7 research outputs found
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
Left-Invariant Diffusion on the Motion Group in terms of the Irreducible Representations of SO(3)
In this work we study the formulation of convection/diffusion equations on
the 3D motion group SE(3) in terms of the irreducible representations of SO(3).
Therefore, the left-invariant vector-fields on SE(3) are expressed as linear
operators, that are differential forms in the translation coordinate and
algebraic in the rotation. In the context of 3D image processing this approach
avoids the explicit discretization of SO(3) or , respectively. This is
particular important for SO(3), where a direct discretization is infeasible due
to the enormous memory consumption. We show two applications of the framework:
one in the context of diffusion-weighted magnetic resonance imaging and one in
the context of object detection
Building connectomes using diffusion MRI: why, how and but
Why has diffusion MRI become a principal modality for mapping connectomes in vivo? How do different image acquisition parameters, fiber tracking algorithms and other methodological choices affect connectome estimation? What are the main factors that dictate the success and failure of connectome reconstruction? These are some of the key questions that we aim to address in this review. We provide an overview of the key methods that can be used to estimate the nodes and edges of macroscale connectomes, and we discuss open problems and inherent limitations. We argue that diffusion MRI-based connectome mapping methods are still in their infancy and caution against blind application of deep white matter tractography due to the challenges inherent to connectome reconstruction. We review a number of studies that provide evidence of useful microstructural and network properties that can be extracted in various independent and biologically-relevant contexts. Finally, we highlight some of the key deficiencies of current macroscale connectome mapping methodologies and motivate future developments
Diffusion, convection and erosion on R3 x S2 and their application to the enhancement of crossing fibers
In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jacobi equations (erosions) on the space R3 x S2 of 3D-positions and orientations naturally embedded in the group SE(3) of 3D-rigid body movements. The general motivation for these (convection-)diffusions and erosions is to obtain crossing-preserving fiber enhancement on probability densities defined on the space of positions and orientations. The linear left-invariant (convection-)diffusions are forward Kolmogorov equations of Brownian motions on R3 x S2 and can be solved by R3 x S2-convolution with the corresponding Greenâs functions or by a finite difference scheme. The left-invariant Hamilton-Jacobi equations are Bellman equations of cost processes on R3 x S2 and they are solved by a morphological R3 x S2-convolution with the corresponding Greenâs functions. We will reveal the remarkable analogy between these erosions/dilations and diffusions. Furthermore, we consider pseudo-linear scale spaces on the space of positions and orientations that combines dilation and diffusion in a single evolution. In our design and analysis for appropriate linear, non-linear, morphological and pseudo-linear scale spaces on R3 x S2 we employ the underlying differential geometry on SE(3), where the frame of left-invariant vector fields serves as a moving frame of reference. Furthermore, we will present new and simpler finite difference schemes for our diffusions, which are clear improvements of our previous finite difference schemes. We apply our theory to the enhancement of fibres in magnetic resonance imaging (MRI) techniques (HARDI and DTI) for imaging water diffusion processes in fibrous tissues such as brain white matter and muscles. We provide experiments of our crossing-preserving (non-linear) left-invariant evolutions on neural images of a human brain containing crossing fibers
Left-invariant diffusions on R^3 x S^2 and their application to crossing-preserving smoothing on HARDI-images
In previous work we studied linear and nonlinear left-invariant diffusion equations on the 2D Euclidean motion group SE(2), for the purpose of crossing-preserving coherence-enhancing diffusion on 2D images. In this article we study left-invariant diffusion on the 3D Euclidean motion group SE(3) and its application to crossing-preserving smoothing of high angular resolution diffusion imaging (HARDI), which is a recent magnetic resonance imaging (MRI) technique for imaging water diffusion processes in fibrous tissues such as brain white matter and muscles. The linear left-invariant (convection-)diffusions are forward Kolmogorov equations of Brownian motions on the space R3 o S2 of positions and orientations embedded in SE(3) and can be solved by R3 o S2-convolution with the corresponding Greenâs functions. We provide analytic approximation formulae and explicit sharp Gaussian estimates for these Greenâs functions. In our design and analysis for appropriate (non-linear) convection-diffusions on HARDI-data we put emphasis on the underlying differential geometry on SE(3). We write our left-invariant diffusions in covariant derivatives on SE(3) using the Cartan-connection. This Cartan-connection has constant curvature and constant torsion, and so have the exponential curves which are the auto-parallels along which our left-invariant diffusion takes place. We provide experiments of our crossing-preserving Euclidean-invariant diffusions on artificial HARDI-data containing crossing-fibers