Daniel C. Alexander

NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain.

This paper introduces neurite orientation dispersion and density imaging (NODDI), a practical diffusion MRI technique for estimating the microstructural complexity of dendrites and axons in vivo on clinical MRI scanners. Such indices of neurites relate more directly to and provide more specific markers of brain tissue microstructure than standard indices from diffusion tensor imaging, such as fractional anisotropy (FA). Mapping these indices over the whole brain on clinical scanners presents new opportunities for understanding brain development and disorders. The proposed technique enables such mapping by combining a three-compartment tissue model with a two-shell high-angular-resolution diffusion imaging (HARDI) protocol optimized for clinical feasibility. An index of orientation dispersion is defined to characterize angular variation of neurites. We evaluate the method both in simulation and on a live human brain using a clinical 3T scanner. Results demonstrate that NODDI provides sensible neurite density and orientation dispersion estimates, thereby disentangling two key contributing factors to FA and enabling the analysis of each factor individually. We additionally show that while orientation dispersion can be estimated with just a single HARDI shell, neurite density requires at least two shells and can be estimated more accurately with the optimized two-shell protocol than with alternative two-shell protocols. The optimized protocol takes about 30 min to acquire, making it feasible for inclusion in a typical clinical setting. We further show that sampling fewer orientations in each shell can reduce the acquisition time to just 10 min with minimal impact on the accuracy of the estimates. This demonstrates the feasibility of NODDI even for the most time-sensitive clinical applications, such as neonatal and dementia imaging.

Evidence for Segregated and Integrative Connectivity Patterns in the Human Basal Ganglia

Detailed knowledge of the anatomy and connectivity pattern of cortico-basal ganglia circuits is essential to an understanding of abnormal cortical function and pathophysiology associated with a wide range of neurological and neuropsychiatric diseases. We aim to study the spatial extent and topography of human basal ganglia connectivity in vivo. Additionally, we explore at an anatomical level the hypothesis of coexistent segregated and integrative cortico-basal ganglia loops. We use probabilistic tractography on magnetic resonance diffusion weighted imaging data to segment basal ganglia and thalamus in 30 healthy subjects based on their cortical and subcortical projections. We introduce a novel method to define voxel-based connectivity profiles that allow representation of projections from a source to more than one target region. Using this method, we localize specific relay nuclei within predefined functional circuits. We find strong correlation between tractography-based basal ganglia parcellation and anatomical data from previously reported invasive tracing studies in nonhuman primates. Additionally, we show in vivo the anatomical basis of segregated loops and the extent of their overlap in prefrontal, premotor, and motor networks. Our findings in healthy humans support the notion that probabilistic diffusion tractography can be used to parcellate subcortical gray matter structures on the basis of their connectivity patterns. The coexistence of clearly segregated and also overlapping connections from cortical sites to basal ganglia subregions is a neuroanatomical correlate of both parallel and integrative networks within them. We believe that this method can be used to examine pathophysiological concepts in a number of basal ganglia-related disorders.

Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data.

This work details the observation of non‐Gaussian apparent diffusion coefficient (ADC) profiles in multi‐direction, diffusion‐weighted MR data acquired with easily achievable imaging parameters (b ≈ 1000 s/mm2). A technique is described for modeling the profile of the ADC over the sphere, which can capture non‐Gaussian effects that can occur at, for example, intersections of different tissue types or white matter fiber tracts. When these effects are significant, the common diffusion tensor model is inappropriate, since it is based on the assumption of a simple underlying diffusion process, which can be described by a Gaussian probability density function. A sequence of models of increasing complexity is obtained by truncating the spherical harmonic (SH) expansion of the ADC measurements at several orders. Further, a method is described for selection of the most appropriate of these models, in order to describe the data adequately but without overfitting. The combined procedure is used to classify the profile at each voxel as isotropic, anisotropic Gaussian, or non‐Gaussian, each with reference to the underlying probability density function of displacement of water molecules. We use it to show that non‐Gaussian profiles arise consistently in various regions of the human brain where complex tissue structure is known to exist, and can be observed in data typical of clinical scanners. The performance of the procedure developed is characterized using synthetic data in order to demonstrate that the observed effects are genuine. This characterization validates the use of our method as an indicator of pathology that affects tissue structure, which will tend to reduce the complexity of the selected model. Magn Reson Med 48:331–340, 2002.

Orientationally invariant indices of axon diameter and density from diffusion MRI

This paper proposes and tests a technique for imaging orientationally invariant indices of axon diameter and density in white matter using diffusion magnetic resonance imaging. Such indices potentially provide more specific markers of white matter microstructure than standard indices from diffusion tensor imaging. Orientational invariance allows for combination with tractography and presents new opportunities for mapping brain connectivity and quantifying disease processes. The technique uses a four-compartment tissue model combined with an optimized multishell high-angular-resolution pulsed-gradient-spin-echo acquisition. We test the method in simulation, on fixed monkey brains using a preclinical scanner and on live human brains using a clinical 3T scanner. The human data take about one hour to acquire. The simulation experiments show that both monkey and human protocols distinguish distributions of axon diameters that occur naturally in white matter. We compare the axon diameter index with the mean axon diameter weighted by axon volume. The index differs from this mean and is protocol dependent, but correlation is good for the monkey protocol and weaker, but discernible, for the human protocol where greater diffusivity and lower gradient strength limit sensitivity to only the largest axons. Maps of axon diameter and density indices from the monkey and human data in the corpus callosum and corticospinal tract reflect known trends from histology. The results show orientationally invariant sensitivity to natural axon diameter distributions for the first time with both specialist and clinical hardware. This demonstration motivates further refinement, validation, and evaluation of the precise nature of the indices and the influence of potential confounds.

Hemispheric asymmetries in language-related pathways: A combined functional MRI and tractography study

Functional lateralization is a feature of human brain function, most apparent in the typical left-hemisphere specialization for language. A number of anatomical and imaging studies have examined whether structural asymmetries underlie this functional lateralization. We combined functional MRI (fMRI) and diffusion-weighted imaging (DWI) with tractography to study 10 healthy right-handed subjects. Three language fMRI paradigms were used to define language-related regions in inferior frontal and superior temporal regions. A probabilistic tractography technique was then employed to delineate the connections of these functionally defined regions. We demonstrated consistent connections between Brocas and Wernickes areas along the superior longitudinal fasciculus bilaterally but more extensive fronto-temporal connectivity on the left than the right. Both tract volumes and mean fractional anisotropy (FA) were significantly greater on the left than the right. We also demonstrated a correlation between measures of structure and function, with subjects with more lateralized fMRI activation having a more highly lateralized mean FA of their connections. These structural asymmetries are in keeping with the lateralization of language function and indicate the major structural connections underlying this function.

Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue

Recently developed methods to extract the persistent angular structure (PAS) of axonal fibre bundles from diffusion-weighted magnetic resonance imaging (MRI) data are applied to drive probabilistic fibre tracking, designed to provide estimates of anatomical cerebral connectivity. The behaviour of the PAS function in the presence of realistic data noise is modelled for a range of single and multiple fibre configurations. This allows probability density functions (PDFs) to be generated that are parametrized according to the anisotropy of individual fibre populations. The PDFs are incorporated in a probabilistic fibre-tracking method to allow the estimation of whole-brain maps of anatomical connection probability. These methods are applied in two exemplar experiments in the corticospinal tract to show that it is possible to connect the entire primary motor cortex (M1) when tracing from the cerebral peduncles, and that the reverse experiment of tracking from M1 successfully identifies high probability connection via the pyramidal tracts. Using the extracted PAS in probabilistic fibre tracking allows higher specificity and sensitivity than previously reported fibre tracking using diffusion-weighted MRI in the corticospinal tract.

Persistent angular structure: new insights from diffusion magnetic resonance imaging data

We determine a statistic called the (radially) persistent angular structure (PAS) from samples of the Fourier transform of a three-dimensional function. The method has applications in diffusion magnetic resonance imaging (MRI), which samples the Fourier transform of the probability density function of particle displacements. The PAS is then a representation of the relative mobility of particles in each direction. In PAS-MRI, we compute the PAS in each voxel of an image. This technique has biomedical applications, where it reveals the orientations of microstructural fibres, such as white-matter fibres in the brain. Scanner time is a significant factor in determining the amount of data available in clinical brain scans. Here, we use measurements acquired for diffusion-tensor MRI, which is a routine diffusion imaging technique, but extract richer information. In particular, PAS-MRI can resolve the orientations of crossing fibres. We test PAS-MRI on human brain data and on synthetic data. The human brain data set comes from a standard acquisition scheme for diffusion-tensor MRI in which the samples in each voxel lie on a sphere in Fourier space.

Probabilistic Monte Carlo Based Mapping of Cerebral Connections Utilising Whole-Brain Crossing Fibre Information

A methodology is presented for estimation of a probability density function of cerebral fibre orientations when one or two fibres are present in a voxel. All data are acquired on a clinical MR scanner, using widely available acquisition techniques. The method models measurements of water diffusion in a single fibre by a Gaussian density function and in multiple fibres by a mixture of Gaussian densities. The effects of noise on complex MR diffusion weighted data are explicitly simluated and parameterised. This information is used for standard and Monte Carlo streamline methods. Deterministic and probabilistic maps of anatomical voxel scale connectivity between brain regions are generated.

Multiple-fiber reconstruction algorithms for diffusion MRI

This chapter reviews multiple‐fiber reconstruction algorithms for diffusion magnetic resonance imaging (MRI) and provides some initial comparative results for two such algorithms, q‐ball imaging and PASMRI, on data from a typical clinical diffusion MRI acquisition. The chapter highlights the problems with standard approaches, such as diffusion‐tensor MRI, to motivate a recent set of alternative approaches. The review concentrates on the software implementation of the new techniques. Results of the preliminary comparison show that PASMRI recovers the principal directions of simple test functions more consistently than q‐ball imaging and produces qualitatively better results on the test data set. Further simulations suggest that a moderate increase in data quality allows q‐ball, which is much faster to run, to recover directions with consistency comparable to that of PASMRI on the test data.

Compartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison

This paper aims to identify the minimum requirements for an accurate model of the diffusion MR signal in white matter of the brain. We construct a taxonomy of multi-compartment models of white matter from combinations of simple models for the intra- and the extra-axonal spaces. We devise a new diffusion MRI protocol that provides measurements with a wide range of imaging parameters for diffusion sensitization both parallel and perpendicular to white matter fibres. We use the protocol to acquire data from two fixed rat brains, which allows us to fit, study and compare the different models. The study examines a total of 47 analytic models, including several well-used models from the literature, which we place within the taxonomy. The results show that models that incorporate intra-axonal restriction, such as ball and stick or CHARMED, generally explain the data better than those that do not, such as the DT or the biexponential models. However, three-compartment models which account for restriction parallel to the axons and incorporate pore size explain the measurements most accurately. The best fit comes from combining a full diffusion tensor (DT) model of the extra-axonal space with a cylindrical intra-axonal component of single radius and a third spherical compartment of non-zero radius. We also measure the stability of the non-zero radius intra-axonal models and find that single radius intra-axonal models are more stable than gamma distributed radii models with similar fitting performance.