them using Monte-Carlo simulations and in vivo human brain data. RESULTS: The time-varying diffusivities are able to distinguish the synthetic structures in the Monte-Carlo simulations. There is also strong statistical evidence about time-varying diffusivity from the in vivo human data set. CONCLUSION: The proposed theory provides new insights into our understanding of the time-varying diffusivity using different gradient sequences. The proposed models for representing time-varying diffusivity can be utilized to study time-varying diffusivity using in vivo human brain diffusion MRI data. 

Shaffer JJ, Ghayoor A, Long JD, Kim RE-Y, Lourens S, O'Donnell LJ, Westin C-F, Rathi Y, Magnotta V, Paulsen JS, et al. Longitudinal Diffusion Changes in Prodromal and Early HD: Evidence of White-matter Tract Deterioration. Hum Brain Mapp. 2017;38 (3) :1460-77.Abstract

INTRODUCTION: Huntington's disease (HD) is a genetic neurodegenerative disorder that primarily affects striatal neurons. Striatal volume loss is present years before clinical diagnosis; however, white matter degradation may also occur prior to diagnosis. Diffusion-weighted imaging (DWI) can measure microstructural changes associated with degeneration that precede macrostructural changes. DWI derived measures enhance understanding of degeneration in prodromal HD (pre-HD). METHODS: As part of the PREDICT-HD study, N = 191 pre-HD individuals and 70 healthy controls underwent two or more (baseline and 1-5 year follow-up) DWI, with n = 649 total sessions. Images were processed using cutting-edge DWI analysis methods for large multicenter studies. Diffusion tensor imaging (DTI) metrics were computed in selected tracts connecting the primary motor, primary somato-sensory, and premotor areas of the cortex with the subcortical caudate and putamen. Pre-HD participants were divided into three CAG-Age Product (CAP) score groups reflecting clinical diagnosis probability (low, medium, or high probabilities). Baseline and longitudinal group differences were examined using linear mixed models. RESULTS: Cross-sectional and longitudinal differences in DTI measures were present in all three CAP groups compared with controls. The high CAP group was most affected. CONCLUSIONS: This is the largest longitudinal DWI study of pre-HD to date. Findings showed DTI differences, consistent with white matter degeneration, were present up to a decade before predicted HD diagnosis. Our findings indicate a unique role for disrupted connectivity between the premotor area and the putamen, which may be closely tied to the onset of motor symptoms in HD. 

Fan Z, Peter S, Cai W, Song Y, Verma R, Carl-Fredrik W, O'Donnell LJ. Fiber Clustering Based White Matter Connectivity Analysis for Prediction of Autism Spectrum Disorder using Diffusion Tensor Imaging. IEEE Int Symp Biomed Imaging. 2016.Abstract
Autism Spectrum Disorder (ASD) has been suggested to associate with alterations in brain connectivity. In this study, we focus on a fiber clustering tractography segmentation strategy to observe white matter connectivity alterations in ASD. Compared to another popular parcellation-based approach for tractography segmentation based on cortical regions, we hypothesized that the clustering-based method could provide a more anatomically correspondent division of white matter. We applied this strategy to conduct a population-based group statistical analysis for the automated prediction of ASD. We obtained a maximum classification accuracy of 81.33% be- tween ASDs and controls, compared to the results of 78.00% from the parcellation-based method.
 
Mirzaalian H, Ning L, Savadjiev P, Pasternak O, Bouix S, Michailovich O, Grant G, Marx CE, Morey RA, Flashman LA, et al. Inter-site and Inter-scanner Diffusion MRI Data Harmonization. Neuroimage. 2016;135 :311-23.Abstract

We propose a novel method to harmonize diffusion MRI data acquired from multiple sites and scanners, which is imperative for joint analysis of the data to significantly increase sample size and statistical power of neuroimaging studies. Our method incorporates the following main novelties: i) we take into account the scanner-dependent spatial variability of the diffusion signal in different parts of the brain; ii) our method is independent of compartmental modeling of diffusion (e.g., tensor, and intra/extra cellular compartments) and the acquired signal itself is corrected for scanner related differences; and iii) inter-subject variability as measured by the coefficient of variation is maintained at each site. We represent the signal in a basis of spherical harmonics and compute several rotation invariant spherical harmonic features to estimate a region and tissue specific linear mapping between the signal from different sites (and scanners). We validate our method on diffusion data acquired from seven different sites (including two GE, three Philips, and two Siemens scanners) on a group of age-matched healthy subjects. Since the extracted rotation invariant spherical harmonic features depend on the accuracy of the brain parcellation provided by Freesurfer, we propose a feature based refinement of the original parcellation such that it better characterizes the anatomy and provides robust linear mappings to harmonize the dMRI data. We demonstrate the efficacy of our method by statistically comparing diffusion measures such as fractional anisotropy, mean diffusivity and generalized fractional anisotropy across multiple sites before and after data harmonization. We also show results using tract-based spatial statistics before and after harmonization for independent validation of the proposed methodology. Our experimental results demonstrate that, for nearly identical acquisition protocol across sites, scanner-specific differences can be accurately removed using the proposed method.

Tax CMW, Dela Haije T, Fuster A, Westin C-F, Viergever MA, Florack L, Leemans A. Sheet Probability Index (SPI): Characterizing the Geometrical Organization of the White Matter with Diffusion MRI. Neuroimage. 2016;142 :260-79.Abstract

The question whether our brain pathways adhere to a geometric grid structure has been a popular topic of debate in the diffusion imaging and neuroscience societies. Wedeen et al. (2012a, b) proposed that the brain's white matter is organized like parallel sheets of interwoven pathways. Catani et al. (2012) concluded that this grid pattern is most likely an artifact, resulting from methodological biases that cause the tractography pathways to cross in orthogonal angles. To date, ambiguities in the mathematical conditions for a sheet structure to exist (e.g. its relation to orthogonal angles) combined with the lack of extensive quantitative evidence have prevented wide acceptance of the hypothesis. In this work, we formalize the relevant terminology and recapitulate the condition for a sheet structure to exist. Note that this condition is not related to the presence or absence of orthogonal crossing fibers, and that sheet structure is defined formally as a surface formed by two sets of interwoven pathways intersecting at arbitrary angles within the surface. To quantify the existence of sheet structure, we present a novel framework to compute the sheet probability index (SPI), which reflects the presence of sheet structure in discrete orientation data (e.g. fiber peaks derived from diffusion MRI). With simulation experiments we investigate the effect of spatial resolution, curvature of the fiber pathways, and measurement noise on the ability to detect sheet structure. In real diffusion MRI data experiments we can identify various regions where the data supports sheet structure (high SPI values), but also areas where the data does not support sheet structure (low SPI values) or where no reliable conclusion can be drawn. Several areas with high SPI values were found to be consistent across subjects, across multiple data sets obtained with different scanners, resolutions, and degrees of diffusion weighting, and across various modeling techniques. Under the strong assumption that the diffusion MRI peaks reflect true axons, our results would therefore indicate that pathways do not form sheet structures at every crossing fiber region but instead at well-defined locations in the brain. With this framework, sheet structure location, extent, and orientation could potentially serve as new structural features of brain tissue. The proposed method can be extended to quantify sheet structure in directional data obtained with techniques other than diffusion MRI, which is essential for further validation.

Ning L, Westin C-F, Rathi Y. Estimation of Bounded and Unbounded Trajectories in Diffusion MRI. Front Neurosci. 2016;10 :129.Abstract

Disentangling the tissue microstructural information from the diffusion magnetic resonance imaging (dMRI) measurements is quite important for extracting brain tissue specific measures. The autocorrelation function of diffusing spins is key for understanding the relation between dMRI signals and the acquisition gradient sequences. In this paper, we demonstrate that the autocorrelation of diffusion in restricted or bounded spaces can be well approximated by exponential functions. To this end, we propose to use the multivariate Ornstein-Uhlenbeck (OU) process to model the matrix-valued exponential autocorrelation function of three-dimensional diffusion processes with bounded trajectories. We present detailed analysis on the relation between the model parameters and the time-dependent apparent axon radius and provide a general model for dMRI signals from the frequency domain perspective. For our experimental setup, we model the diffusion signal as a mixture of two compartments that correspond to diffusing spins with bounded and unbounded trajectories, and analyze the corpus-callosum in an ex-vivo data set of a monkey brain.

O'Donnell LJ, Suter Y, Rigolo L, Kahali P, Zhang F, Norton I, Albi A, Olubiyi O, Meola A, Essayed WI, et al. Automated White Matter Fiber Tract Identification in Patients with Brain Tumors. Neuroimage Clin. 2016;13 :138-53.Abstract

We propose a method for the automated identification of key white matter fiber tracts for neurosurgical planning, and we apply the method in a retrospective study of 18 consecutive neurosurgical patients with brain tumors. Our method is designed to be relatively robust to challenges in neurosurgical tractography, which include peritumoral edema, displacement, and mass effect caused by mass lesions. The proposed method has two parts. First, we learn a data-driven white matter parcellation or fiber cluster atlas using groupwise registration and spectral clustering of multi-fiber tractography from healthy controls. Key fiber tract clusters are identified in the atlas. Next, patient-specific fiber tracts are automatically identified using tractography-based registration to the atlas and spectral embedding of patient tractography. Results indicate good generalization of the data-driven atlas to patients: 80% of the 800 fiber clusters were identified in all 18 patients, and 94% of the 800 fiber clusters were found in 16 or more of the 18 patients. Automated subject-specific tract identification was evaluated by quantitative comparison to subject-specific motor and language functional MRI, focusing on the arcuate fasciculus (language) and corticospinal tracts (motor), which were identified in all patients. Results indicate good colocalization: 89 of 95, or 94%, of patient-specific language and motor activations were intersected by the corresponding identified tract. All patient-specific activations were within 3mm of the corresponding language or motor tract. Overall, our results indicate the potential of an automated method for identifying fiber tracts of interest for neurosurgical planning, even in patients with mass lesions.

Wassermann D, Makris N, Rathi Y, Shenton M, Kikinis R, Kubicki M, Westin C-F. The White Matter Query Language: A Novel Approach for Describing Human White Matter Anatomy. Brain Struct Funct. 2016;221 (9) :4705-4721.Abstract

We have developed a novel method to describe human white matter anatomy using an approach that is both intuitive and simple to use, and which automatically extracts white matter tracts from diffusion MRI volumes. Further, our method simplifies the quantification and statistical analysis of white matter tracts on large diffusion MRI databases. This work reflects the careful syntactical definition of major white matter fiber tracts in the human brain based on a neuroanatomist's expert knowledge. The framework is based on a novel query language with a near-to-English textual syntax. This query language makes it possible to construct a dictionary of anatomical definitions that describe white matter tracts. The definitions include adjacent gray and white matter regions, and rules for spatial relations. This novel method makes it possible to automatically label white matter anatomy across subjects. After describing this method, we provide an example of its implementation where we encode anatomical knowledge in human white matter for ten association and 15 projection tracts per hemisphere, along with seven commissural tracts. Importantly, this novel method is comparable in accuracy to manual labeling. Finally, we present results applying this method to create a white matter atlas from 77 healthy subjects, and we use this atlas in a small proof-of-concept study to detect changes in association tracts that characterize schizophrenia.

Ning L, Setsompop K, Michailovich O, Makris N, Shenton ME, Westin C-F, Rathi Y. A Joint Compressed-sensing and Super-resolution Approach for Very High-resolution Diffusion Imaging. Neuroimage. 2016;125 :386-400.Abstract

Diffusion MRI (dMRI) can provide invaluable information about the structure of different tissue types in the brain. Standard dMRI acquisitions facilitate a proper analysis (e.g. tracing) of medium-to-large white matter bundles. However, smaller fiber bundles connecting very small cortical or sub-cortical regions cannot be traced accurately in images with large voxel sizes. Yet, the ability to trace such fiber bundles is critical for several applications such as deep brain stimulation and neurosurgery. In this work, we propose a novel acquisition and reconstruction scheme for obtaining high spatial resolution dMRI images using multiple low resolution (LR) images, which is effective in reducing acquisition time while improving the signal-to-noise ratio (SNR). The proposed method called compressed-sensing super resolution reconstruction (CS-SRR), uses multiple overlapping thick-slice dMRI volumes that are under-sampled in q-space to reconstruct diffusion signal with complex orientations. The proposed method combines the twin concepts of compressed sensing and super-resolution to model the diffusion signal (at a given b-value) in a basis of spherical ridgelets with total-variation (TV) regularization to account for signal correlation in neighboring voxels. A computationally efficient algorithm based on the alternating direction method of multipliers (ADMM) is introduced for solving the CS-SRR problem. The performance of the proposed method is quantitatively evaluated on several in-vivo human data sets including a true SRR scenario. Our experimental results demonstrate that the proposed method can be used for reconstructing sub-millimeter super resolution dMRI data with very good data fidelity in clinically feasible acquisition time.

Szczepankiewicz F, van Westen D, Englund E, Westin C-F, Ståhlberg F, Lätt J, Sundgren PC, Nilsson M. The Link between Diffusion MRI and Tumor Heterogeneity: Mapping Cell Eccentricity and Density by Diffusional Variance Decomposition (DIVIDE). Neuroimage. 2016;142 :522-32.Abstract

The structural heterogeneity of tumor tissue can be probed by diffusion MRI (dMRI) in terms of the variance of apparent diffusivities within a voxel. However, the link between the diffusional variance and the tissue heterogeneity is not well-established. To investigate this link we test the hypothesis that diffusional variance, caused by microscopic anisotropy and isotropic heterogeneity, is associated with variable cell eccentricity and cell density in brain tumors. We performed dMRI using a novel encoding scheme for diffusional variance decomposition (DIVIDE) in 7 meningiomas and 8 gliomas prior to surgery. The diffusional variance was quantified from dMRI in terms of the total mean kurtosis (MKT), and DIVIDE was used to decompose MKT into components caused by microscopic anisotropy (MKA) and isotropic heterogeneity (MKI). Diffusion anisotropy was evaluated in terms of the fractional anisotropy (FA) and microscopic fractional anisotropy (μFA). Quantitative microscopy was performed on the excised tumor tissue, where structural anisotropy and cell density were quantified by structure tensor analysis and cell nuclei segmentation, respectively. In order to validate the DIVIDE parameters they were correlated to the corresponding parameters derived from microscopy. We found an excellent agreement between the DIVIDE parameters and corresponding microscopy parameters; MKA correlated with cell eccentricity (r=0.95, p<10(-7)) and MKI with the cell density variance (r=0.83, p<10(-3)). The diffusion anisotropy correlated with structure tensor anisotropy on the voxel-scale (FA, r=0.80, p<10(-3)) and microscopic scale (μFA, r=0.93, p<10(-6)). A multiple regression analysis showed that the conventional MKT parameter reflects both variable cell eccentricity and cell density, and therefore lacks specificity in terms of microstructure characteristics. However, specificity was obtained by decomposing the two contributions; MKA was associated only to cell eccentricity, and MKI only to cell density variance. The variance in meningiomas was caused primarily by microscopic anisotropy (mean±s.d.) MKA=1.11±0.33 vs MKI=0.44±0.20 (p<10(-3)), whereas in the gliomas, it was mostly caused by isotropic heterogeneity MKI=0.57±0.30 vs MKA=0.26±0.11 (p<0.05). In conclusion, DIVIDE allows non-invasive mapping of parameters that reflect variable cell eccentricity and density. These results constitute convincing evidence that a link exists between specific aspects of tissue heterogeneity and parameters from dMRI. Decomposing effects of microscopic anisotropy and isotropic heterogeneity facilitates an improved interpretation of tumor heterogeneity as well as diffusion anisotropy on both the microscopic and macroscopic scale.

Westin C-F, Knutsson H, Pasternak O, Szczepankiewicz F, Özarslan E, van Westen D, Mattisson C, Bogren M, O'Donnell LJ, Kubicki M, et al. Q-space Trajectory Imaging for Multidimensional Diffusion MRI of the Human Brain. Neuroimage. 2016;135 :345-62.Abstract

This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture.

Szczepankiewicz F, Lasič S, van Westen D, Sundgren PC, Englund E, Westin C-F, Ståhlberg F, Lätt J, Topgaard D, Nilsson M. Quantification of Microscopic Diffusion Anisotropy Disentangles Effects of Orientation Dispersion from Microstructure: Applications in Healthy Volunteers and in Brain Tumors. Neuroimage. 2015;104 :241-52.Abstract
The anisotropy of water diffusion in brain tissue is affected by both disease and development. This change can be detected using diffusion MRI and is often quantified by the fractional anisotropy (FA) derived from diffusion tensor imaging (DTI). Although FA is sensitive to anisotropic cell structures, such as axons, it is also sensitive to their orientation dispersion. This is a major limitation to the use of FA as a biomarker for "tissue integrity", especially in regions of complex microarchitecture. In this work, we seek to circumvent this limitation by disentangling the effects of microscopic diffusion anisotropy from the orientation dispersion. The microscopic fractional anisotropy (μFA) and the order parameter (OP) were calculated from the contrast between signal prepared with directional and isotropic diffusion encoding, where the latter was achieved by magic angle spinning of the q-vector (qMAS). These parameters were quantified in healthy volunteers and in two patients; one patient with meningioma and one with glioblastoma. Finally, we used simulations to elucidate the relation between FA and μFA in various micro-architectures. Generally, μFA was high in the white matter and low in the gray matter. In the white matter, the largest differences between μFA and FA were found in crossing white matter and in interfaces between large white matter tracts, where μFA was high while FA was low. Both tumor types exhibited a low FA, in contrast to the μFA which was high in the meningioma and low in the glioblastoma, indicating that the meningioma contained disordered anisotropic structures, while the glioblastoma did not. This interpretation was confirmed by histological examination. We conclude that FA from DTI reflects both the amount of diffusion anisotropy and orientation dispersion. We suggest that the μFA and OP may complement FA by independently quantifying the microscopic anisotropy and the level of orientation coherence.
Pasternak O, Westin C-F, Dahlben B, Bouix S, Kubicki M. The Extent of Diffusion MRI Markers of Neuroinflammation and White Matter Deterioration in Chronic Schizophrenia. Schizophr Res. 2015;161 (1) :113-8.Abstract
In a previous study we have demonstrated, using a novel diffusion MRI analysis called free-water imaging, that the early stages of schizophrenia are more likely associated with a neuroinflammatory response and less so with a white matter deterioration or a demyelination process. What is not known is how neuroinflammation and white matter deterioration change along the progression of the disorder. In this study we apply the free-water measures on a population of 29 chronic schizophrenia subjects and compare them with 25 matching controls. Our aim was to compare the extent of free-water imaging abnormalities in chronic subjects with the ones previously obtained for subjects at their first psychotic episode. We find that chronic subjects showed a limited extent of abnormal increase in the volume of the extracellular space, suggesting a less extensive neuroinflammatory response relative to patients at the onset of schizophrenia. At the same time, the chronic schizophrenia subjects had greater extent of reduced fractional anisotropy compared to the previous study, suggesting increased white matter deterioration along the progression of the disease. Our findings substantiate the role of neuroinflammation in the earlier stages of the disorder, and the effect of neurodegeneration that is worsening in the chronic phase.
Ning L, Westin C-F, Rathi Y. Estimating diffusion propagator and its moments using directional radial basis functions. IEEE Trans Med Imaging. 2015;34 (10) :2058-78.Abstract
The ensemble average diffusion propagator (EAP) obtained from diffusion MRI (dMRI) data captures important structural properties of the underlying tissue. As such, it is imperative to derive an accurate estimate of the EAP from the acquired diffusion data. In this work, we propose a novel method for estimating the EAP by representing the diffusion signal as a linear combination of directional radial basis functions scattered in q-space. In particular, we focus on a special case of anisotropic Gaussian basis functions and derive analytical expressions for the diffusion orientation distribution function (ODF), the return-to-origin probability (RTOP), and mean-squared-displacement (MSD). A significant advantage of the proposed method is that the second and the fourth order moment tensors of the EAP can be computed explicitly. This allows for computing several novel scalar indices (from the moment tensors) such as mean-fourth-order-displacement (MFD) and generalized kurtosis (GK)-which is a generalization of the mean kurtosis measure used in diffusion kurtosis imaging. Additionally, we also propose novel scalar indices computed from the signal in q-space, called the q-space mean-squared-displacement (QMSD) and the q-space mean-fourth-order-displacement (QMFD), which are sensitive to short diffusion time scales. We validate our method extensively on data obtained from a physical phantom with known crossing angle as well as on in-vivo human brain data. Our experiments demonstrate the robustness of our method for different combinations of b-values and number of gradient directions.
Eriksson S, Lasič S, Nilsson M, Westin C-F, Topgaard D. NMR Diffusion-Encoding with Axial Symmetry and Variable Anisotropy: Distinguishing Between Prolate and Oblate Microscopic Diffusion Tensors with Unknown Orientation Distribution. J Chem Phys. 2015;142 (10) :104201.Abstract
We introduce a nuclear magnetic resonance method for quantifying the shape of axially symmetric microscopic diffusion tensors in terms of a new diffusion anisotropy metric, DΔ, which has unique values for oblate, spherical, and prolate tensor shapes. The pulse sequence includes a series of equal-amplitude magnetic field gradient pulse pairs, the directions of which are tailored to give an axially symmetric diffusion-encoding tensor b with variable anisotropy bΔ. Averaging of data acquired for a range of orientations of the symmetry axis of the tensor b renders the method insensitive to the orientation distribution function of the microscopic diffusion tensors. Proof-of-principle experiments are performed on water in polydomain lyotropic liquid crystals with geometries that give rise to microscopic diffusion tensors with oblate, spherical, and prolate shapes. The method could be useful for characterizing the geometry of fluid-filled compartments in porous solids, soft matter, and biological tissues.

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