Diffusion basis functions decomposition for estimating white matter intravoxel fiber geometry.
In this paper, we present a new formulation for recovering the fiber tract geometry within a voxel from diffusion weighted magnetic resonance imaging (MRI) data, in the presence of single or multiple neuronal fibers. To this end, we define a discrete set of diffusion basis functions. The intravoxel information is recovered at voxels containing fiber crossings or bifurcations via the use of a linear combination of the above mentioned basis functions. Then, the parametric representation of the intravoxel fiber geometry is a discrete mixture of Gaussians. Our synthetic experiments depict several advantages by using this discrete schema: the approach uses a small number of diffusion weighted images (23) and relatively small b values (1250 s/mm2), i.e., the intravoxel information can be inferred at a fraction of the acquisition time required for datasets involving a large number of diffusion gradient orientations. Moreover our method is robust in the presence of more than two fibers within a voxel, improving the state-of-the-art of such parametric models. We present two algorithmic solutions to our formulation: by solving a linear program or by minimizing a quadratic cost function (both with non-negativity constraints). Such minimizations are efficiently achieved with standard iterative deterministic algorithms. Finally, we present results of applying the algorithms to synthetic as well as real data.
Ramirez-Manzanares
Alonso
A
Computer Science Department, Centro de Investigacion en Matematicas A.C., Guanajuato 36000, Mexico. alram@cimat.mx
Rivera
Mariano
M
Vemuri
Baba C
BC
Carney
Paul
P
Mareci
Thomas
T
D000465:Algorithms; D000818:Animals; D001921:Brain / Q000166:cytology*; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D009413:Nerve Fibers, Myelinated / Q000648:ultrastructure*; D051381:Rats; D017207:Rats, Sprague-Dawley; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity