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

Abstract

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.

Introduction

Dendrites and axons, known collectively as neurites, are projections of neurons. They are the cellular building blocks of the computational circuitry of the brain. Quantifying neurite morphology in terms of its density and orientation distribution provides a window into the structural basis of brain function both in normal populations and in populations with brain disorders. For example, the branching complexity of the dendritic trees, measured in terms of dendritic density, reflects the nature of their computation and hence their function: the areas of the cortex with less complex dendritic structures engage in the early stages of information processing while the regions with more complex dendritic structures participate in the later stages of processing (Jacobs et al., 2001). Neurite morphology is also a key marker of brain development and aging. An increase in the dispersion of neurite orientation distribution is associated with brain development (Conel, 1939), whereas a reduction in the dendritic density is linked with the aging of the brain (Jacobs et al., 1997). Changes in neurite morphology are additionally implicated in numerous neurological disorders, including multiple sclerosis (Evanglou et al., 2000), amyotrophic lateral sclerosis (Bruijn et al., 2004), and Alzheimer's disease (Paula-Barbosa et al., 1980). However, due to its reliance on scarcely available postmortem tissue samples, the quantitative analysis of neurite morphology, despite its importance, is not widely applied. The development of a non-invasive imaging-based solution holds the key to realize such quantification in vivo.

Diffusion magnetic resonance imaging (MRI) provides unique insight into tissue microstructure and is arguably the most promising candidate for in vivo quantification of neurite morphology. It works by sensitizing MRI measurements to the displacement pattern of water molecules undergoing diffusion. As the water displacement pattern is influenced by tissue microstructure, by measuring this displacement pattern, diffusion MRI is able to distinguish different microstructural environments. In the case of neuronal tissues, during the typical time scale of a diffusion MRI experiment, two kinds of microstructural environments can be identified, which are characterized by either hindered or restricted diffusion (Assaf and Cohen, 2000). Hindered diffusion refers to the diffusion of water with a Gaussian displacement pattern. It characterizes the water in the extra-cellular space defined by cellular membranes of somas and glial cells. Restricted diffusion refers to the diffusion of water in restricted geometries. It is characterized by a non-Gaussian pattern of displacement and describes the water in the intra-cellular space bounded for example by axonal or dendritic membranes. The differentiation of intra- and extra-cellular water forms the basis of measuring neurite morphology via diffusion MRI.

Currently, the standard clinical diffusion MRI technique is diffusion tensor imaging (DTI) (Basser et al., 1994). This technique provides sensitivity to tissue microstructure but lacks specificity for individual tissue microstructure features (Pierpaoli et al., 1996). DTI provides simple markers, such as mean diffusivity (MD) and fractional anisotropy (FA), that are widely used as surrogate measures of microstructural tissue change during normal brain development and aging, or during the onset and progression of neurological disorders (see, e.g., Salat et al. (2009) and Bodini and Ciccarelli (2009) for reviews). However, despite their sensitivity, these markers are inherently non-specific (Pierpaoli et al., 1996). For instance, the observation of a reduction in FA may be caused by a reduction in neurite density, an increase in the dispersion of neurite orientation distribution, as well as various other tissue microstructural changes (Beaulieu, 2009). Hence, a change in these statistics may not be attributed to specific changes in tissue microstructure.

Towards in vivo quantification of neurite morphology, the recent trend in diffusion MRI is in developing more advanced techniques that can measure tissue microstructure features directly (see Assaf and Cohen (2009) for a review). A particularly successful approach, pioneered by Stanisz et al. (1997), is the model-based strategy in which a geometric model of the microstructure of interest predicts the MR signal from water diffusion within. The authors propose a model of white matter microstructure that consists of individual compartments for glial cells, axons, and extra-cellular space. The glial and axon compartments have restricted diffusion; extra-cellular diffusion is hindered with apparent diffusivities calculated via a tortuosity model. The model allows the exchange of water between the intra-cellular and extra-cellular compartments.

Subsequent white matter models include the ball-and-stick model (Behrens et al., 2003), which represents the intra-cellular compartment as cylinders of zero radius and extra-cellular diffusion as isotropic and unrestricted. The composite hindered and restricted water diffusion (CHARMED) model (Assaf and Basser, 2005, Assaf et al., 2004) represents the intra-cellular compartment as impermeable parallel cylinders with a gamma distribution of radii. The signal for the extra-cellular compartment comes from an anisotropic diffusion tensor model. In the original model, the distribution of radii is fixed to a biologically plausible distribution, but subsequent work (Assaf et al., 2008) fits these parameters. Barazany et al. (2009) add a free-water compartment necessary for in vivo imaging data. Alexander (2008) reduces the CHARMED model to a single radius, and subsequently Alexander et al. (2010) include tortuosity models and isotropically restricted compartments, in a similar way to Stanisz et al. (1997), and a free-water compartment as in Barazany et al. (2009), to obtain the minimal model of white matter diffusion (MMWMD). Most recently, Panagiotaki et al. (2012) construct a taxonomy of compartment models for white matter including those above and a range of intermediate and additional compartment combinations. They compare them with each other and with various multi-exponential models using fixed-brain data to demonstrate the need for both a restricted axonal compartment and an isotropically restricted compartment as in Stanisz et al. (1997), Alexander et al. (2010).

Assaf and Basser (2005) demonstrate for the first time that the CHARMED model can provide sensible maps of the volume fraction of intra-cellular space, the axon density, in in vivo human brain imaging on a clinical MRI scanner. However, by representing axons as parallel cylinders, models such as ball-and-stick (Behrens et al., 2003), CHARMED, MMWMD, and the entire hierarchy of compartment models in (Panagiotaki et al., 2012) cannot recover the effect of axonal-orientation dispersion due to bending and fanning of axon bundles widespread throughout the brain (Bürgel et al., 2006, House and Pansky, 1960). By relaxing this constraint, more recent models (Kaden et al., 2007, Sotiropoulos et al., 2012, Zhang et al., 2011) support a more realistic description of white matter beyond the most coherently-oriented structures, such as the corpus callosum, and provide an estimate of orientation dispersion.

Going beyond the modeling of white matter, Jespersen et al. (2007) propose an analytic model of neurites that support the modeling of both gray and white matter. Using a truncated spherical harmonic series, the neurite model approximates an arbitrary orientation distribution of dendrites and axons, which is essential for modeling both low-to-moderately dispersed axons in white matter and highly dispersed dendritic trees in gray matter. Using data from ex vivo imaging of a baboon brain sample, the authors demonstrate for the first time that both neurite density and its orientation distribution can be quantified using diffusion MRI. However, the imaging protocol consists of 153 diffusion-weighted images spread over 17 b-values with the largest equal to 15,000 s/mm², making it impractical for clinical translation.

Despite the lack of clinically feasible imaging protocols, emerging evidence suggests that, in both gray and white matter, neurite morphology determined from diffusion MRI is comparable to independent measures derived from histology. Jespersen et al. (2010) show that neurite density estimates, determined using the model in Jespersen et al. (2007), correlate more strongly with both optical myelin staining intensity and stereological estimation of neurite density using electronmicroscopy than with DTI-derived markers. More recently, Jespersen et al. (2012) demonstrate that neurite orientation distributions derived from diffusion MRI show excellent agreement to those quantified using a quantitative Golgi analysis. These recent findings are extremely encouraging and motivate the current work.

The aim of this work is to develop a clinically feasible technique for in vivo neurite orientation dispersion and density imaging, which we refer to hereafter as NODDI. Our approach is to first choose a model that is sufficiently simple, yet complex enough to capture the key features of neurite morphology, then identify the optimal acquisition protocol for such a model under scanner hardware and acquisition time constraints typical in a clinical setting. Specifically, NODDI adapts the orientation-dispersed cylinder model in Zhang et al. (2011) to estimate only neurite density and orientation dispersion. The acquisition protocol is determined using the experiment design optimization in Alexander (2008) under an acquisition time constraint of 30 min. Using both synthetic and in vivo human brain data, we assess the performance of the optimized protocol, in terms of the accuracy and precision of its microstructure parameter estimates, against alternative protocols.

The rest of the paper is organized as follows: the Materials and methods section describes the NODDI tissue model, protocol optimization, data acquisition, model fitting, and preprocessing; the Experiments and results section gives the experimental design and results; and the Discussion section summarizes the contribution and discusses future work.