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NIH Pediatric Neuroimaging - Diffusion Tensor MRI Center
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If you use our software in your research, the algorithms listed below have been published elsewhere. Downloadable pdf copies of the articles are available by clicking the download links. Please cite the appropriate references in your work. A general reference for TORTOISE is shown below. 1

DIFF_CALC is a software package for the estimation of the diffusion tensor in each voxel and for the computation of tensor-derived quantities. Functions include:

  • Automated 2,14 and manual (ROI based) image noise estimation
  • Tensor computation approaches including weighted and unweighted linear, non-linear, 3 and robust fitting including RESTORE 5 and informed RESTORE 14
  • Future support of dual compartment, 6 and Newton constrained fitting 7
  • Proper weighting in the tensor fitting to account for changes in the statistical properties of the image due to interpolation from image registration 8,9
  • Goodness of fit analysis with display of the residuals of the fitting
  • Tensor derived quantities in analyze and nifti formats including Trace(D), eignevalues, eigenvectors, fractional anisotropy, relative anisotropy, volume ratio, 10 lattice index, 11 directionally encoded color (DEC) maps, 12 Westin's measures, 13 skewness, 1 linefield representation of principal eigenvector, etc.
  • ROI analysis including orthogonal viewer for 3D Volume of Interest (VOI) analysis
  • Export modules for diffusion weighted images and/or diffusion tensor to: FSL, Camino, TrackVis, Slicer, DTI-TK, NRRD, VTK, DTI Studio

For access to the Software Guide click here
For a list of the outputs of the tensor fitting click here

For frequently asked questions, please visit our FAQ


  1. C. Pierpaoli, L. Walker, M. O. Irfanoglu, A. Barnett, P. Basser, L-C. Chang, C. Koay, S. Pajevic, G. Rohde, J. Sarlls, and M. Wu, 2010, TORTOISE: an integrated software package for processing of diffusion MRI data, ISMRM 18th annual meeting, Stockholm, Sweden, #1597 pdf
  2. Koay CG, Özarslan E and Basser PJ. A signal transformational framework for breaking the noise floor and its applications in MRI. J Magn Reson 2009; 197: 108-119. pdf
  3. Basser, P.J., Mattiello, J., and LeBihan, D. (1994) Estimation of the effective self-diffusion tensor from the NMR spin echo. J Magn Reson B 103:247-254 pdf
  4. Mangin JF, Poupon C, Clark C, Le Bihan D, Bloch I. (2002) Distortion correction and robust tensor estimation for MR diffusion imaging. Med Image Anal. 6(3):191-8. abstract
  5. Chang, L.C., Jones, D.K., and Pierpaoli, C. (2005) RESTORE: Robust estimation of tensors by outlier rejection. Magn Reson Med. 53:1088-1095 pdf
  6. Kim, S., et al. (2005) Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart. 13th Annual ISMRM, Miami Beach, Florida, USA #1285
  7. Koay, C.G., Chang, L-C., Carew, J.D., Pierpaoli, C., and Basser, P.J. (2006) A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging. J Magn Reson. 182:115-125 pdf
  8. Rohde, G.K., Barnett, A.S., Basser, P.J., and Pierpaoli, C. (2005) Estimating intensity variance due to noise in registered images: Applications to diffusion tensor MRI. Neuroimage 26:673-684 pdf
  9. Irfanoglu, M. O., Walker, L., Machiraju, R., Pierpaoli, C. (2011). Accounting for changes in signal variance in diffusion weighted images following interpolation for motion and distortion correction. ISMRM 19th Annual Meeting and Exhibition, Montreal, Canada.
  10. Basser, P.J. and Pierpaoli, C. (1996) Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J Magn Reson B. 111:209-219 pdf
  11. Pierpaoli, C. and Basser, P.J. (1996) Toward a quantitative assessment of diffusion anisotropy. Magn Reson Med. 36:893-906 pdf
  12. Pajevic, S. and Pierpaoli, C. (1999) Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain. Magn Reson Med. 42:526-540 pdf
  13. Peled S, Gudbjartsson H, Westin CF, Kikinis R, Jolesz FA. (1998) Magnetic resonance imaging shows orientation and asymmetry of white matter fiber tracts. Brain Res. 5;780(1):27-33 abstract
  14. Chang, L.C., Walker, L., Pierpaoli, C., (2012) Informed RESTORE: A Method for Robust Estimation of Diffusion Tensor from Low Redundancy Datasets in the Presence of Physiological Noise Artifacts. MRM. In Press