| 1. |
- Alipoor, Mohammad, 1983, et al.
(författare)
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Optimal Gradient Encoding Schemes for Diffusion Tensor and Kurtosis Imaging
- 2016
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Ingår i: IEEE transactions on Computational Imaging. - 2333-9403. ; 2:3, s. 375-391
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Tidskriftsartikel (refereegranskat)abstract
- Diffusion-derived parameters find application in characterizing pathological and developmental changes in living tissues. Robust estimation of these parameters is important because they are used for medical diagnosis. An optimal gradient encoding scheme (GES) is one that minimizes the variance of the estimated diffusion parameters. This paper proposes a method for optimal GES design for two diffusion models: high-order diffusion tensor (HODT) imaging and diffusion kurtosis imaging (DKI). In both cases, the optimal GES design problem is formulated as a D-optimal (minimum determinant) experiment design problem. Then, using convex relaxation, it is reformulated as a semidefinite programming problem. Solving these problems we show that: 1) there exists a D-optimal solution for DKI that is simultaneously D-optimal for second- and fourth-order diffusion tensor imaging (DTI); 2) the traditionally used icosahedral scheme is approximately D-optimal for DTI and DKI; 3) the proposed D-optimal design is rotation invariant; 4) the proposed method can be used to compute the optimal design ($b$ -values and directions) for an arbitrary number of measurements and shells; and 5) using the proposed method one can obtain uniform distribution of gradient encoding directions for a typical number of measurements. Importantly, these theoretical findings provide the first mathematical proof of the optimality of uniformly distributed GESs for DKI and HODT imaging. The utility of the proposed method is further supported by the evaluation results and comparisons with with existing methods.
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| 2. |
- Alipoor, Mohammad, 1983, et al.
(författare)
-
Optimal Diffusion Tensor Imaging with Repeated Measurements
- 2013
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Ingår i: Lecture Notes in Computer Science: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2013. 16th International Conference, Nagoya, Japan, September 22-26, 2013, Proceedings, Part I. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 0302-9743 .- 1611-3349. - 9783642408106 ; 8149, s. 687-694
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Konferensbidrag (refereegranskat)abstract
- Several data acquisition schemes for diffusion MRI have been proposed and explored to date for the reconstruction of the 2nd order tensor. Our main contributions in this paper are: (i) the definition of a new class of sampling schemes based on repeated measurements in every sampling point; (ii) two novel schemes belonging to this class; and (iii) a new reconstruction framework for the second scheme. We also present an evaluation, based on Monte Carlo computer simulations, of the performances of these schemes relative to known optimal sampling schemes for both 2nd and 4th order tensors. The results demonstrate that tensor estimation by the proposed sampling schemes and estimation framework is more accurate and robust.
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| 3. |
- Alipoor, Mohammad, 1983, et al.
(författare)
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On High Order Tensor-based Diffusivity Profile Estimation
- 2013
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Ingår i: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS. - 1557-170X. - 9781457702167 ; , s. 93-96, s. 4-
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Konferensbidrag (refereegranskat)abstract
- Diffusion weighted magnetic resonance imaging (dMRI) is used to measure, in vivo, the self-diffusion of water molecules in biological tissues. High order tensors (HOTs) are used to model the apparent diffusion coefficient (ADC) profile at each voxel from the dMRI data. In this paper we propose: (i) A new method for estimating HOTs from dMRI data based on weighted least squares (WLS) optimization; and (ii) A new expression for computing the fractional anisotropy from a HOT that does not suffer from singularities and spurious zeros. We also present an empirical evaluation of the proposed method relative to the two existing methods based on both synthetic and real human brain dMRI data. The results show that the proposed method yields more accurate estimation than the competing methods.
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