The 4D hyperspherical diffusion wavelet: A new method for the detection of localized anatomical variation.

Recently, the HyperSPHARM algorithm was proposed to parameterize multiple disjoint objects in a holistic manner using the 4D hyperspherical harmonics. The HyperSPHARM coefficients are global; they cannot be used to directly infer localized variations in signal. In this paper, we present a unified wavelet framework that links Hyper-SPHARM to the diffusion wavelet transform.

Diffeomorphic metric mapping and probabilistic atlas generation of hybrid diffusion imaging based on BFOR signal basis.

We first propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI). We denote this algorithm as LDDMM-HYDI. We then propose a Bayesian probabilistic model for estimating the white matter atlas from HYDIs.

A 4D hyperspherical interpretation of q-space.

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we analytically derive several quantitative indices and numerically estimate the diffusion ODF.

4D hyperspherical harmonic (HyperSPHARM) representation of multiple disconnected brain subcortical structures.

We present a novel surface parameterization technique using hyperspherical harmonics (HSH) in representing compact, multiple, disconnected brain subcortical structures as a single analytic function. The proposed hyperspherical harmonic representation (HyperSPHARM) has many advantages over the widely used spherical harmonic (SPHARM) parameterization technique. SPHARM requires flattening 3D surfaces to 3D sphere which can be time consuming for large surface meshes, and can't represent multiple disconnected objects with single parameterization.

Extracting quantitative measures from EAP: a small clinical study using BFOR.

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents, and hence providing rich information about complex tissue microstructure properties. Bessel Fourier orientation reconstruction (BFOR) is one of several analytical, non-Cartesian EAP reconstruction schemes employing multiple shell acquisitions that have recently been proposed. Such modeling bases have not yet been fully exploited in the extraction of rotationally invariant q-space indices that describe the degree of diffusion anisotropy/restrictivity.

Diffeomorphic metric mapping of hybrid diffusion imaging based on BFOR signal basis.

In this paper, we propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI), denoted as LDDMM-HYDI. We adopt the work given in Hosseinbor et al. (2012) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis.

Bessel Fourier Orientation Reconstruction (BFOR): an analytical diffusion propagator reconstruction for hybrid diffusion imaging and computation of q-space indices.

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI).

Characterization of cerebral white matter properties using quantitative magnetic resonance imaging stains.

The image contrast in magnetic resonance imaging (MRI) is highly sensitive to several mechanisms that are modulated by the properties of the tissue environment. The degree and type of contrast weighting may be viewed as image filters that accentuate specific tissue properties. Maps of quantitative measures of these mechanisms, akin to microstructural/environmental-specific tissue stains, may be generated to characterize the MRI and physiological properties of biological tissues.

Bessel Fourier orientation reconstruction: an analytical EAP reconstruction using multiple shell acquisitions in diffusion MRI.

The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed.