6,996 research outputs found
Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization
Spherical deconvolution (SD) methods are widely used to estimate the
intra-voxel white-matter fiber orientations from diffusion MRI data. However,
while some of these methods assume a zero-mean Gaussian distribution for the
underlying noise, its real distribution is known to be non-Gaussian and to
depend on the methodology used to combine multichannel signals. Indeed, the two
prevailing methods for multichannel signal combination lead to Rician and
noncentral Chi noise distributions. Here we develop a Robust and Unbiased
Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with
realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to
Rician and noncentral Chi likelihood models. To quantify the benefits of using
proper noise models, RUMBA-SD was compared with dRL-SD, a well-established
method based on the RL algorithm for Gaussian noise. Another aim of the study
was to quantify the impact of including a total variation (TV) spatial
regularization term in the estimation framework. To do this, we developed TV
spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The
evaluation was performed by comparing various quality metrics on 132
three-dimensional synthetic phantoms involving different inter-fiber angles and
volume fractions, which were contaminated with noise mimicking patterns
generated by data processing in multichannel scanners. The results demonstrate
that the inclusion of proper likelihood models leads to an increased ability to
resolve fiber crossings with smaller inter-fiber angles and to better detect
non-dominant fibers. The inclusion of TV regularization dramatically improved
the resolution power of both techniques. The above findings were also verified
in brain data
NODDI-SH: a computational efficient NODDI extension for fODF estimation in diffusion MRI
Diffusion Magnetic Resonance Imaging (DMRI) is the only non-invasive imaging
technique which is able to detect the principal directions of water diffusion
as well as neurites density in the human brain. Exploiting the ability of
Spherical Harmonics (SH) to model spherical functions, we propose a new
reconstruction model for DMRI data which is able to estimate both the fiber
Orientation Distribution Function (fODF) and the relative volume fractions of
the neurites in each voxel, which is robust to multiple fiber crossings. We
consider a Neurite Orientation Dispersion and Density Imaging (NODDI) inspired
single fiber diffusion signal to be derived from three compartments:
intracellular, extracellular, and cerebrospinal fluid. The model, called
NODDI-SH, is derived by convolving the single fiber response with the fODF in
each voxel. NODDI-SH embeds the calculation of the fODF and the neurite density
in a unified mathematical model providing efficient, robust and accurate
results. Results were validated on simulated data and tested on
\textit{in-vivo} data of human brain, and compared to and Constrained Spherical
Deconvolution (CSD) for benchmarking. Results revealed competitive performance
in all respects and inherent adaptivity to local microstructure, while sensibly
reducing the computational cost. We also investigated NODDI-SH performance when
only a limited number of samples are available for the fitting, demonstrating
that 60 samples are enough to obtain reliable results. The fast computational
time and the low number of signal samples required, make NODDI-SH feasible for
clinical application
Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution
We propose two strategies to improve the quality of tractography results
computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both
methods are based on the same PDE framework, defined in the coupled space of
positions and orientations, associated with a stochastic process describing the
enhancement of elongated structures while preserving crossing structures. In
the first method we use the enhancement PDE for contextual regularization of a
fiber orientation distribution (FOD) that is obtained on individual voxels from
high angular resolution diffusion imaging (HARDI) data via constrained
spherical deconvolution (CSD). Thereby we improve the FOD as input for
subsequent tractography. Secondly, we introduce the fiber to bundle coherence
(FBC), a measure for quantification of fiber alignment. The FBC is computed
from a tractography result using the same PDE framework and provides a
criterion for removing the spurious fibers. We validate the proposed
combination of CSD and enhancement on phantom data and on human data, acquired
with different scanning protocols. On the phantom data we find that PDE
enhancements improve both local metrics and global metrics of tractography
results, compared to CSD without enhancements. On the human data we show that
the enhancements allow for a better reconstruction of crossing fiber bundles
and they reduce the variability of the tractography output with respect to the
acquisition parameters. Finally, we show that both the enhancement of the FODs
and the use of the FBC measure on the tractography improve the stability with
respect to different stochastic realizations of probabilistic tractography.
This is shown in a clinical application: the reconstruction of the optic
radiation for epilepsy surgery planning
Bayesian Estimation of White Matter Atlas from High Angular Resolution Diffusion Imaging
We present a Bayesian probabilistic model to estimate the brain white matter
atlas from high angular resolution diffusion imaging (HARDI) data. This model
incorporates a shape prior of the white matter anatomy and the likelihood of
individual observed HARDI datasets. We first assume that the atlas is generated
from a known hyperatlas through a flow of diffeomorphisms and its shape prior
can be constructed based on the framework of large deformation diffeomorphic
metric mapping (LDDMM). LDDMM characterizes a nonlinear diffeomorphic shape
space in a linear space of initial momentum uniquely determining diffeomorphic
geodesic flows from the hyperatlas. Therefore, the shape prior of the HARDI
atlas can be modeled using a centered Gaussian random field (GRF) model of the
initial momentum. In order to construct the likelihood of observed HARDI
datasets, it is necessary to study the diffeomorphic transformation of
individual observations relative to the atlas and the probabilistic
distribution of orientation distribution functions (ODFs). To this end, we
construct the likelihood related to the transformation using the same
construction as discussed for the shape prior of the atlas. The probabilistic
distribution of ODFs is then constructed based on the ODF Riemannian manifold.
We assume that the observed ODFs are generated by an exponential map of random
tangent vectors at the deformed atlas ODF. Hence, the likelihood of the ODFs
can be modeled using a GRF of their tangent vectors in the ODF Riemannian
manifold. We solve for the maximum a posteriori using the
Expectation-Maximization algorithm and derive the corresponding update
equations. Finally, we illustrate the HARDI atlas constructed based on a
Chinese aging cohort of 94 adults and compare it with that generated by
averaging the coefficients of spherical harmonics of the ODF across subjects
Diffeomorphic Metric Mapping of High Angular Resolution Diffusion Imaging based on Riemannian Structure of Orientation Distribution Functions
In this paper, we propose a novel large deformation diffeomorphic
registration algorithm to align high angular resolution diffusion images
(HARDI) characterized by orientation distribution functions (ODFs). Our
proposed algorithm seeks an optimal diffeomorphism of large deformation between
two ODF fields in a spatial volume domain and at the same time, locally
reorients an ODF in a manner such that it remains consistent with the
surrounding anatomical structure. To this end, we first review the Riemannian
manifold of ODFs. We then define the reorientation of an ODF when an affine
transformation is applied and subsequently, define the diffeomorphic group
action to be applied on the ODF based on this reorientation. We incorporate the
Riemannian metric of ODFs for quantifying the similarity of two HARDI images
into a variational problem defined under the large deformation diffeomorphic
metric mapping (LDDMM) framework. We finally derive the gradient of the cost
function in both Riemannian spaces of diffeomorphisms and the ODFs, and present
its numerical implementation. Both synthetic and real brain HARDI data are used
to illustrate the performance of our registration algorithm
Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space
High angular resolution diffusion imaging data is the observed characteristic
function for the local diffusion of water molecules in tissue. This data is
used to infer structural information in brain imaging. Nonparametric scalar
measures are proposed to summarize such data, and to locally characterize
spatial features of the diffusion probability density function (PDF), relying
on the geometry of the characteristic function. Summary statistics are defined
so that their distributions are, to first-order, both independent of nuisance
parameters and also analytically tractable. The dominant direction of the
diffusion at a spatial location (voxel) is determined, and a new set of axes
are introduced in Fourier space. Variation quantified in these axes determines
the local spatial properties of the diffusion density. Nonparametric hypothesis
tests for determining whether the diffusion is unimodal, isotropic or
multi-modal are proposed. More subtle characteristics of white-matter
microstructure, such as the degree of anisotropy of the PDF and symmetry
compared with a variety of asymmetric PDF alternatives, may be ascertained
directly in the Fourier domain without parametric assumptions on the form of
the diffusion PDF. We simulate a set of diffusion processes and characterize
their local properties using the newly introduced summaries. We show how
complex white-matter structures across multiple voxels exhibit clear
ellipsoidal and asymmetric structure in simulation, and assess the performance
of the statistics in clinically-acquired magnetic resonance imaging data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Fast Fiber Orientation Estimation in Diffusion MRI from kq-Space Sampling and Anatomical Priors
High spatio-angular resolution diffusion MRI (dMRI) has been shown to provide
accurate identification of complex fiber configurations, albeit at the cost of
long acquisition times. We propose a method to recover intra-voxel fiber
configurations at high spatio-angular resolution relying on a kq-space
under-sampling scheme to enable accelerated acquisitions. The inverse problem
for reconstruction of the fiber orientation distribution (FOD) is regularized
by a structured sparsity prior promoting simultaneously voxelwise sparsity and
spatial smoothness of fiber orientation. Prior knowledge of the spatial
distribution of white matter, gray matter and cerebrospinal fluid is also
assumed. A minimization problem is formulated and solved via a forward-backward
convex optimization algorithmic structure. Simulations and real data analysis
suggest that accurate FOD mapping can be achieved from severe kq-space
under-sampling regimes, potentially enabling high spatio-angular dMRI in the
clinical setting.Comment: 10 pages, 5 figures, Supplementary Material
- …