The estimation of principal diffusion directions in brain white matter has been extensively studied by processing Diffusion Weighted Magnetic Resonance Images. Those studies present competitive ...results for both, a single diffusion orientation, as well as for multiple diffusion orientations at voxels where the axon fibers cross or split. However, in the best of our knowledge, all the available methods are unable to estimate the an isotropic indexes in the multiple diffusion direction case. Those an isotropic indexes are used to determine properties of the axon packs in the brain, thus are related to the diagnosis of brain diseases. In this paper we propose a new method based on the selection of Diffusion Basis Functions which is capable to detect the an isotropic indexes. Our approach is composed of two steps: the first stage estimates the diffusion orientation based on a raw an isotropic model, the second stage estimates the an isotropic indexes by setting a high resolution Diffusion Basis built from statistical analysis of parallel and radial diffusion coefficients on the brain white matter. Our experiments are presented on synthetic diffusion weighted data.
A large number of mathematical models have been proposed to describe the measured signal in diffusion-weighted (DW) magnetic resonance imaging (MRI) and infer properties about the white matter ...microstructure. However, a head-to-head comparison of DW-MRI models is critically missing in the field. To address this deficiency, we organized the "White Matter Modeling Challenge" during the International Symposium on Biomedical Imaging (ISBI) 2015 conference. This competition aimed at identifying the DW-MRI models that best predict unseen DW data. in vivo DW-MRI data was acquired on the Connectom scanner at the A.A.Martinos Center (Massachusetts General Hospital) using gradients strength of up to 300 mT/m and a broad set of diffusion times. We focused on assessing the DW signal prediction in two regions: the genu in the corpus callosum, where the fibres are relatively straight and parallel, and the fornix, where the configuration of fibres is more complex. The challenge participants had access to three-quarters of the whole dataset, and their models were ranked on their ability to predict the remaining unseen quarter of data. In this paper we provide both an overview and a more in-depth description of each evaluated model, report the challenge results, and infer trends about the model characteristics that were associated with high model ranking. This work provides a much needed benchmark for DW-MRI models. The acquired data and model details for signal prediction evaluation are provided online to encourage a larger scale assessment of diffusion models in the future.
In this work, we applied the basis pursuit (BP) methodology for recovering the intra-voxel information in diffusion weighted MR images (DW-MRI). We compare the proposed BP approach with the diffusion ...basis function estimation (DBFE) algorithm. DBFE approach was previously applied to recover intra-voxel diffusion information in brain DW-MRI. The intra-voxel information is recovered at voxels that contain axon fiber crosses or bifurcations by means of a linear combination of a known diffusion functions. We state the DBFE solution in the signal decomposition context, i.e., the measured DW-MRI signal is decomposed as a linear combination of signals that belongs to a base of diffusion functions (BDF). In such a BDF, each signal is an M-dimensional vector, where each component indicates the water diffusion coefficient in a known three-dimensional orientation. In this work, we analyze and compare the solution given by DBFE method with the BP methodology. The BP methodology is used in order to select the set of base signals (which are taken from a dictionary) that best explain a given arbitrary signal. Moreover, solution strategies used in the BP and DBFE algorithm are compared and discussed. Examples in synthetic and real images are shown in order to demonstrate the performance of the compared methods.
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