Computational Diffusion MRI

Over the last decade, the number of models used to analyse and interpret diffusion MRI data has increased dramatically. Exponentials and biexponentials have been joined by stretched exponentials, HARDI methods, compartment-based microstructure models and effective medium theories. At the same time, the field has experienced a cultural shift away from MR physics and towards computer science, emphasising Bayesian statistics and Machine Learning. This has meant that understanding imaging methodology whilst still keeping in mind the underlying physical assumptions can be challenging. This chapter reviews the Diffusion MR modelling literature from the point of view of the underlying physics. We show how the Bloch-Torrey equation can be derived, and then how different physical assumptions and formulations lead to different models. The intention is to show the different assumptions made in different models, to aid understanding and model selection.

The non-Gaussian noise distribution in magnitude Diffusion-Weighted Images (DWIs) can severely affect the estimation and reconstruction of the true diffusion signal. As a consequence, also the estimated diffusion metrics can be biased. We study the effect of phase correction, a procedure that re-establishes the Gaussianity of the noise distribution in DWIs by taking into account the corresponding phase images. We quantify the debiasing effects of phase correction in terms of diffusion signal estimation and calculated metrics. We perform in silico experiments based on a MGH Human Connectome Project dataset and on a digital phantom, accounting for different acquisition schemes, diffusion-weightings, signal to noise ratios, and for metrics based on Diffusion Tensor Imaging and on Mean Apparent Propagator Magnetic Resonance Imaging, i.e. q-space metrics. We show that phase correction is still a challenge, but also an effective tool to debias the estimation of diffusion signal and metrics from DWIs, especially at high b-values.

This paper presents a new compressed sensing framework for multishell HARDI. Unlike methods that model diffusion signals using analytical bases, we learn a dictionary of multishell diffusion signals, with a proposed regularization term to handle low signal-to-noise ratios at high b values. We combine the dictionary model for diffusion signals together with a multiscale (wavelet-based) spatial model on images for compressed sensing. To control overfitting of the dictionary to tracts with unknown orientations, we use a strong non-sparsity penalty that behaves close to the desirable L ⁰ pseudo-norm. Our framework allows undersampling gradient directions, shells, and k-space. The results show improved reconstructions from our framework, over the state of the art.

Noise in diffusion-weighted (DW) images increases the complexity of quantitative analysis and decreases the reliability of inferences. Hence, to improve analysis, it is often desirable to remove noise and at the same time preserve relevant image features. In this paper, we propose a tight wavelet frame based approach for edge-preserving denoising of DW images. Our approach (1) employs the unitary extension principle (UEP) to generate frames that are discrete analogues to differential operators of various orders; (2) introduces a very efficient method for solving an ℓ ₀ denoising problem that involves only thresholding and solving a trivial inverse problem; and (3) groups DW images acquired with neighboring gradient directions for collaborative denoising. Experiments using synthetic data with noncentral chi noise and real data with repeated scans confirm that our method yields superior performance compared with denoising using state-of-the-art methods such as non-local means.

High Angular Resolution Diffusion Imaging makes it possible to capture information about the course and location of complex fiber structures in the human brain. Ideally, multi-shell sampling would be applied, which however increases the acquisition time. Therefore, multi-shell acquisitions are considered infeasible for practical use in a clinical setting. In this work, we present a data-driven approach that is able to augment single-shell signals to multi-shell signals based on Deep Neural Networks and Spherical Harmonics. The proposed concept is evaluated on synthetic data to investigate the impact of noise and number of gradients. Moreover, it is evaluated on human brain data from the Human Connectome Project, comprising 100 scans from different subjects. The proposed approach makes it possible to drastically reduce the signal acquisition time and performs equally well on both synthetic as well as real human brain data.

Effective representation of the diffusion signal’s dependence on diffusion time is a sought-after, yet still unsolved, challenge in diffusion MRI (dMRI). We propose a functional basis approach that is specifically designed to represent the dMRI signal in this four-dimensional space—varying over gradient strength, direction and diffusion time. In particular, we provide regularization tools imposing signal sparsity and signal smoothness to drastically reduce the number of measurements we need to probe the properties of this multi-spherical space. We illustrate a novel application of our approach, which is the estimation of time-dependent q -space indices, on both synthetic data generated using Monte-Carlo simulations and in vivo data acquired from a C57Bl6 wild-type mouse. In both cases, we find that our regularization approach stabilizes the signal fit and index estimation as we remove samples, which may bring multi-spherical diffusion MRI within the reach of clinical application.

Axon diameter can play a key role in the function and performance of nerve pathways of the central and peripheral nervous system. Previously, a number of techniques to measure axon diameter using diffusion MR I have been proposed, majority of which uses single diffusion encoding (SDE) spin-echo sequence. However, recent theoretical research suggests that low-frequency oscillating gradient spin echo (OGSE ) offers benefits over SDE for imaging diameters when fibres are of unknown orientation. Furthermore, it suggests that resolution limit for clinical scanners (gradient strength of 60–80 mT/m) is ≈ 6 μm. Here we investigate the sensitivity of OGSE to fibre diameters experimentally on a clinical scanner, using microcapillaries of unknown orientation. We use the orientationally invariant OGSE ActiveAx method to image microcapillaries with diameters of 5, 10 or 20 μm. As predicted by theory, we find that 5 μm diameters are undistinguishable from zero. Furthermore, we find accurate and precise estimates for 10 and 20 μm. Finally, we find that low frequency oscillating gradient waveforms are optimal for accurate diameter estimation.

Construction of brain atlases is generally carried out using a two-step procedure involving registering a population of images to a common space and then fusing the aligned images to form an atlas. In practice, image registration is not perfect and simple averaging of the images will blur structures and cause artifacts. In diffusion MRI, this is further complicated by the possibility of within-voxel fiber misalignment due to natural inter-subject orientation dispersion. In this paper, we propose a method to improve the construction of diffusion atlases in light of inter-subject fiber dispersion. Our method involves a novel q-space (i.e., wavevector space) patch matching mechanism that is incorporated in a mean shift algorithm to seek the most probable signal at each point in q-space. Our method relies on the fact that the mean shift algorithm is a mode seeking algorithm that converges to the mode of a distribution and is hence robustness to outliers. Our method is therefore in effect seeking the most probable signal profile at each voxel given a distribution of profiles. Experimental results confirm that our method yields cleaner fiber orientation distribution functions with less artifacts caused by dispersion.

Amygdala plays an important role in fear and emotional learning, which are critical for human survival. Despite the functional relevance and unique circuitry of each human amygdaloid subnuclei, there has yet to be an efficient imaging method for identifying these regions in vivo. A data-driven approach without prior knowledge provides advantages of efficient and objective assessments. The present study uses high angular and high spatial resolution diffusion magnetic resonance imaging to generate orientation distribution function, which bears distinctive microstructural features. The features were extracted using spherical harmonic decomposition to assess microstructural similarity within amygdala subfields that are identified via similarity matrices using spectral k-mean clustering. The approach was tested on 32 healthy volunteers and three distinct amygdala subfields were identified including medial, posterior-superior lateral, and anterior-inferior lateral.

Recent years have brought about impressive reconstructions of white matter architecture, due to the advance of increasingly sophisticated MRI based acquisition methods and modeling techniques. These result in extremely large sets of streamelines (fibers) for each subject. The sets require large amount of storage and are often unwieldy and difficult to manipulate and analyze. We propose to use sparse representations for fibers to achieve a more compact representation. We also propose the means for calculating inter-fiber similarities in the compressed space using a measure, which we term: Cosine with Dictionary Similarity Weighting (CWDS). The performance of both sparse representations and CWDS is evaluated on full brain fiber-sets of 15 healthy subjects. The results show that a reconstruction error of slightly below 2 mm is achieved, and that CWDS is highly correlated with the cosine similarity in the original space.

Cortical parcellations provide valuable localisation resources for other neuroimaging modalities such as fMRI as well as insight into the structure-function relationship of the brain. The venerable but now dated ex vivo Brodmann map is currently being superseded by in vivo techniques that can better take into account intersubject variability. One popular in vivo method focusses on myeloarchitecture by measuring T1. This, however, probes only one aspect of cortical microstructure and is less useful in regions of low myelination. In contrast, diffusion MRI (dMRI) is sensitive to several additional microstructural features and can potentially provide a richer set of information regarding the architecture of grey matter microcircuitry. The following study used 3T HARDI data of multiple subjects to produce an entirely unsupervised, hemisphere-wide, group-average, parcellation. A qualitative assessment of the resulting cortical parcellation demonstrates several spatially coherent clusters in areas corresponding to well known functional anatomical areas. In addition, it exhibits some cluster boundaries that correlate with independently derived myelin mapping data for the same set of subjects, whilst also providing distinct clusters in areas (e.g., within MT+) where myelination is a less informative measurement.

Microstructural measures from diffusion MRI have been used for classification purposes in neurodegenerative and psychiatric conditions. Novel diffusion reconstruction models can lead to better and more accurate measures of tissue properties: each measure provides different information on white matter microstructure in the brain, revealing different signs of disease. The diversity of computable measures makes it necessary to develop novel classification procedures to capture all of the available information from each measure. Here we introduce a multichannel regularized logistic regression algorithm that classifies individuals’ diagnostic status based on several microstructural measures, derived from their diffusion MRI scans. With the aid of a TV-L1 prior, which ensures sparsity in the classification model, the resulting linear models point to the most classifying brain regions for each of the diffusion MRI measures, giving the method additional descriptive power. We apply our regularized regression approach to classify Alzheimer’s disease patients and healthy controls in the ADNI dataset, based on their diffusion MRI data.

SWEDD (scans without evidence of dopaminergic deficit) patients often are misdiagnosed as having Parkinson disease (PD) but later prove to have distinct features from PD. A commonly found symptom of these patients being focal and unilateral dystonia. SWEDD patients do not respond to dopaminergic therapy and may in turn benefit from management of adult onset dystonia, therefore early differential diagnosis from PD is important in order to avoid over diagnosis of PD and mismanagement of these patients. Along with a different pattern of tremor from PD, SWEDD patients do not show the non-motor symptoms associated with different stages of PD, do not exhibit cognitive deficit and depict a and task specificity of the motor symptoms without any deterioration along time. We hypothesized that the cingulum which is both functional in cognitive control and task set performance and is structurally affected in early stages of PD and is implicated in other non-motor symptoms of PD might be differentially affected in PD and SWEDD group. The diffusion imaging data from 39 PD, 28 SWEDD and 21 normal subjects were reconstructed in the MNI space using q-space diffeomorphic reconstruction (QSDR) to assess association of quantitative anisotropy (QA) and generalized fractional anisotropy (GFA) of left and right cingulum with the PD and SWEDD groups in the baseline level (diagnosis of PD or SWEDD) and age-sex matched controls. We found significant difference between GFA and QA of the left cingulum and QA of the right cingulum in SWEDD and control group versus the PD group. These results suggest a diagnostic value for the cingulum in early PD/SWEDD and also reveal that the diffusion metric parameters of cingulum that are not necessarily sensitive to axonal loss (GFA) might be a better indicator of microstructural changes in early PD/SWEDD.

In this work, we investigated the link between the blood-oxygen-level dependant (BOLD) effect observed using functional magnetic resonance imaging (fMRI) and the neurite density inferred from the Neurite Orientation Dispersion and Density Imaging (NODDI) model in some well-known lateralized cortical areas. We found a strong colocalization between those two parameters in lateralized areas such as the primary motor cortex, the language network, but also the primary visual cortex, which might indicate a strong link between microstructure and functional activity.

In this study, we assessed the evolution of diffusion MRI (dMRI) derived markers from different white matter models as progressive neurodegeneration occurs in transgenic Alzheimer rats (TgF344-AD) at 10, 15 and 24 months. We compared biomarkers reconstructed from Diffusion Tensor Imaging (DTI), Neurite Orientation Dispersion and Density Imaging (NODDI) and Mean Apparent Propagator (MAP)-MRI in the hippocampus, cingulate cortex and corpus callosum using multi-shell dMRI. We found that NODDI’s dispersion and MAP-MRI’s anisotropy markers consistently changed over time, possibly indicating that these measures are sensitive to age-dependent neuronal demise due to amyloid accumulation. Conversely, we found that DTI’s mean diffusivity, NODDI’s isotropic volume fraction and MAP-MRI’s restriction-related metrics all followed a two-step progression from 10 to 15 months, and from 15 to 24 months. This two-step pattern might be linked with a neuroinflammatory response that may be occurring prior to, or during microstructural breakdown. Using our approach, we are able to provide—for the first time—preliminary and valuable insight on relevant biomarkers that may directly describe the underlying pathophysiology in Alzheimer’s disease.

Schizophrenia is a kind of psychosis accompanied by cognitive deficits. In addition, white matter abnormalities are observed in various brain regions and tracts in the disease. Association of some tracts like superior longitudinal fasciculus (SLF), inferior longitudinal fasciculus (ILF), inferior fronto-occipital fasciculus (IFOF) with working memory function have been observed using diffusion MRI analysis methods such as tract-based spatial statistics (TBSS). Thus, we applied connectometry, not suffering from some limitations of tract specific analysis, in a group of 29 patients and 32 healthy controls to investigate association of working memory performance (as measured by letter-number sequencing test) with white matter integrity in recent-onset schizophrenic patients, who are less affected by antipsychotic medications. Connectometry is a recently introduced approach utilized to associate local connectomes with a study variable along the fiber pathways themselves instead of finding the difference in the whole fiber pathways. This study showed that lesser integrity of some fiber tracts like the arcuate fasciculus, the inferior longitudinal fasciculus, the body of corpus callosum and also some fibers of corticospinal tract, IFOF, and cingulum bundle associated with working memory deficits in schizophrenic patients while healthy controls did not show any correlation unless the percentage threshold was increased up to 45%. These results are consistent with previous ones to a large extent but we also found some fiber tracts other than previous studies like the body of corpus callosum and some fibers of corticospinal tract. On the whole, Our study further supports disconnectivity hypothesis in schizophrenia, playing a major role in cognitive dysfunction.