1,742 research outputs found
Bayesian uncertainty quantification in linear models for diffusion MRI
Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue
microstructure. By fitting a model to the dMRI signal it is possible to derive
various quantitative features. Several of the most popular dMRI signal models
are expansions in an appropriately chosen basis, where the coefficients are
determined using some variation of least-squares. However, such approaches lack
any notion of uncertainty, which could be valuable in e.g. group analyses. In
this work, we use a probabilistic interpretation of linear least-squares
methods to recast popular dMRI models as Bayesian ones. This makes it possible
to quantify the uncertainty of any derived quantity. In particular, for
quantities that are affine functions of the coefficients, the posterior
distribution can be expressed in closed-form. We simulated measurements from
single- and double-tensor models where the correct values of several quantities
are known, to validate that the theoretically derived quantiles agree with
those observed empirically. We included results from residual bootstrap for
comparison and found good agreement. The validation employed several different
models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI)
and Constrained Spherical Deconvolution (CSD). We also used in vivo data to
visualize maps of quantitative features and corresponding uncertainties, and to
show how our approach can be used in a group analysis to downweight subjects
with high uncertainty. In summary, we convert successful linear models for dMRI
signal estimation to probabilistic models, capable of accurate uncertainty
quantification.Comment: Added results from a group analysis and a comparison with residual
bootstra
Fast, Model-Free , Analytical ODF Reconstruction from the Q-Space Signal
International audienceThe orientation distribution function (ODF) is very important in diffusion MRI. There are two types of ODFs. One is proposed using radial projection in Q-ball imaging [7]. Another one is the marginal pdf proposed in diffusion spectrum imaging (DSI) [8]. Since the marginal pdf is much sharper and mathematically correct, it could be more useful. Recently some reconstruction methods were proposed for this kind of ODF [1, 6]. They are both based on mono-exponential model, globally or locally, which has some intrinsic modeling error [4]. Although the authors in [1] extended the mono-exponential model to multi-exponential model, this multi-exponential model needs to be estimated non-linearly for every voxel and only in some special sampling scheme it has a analytical solution. Here we give a model-free analytical reconstruction method based on the Spherical Polar Fourier expression of the signal. It can estimate the ODF fast and analytically from the signal
Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS
In this article we present a noise reduction method (msPOAS) for multi-shell diffusion-weighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed position-orientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted data measured on a single shell and on multiple shells
Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS
In this article we present a noise reduction method (msPOAS) for
multi-shell diffusionweighted magnetic resonance data. To our knowledge, this
is the first smoothing method which allows simultaneous smoothing of all
q-shells. It is applied directly to the diffusion weighted data and
consequently allows subsequent analysis by any model. Due to its adaptivity,
the procedure avoids blurring of the inherent structures and preserves
discontinuities. MsPOAS extends the recently developed positionorientation
adaptive smoothing (POAS) procedure to multi-shell experiments. At the same
time it considerably simplifies and accelerates the calculations. The
behavior of the algorithm msPOAS is evaluated on diffusion-weighted data
measured on a single shell and on multiple shells
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
Non-parametric representation and prediction of single- and multi-shell diffusion-weighted MRI data using Gaussian processes
Diffusion MRI offers great potential in studying the human brain microstructure and connectivity. However, diffusion images are marred by technical problems, such as image distortions and spurious signal loss. Correcting for these problems is non-trivial and relies on having a mechanism that predicts what to expect. In this paper we describe a novel way to represent and make predictions about diffusion MRI data. It is based on a Gaussian process on one or several spheres similar to the Geostatistical method of “Kriging”. We present a choice of covariance function that allows us to accurately predict the signal even from voxels with complex fibre patterns. For multi-shell data (multiple non-zero b-values) the covariance function extends across the shells which means that data from one shell is used when making predictions for another shell
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