Alonso Ramirez-Manzanares

Diffusion Basis Functions Decomposition for Estimating White Matter Intravoxel Fiber Geometry

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/mm2 ), 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.

Quantitative Comparison of Reconstruction Methods for Intra-Voxel Fiber Recovery From Diffusion MRI

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the “HARDI reconstruction challenge” organized in the context of the “ISBI 2012” conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

Basis Tensor Decomposition for Restoring Intra-Voxel Structure and Stochastic Walks for Inferring Brain Connectivity in DT-MRI

We present a regularized method for solving an inverse problem in Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data. In the case of brain images, DT-MR imagery technique produces a tensor field that indicates the local orientation of nerve bundles. Now days, the spatial resolution of this technique is limited by the partial volume effect produced in voxels that contain fiber crossings or bifurcations. In this paper, we proposed a method for recovering the intra-voxel information and inferring the brain connectivity. We assume that the observed tensor is a linear combination of a given tensor basis, therefore, the aim of our approach is the computation of the unknown coefficients of this linear combination. By regularizing the problem, we introduce the needed prior information about the piecewise smoothness of nerve bundles orientation. As a result, we recover a multi-tensor field. Moreover, for estimating the nerve bundles trajectory, we propose a method based on stochastic walks of particles through the computed multi-tensor field. The performance of the method is demonstrated by experiments in both synthetic and real data.

A hierarchical algorithm for molecular similarity (H-FORMS)

A new hierarchical method to determine molecular similarity is introduced. The goal of this method is to detect if a pair of molecules has the same structure by estimating a rigid transformation that aligns the molecules and a correspondence function that matches their atoms. The algorithm firstly detect similarity based on the global spatial structure. If this analysis is not sufficient, the algorithm computes novel local structural rotation‐invariant descriptors for the atom neighborhood and uses this information to match atoms. Two strategies (deterministic and stochastic) on the matching based alignment computation are tested. As a result, the atom‐matching based on local similarity indexes decreases the number of testing trials and significantly reduces the dimensionality of the Hungarian assignation problem. The experiments on well‐known datasets show that our proposal outperforms state‐of‐the‐art methods in terms of the required computational time and accuracy.

Resolving axon fiber crossings at clinical b-values: An evaluation study

PURPOSE Diffusion tensor magnetic resonance imaging is widely used to study the structure of the fiber pathways of brain white matter. However, the diffusion tensor cannot capture complex intravoxel fiber architecture such as fiber crossings of bifurcations. Consequently, a number of methods have been proposed to recover intravoxel fiber bundle orientations from high angular resolution diffusion imaging scans, optimized to resolve fiber crossings. It is important to improve the brain tractography by applying these multifiber methods to diffusion tensor protocols with a clinical b- value (low), which are optimized on computing tensor scalar statistics. In order to characterize the variance among different methods, consequently to be able to select the most appropriate one for a particular application, it is desirable to compare them under identical experimental conditions. METHODS In this work, the authors study how QBall, spherical deconvolution, persistent angular structure, stick and ball, diffusion basis functions, and analytical QBall methods perform under clinically-realistic scanning conditions, where the b-value is typically lower (around 1000 s∕mm(2)), and the number of diffusion encoding orientations is fewer (30-60) than in dedicated high angular resolution diffusion imaging scans. To characterize the performance of the methods, they consider the accuracy of the estimated number of fibers, the relative contribution of each fiber population to the total magnetic resonance signal, and the recovered orientation error for each fiber bundle. To this aim, they use four different sources of data: synthetic data from Gaussian mixture model, cylinder restricted model, and in vivo data from two different acquisition schemes. RESULTS Results of their experiments indicate that: (a) it is feasible to apply only a subset of these methods to clinical data sets and (b) it allows one to characterize the performance of each method. In particular, two methods are not feasible to the kind of magnetic resonance diffusion data they test. By the characterization of their systematic behavior, among other conclusions, they report the method which better performs for the estimation of the number of diffusion peaks per voxel, also the method which better estimates the diffusion orientation. CONCLUSIONS The framework they propose for comparison allows one to effectively characterize and compare the performance of the most frequently used multifiber algorithms under realistic medical settings and realistic signal-to-noise ratio environments. The framework is based on several crossings with a non-orientational bias and different signal models. The results they present are relevant for medical doctors and researchers, interested in the use of the multifiber solution for tractography.

Sparse and Adaptive Diffusion Dictionary (SADD) for recovering intra-voxel white matter structure.

On the analysis of the Diffusion-Weighted Magnetic Resonance Images, multi-compartment models overcome the limitations of the well-known Diffusion Tensor model for fitting in vivo brain axonal orientations at voxels with fiber crossings, branching, kissing or bifurcations. Some successful multi-compartment methods are based on diffusion dictionaries. The diffusion dictionary-based methods assume that the observed Magnetic Resonance signal at each voxel is a linear combination of the fixed dictionary elements (dictionary atoms). The atoms are fixed along different orientations and diffusivity profiles. In this work, we present a sparse and adaptive diffusion dictionary method based on the Diffusion Basis Functions Model to estimate in vivo brain axonal fiber populations. Our proposal overcomes the following limitations of the diffusion dictionary-based methods: the limited angular resolution and the fixed shapes for the atom set. We propose to iteratively re-estimate the orientations and the diffusivity profile of the atoms independently at each voxel by using a simplified and easier-to-solve mathematical approach. As a result, we improve the fitting of the Diffusion-Weighted Magnetic Resonance signal. The advantages with respect to the former Diffusion Basis Functions method are demonstrated on the synthetic data-set used on the 2012 HARDI Reconstruction Challenge and in vivo human data. We demonstrate that improvements obtained in the intra-voxel fiber structure estimations benefit brain research allowing to obtain better tractography estimations. Hence, these improvements result in an accurate computation of the brain connectivity patterns.

A Comparison of Methods for Recovering Intra-voxel White Matter Fiber Architecture from Clinical Diffusion Imaging Scans

Diffusion tensor magnetic resonance imaging is widely used to study the structure of the fiber pathways of brain white matter. However, the diffusion tensor cannot capture complex intra-voxel fiber architecture such as fiber crossings. Consequently, a number of methods have been proposed to recover intra-voxel fiber bundle orientations from high angular-resolution diffusion imaging scans, which are optimized to resolve fiber crossings. In this work we study how multi-tensor, spherical deconvolution, analytical QBall and diffusion basis function methods perform under clinical scanning conditions. Our experiments indicate that it is feasible to apply some of these methods in clinical data sets.

A flocking based method for brain tractography

We propose a new method to estimate axonal fiber pathways from Multiple Intra-Voxel Diffusion Orientations. Our method uses the multiple local orientation information for leading stochastic walks of particles. These stochastic particles are modeled with mass and thus they are subject to gravitational and inertial forces. As result, we obtain smooth, filtered and compact trajectory bundles. This gravitational interaction can be seen as a flocking behavior among particles that promotes better and robust axon fiber estimations because they use collective information to move. However, the stochastic walks may generate paths with low support (outliers), generally associated to incorrect brain connections. In order to eliminate the outlier pathways, we propose a filtering procedure based on principal component analysis and spectral clustering. The performance of the proposal is evaluated on Multiple Intra-Voxel Diffusion Orientations from two realistic numeric diffusion phantoms and a physical diffusion phantom. Additionally, we qualitatively demonstrate the performance on in vivo human brain data.

Diffusion MRI microstructure models with in vivo human brain Connectome data: results from a multi‐group comparison

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 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 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.

Spatial Sampling for Image Segmentation

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.