| 1. |
- Alipoor, Mohammad, 1983, et al.
(författare)
-
On High Order Tensor-based Diffusivity Profile Estimation
- 2013
-
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-
-
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.
|
|
| 2. |
- Alipoor, Mohammad, 1983, et al.
(författare)
-
K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging
- 2015
-
Ingår i: Biomed Research International. - : Hindawi Limited. - 2314-6133 .- 2314-6141.
-
Tidskriftsartikel (refereegranskat)abstract
- The design of an optimal gradient encoding scheme (GES) is a fundamental problem in diffusion MRI. It is well studied for the case of second-order tensor imaging (Gaussian diffusion). However, it has not been investigated for the wide range of non-Gaussian diffusion models. The optimal GES is the one that minimizes the variance of the estimated parameters. Such a GES can be realized by minimizing the condition number of the design matrix (K-optimal design). In this paper, we propose a new approach to solve the K-optimal GES design problem for fourth-order tensor-based diffusion profile imaging. The problem is a nonconvex experiment design problem. Using convex relaxation, we reformulate it as a tractable semidefinite programming problem. Solving this problem leads to several theoretical properties of K-optimal design: (i) the odd moments of the K-optimal design must be zero; (ii) the even moments of the K-optimal design are proportional to the total number of measurements; (iii) the K-optimal design is not unique, in general; and (iv) the proposed method can be used to compute the K-optimal design for an arbitrary number of measurements. Our Monte Carlo simulations support the theoretical results and show that, in comparison with existing designs, the K-optimal design leads to the minimum signal deviation.
|
|
| 3. |
- Alipoor, Mohammad, 1983, et al.
(författare)
-
Optimal Diffusion Tensor Imaging with Repeated Measurements
- 2013
-
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
-
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.
|
|
| 4. |
- Alipoor, Mohammad, 1983, et al.
(författare)
-
Optimal Gradient Encoding Schemes for Diffusion Tensor and Kurtosis Imaging
- 2016
-
Ingår i: IEEE transactions on Computational Imaging. - 2333-9403. ; 2:3, s. 375 - 391
-
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.
|
|
| 5. |
- Ferizi, U., et al.
(författare)
-
Diffusion MRI microstructure models with in vivo human brain Connectome data: results from a multi-group comparison
- 2017
-
Ingår i: NMR in Biomedicine. - : Wiley. - 0952-3480 .- 1099-1492. ; 30:9, s. Article no e3734 -
-
Tidskriftsartikel (refereegranskat)abstract
- A large number of mathematical models have been proposed to describe the measured signal in diffusion-weighted (DW) magnetic resonance imaging (MRI). However, model comparison to date focuses only on specific subclasses, e.g. compartment models or signal models, and little or no information is available in the literature on how performance varies among the different types of models. To address this deficiency, we organized the White Matter Modeling Challenge' during the International Symposium on Biomedical Imaging (ISBI) 2015 conference. This competition aimed to compare a range of different kinds of models in their ability to explain a large range of measurable in vivo DW human brain data. Specifically, we assessed the ability of models to predict the DW signal accurately for new diffusion gradients and b values. We did not evaluate the accuracy of estimated model parameters, as a ground truth is hard to obtain. We used the Connectome scanner at the Massachusetts General Hospital, using gradient strengths of up to 300mT/m and a broad set of diffusion times. We focused on assessing the DW signal prediction in two regions: the genu in the corpus callosum, where the fibres are relatively straight and parallel, and the fornix, where the configuration of fibres is more complex. The challenge participants had access to three-quarters of the dataset and their models were ranked on their ability to predict the remaining unseen quarter of the data. The challenge provided a unique opportunity for a quantitative comparison of diverse methods from multiple groups worldwide. The comparison of the challenge entries reveals interesting trends that could potentially influence the next generation of diffusion-based quantitative MRI techniques. The first is that signal models do not necessarily outperform tissue models; in fact, of those tested, tissue models rank highest on average. The second is that assuming a non-Gaussian (rather than purely Gaussian) noise model provides little improvement in prediction of unseen data, although it is possible that this may still have a beneficial effect on estimated parameter values. The third is that preprocessing the training data, here by omitting signal outliers, and using signal-predicting strategies, such as bootstrapping or cross-validation, could benefit the model fitting. The analysis in this study provides a benchmark for other models and the data remain available to build up a more complete comparison in the future.
|
|
| 6. |
- Kuczera, Stefan, et al.
(författare)
-
Optimized bias and signal inference in diffusion-weighted image analysis (OBSIDIAN)
- 2021
-
Ingår i: Magnetic Resonance in Medicine. - : Wiley. - 0740-3194 .- 1522-2594. ; 86:5, s. 2716-2732
-
Tidskriftsartikel (refereegranskat)abstract
- Purpose Correction of Rician signal bias in magnitude MR images. Methods A model-based, iterative fitting procedure is used to simultaneously estimate true signal and underlying Gaussian noise with standard deviation sigma g on a pixel-by-pixel basis in magnitude MR images. A precomputed function that relates absolute residuals between measured signals and model fit to sigma g is used to iteratively estimate sigma g. The feasibility of the method is evaluated and compared to maximum likelihood estimation (MLE) for diffusion signal decay simulations and diffusion-weighted images of the prostate considering 21 linearly spaced b-values from 0 to 3000 s/mm(2). A multidirectional analysis was performed with publically available brain data. Results Model simulations show that the Rician bias correction algorithm is fast, with an accuracy and precision that is on par to model-based MLE and direct fitting in the case of pure Gaussian noise. Increased accuracy in parameter prediction in a low signal-to-noise ratio (SNR) scenario is ideally achieved by using a composite of multiple signal decays from neighboring voxels as input for the algorithm. For patient data, good agreement with high SNR reference data of diffusion in prostate is achieved. Conclusions OBSIDIAN is a novel, alternative, simple to implement approach for rapid Rician bias correction applicable in any case where differences between true signal decay and underlying model function can be considered negligible in comparison to noise. The proposed composite fitting approach permits accurate parameter estimation even in typical clinical scenarios with low SNR, which significantly simplifies comparison of complex diffusion parameters among studies.
|
|
