Magnetic Resonance in Medicine 65:138–145 (2011) More Accurate Estimation of Diffusion Tensor Parameters Using Diffusion Kurtosis Imaging Jelle Veraart, 1* Dirk H. J. Poot, 1,2 Wim Van Hecke, 3,4 Ines Blockx, 5 Annemie Van der Linden, 5 Marleen Verhoye, 5 and Jan Sijbers 1 With diffusion tensor imaging, the diffusion of water molecules through brain structures is quantified by parameters, which are estimated assuming monoexponential diffusion-weighted sig- nal attenuation. The estimated diffusion parameters, however, depend on the diffusion weighting strength, the b-value, which hampers the interpretation and comparison of various diffusion tensor imaging studies. In this study, a likelihood ratio test is used to show that the diffusion kurtosis imaging model pro- vides a more accurate parameterization of both the Gaussian and non-Gaussian diffusion component compared with diffusion tensor imaging. As a result, the diffusion kurtosis imaging model provides a b-value-independent estimation of the widely used diffusion tensor parameters as demonstrated with diffusion- weighted rat data, which was acquired with eight different b-values, uniformly distributed in a range of [0,2800 sec/mm 2 ]. In addition, the diffusion parameter values are significantly increased in comparison to the values estimated with the dif- fusion tensor imaging model in all major rat brain structures. As incorrectly assuming additive Gaussian noise on the diffusion- weighted data will result in an overestimated degree of non- Gaussian diffusion and a b-value-dependent underestimation of diffusivity measures, a Rician noise model was used in this study. Magn Reson Med 65:138–145, 2011. © 2010 Wiley-Liss, Inc. Key words: DKI; likelihood ratio test; b-value dependency; parameter estimation Diffusion tensor magnetic resonance imaging (DTI) is an important medical imaging modality in neuroscience research, because it allows the study of the complex net- work of myelinated axons, in vivo and noninvasively (1,2). In DTI, the diffusion of water molecules through brain structures is mathematically described by a second order 3D diffusion tensor (DT). It is generally accepted that the first eigenvector of the tensor, corresponding to the direction of maximal diffusion, is aligned with the underlying fiber structures. Furthermore, the diffusion 1 Visionlab, Department of Physics, University of Antwerp, Wilrijk, Antwerp, Belgium 2 Biomedical Imaging Group Rotterdam, Erasmus MC, Rotterdam, The Nether- lands 3 Department of Radiology, University Hospital Antwerp, University of Antwerp, Edegem, Antwerp, Belgium 4 Department of Radiology, University Hospitals of the Catholic University of Leuven, Leuven, Belgium 5 Bio-Imaging Lab, Department of Biomedical Sciences, University of Antwerp, Antwerp, Belgium Grant sponsor:SBO “Quantiviam” of IWT; Grant number: 060819 Grant sponsor: IAP-Grant of the Belgian Science Policy; Grant number: P6/38 *Correspondence to: Jelle Veraart, Visionlab, M.S., Department of Physics, University of Antwerp, Universiteitsplein 1, N 1.16, B-2610 Wilrijk, Belgium. E-mail: jelle.veraart@ua.ac.be Received 5 March 2010; revised 15 July 2010; accepted 20 July 2010. DOI 10.1002/mrm.22603 Published online 27 September 2010 in Wiley Online Library (wileyonlinelibrary.com). is often quantified with diffusion parameters (i.e., frac- tional anisotropy (FA) and mean (MD), radial (D ⊥ ) and axial (D ‖ ) diffusivity), which provide insight in the orga- nization, structural integrity, and development of white matter (WM) structures of the normal and pathological brain (3–9). In DTI, the diffusion of water molecules along a certain gradient direction is assumed to occur in an unrestricted environment. Consequently, the molecules’ probability of diffusing from one location to another in a given time is described by a Gaussian distribution of which the stan- dard deviation relates to the apparent diffusion coefficient (ADC). As a result, the normalized diffusion-weighted sig- nal that is measured along a certain axis can be described by a monoexponential function; the exponent equals the ADC, weighted by the diffusion weighting strength that is given by the b-value. Several DTI studies, however, reported that the estimation of diffusion parameters depends on the b-value that is used during data acquisition. Therefore, the comparison and interpretation of various DTI stud- ies are hampered. Jones and Basser (10) and Andersson (11) attributed the b-value dependency to the use of an inaccurate, Gaussian noise model while estimating diffu- sion parameters with a (weighted) least squares estimator, as MR images are corrupted with Rician noise (12,13). Other related work addressed the b-value dependency of the quantification of DTI measures in biological tissue to the complex relation between the diffusion-weighted signal and the b-value due to factors such as cerebral perfusion, restricted diffusion, membrane permeability, and extra- and intracellular water compartments (8,14, 15). As a result, the diffusion will appear non-Gaussian and hence cannot be approximated accurately by a DTI model (8,16,17). Recently, Jensen et al. (17) and Lu et al. (18) intro- duced diffusion kurtosis imaging (DKI), a higher order diffusion model that is a straightforward extension of the DTI model. DKI approximates the diffusion-weighted sig- nal attenuation more accurately by quantifying the degree of non-Gaussian diffusion. To this end, the exponent of the DTI model is extended with a quadratic term in the b-value. The coefficient of the additional term relates to the apparent excess kurtosis (AKC), a dimensionless metric quantifying the non-gaussianity. By measuring the AKC in at least 15 different gradient directions, a fourth-order 3D, fully sym- metric tensor—the diffusion kurtosis tensor (DKT)—can be calculated in addition to the DT. As the DKI model is param- eterized by 22 elements: nondiffusion-weighted signal b 0 , six independent DT elements, and 15 independent DKT elements, it requires at least diffusion weighting along 15 noncollinear gradient directions with one or two nonzero b-values in such a way that a total of 22 diffusion-weighted © 2010 Wiley-Liss, Inc. 138 Personal use of this material is permitted. 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