Q-ball imaging (QBI) is a high angular resolution diffusion imaging (HARDI) technique which has been proven very successful in resolving multiple intravoxel fiber orientations in MR images. The standard computation of the orientation distribution function (ODF, the probability of diffusion in a given direction) from q-ball uses linear radial projection, neglecting the change in the volume eleme...

BACKGROUND A number of imaging factors can affect the orientation distribution function (ODF) reconstruction in high angular resolution diffusion imaging (HARDI). The aim of this study was to investigate the effect of the b-value on the HARDI reconstruction and to seek for the appropriate b-value for ODF reconstruction from clinical HARDI data. METHODS Diffusion MRI data with various b-values...

Polycrystalline materials, such as metals, are composed of heterogeneously oriented crystals. Observed crystal orientations modelled a sample from an orientation distribution function (ODF), which determines variety material properties and is therefore great interest to practitioners. Observations consist quaternions, four-dimensional unit vectors reflecting both rotation single crystal. Thus, ...

In High Angular Resolution Diffusion Imaging (HARDI), Orientation Distribution Function (ODF) and Ensemble Average Propagator (EAP) are two important Probability Density Functions (PDFs) which reflect the water diffusion and fiber orientations. Spherical Polar Fourier Imaging (SPFI) is a recent model-free multi-shell HARDI method which estimates both EAP and ODF from the diffusion signals with ...

In this paper we describe the capabilities for texture measurements of the new neutron time-offlight diffractometer HIPPO at the Los Alamos Neutron Science Center (LANSCE). The orientation distribution function (ODF) is extracted from multiple neutron time-of-flight histograms using the full-pattern analysis first described by Rietveld. Both, the well-established description of the ODF using sp...

In this paper, the spherical harmonic convolution approach for HCP materials [1] is extended into a generalised form for the principal purpose of bulk texture determination in cubic polycrystals from ultrasonic wave speed measurements. It is demonstrated that the wave speed function of a general single crystal convolves with the polycrystal Orientation Distribution Function (ODF) to make the re...

In this paper we extract the geometric characteristics from an antipodally symmetric spherical function (ASSF), which can be described equivalently in the spherical harmonic (SH) basis, in the symmetric tensor (ST) basis constrained to the sphere, and in the homogeneous polynomial (HP) basis constrained to the sphere. All three bases span the same vector space and are bijective when the rank of...

The uniaxial orientational order in a macromolecular system is usually specified using the Hermans factor which equivalent to second moment of system's orientation distribution function (ODF) expanded terms Legendre polynomials. In this work, we show that for aligned materials are two-dimensional (2D) or have measurable 2D intensity distribution, such as carbon nanotube (CNT) textiles, not appr...

A novel method for estimating a field of orientation distribution functions (ODF) from a given set of DW-MR images is presented. We model the ODF by Cartesian tensor basis using a parametrization that explicitly enforces the positive definite property to the computed ODF. The computed Cartesian tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite tensors whose coeffici...

The response of polycrystals to deterministic and random deformations is investigated with respect to the evolution of the crystallographic orientation and its probability density function, the ODF. The crystals analyzed are highly simplified, being two-dimensional and with only two active slip systems. A differential equation is derived which governs the evolution of the orientation under arbi...