White matter characterization with diffusional kurtosis imaging
Highlights
► DKI is a clinically feasible extension of DTI to probe restricted diffusion in tissue. ► We provide a physically meaningful interpretation of DKI metrics in white matter. ► White matter parameters: intra- and extra-axonal diffusivities, axonal water fraction. ► White matter parameters estimated in vivo in healthy brain agree with prior knowledge. ► Convenient method for the clinical assessment of white matter in health and disease.
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.
Section snippets
Methods
In this section, we first describe the WM model, discuss the validity of its assumptions, and outline its relation to DKI. We then specify the datasets, imaging protocols and data processing needed to evaluate the derived WM parameters.
Results
This section shows the results of testing the new WM DKI model; first we evaluate the parametric maps of three healthy young adults, then we show the comparison between the DKI-derived AWF and the slow diffusion fraction as obtained from biexponential fitting in WM regions where the biexponential model is physically justified.
Discussion
DKI has been introduced as a clinically feasible technique to study restricted diffusion in brain WM (Jensen and Helpern, 2010, Jensen et al., 2005). It is a fast and robust method that quantifies the diffusion coefficient and diffusional kurtosis, both physically well-defined, model independent, diffusion metrics. In this work, we provide a physical interpretation for the diffusional kurtosis by augmenting the DKI metrics with an idealized model for WM tissue, as described in detail in Model
Conclusion
We have proposed an idealized two-compartment no exchange diffusion model of white matter suitable for analysis with diffusional kurtosis imaging (DKI) diffusion metrics. Based on this model, standard DKI metrics can be used to estimate the intra- and extra-axonal diffusivities, the axonal water fraction, and the tortuosity of the extra-axonal geometry. Values for these parameters obtained in healthy young adults agree well with those of prior studies. The axonal water fraction and the
Acknowledgments
We thank Caixa Hu, Dmitry Novikov and Ali Tabesh for technical assistance and discussions. This work was supported by National Institutes of Health research grants (1R01AG027852 and 1R01EB007656 (to J.A.H)), the Litwin Foundation (to J.A.H.) and the King Baudouin Foundation (Henri Benedictus Fund (to E.F.)).
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Present address: Department of Radiology and Radiological Science, Medical University of South Carolina, Charleston. SC, USA.