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High Angular Resolution Diffusion Imaging (HARDI) Tools

Authors: Erick J. Canales-Rodrí­guez, Lester Melie-Garcí­a, Yasser Iturria-Medina, Yasser Alemán-Gómez

Date: 2013, Version: 1.2


This is a collection of Matlab routines for the analysis of High Angular Resolution Diffusion Imaging (HARDI) data. It is a subset of the code internally used in the FIDMAG Research Foundation (unit of research at the Benito Menni Hospital, Barcelona, Spain), the Cuban Neuroscience Center (Havana, Cuba), and the Medical Imaging Laboratory at Gregorio Marañón Hospital (Madrid, Spain).

List of reconstruction methods currently included:

  1. Q-Ball Imaging (QBI) (see Refs. [2,3,4])
  2. Mono-Exponential-Exact Q-Ball Imaging (MeEQBI) (see Ref. [9])
  3. Q-Ball Imaging in Constant Solid Angle (CSA-QBI) (see Refs. [13,14,8])
  4. Diffusion Orientation Transform (DOT) (see Ref. [5])
  5. Revisited version of the DOT method (DOT-R1 and DOT-R2) (see Ref. [8])
  6. Spherical deconvolution method (using standard and Damped R-L) (see Ref. [15])
  7. Diffusion Spectrum Imaging (DSI) (see Ref. [11])
  8. Deconvolved DSI (DDSI) (using standard and Damped R-L, and R-L with TV regularization) (see Ref. [12])

Most of the reconstructions are based on real-valued spherical harmonics expansions. Some useful free spherical harmonics tools provided by Bing Jian PhD are included in this collection. The codes illustrate the use and performance of the above listed methods in simulated data, generated from a multi-tensor diffusion model for a single voxel under experimental noise (Rician). To use the above methods in real data it is mandatory to convert the raw diffusion MRI data (DICOM/ANALYZE) to Matlab matrix format .mat (using for example SPM tools : spm_vol and spm_read_vols functions) and then compute the implemented algorithms for each voxel in the brain-image.

Download the software

In this web we provide some of the implementations used in our laboratories, under the aim to make our research reproducible. By providing these codes we hope that: (1) other people who want to do research in the field can really start from the current state of the art, instead of spending months trying to implement the methods, and (2) the task of comparing a new method to existing methods becomes easier.

If you want to include a new method in this web, feel free to contact the authors. Do not hesitate to use them for your own research. As always, any feedback will be greatly appreciated:

Please, if you are using these tools for your own research, cite this web site.


Examples of usage

Firstly you need to add the main folder and all it's subdirectories to the Matlab path.

Note: If you already have a previous version of HARDI tools, please, delete the previous version from the Matlab path. (Some functions were modified and renamed)

Then run any of the following test scripts (click on the items to view the html files generated from these codes):


Special Thanks to Joaquim Radua MD, PhD, for generously providing the NeuroimageN web for posting this Toolbox


  1. David S. Tuch, Reese TG, Wiegell MR, et al (2002). "High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity". Magn. Res. Med. 48 (4): 577-582.
  2. David S. Tuch. "Q-ball imaging". Magn. Reson. Med., 52(6):1358-1372, 2004.
  3. Maxime Descoteaux, Elaine Angelino, Shaun Fitzgibbons, and Rachid Deriche. "Regularized, Fast and Robust Analytical Q-Ball Imaging". Magn. Reson. Med., 58:497-510, 2007.
  4. Hess CP, Mukherjee P, Han ET, Xu D, Vigneron DB. "Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis". Magn Reson Med. 2006 Jul;56(1):104-17.
  5. Evren Özarslan, Timothy M. Shepherd, Baba C. Vemuri, Stephen J. Blackband, and Thomas H. Mareci. "Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT)". NeuroImage, 36(3):1086-1103, 2006.
  6. Maxime Descoteaux, Elaine Angelino, Shaun Fitzgibbons, and Rachid Deriche. "Apparent diffusion coefficients from high angular resolution diffusion imaging: Estimation and applications". Magn. Reson. Med., 56(2):395-410, 2006.
  7. Adam W. Anderson. "Measurement of Fiber Orientation Distributions Using High Angular Resolution Diffusion Imaging". Magn. Reson. Med.,54 (5):1194-1206, 2005.
  8. Erick J. Canales-Rodrí­guez, Lin CP., Iturria-Medina Y, Yeh CH., Cho KH., Melie-Garcí­a L. "Diffusion orientation transform revisited". Neuroimage, 2010, Vol 49, 2, 1326-1339.
  9. Erick J. Canales-Rodríguez, Lester Melie-Garcí­a, and Yasser Iturria-Medina. "Mathematical Description of q-Space in Spherical Coordinates: Exact q-Ball Imaging". Magnetic Resonance in Medicine, 2009, Vol 61, 3, 1350-1367.
  10. Lester Melie-Garcí­a, Erick J. Canales-Rodríguez, Yasser Alemán-Gómez, Ching-Po Lin, Yasser Iturria-Medina, and Pedro Valdés-Hernández. "A Bayesian framework to identify principal intravoxel diffusion profiles based on Diffusion-Weighted MR Imaging". Neuroimage, 2008, Vol 42, 2, 750-770.
  11. Wedeen V.J., Hagmann P., Tseng W.Y., Reese T.G., Weisskoff R.M. "Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging". Magn Reson Med. 2005 Dec;54(6):1377-86.
  12. Erick J. Canales-Rodríguez, Y. Iturria-Medina, Y. Alemán-Gómez, L. Melie-García. "Deconvolution in diffusion spectrum imaging". Neuroimage. 2010 Mar;50(1):136-49.
  13. 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 Aug;64(2):554-66.
  14. Tristán-Vega A, Westin CF, Aja-Fernández S. "A new methodology for the estimation of fiber populations in the white matter of the brain with the Funk-Radon transform". Neuroimage. 2010 Jan 15;49(2):1301-15.
  15. Dell'acqua F, Scifo P, Rizzo G, Catani M, Simmons A, Scotti G, Fazio F. "A modified damped Richardson-Lucy algorithm to reduce isotropic background effects in spherical deconvolution." Neuroimage. 2010 Jan 15;49(2):1446-58.