Computational Diffusion MRI: Optimal Gradient Encoding Schemes

• Diffusion-weighted magnetic resonance imaging (dMRI) is a non-invasivestructural imaging technique that provides information about tissue microstructures.Quantitative measures derived from dMRI reflect pathologicaland developmental changes in living tissues such as human brain. Such parametersare increasingly used in diagnostic and prognostic procedures andthis has motivated several studies to investigate their estimation accuracyand precision. The precision of an estimated parameter is dependent on theapplied gradient encoding scheme (GES). An optimal GES is one that minimizesthe variance of the estimated parameter(s). This thesis focuses onoptimal GES design for the following dMRI models: second and fourth-orderdiffusion tensor imaging (DTI), ADC imaging and diffusion kurtosis imaging(DKI). A unified framework is developed that comprises three steps. Inthe first step, the original problem is formulated as an optimal experimentdesign problem. The optimal experiment design is the one that minimizesthe condition number (K-optimal) or the determinant (D-optimal) of thecovariance matrix of the estimated parameters. This yields a non-convexoptimization problem. In the second step, the problem is re-formulated as asemi-definite programming (SDP) problem by introducing new decision variablesand convex relaxation. In the final step, the SDP problem is solvedand the original decision variables are recovered. The proposed framework iscomprehensive; it can be applied to DTI, DKI, K-optimal design, D-optimaldesign, single-shell and multi-shell acquisitions and to optimizing directionsand b-values.The main contributions of this thesis include: (i) proof that by uniformlydistributing gradient encoding directions one obtains a D-optimal designboth for DKI and DTI; (ii) proof that the traditionally used icosahedral GESis D-optimal for DTI; (iii) proof that there exist rotation-invariant GESs thatare not uniformly distributed; and (iv) proof that there exist GESs that areD-optimal for DTI and DKI simultaneously. A simple algorithm is presntedthat can compute uniformly distributed GESs. In contrast to previousmethods, the proposed solution is strictly rotation-invariant. The practicalimpact/utility of the proposed method is demonstrated using Monte Carlosimulations. The results show that the precision of parameters estimatedusing the proposed approach can be as much as 25% better than that estimatedby state-of-the-art methods. Validation of these findings using realdata and extension to non-linear estimators/diffusion models provide scopefor future work.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Medicinteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Medical Engineering (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)

Nyckelord

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

Publikations- och innehållstyp

dok (ämneskategori)

vet (ämneskategori)