| 1. |
- Alipoor, Mohammad, 1983, et al.
(författare)
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A Novel Framework for repeated measurements in diffusion tensor imaging
- 2016
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Ingår i: 3rd (ACM) Int'l Conf. on Biomedical and Bioinformatics Engineering (ICBBE 2016). - New York, NY, USA : ACM. - 9781450348249 ; Part F125793, s. 1-6
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Konferensbidrag (refereegranskat)abstract
- In the context of diffusion tensor imaging (DTI), the utility of making repeated measurements in each diffusion sensitizing direction has been the subject of numerous stud-ies. One can estimate the true signal value using either the raw complex-valued data or the real-valued magnitudesignal. While conventional methods focus on the former strategy, this paper proposes a new framework for acquiring/processing repeated measurements based on the latter strategy. The aim is to enhance the DTI processing pipeline by adding a diffusion signal estimator (DSE). This permits us to exploit the knowledge of the noise distribution to estimate the true signal value in each direction. An extensive study of the proposed framework, including theoretical analysis, experiments with synthetic data, performance evaluation and comparisons is presented.Our results show that the precision of estimated diffusionparameters is dependent on the number of available samplesand the manner in which the DSE accounts for noise. Theproposed framework improves the precision in estimationof diffusion parameters given a sufficient number of uniquemeasurements. This encourages future work with rich realdatasets and downstream applications.
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| 2. |
- Alipoor, Mohammad, 1983
(författare)
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Computational Diffusion MRI: Optimal Gradient Encoding Schemes
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 3. |
- Alipoor, Mohammad, 1983, et al.
(författare)
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Determinant of the information matrix: a new rotation invariant optimality metric to design gradient encoding schemes
- 2015
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Ingår i: 12th IEEE International Symposium on Biomedical Imaging, ISBI 2015, Brooklyn, United States, 16-19 April 2015. - 1945-8452. - 9781479923748 ; 2015-July, s. 462-465
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Konferensbidrag (refereegranskat)abstract
- Minimum condition number (CN) gradient encoding schemewas introduced to diffusion MRI community more than adecade ago. It’s computation requires tedious numerical optimization which usually leads to sub-optimal solutions. TheCN does not reflect any benefits in acquiring more measurements, i.e. it’s optimal value is constant for any numberof measurements. Further, it is variable under rotation. Inthis paper we (i) propose an accurate method to computeminimum condition number scheme; and (ii) introduce determinant of the information matrix (DIM) as a new optimality metric that scales with number of measurements anddoes reflect what one would gain from acquiring more measurements. Theoretical analysis shows that DIM is rotationinvariant. Evaluations on state-of-the-art encoding schemesproves the relevance and superiority of the proposed metriccompared to condition number.
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| 4. |
- Alipoor, Mohammad, 1983, et al.
(författare)
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Fourth order tensor-based diffusion MRI signal modeling
- 2015
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Ingår i: International symposium on biomedical imaging, White Matter Modeling Challenge. 16-19 April 2015, New York, USA..
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This abstract describes forth order tensor-based diffusion signal modeling as proposed in [1].
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| 5. |
- Alipoor, Mohammad, 1983, et al.
(författare)
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Icosahedral gradient encoding scheme for an arbitrary number of measurements
- 2015
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Ingår i: International symposium on biomedical imaging. - 1945-8452. - 9781479923748 ; 2015-July, s. 959-962
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Konferensbidrag (refereegranskat)abstract
- The icosahedral gradient encoding scheme (GES) is widelyused in diffusion MRI community due to its uniformly distributed orientations and rotationally invariant condition number. The major drawback with this scheme is that it is notavailable for arbitrary number of measurements. In this paper(i) we propose an algorithm to find the icosahedral schemefor any number of measurements. Performance of the obtained GES is evaluated and compared with that of Jones andtraditional icosahedral schemes in terms of condition number,standard deviation of the estimated fractional anisotropy anddistribution of diffusion sensitizing directions; and (ii) we introduce minimum eigenvalue of the information matrix as anew optimality metric to replace condition number. Unlikecondition number, it is proportional to the number of measurements and thus in agreement with the intuition that moremeasurements leads to more robust tensor estimation. Furthermore, it may independently be maximized to design GESsfor different diffusion imaging techniques.
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| 6. |
- Alipoor, Mohammad, 1983, et al.
(författare)
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K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging
- 2015
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Ingår i: Biomed Research International. - : Hindawi Limited. - 2314-6133 .- 2314-6141.
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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.
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| 7. |
- Alipoor, Mohammad, 1983, et al.
(författare)
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Optimal Experiment Design for Mono-Exponential Model Fitting: Application to Apparent Diffusion Coefficient Imaging
- 2015
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Ingår i: BioMed Research International. - : Hindawi Limited. - 2314-6133 .- 2314-6141. ; 2015
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Tidskriftsartikel (refereegranskat)abstract
- The mono-exponential model is widely used in quantitative biomedical imaging. Notable applications include apparent diffusion coefficient (ADC) imaging and pharmacokinetics.The application of ADC imaging to the detection of malignant tissue has in turn prompted several studies concerning optimal experiment design for mono-exponential model fitting. In this paper, we propose a new experiment design method that is based on minimizing the determinant of the covariance matrix of the estimated parameters (?-optimal design). In contrast to previous methods, ?-optimal design is independent of the imaged quantities. Applying this method to ADC imaging, we demonstrate its steady performance for the whole range of input variables (imaged parameters, number of measurements, range of ?-values). Using Monte Carlo simulations we show that the ?-optimal design outperforms existing experiment design methods in terms of accuracy and precision of the estimated parameters.
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| 8. |
- 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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| 9. |
- Ferizi, U., et al.
(författare)
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Diffusion MRI microstructure models with in vivo human brain Connectome data: results from a multi-group comparison
- 2017
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Ingår i: NMR in Biomedicine. - : Wiley. - 0952-3480 .- 1099-1492. ; 30:9, s. Article no e3734 -
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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.
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