Document Type : Full Research Paper


1 Ph.D student, Department of Electrical Engineering, Biomedical Signal and Image Processing Laboratory (BiSIPL), Sharif University of Technology

2 Assistant Professor, Department of Electrical Engineering, Biomedical Signal and Image Processing Laboratory (BiSIPL), Sharif University of Technology

3 Professor, Control and Intelligent Processing Center of Excellence (CIPCE), School of Electrical and Computer Engineering, University of Tehran. Image Analysis Laboratory, Radiology Department, Henry Ford Health System, Detroit, Michigan, USA



Diffusion tensor magnetic resonance imaging (DTMRI) is a non-invasive method for investigating the brain white matter structure. It can be used to evaluate fiber bundles in the brain but in the regions with crossing fibers, it fails. To resolve this problem, high angular resolution diffusion imaging (HARDI) with a large number of diffusion encoding directions is used and for reconstruction, the Q-ball method is applied. In this method, orientation distribution function (ODF) of fibers can be calculated. Mathematical models play a crucial role in the field of ODF. For instance, in registering Q-ball images for applications like group analysis or atlas construction, one needs to interpolate ODFs. To this end, principal diffusion directions (PDDs) of each ODF are needed. In this paper, PDDs are defined as vectors that connect the corresponding local maxima of ODF values. Then, ODFs are interpolated using PDDs.We find the principal direction of ODF of the dataset to be interpolated and then rotate it to lie in the direction of the reference dataset. Now that ODFs are parallel, we apply linear interpolation to generate interpolated data. The proposed method is evaluated and compared with previous protocols. Experimental results show that the proposed interpolation algorithm preserves the principal direction of fiber tracts without producing any deviations in the tracts.  It is shown that changes in the entropy of the interpolated ODFs are almost linear and the bloating effect (blurring of the principal directions) can be removed. 


Main Subjects

[1]     Basser P., Mattiello J., LeBihan D., Estimation of the effective self-diffusion tensor from the NMR spin echo; J. Magn. Reson., 1994; 103: 247–254.
[2]     Basser P., Pajevic S., Pierpaoli C., Duda J., Aldroubi A., In vivo fiber tractography using DT-MRI data; Magn. Reson. Med., 2000; 44: 625–632.
[3]     Hagmann P., Thiran J., Jonasson L., Vandergheynst P., Clarke S., Maeder P., Meuli R., DTI mapping of human brain connectivity: statistical fibre tracking and virtual dissection; Neuroimage, 2003; 19: 545–554.
[4]     Tuch D.S., High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity; Magn. Reson. Med., 2002; 48: 577–582.
[5]     Barmpoutis A., Hwang M., Howland D., Forder J., Vemuri B., Regularized positive-definite fourth order tensor field estimation from DW-MRI; Neuroimage, 2009; 45: 153–162.
[6]     Ghosh A., Descoteaux M., Deriche R., Riemannian framework for estimating symmetric positive definite 4th order diffusion tensors; Medical Image Computing and Computer-Assisted Intervention, 2008; pp. 858–865.
[7]     Tuch D.S., Q-Ball Imaging; Magnetic Resonance in Medicine, 2004; 52: 1358–1372.
[8]     Özarslan E., Mareci T., Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging; Magn. Reson. Med., 2003; 50: 955–965.
[9]     Descoteaux M., Angelino E., Fitzgibbons S., Deriche R., Regularized, fast and robust analytical Q-ball imaging; Magn. Reson. Med.,2007; 58: 497–510.
[10] Frank L.R., Characterization of anisotropy in high angular resolution diffusion weighted MRI; Magn. Reson. Med., 2002; 47: 1083–1099.
[11] Hess C.P., Mukherjee P., Han E.T., Xu D., Vigneron D.B., Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis; Magn. Reson. Med., 2006; 56: 104–117.
[12] Aganj I., Lenglet C., Sapiro G., Yacoub E., Ugurbil K., Harel N., Reconstruction of the Orientation Distribution Function in Single and Multiple Shell Q-Ball Imaging within Constant Solid Angle; Magn Reson Med., 2010; 64: 554–566.
[13] Chiang M.C., Barysheva M., Lee A.D., Madsen S., Klunder A.D., Toga A.W., McMahon K.L., Zubicaray G.I., Meredith M., Wright M.J., Srivastava A., Balov N., Thompson P.M., Brain Fiber Architecture, Genetics, and Intelligence: A High Angular Resolution Diffusion Imaging (HARDI) Study; MICCAI 2008.
[14] Goh A., Lenglet C., Thompson P.M., Vidal R., A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry; NeuroImage, 2011; 56: 1181–1201.
[15] Ncube S., Srivastava A., A Geometric Analysis of ODFs As Oriented Surfaces for Interpolation, Averaging and Denoising in HARDI Data; MMBIA 2012.
[16] Nazem-Zadeh M.R., Jafari-Khouzani K., Davoodi-Bojd E., Jiang Q., Soltanian-Zadeh H., Clustering method for estimating principal diffusion directions; NeuroImage, 2011; 57: 825–838.
[17] Cetingul H.E., Afsari B., Wright M.J., Thompson P.M., Vidal R., Group Action Induced Averaging for HARDI Processing; ISBI 2012.