Towards better MR characterization of neural tissues using directional diffusion kurtosis analysis
Introduction
Diffusion kurtosis imaging (DKI) was recently proposed to characterize the non-Gaussian water diffusion behavior in neural tissues (Fieremans et al., 2008, Jensen et al., 2005, Lu et al., 2006). Biological tissues are heterogeneous in nature comprising multiple compartments (Le Bihan, 1991). Thus the Gaussian distribution generally assumed for free or unrestricted water diffusion is insufficient to describe the diffusion process in biological environment (Karger, 1985). In addition, the dependency of diffusion-weighted (DW) signal on b-value has been observed to be non-monoexponential in neural tissues (Basser and Jones, 2002, Mulkern et al., 1999, Niendorf et al., 1996). To characterize such non-Gaussian diffusion behavior, kurtosis, the 4th central moment of the diffusion distribution (Balanda and Macgillivray, 1988), was introduced (Jensen et al., 2005). It is a dimensionless measure that can be either positive or negative. Positive kurtosis means that distribution is more sharply peaked than Gaussian. The higher the diffusion kurtosis, the more the water molecule diffusion deviates from Gaussian distribution, indicative of a more restricted diffusion environment. Apparent diffusion kurtosis has been estimated by acquiring DW signals at multiple b-values up to a maximum of 2500 s/mm2 in humans (Jensen et al., 2005, Lu et al., 2006). Because the 4th order diffusion kurtosis tensor (KT) is fully symmetric and has 15 independent components, DKI experiments are typically performed in more than 15 directions to obtain the full KT.
Several approaches have been proposed to study the non-monoexponential diffusion behavior. They include the multi-compartment model (Clark et al., 2002), statistical diffusion model (Yablonskiy et al., 2003), generalized diffusion tensors (Liu et al., 2004, Ozarslan and Mareci, 2003) and q-space imaging (Callaghan, 1991). Among them, q-space imaging, in which water diffusion displacement probability profile is estimated, is deemed to provide a robust characterization of the diffusion related structural changes in diseased neural tissues (Assaf et al., 2005, Assaf et al., 2003, Biton et al., 2006, Nossin-Manor et al., 2007). Despite of the advantage of quantitatively measuring the water displacement, q-space imaging often requires a long scan time, large b-values and a strong gradient. The DKI approach largely circumvents these limitations, offering a more practical means to investigate the non-Gaussian diffusion behavior with relative ease and reasonable speed. It utilizes the non-monoexponential dependence of DW signals on b-values to map the diffusion kurtosis as a biomarker for microstructural changes in various neural tissues, including both white and gray matters.
Recent experimental findings in human DKI studies were promising (Falangola et al., 2007a, Falangola et al., 2007b, Helpern et al., 2007, Jensen et al., 2005, Lu et al., 2006, Ramani et al., 2007). Mean kurtosis (MK), the average apparent kurtosis along all diffusion gradient encoding directions, was measured and demonstrated to offer an improved sensitivity in detecting developmental and pathological changes in neural tissues as compared to the conventional diffusion tensor imaging (DTI). One might argue that by simply taking the mean of the apparent kurtoses measured along all diffusion directions it would reduce the sensitivity and specificity in probing diffusion kurtosis change occurring along a specific direction, for instance, parallel or perpendicular to the principal diffusion eigenvector as denoted as axial or radial direction, respectively. Given that axial and radial diffusivity analyses have been successfully employed in numerous studies to elucidate the specific neural tissue pathologies in animal models (Song et al., 2003, Song et al., 2002, Sun et al., 2006) and humans (Trip et al., 2006), it is valuable to analyze the directional kurtoses by obtaining the water diffusion kurtoses along these two directions. Such directional diffusion kurtosis analysis may provide unique and complementary information regarding the biological systems, thus improving the MR diffusion characterization of neural tissues in normal, developmental or pathological states.
In this study, an orthogonal transformation of the 4th order KT was proposed to compute the diffusion kurtoses along the directions of the three diffusion eigenvectors. Histological fixation is known to alter the cellular structure and hence the restriction to water diffusion (Does et al., 2003, Schwartz et al., 2005, Takahashi et al., 2002, Thelwall et al., 2006, Yong-Hing et al., 2005), likely leading to varying extents of water diffusion restriction along the axial and radial directions. Therefore, DKI experiments were performed in both normal and formalin-fixed adult rat brains to document both DKI and DTI estimates in various brain tissues, and to evaluate whether directional kurtosis analysis improves tissue characterization.
Section snippets
Theory
In conventional DTI, the 2nd order diffusion tensor (DT) is fully characterized by its eigenvalues (λi with i = 1, 2 3 and λ1 > λ2 > λ3) and the corresponding orthonormal eigenvectors that can be obtained by matrix diagonalization (Basser et al., 1994). In DKI (Jensen et al., 2005, Lu et al., 2006), both apparent diffusion coefficient (Dapp) and apparent diffusion kurtosis (Kapp) along each applied diffusion gradient direction are estimated together by fitting the following equation with the multiple
DTI- and DKI-derived parametric maps
Fig. 1, Fig. 2 illustrate the typical MD, λ//, λ┴, FA, color-coded FA direction, MK, K//, K┴, FAK and ME maps from an intact in vivo rat brain and a formalin-fixed ex vivo rat brain, respectively, with Fig. 3 showing the maps from the first slice only. Different contrasts were generally observed between various DTI and DKI maps, particularly between the directional diffusivity and kurtosis maps. The image contrasts of both DTI- and DKI-derived parametric maps were found to alter under formalin
Discussions
Numerous DTI studies have been performed successfully by utilizing the directional diffusion analysis to detect and monitor various pathophysiological changes in neural tissues, including brain and spinal cord (Basser and Pierpaoli, 1996, Kim et al., 2007, Song et al., 2003, Sun et al., 2006). Water molecule diffusion in vivo is a complex process with restriction incurred by numerous determinants such as intra-/extracellular compartments, permeability or water exchange, and potentially other
Conclusions
Directional diffusion kurtosis analysis was presented to study the non-Gaussian diffusion behavior along the three eigenvectors of the conventional diffusion tensor. Radial and axial kurtoses were derived for the first time and applied to DKI study of rodent brains under in vivo and formalin-fixed conditions. Various kurtosis estimates were documented for WM and GM tissues, and compared to the diffusion tensor estimates. The results demonstrated that kurtosis estimates can reveal different
Acknowledgments
The authors would like to thank Drs. Jens H. Jensen and Joseph A. Helpern at New York University School of Medicine in New York, and Dr. Hanzhang Lu at UT Southwestern Medical Center in Dallas for providing assistance with data processing procedures. This work was supported in part by the University of Hong Kong Committee on Research and Conference Grants and Hong Kong Research Grant Council.
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