White matter characterization with diffusional kurtosis imaging

Abstract

Diffusional kurtosis imaging (DKI) is a clinically feasible extension of diffusion tensor imaging that probes restricted water diffusion in biological tissues using magnetic resonance imaging. Here we provide a physically meaningful interpretation of DKI metrics in white matter regions consisting of more or less parallel aligned fiber bundles by modeling the tissue as two non-exchanging compartments, the intra-axonal space and extra-axonal space. For the b-values typically used in DKI, the diffusion in each compartment is assumed to be anisotropic Gaussian and characterized by a diffusion tensor. The principal parameters of interest for the model include the intra- and extra-axonal diffusion tensors, the axonal water fraction and the tortuosity of the extra-axonal space. A key feature is that these can be determined directly from the diffusion metrics conventionally obtained with DKI. For three healthy young adults, the model parameters are estimated from the DKI metrics and shown to be consistent with literature values. In addition, as a partial validation of this DKI-based approach, we demonstrate good agreement between the DKI-derived axonal water fraction and the slow diffusion water fraction obtained from standard biexponential fitting to high b-value diffusion data. Combining the proposed WM model with DKI provides a convenient method for the clinical assessment of white matter in health and disease and could potentially provide important information on neurodegenerative disorders.

Introduction

Diffusion weighted imaging (DWI) is a widely applied and clinically important MRI method used to measure the micron-scale displacement of water molecules in the brain. Diffusion on this length scale is very sensitive to the microstructure of neural tissue, being strongly affected by the number, orientation and permeability of barriers (e.g. myelin) and the presence of various cell types and organelles (e.g. neurons, dendrites, axons, neurofilaments and microtubules) (Beaulieu, 2002). Moreover, as the tissue microarchitecture is closely associated with function, DWI offers a unique and very powerful method to study brain pathology.

By far the most widely applied DWI technique to date is diffusion tensor imaging (DTI), in which the apparent diffusion tensor is estimated from the measurement of the apparent diffusion coefficient (ADC) along multiple directions (Basser et al., 1994). Several rotationally invariant diffusion metrics can be extracted from a DTI-analysis, including the mean diffusivity (MD) and the fractional anisotropy (FA), which are both popular markers of white matter (WM) integrity (Pierpaoli and Basser, 1996). In addition, DTI is also a commonly used method for fiber tractography, i.e. reconstructing the pathways of major WM fiber tracts through the brain (Basser et al., 2000). Although DTI is an important technique for investigating mechanisms of health and disease in brain WM (Thomason and Thompson, 2011), among its limitations are the inability of DTI-based fiber tractography to resolve fiber crossings, and the lack of specificity to histological features.

While DWI has the potential to fully characterize the water diffusion properties of the brain, it is well recognized that DTI yields only a fraction of the information potentially accessible with DWI, which is mainly due to the fact that DTI is based upon a Gaussian approximation of the diffusion displacement probability function. Non-Gaussian diffusion is readily observed in the brain when applying diffusion gradients such that the corresponding b-value (diffusion weighting) is significantly higher than the typical DTI b-value of 1000 s/mm² (Assaf and Cohen, 1998, Niendorf et al., 1996). The non-Gaussian diffusion effects in the brain are believed to arise from diffusion restricted by barriers, such as cell membranes and organelles, as well as the presence of distinct water compartments with differing diffusivities.

Several techniques for assessing non-Gaussian diffusion have been developed (Alexander et al., 2002, Jensen and Helpern, 2010, Liu et al., 2004, Maier et al., 2004, Tuch, 2004, Wedeen et al., 2005). Among them, diffusional kurtosis imaging (DKI) has been proposed as a minimal extension of DTI that enables the quantification of non-Gaussian diffusion through the estimation of the diffusional kurtosis, a quantitative measure of the non-Gaussianity of the diffusion process (Jensen et al., 2011, Jensen et al., 2005, Lu et al., 2006). A typical DKI-protocol for brain requires a maximum b-value of 2000 s/mm² and DWI measurements along a minimum of 15 different directions (Tabesh et al., 2011). Quantitative rotationally invariant diffusion metrics can be extracted from the DKI-analysis, such as the mean kurtosis (MK), radial kurtosis and axial kurtosis, that are of potential interest to the study of white and gray matter integrity. So far, DKI has shown promising preliminary results for several brain diseases including stroke (Jensen et al., 2011), attention-deficit hyperactivity disorder (ADHD) (Helpern et al., 2011), the staging of glioblastomas (Raab et al., 2010), as well as normal aging (Falangola et al., 2008). Additionally, DKI is potentially useful in tractography for resolving crossing fibers (Lazar et al., 2008). However, similar to DTI, DKI metrics of non-Gaussianity are pure diffusion measures and lack microstructural and pathological specificity. Furthermore, a clear explanation for the microscopic origin of the diffusional kurtosis in WM has not been previously given.

The extraction of cell properties and histological details of WM necessarily relies on biophysical modeling of the DWI signal, and on the subsequent interpretation of the model parameters in terms of intrinsic tissue properties. The most basic model used to analyze high b-value data is the biexponential model that is based on the assumption of two non-exchanging compartments: one exhibiting fast diffusion, and the other slow diffusion. Despite good fits of the DWI signal, the original attempt to assign the two compartments to the intra- and extracellular space is still a subject of a debate (Assaf and Cohen, 1998, Clark and Le Bihan, 2000, Kiselev and Il'yasov, 2007, Maier et al., 2004, Mulkern et al., 2000, Niendorf et al., 1996). However, for the WM, assigning the highly restricted water diffusion inside the axons to the slow compartment and the less hindered diffusion in the extra-axonal space to the fast compartment has been justified experimentally (Assaf and Basser, 2005, Assaf and Cohen, 2000, Assaf et al., 2004) and theoretically (Fieremans et al., 2010b).

A number of advanced morphology-based models have been proposed to interpret DWI in brain WM. As an early and comprehensive model, Stanisz et al. represented bovine optic nerve tissue by three compartments formed by spherical glial cells, prolate ellipsoidal axons and the extracellular space. By using this analytical model, the compartment parameters, such as volume fractions, compartment size, membrane permeability and diffusivity, could be estimated for fixed tissue (Stanisz et al., 1997). The less elaborate CHARMED model (Assaf and Basser, 2005, Assaf et al., 2004) assumes two types of diffusion in the brain: restricted diffusion inside impermeable cylindrical axons and hindered diffusion in the extra-axonal space, allowing estimation of the compartment volume fractions and diffusivities for the human brain in vivo. In the framework of “Axcaliber,” the CHARMED model was further developed to extract the axonal diameter distribution, which was evaluated ex vivo on pig spinal cord (Assaf et al., 2008) and in vivo in the corpus callosum of a rat (Barazany et al., 2009). A similar model of two non-exchanging compartments has been developed by Jespersen et al., wherein the restricted diffusion component arises from an angular distribution of narrow cylinders (representing the axons and dendrites), allowing one to estimate the compartment volume fractions and diffusivities, as well as the intra-voxel distribution of fiber orientations, as demonstrated in fixed brain tissue of the rat and baboon (Jespersen et al., 2010, Jespersen et al., 2007). Recently, Alexander et al. proposed a four-compartment brain WM model that allows the axon diameter and density to be derived, as illustrated in fixed monkey brain and in vivo human brain (Alexander et al., 2010).

To extract all the features of the models summarized above, DWI data are needed for several high b-values (i.e., b ≥ 3000 s/mm²), multiple diffusion gradient directions and/or different diffusion times, which necessitates long scan times and limits the applicability of these models for most clinical studies. Alternatively, DKI is a clinically feasible technique with acquisition times only a few minutes longer than conventional DTI. However, as DKI metrics of non-Gaussianity are model-independent, they must be augmented with a tissue model to help interpret the physical meaning of any changes associated with disease processes.

In this work, we focus on WM regions consisting of more or less parallel aligned fiber bundles and propose a model of diffusion in the WM that is suitable for DKI analysis and provides a more meaningful physical interpretation of DKI diffusion metrics in WM. We first introduce the WM diffusion model of two non-exchanging compartments: the intra-axonal space, consisting of impermeable cylindrical axons (IAS), and the extra-axonal space (EAS). Next, we demonstrate how the diffusion in each compartment appears to be Gaussian for the b-values typically used in DKI and hence can be described by compartment-specific diffusion tensors. Combining this model with DKI provides analytical expressions for the intra- and extra-axonal diffusion tensors, and allows for quantification of the axonal water fraction (AWF) and of the tortuosity of the EAS. We use then the newly proposed model to characterize human brain WM in vivo and discuss the biological significance of the tissue parameters as derived using DKI. Finally, we compare the AWF obtained from DKI-analysis to the slow diffusion fraction obtained from conventional biexponential fitting to high b-value diffusion data.