Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data.

In this paper, we propose a new and accurate technique for uncertainty analysis and uncertainty visualization based on fiber orientation distribution function (ODF) glyphs, associated with high angular resolution diffusion imaging (HARDI). Our visualization applies volume rendering techniques to an ensemble of 3D ODF glyphs, which we call SIP functions of diffusion shapes, to capture their variability due to underlying uncertainty. This rendering elucidates the complex heteroscedastic structural variation in these shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. Our uncertainty analysis and visualization framework is then applied to synthetic data, as well as to HARDI human-brain data, to study the impact of various image acquisition parameters and background noise levels on the diffusion shapes.

Abstract. In this paper, we propose three metrics to quantify the differences between the results of diffusion tensor magnetic resonance imaging (DT-MRI) fiber tracking algorithms: the area between corresponding fibers of each bundle, the Earth Mover's Distance (EMD) between two fiber bundle volumes, and the current distance between two fiber bundle volumes. We also discuss an interactive fiber track comparison visualization toolkit we have developed based on the three proposed fiber difference metrics and have tested on six widely-used fiber tracking algorithms. To show the effectiveness and robustness of our metrics and visualization toolkit, we present results on both synthetic data and high resolution monkey brain DT-MRI data. Our toolkit can be used for testing the noise effects on fiber tracking analysis and visualization and to quantify the difference between any pair of DT-MRI techniques, compare single subjects within an image atlas.

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This paper reports fabrication of a magnetic resonance imaging (MRI) phantom created by stacking of multiple thin polydimethylsiloxane (PDMS) layers. PDMS is spin coated on SU-8 molds to obtain the desired layer thickness and imprints of the microchannel patterns that define the phantom geometry. This paper also identifies the unique challenges related to the fabrication and assembly of multiple thin layers and reports for the first time assembly of a large number of thin laminates of this nature. Use of photolithography techniques allows us to create a wide range of phantom geometries. The target dimensions of the phantoms reported here are (i) a stack of 30 thin PDMS layers of 10 µm thickness (ii) curved 5 µm × 5 µm microchannels with 8.7 µm spacing, and (iii) straight 5 µm × 5 µm microchannels with 3.6 µm spacing. SEM scans of the assembled phantoms show open microchannels and a monolithic cross-section with no visible interface between PDMS layers. Based on the results of diffusion tensor magnetic resonance imaging (DT-MRI) scan, the anisotropic diffusion of water molecules due to the physical restriction of the microchannels was detected, which means that the phantom can be used to calibrate and optimize MRI instrumentation.