Estimation of Multiple Fibre Orientations Using Convex Optimization

¹Engineering School, Universidad de los Andes, Santiago, RM, Chile; ²Danish Research Centre for Magnetic Resonance, Copenhagen University Hospital Hvidovre, Hvidovre, Denmark; ³Center for Mathematical Modelling, Universidad de Chile, Santiago, Chile; ⁴Neurosurgery Institute, Universidad de Chile, Santiago, Chile; ⁵Clinica Santa Maria, Radiology, Santiago, Chile

A method is presented that is capable of determining more than one fibre orientation within a single voxel from diffusion weighted MR images of the brain. The method can identify voxels with directional heterogeneity and assess the relevance of each direction in the signal. The method describes the diffusion weighted dataset as a combination of one isotropic compartment and a large pre-specified set of anisotropic compartments, and uses regularized least squares to find the amplitude of each component, reducing overfitting i.e. the use of unnecessary degrees of freedom. The result is a sparse representation of the diffusion signal in terms of a few anisotropic compartments. Using diffusion weighted MR datasets, we show that the multiple orientation method gives robust results across a wide range of b-values, and can be further enhanced using multi-channel denoising on the raw datasets. The method is fast and uses standard optimization algorithms. Results of this methodology can potentially improve results of multi-fibre tractography.