Does diffusion kurtosis imaging lead to better neural tissue characterization? A rodent brain maturation study
Introduction
Magnetic resonance (MR) diffusion tensor imaging (DTI) has been shown to provide unique structural information in characterizing tissue microstructure (Basser, 1995, Basser and Pierpaoli, 1996), which cannot be easily revealed non-invasively by other modalities. The three-dimensional water diffusion probability distribution in an anisotropic medium has been quantified by a rank 2 tensor in DTI (Basser, 1995) where the three eigenvectors correspond to the axes of a tri-axial diffusivity ellipsoid. The commonly employed rotationally invariant parameters derived from the diffusion tensor (DT) include the mean diffusivity (MD), fractional anisotropy (FA), axial diffusivity (λ//) and radial diffusivity (λ⊥). It has been observed that water diffusion is anisotropic in the central nervous system (Moseley et al., 1990). The origin of the anisotropy in white matter (WM) nerve fibers can be complex and it cannot be solely ascribed to myelination (Beaulieu, 2002). Inherent structures of axons can also alter the diffusion properties. The degree of anisotropy and the directional diffusivities have been shown to correlate well with microstructural changes of neural tissues in certain pathological states (Beaulieu et al., 1996, Song et al., 2003, Sun et al., 2006).
The orientational neuroarchitecture can be inferred from DTI, but it is inadequate to resolve the heterogeneity within a voxel (Tuch et al., 2002). For instance, crossing or diverging WM fibers can appear to be isotropic and DTI may fail to sensitively probe these structures. Moreover, the gray matter (GM) is relatively isotropic and DTI is not truly effective in characterizing water diffusion changes in GM. Apart from the inability to resolve the heterogeneity, the assumption of monoexponential signal attenuation in DTI due to diffusion was observed to be invalid when a high b-value was employed (Assaf and Cohen, 1998, Basser and Jones, 2002, Mulkern et al., 1999, Niendorf et al., 1996). DTI estimation of diffusivity is based on the implicit assumption that diffusion occurs in an unrestricted environment. In biological tissues, there is always structural hindrance or restriction that prohibits truly free water diffusion and hence we can apply a higher b-value to probe such restricted diffusion. The deviation from the monoexponential decay leads to the fact that the apparent diffusion coefficient depends on the b-values chosen, complicating quantitative and comparative studies. There are various approaches to characterize or quantify this non-monoexponential decay. As there are at least two types of compartments (intra- and extra-cellular) in the tissue, a bi-exponential model was proposed (Mulkern et al., 1999, Niendorf et al., 1996). Despite the good fit of the signal attenuation, the estimated volume fractions of the fast and slow diffusion components were found to be inconsistent with the known ratio between the intra-cellular and extra-cellular compartments (Clark et al., 2002, Clark and Le Bihan, 2000, Minati et al., 2007, Niendorf et al., 1996).
More generalized approaches have been attempted. Q-space imaging estimates the water diffusion displacement probability profile (Callaghan, 1991) and it has been shown that structural changes in diseased neural tissues can be detected. (Assaf et al., 2003, Assaf et al., 2005, Biton et al., 2006, Nossin-Manor et al., 2007). Although q-space can fully describe the diffusion profile, it often requires prohibitively long scan time and is hardware demanding. The Bloch–Torrey equation for diffusion has been generalized for a multiple rank tensor in generalized DTI (GDTI) (Liu et al., 2004, Ozarslan and Mareci, 2003). Formulations have been introduced, but they have not shown much success in practice because the approach lacks physical relevance and interpretation is problematic. Diffusion kurtosis imaging (DKI) has been proposed recently to probe non-Gaussian diffusion property (Jensen and Helpern, 2003, Jensen et al., 2005, Lu et al., 2006). DKI provides a second-order approximation of water displacement distribution, in which both the apparent diffusion coefficient and apparent diffusion kurtosis can be obtained. Kurtosis here refers to the excess kurtosis and is the normalized and standardized fourth central moment of water displacement distribution (Jensen et al., 2005). It is a dimensionless measure quantifying the deviation of the water diffusion profile from Gaussian distribution (that is inherent to free or unrestricted diffusion), and hence revealing the degree of diffusion restriction. A positive kurtosis implies that the distribution is more sharply peaked than a Gaussian one. Both diffusivity and kurtosis are fitted from a non-monoexponential equation in DKI. The diffusivity estimated is different from that computed using the monoexponential model unless the kurtosis is zero. Although in theory DKI is robust, the sensitivity of this approach for tissue characterization has not yet been evaluated.
There were a few human brain studies that measured mean kurtosis (MK) to detect pathological changes in neural tissues (Falangola et al., 2007a, Falangola et al., 2007b, Helpern et al., 2007, Jensen et al., 2005, Latt et al., 2008, Lu et al., 2006, Minati et al., 2007, Ramani et al., 2007). They demonstrated that MK can yield information different from the FA obtained with DTI and that MK can detect pathophysiological changes. In recent studies, directional kurtosis analysis was formulated and applied to examine the effect of rat brain fixation (Hui et al., 2008, Qi et al., 2008). Directional kurtoses along the eigenvectors of DT were computed by orthogonal transformation (Hui et al., 2008, Qi et al., 2008), providing directionally specific kurtosis information. The study demonstrated that various kurtosis estimates can reveal information different from diffusivity estimates, and the effect of fixation was documented. Due to the dramatic structural changes involved in fixation, the study cannot directly evaluate how sensitive DKI can detect neural tissue alterations. In the current study, in vivo rat brain maturation was studied by DKI to investigate the efficacy of DKI in detecting subtle morphological changes in neural tissues.
There are various biological events that can affect water diffusion properties in both WM and GM during normal brain maturation. DTI has been applied in various human (Dubois et al., 2006, Huang et al., 2006, Huppi and Dubois, 2006, Neil et al., 2002, Suzuki et al., 2003) and rodent studies (Bockhorst et al., 2008, Chahboune et al., 2007, Harsan et al., 2006, Larvaron et al., 2007, Mori et al., 2001, Sizonenko et al., 2007, Verma et al., 2005, Zhang et al., 2003) and it was found to be sensitive to brain development. WM maturation processes include denser packing of fiber bundles and axons, increased axon diameter and number of neurofibrils, and changes of axonal membrane permeability (Dubois et al., 2006, Huppi and Dubois, 2006, Larvaron et al., 2007, Neil et al., 2002, Suzuki et al., 2003). There is also increased complexity in extracellular matrix and microtubule associated proteins (Huppi and Dubois, 2006, Neil et al., 2002, Suzuki et al., 2003). In GM, apart from the addition of basal dendrites, modification in tissue water content and cell packing density, it is known that changes in cortical cytoarchitecture affect the water diffusion behavior (Bockhorst et al., 2008, Huppi and Dubois, 2006, Sizonenko et al., 2007). The anisotropic diffusion observed in immature cortex is believed to be caused by radial glial cells. The transition of radial glia to astrocytic neuropil is shown to reduce the anisotropy when the brain matures (Bockhorst et al., 2008, Sizonenko et al., 2007). These subtle developmental changes in normal rat brain maturation can provide an effective biological platform to evaluate the sensitivity of DKI. Furthermore, hypoxic–ischemic insults in neonates cause mild but persistent injuries in both WM and GM (Wang et al., 2008, Wang et al., 2006, Yang et al., 2008, Yang and Wu, 2008). To study these pathological changes in neonates, normal brain developmental changes have to be documented in depth (Bockhorst et al., 2008). A recent longitudinal study of normal rat brain development showed that DTI parameters were correlated with the maturation processes (Bockhorst et al., 2008). However, the use of a single non-zero b-value in the study might limit the interpretation of the DTI findings in view of the complex maturation processes. Most of the other rodent brain developmental studies were either performed ex vivo or focused on few particular structures. However, ex vivo studies may not truly exploit the power of MR diffusion in the study of developmental brain. Although the diffusion anisotropy was maintained after fixation (Sun et al., 2005), directional diffusivities and kurtoses can change substantially and vary with sample temperature (Hui et al., 2008). Thus their absolute values cannot be used for comparison among studies in a robust manner.
In this study, normal postnatal rat brain development was investigated to assess the sensitivity of DKI. Directional kurtosis analysis was employed so that the kurtoses along the DT eigenvectors could be measured. Various WM and GM structures were analyzed for different postnatal stages. In addition, these diffusivity and kurtosis parameters were compared with those derived from the monoexponential model used by conventional DTI.
Section snippets
Theory
Conventional DTI assumes Gaussian (i.e., unrestricted and free) diffusion. The apparent diffusivity (Dapp) is derived by linearly fitting the DW signals acquired with one or more non-zero b-values to the following linear equation:
In DKI, logarithmic expansion of signal decay is used to estimate both apparent diffusivity and diffusion kurtosis (Kapp) (Jensen et al., 2005, Lu et al., 2006). Kurtosis is a quantitative measurement of the deviation from Gaussian form. DW signals
Evolution of DKI parameters with age
The representative normalized DW signal decays in CP and CT observed in the 3 age groups are shown in Fig. 1. The mean normalized signal is the average of the normalized signals along the 30 directions of diffusion encoding gradients, and the error bar indicates the standard deviation (SD). It can be clearly observed that the attenuation was not monoexponential and hence conventional DTI with a single non-zero b-value was not adequate to fully characterize the signal decay. The deviation from
Evolution of DKI parameters with age
In the direction along the principal eigenvector of DT, the generally increased diffusivity may reflect the increase in axoplasmic flow in WM during the myelination period (Suzuki et al., 2003). Yet at the same time, axonal pruning may shorten the axon length and increase restriction (Bockhorst et al., 2008). The competition among these biological events makes it difficult to characterize the changes along axonal direction using conventional DTI. The trends of λ// in normal rodent brain
Conclusions
DKI has been demonstrated to be highly sensitive and directionally specific in detecting brain maturation processes. DKI approach quantifies both diffusivities and kurtoses; together they provided better detection and characterization of the developmental changes in various WM and GM structures studied. K// and K⊥ increased from P13 to P120, indicating generally more restricted diffusion environments. By measuring directional diffusivity and kurtosis, DKI offers a more comprehensive and
Acknowledgments
We thank Dr. Jens H. Jensen at the New York University School of Medicine in New York and Dr. Hanzhang Lu at the UT Southwestern Medical Center in Dallas for assistance with data processing procedures. This work was supported in part by Hong Kong Research Grant Council and the University of Hong Kong Committee on Research and Conference Grants.
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