Computational Diffusion MRI: Optimal Gradient Encoding Schemes
Doktorsavhandling, 2016
Diffusion-weighted magnetic resonance imaging (dMRI) is a non-invasive
structural imaging technique that provides information about tissue microstructures.
Quantitative measures derived from dMRI reflect pathological
and developmental changes in living tissues such as human brain. Such parameters
are increasingly used in diagnostic and prognostic procedures and
this has motivated several studies to investigate their estimation accuracy
and precision. The precision of an estimated parameter is dependent on the
applied gradient encoding scheme (GES). An optimal GES is one that minimizes
the variance of the estimated parameter(s). This thesis focuses on
optimal GES design for the following dMRI models: second and fourth-order
diffusion tensor imaging (DTI), ADC imaging and diffusion kurtosis imaging
(DKI). A unified framework is developed that comprises three steps. In
the first step, the original problem is formulated as an optimal experiment
design problem. The optimal experiment design is the one that minimizes
the condition number (K-optimal) or the determinant (D-optimal) of the
covariance matrix of the estimated parameters. This yields a non-convex
optimization problem. In the second step, the problem is re-formulated as a
semi-definite programming (SDP) problem by introducing new decision variables
and convex relaxation. In the final step, the SDP problem is solved
and the original decision variables are recovered. The proposed framework is
comprehensive; it can be applied to DTI, DKI, K-optimal design, D-optimal
design, single-shell and multi-shell acquisitions and to optimizing directions
and b-values.
The main contributions of this thesis include: (i) proof that by uniformly
distributing gradient encoding directions one obtains a D-optimal design
both for DKI and DTI; (ii) proof that the traditionally used icosahedral GES
is D-optimal for DTI; (iii) proof that there exist rotation-invariant GESs that
are not uniformly distributed; and (iv) proof that there exist GESs that are
D-optimal for DTI and DKI simultaneously. A simple algorithm is presnted
that can compute uniformly distributed GESs. In contrast to previous
methods, the proposed solution is strictly rotation-invariant. The practical
impact/utility of the proposed method is demonstrated using Monte Carlo
simulations. The results show that the precision of parameters estimated
using the proposed approach can be as much as 25% better than that estimated
by state-of-the-art methods. Validation of these findings using real
data and extension to non-linear estimators/diffusion models provide scope
for future work.
Gradient Encoding Scheme
ADC imaging
Diffusion MRI
D-optimal experiment design
Diffusion Tensor Imaging
Optimal Image acquisition
Second and Fourth Order Tensors.
Diffusion Kurtosis Imaging