Apparent Diffusion Coefficient Approximation and Diffusion Anisotropy Characterization in DWI

We present a new approximation for the apparent diffusion coefficient (ADC) of non-Gaussian water diffusion with at most two fiber orientations within a voxel. The proposed model approximates ADC profiles by product of two spherical harmonic series (SHS) up to order 2 from High Angular Resolution Diffusion-weighted (HARD) MRI data. The coefficients of SHS are estimated and regularized simultaneously by solving a constrained minimization problem. An equivalent but non-constrained version of the approach is also provided to reduce the complexity and increase the efficiency in computation. Moreover we use the Cumulative Residual Entropy (CRE) as a measurement to characterize diffusion anisotropy. By using CRE we can get reasonable results with two thresholds, while the existing methods either can only be used to characterize Gaussian diffusion or need more measurements and thresholds to classify anisotropic diffusion with two fiber orientations. The experiments on HARD MRI human brain data indicate the effectiveness of the method in the recovery of ADC profiles. The characterization of diffusion based on the proposed method shows a consistency between our results and known neuroanatomy.

[1]  Yunmei Chen,et al.  Cumulative residual entropy: a new measure of information , 2004, IEEE Transactions on Information Theory.

[2]  Murali Rao,et al.  More on a New Concept of Entropy and Information , 2005 .

[3]  T. Chenevert,et al.  Anisotropic diffusion in human white matter: demonstration with MR techniques in vivo. , 1990, Radiology.

[4]  D. Parker,et al.  Analysis of partial volume effects in diffusion‐tensor MRI , 2001, Magnetic resonance in medicine.

[5]  V. Wedeen,et al.  Mapping fiber orientation spectra in cerebral white matter with Fourier-transform diffusion MRI , 2000 .

[6]  C. Beaulieu,et al.  The basis of anisotropic water diffusion in the nervous system – a technical review , 2002, NMR in biomedicine.

[7]  L. Frank.  Characterization of anisotropy in high angular resolution diffusion‐weighted MRI , 2002, Magnetic resonance in medicine.

[8]  S. Arridge,et al.  Detection and modeling of non‐Gaussian apparent diffusion coefficient profiles in human brain data , 2002, Magnetic resonance in medicine.

[9]  P. Basser,et al.  MR diffusion tensor spectroscopy and imaging. , 1994, Biophysical journal.

[10]  Baba C. Vemuri,et al.  Estimation, smoothing, and characterization of apparent diffusion coefficient profiles from High Angular Resolution DWI , 2004, CVPR 2004.

[11]  Isabelle Bloch,et al.  Towards inference of human brain connectivity from MR diffusion tensor data , 2001, Medical Image Anal..

[12]  P. Basser.  Inferring microstructural features and the physiological state of tissues from diffusion‐weighted images , 1995, NMR in biomedicine.

[13]  D. Tuch.  High Angular Resolution Diffusion Imaging of the Human Brain , 1999 .

[14]  Zhizhou Wang,et al.  A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI , 2004, IEEE Transactions on Medical Imaging.

[15]  P. Basser,et al.  Estimation of the effective self-diffusion tensor from the NMR spin echo. , 1994, Journal of magnetic resonance. Series B.

[16]  L. Frank.  Anisotropy in high angular resolution diffusion‐weighted MRI , 2001, Magnetic resonance in medicine.

[17]  Yijun Liu,et al.  Recovery of intra-voxel structure from HARD DWI , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).

[18]  Rachid Deriche,et al.  DT-MRI estimation, regularization and fiber tractography , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).

[19]  N. Makris,et al.  High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity , 2002, Magnetic resonance in medicine.

[20]  Daniel C. Alexander,et al.  Probabilistic Monte Carlo Based Mapping of Cerebral Connections Utilising Whole-Brain Crossing Fibre Information , 2003, IPMI.

[21]  J. Schnabel,et al.  Nonlinear smoothing for reduction of systematic and random errors in diffusion tensor imaging , 2000, Journal of magnetic resonance imaging : JMRI.

[22]  T. Mareci,et al.  Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging , 2003, Magnetic resonance in medicine.