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A New Methodology for the Estimation of Fiber Populations in the White Matter of the Brain with the Funk-Radon Transform
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Institution: |
1Laboratory of Image Processing, Universidad de Valladolid, Spain. atriveg@lpi.tel.uva.es 2Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA |
Publisher: |
Elsevier Science |
Publication Date: |
Jan-2010 |
Journal: |
Neuroimage |
Volume Number: |
49 |
Issue Number: |
2 |
Pages: |
1301-1315 |
Citation: |
Neuroimage. 2010 Jan 15;49(2):1301-15. |
PubMed ID: |
19815078 |
Keywords: |
HARDI, Funk–Radon transform, Q-Balls, OPDT |
Appears in Collections: |
NAC, LMI |
Sponsors: |
P41 RR13218 (RR) funded by NCRR NIH HHS R01 MH074794 (MH) funded by NIMH NIH HHS |
Generated Citation: |
Tristan-Vega A., Westin C-F., Aja-Fernandez 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. PMID: 19815078. |
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The Funk-Radon Transform (FRT) is a powerful tool for the estimation of fiber populations with High Angular Resolution Diffusion Imaging (HARDI). It is used in Q-Ball imaging (QBI), and other HARDI techniques such as the recent Orientation Probability Density Transform (OPDT), to estimate fiber populations with very few restrictions on the diffusion model. The FRT consists in the integration of the attenuation signal, sampled by the MRI scanner on the unit sphere, along equators orthogonal to the directions of interest. It is easily proved that this calculation is equivalent to the integration of the diffusion propagator along such directions, although a characteristic blurring with a Bessel kernel is introduced. Under a different point of view, the FRT can be seen as an efficient way to compute the angular part of the integral of the attenuation signal in the plane orthogonal to each direction of the diffusion propagator. In this paper, Stoke's theorem is used to prove that the FRT can in fact be used to compute accurate estimates of the true integrals defining the functions of interest in HARDI, keeping the diffusion model as little restrictive as possible. Varying the assumptions on the attenuation signal, we derive new estimators of fiber orientations, generalizing both Q-Balls and the OPDT. Extensive experiments with both synthetic and real data have been intended to show that the new techniques improve existing ones in many situations.
Additional Material
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Tristan-Vega-Neuroimage2010-fig11.jpg (224.703kB)