•We present a method for the estimation of the intra-voxel bundle-wise diffusion properties for DW-MRI.•Our method overcomes some limitations of most multi-fiber algorithms and extends them to ...estimate the diffusion profiles.•Our method constraints the sparsity of the axon bundles and uses their spatial redundancy to achieve robustness against noise.•We propose a new evaluation metric and a novel methodology for the quantitative evaluation of the methods on in-vivo data.•We present an extensive evaluation on state-of-the-art biophysical synthetic data and on the in-vivo MASSIVE dataset.
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A stable, accurate and robust-to-noise method for the estimation of the intra-voxel bundle-wise diffusion properties for diffusion-weighted magnetic resonance imaging is presented. The proposed method overcomes some of the limitations of most of the multi-fiber algorithms in the literature and extends them to estimate the diffusion profiles, improving the estimation of the intra-voxel geometry at challenging microstructure configurations, that is to say: relatively small crossing angles, different voxel-wise anisotropic diffusion profiles and low SNR. The proposed methodology is based on four key novel ideas: (i) A Multi-Resolution Discrete-Search determines the orientation of the fiber bundles accurately and naturally constrains the sparsity on the recovered solutions; (ii) the determination of the number of fiber bundles using the F-test combined with a Rician bias correction; (iii) a Simultaneous Denoising and Fitting procedure that exploits the spatial redundancy of the axon bundles to achieve robustness with respect to noise; and (iv) a general framework for the estimation of the axial and radial diffusivity parameters independently for each voxel. A new useful evaluation metric is also proposed, which combines the information of the success rate in the estimated number of bundles and the angular error, avoiding in this way, some of the limitations these metrics have individually. A novel methodology for the evaluation of the methods on in-vivo data is also proposed. This work presents an extensive evaluation: the proposed methodology has been tested on state-of-the-art biophysical synthetic data for a variety of conditions, on the challenging spatially coherent phantom used on the HARDI reconstruction Challenge 2012, and on the recently released in-vivo MASSIVE data-set. Our results present significant improvements on the estimation of the number and orientation of the fiber bundles over the Spherical Deconvolution algorithm for multi-shell data, which is one of the most widely used multi-fiber algorithm. The results also show that, by the voxel-wise estimation of the diffusion profiles, the axial and radial diffusivity parameters are robustly estimated, being this essential for a better understanding of the individual bundle diffusion properties at challenging structural configurations.
In this paper, we present a new formulation for recovering the fiber tract geometry within a voxel from diffusion weighted magnetic resonance imaging (MRI) data, in the presence of single or multiple ...neuronal fibers. To this end, we define a discrete set of diffusion basis functions. The intravoxel information is recovered at voxels containing fiber crossings or bifurcations via the use of a linear combination of the above mentioned basis functions. Then, the parametric representation of the intravoxel fiber geometry is a discrete mixture of Gaussians. Our synthetic experiments depict several advantages by using this discrete schema: the approach uses a small number of diffusion weighted images (23) and relatively small b values (1250 s/mm 2 ), i.e., the intravoxel information can be inferred at a fraction of the acquisition time required for datasets involving a large number of diffusion gradient orientations. Moreover our method is robust in the presence of more than two fibers within a voxel, improving the state-of-the-art of such parametric models. We present two algorithmic solutions to our formulation: by solving a linear program or by minimizing a quadratic cost function (both with non-negativity constraints). Such minimizations are efficiently achieved with standard iterative deterministic algorithms. Finally, we present results of applying the algorithms to synthetic as well as real data.
Brain tractography allows estimating in vivo long-range connections between groups of neurons. However, it is well known there is a huge amount of false-positive connections in the estimators that ...are represented as 3D streamlines. The COMMIT framework allows reducing those false positives, however the required computational time may become very long due to the, usually, huge number of streamlines per brain-volume, and the need to process thousands of brain images to increase the statistical power of current medical studies. In this work, we provide a programming model to parallelize the COMMIT framework on the CUDA language framework. Our results demonstrate that it is possible to reduce the computational burden by one order of magnitude by using this proposal.
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, 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 model in their ability to explain measured in vivo DW human brain data. We focus specifically on the challenge of explaining a large range of measurable data. We used the Connectome scanner at the Massachusetts General Hospital, using gradients strengths of up to 300 mT/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 quantitative comparison of a diverse set of methods from multiple groups worldwide. The comparison of the challenge entries reveals important trends and conclusions that influence the next generation of diffusion-based quantitative MRI techniques. The first is that signal models do not necessarily outperform tissue models; in fact tissue models on average rank highest of those tested. The second is that assuming a non-Gaussian (rather than a purely Gaussian) noise model provides little benefit. The third is that preprocessing the training data (here, 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 remains available to build up a more complete comparison over future years.
We present a new regularization approach for Diffusion Basis Functions fitting to estimate in vivo brain the axonal orientation from Diffusion Weighted Magnetic Resonance Images. That method assumes ...that the observed Magnetic Resonance signal at each voxel is a linear combination of a given diffusion basis functions; the aim of the approach is the estimation of the coefficients of the linear combination. An issue with the Diffusion Basis Functions method is the overestimation on the number of tensors (associated with different axon fibers) within a voxel due to noise, namely, the over fitting of the noisy signal. Our proposal overcomes such an overestimation problem. In additionally, we propose a metric to compare the performance of multi-fiber estimation algorithms. The metric is based on the Earth Mover’s Distance and allows us to compare in a single metric the orientation, size compartment and the number of axon bundles between two different estimations. The improvements of our two proposals is shown on synthetic and real experiments.
We present a novel framework for image segmentation based on the maximum likelihood estimator. A common hypothesis for explaining the differences among image regions is that they are generated by ...sampling different likelihood functions called models. In this work, we construct on last hypothesis and, additionally, we assume that such samples come from independent and identically distributed random variables. Thus, the probability (likelihood) that a particular model generates the observed value (at a given pixel) is estimated by computing the likelihood of the sample composed with the surrounding pixels. This simple approach allows us to propose efficient segmentation methods able to deal with textured images. Our approach is naturally extended for combining different features. Experiments in interactive image segmentation, automatic stereo analysis and denoising of brain water diffusion multi-tensor fields demonstrate the capabilities of our approach. PUBLICATION ABSTRACT
We present an extension to the Diffusion Basis Function Model for fitting the in vivo brain axonal orientations from Diffusion Weighted Magnetic Resonance Images. The standard Diffusion Basis ...Functions method assumes that the observed Magnetic Resonance signal at each voxel is a linear combination of a static set of basis functions with equally distributed orientations into the 3D unitary sphere. Our proposal, overcomes the limited angular resolution of the original model by adapting the basis orientations using a sophisticated non-linear optimization procedure. The improvements over the standard Diffusion Basis Functions model estimation by our proposal are demonstrated on the synthetic data-sets used on the 2012 HARDI Reconstruction Challenge.
Heavy periodane Azpiroz, Jon M.; Moreno, Diego; Ramirez-Manzanares, Alonso ...
Journal of molecular modeling,
05/2013, Letnik:
19, Številka:
5
Journal Article
Recenzirano
The potential energy surface of the hypothetical NaMgAlSiPSCl system (heavy periodane) is exhaustively analyzed via the gradient embedded genetic algorithm (GEGA) in combination with density ...functional theory (DFT) computations. The electronegativity differences among the elements in both the second and third rows of the periodic table indicate that low-energy heavy periodane structures are obtained when highly electronegative and electropositive elements are bound together, but the global minimum of the heavy periodane system is completely different to its second-row analog (LiBeBCNOF).
Figure
We propose a variational approach for multi-valued velocity field estimation in transparent sequences. Starting from existing local motion estimators, we show a variational model for integrating in ...space and time these local estimations to obtain a robust estimation of the multi-valued velocity field. With this approach, we can indeed estimate some multi-valued velocity fields which are not necessarily piecewise constant on a layer: Each layer can evolve according to non-parametric optical flow. We show how our approach outperforms some existing approaches, and we illustrate its capabilities on several challenging synthetic/real sequences.
Diffusion Weighted Magnetic Resonance Imaging is widely used to study the structure of the fiber pathways of brain white matter. Though, the recovered axon orientations could be prone to error ...because of the low signal to noise ratio. Spatial regularization can improve the estimations but it must be done carefully such that real information is not removed and false orientations are not introduced. In this work we investigate the advantages to apply an anisotropic filtering based on single and multiple axon bundle orientation kernels. To this aim, we compute local diffusion kernels based on Diffusion Tensor and multi Diffusion Tensor models. We show the benefits of our approach on three different types of DW-MRI Data: synthetic, in vivo human data, and acquired from a diffusion phantom.
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