Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in ...the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.
Focal cortical dysplasias are a type of malformations of cortical development that are a common cause of drug-resistant focal epilepsy. Surgical treatment is a viable option for some of these ...patients, with their outcome being highly related to complete surgical resection of lesions visible in magnetic resonance imaging (MRI). However, subtle lesions often go undetected on conventional imaging. Several methods to analyze MRI have been proposed, with the common goal of rendering subtle cortical lesions visible. However, most image-processing methods are targeted to detect the macroscopic characteristics of cortical dysplasias, which do not always correspond to the microstructural disarrangement of these cortical malformations. Quantitative analysis of diffusion-weighted MRI (dMRI) enables the inference of tissue characteristics, and novel methods provide valuable microstructural features of complex tissue, including gray matter. We investigated the ability of advanced dMRI descriptors to detect diffusion abnormalities in an animal model of cortical dysplasia. For this purpose, we induced cortical dysplasia in 18 animals that were scanned at 30 postnatal days (along with 19 control animals). We obtained multi-shell dMRI, to which we fitted single and multi-tensor representations. Quantitative dMRI parameters derived from these methods were queried using a curvilinear coordinate system to sample the cortical mantle, providing inter-subject anatomical correspondence. We found region- and layer-specific diffusion abnormalities in experimental animals. Moreover, we were able to distinguish diffusion abnormalities related to altered intra-cortical tangential fibers from those associated with radial cortical fibers. Histological examinations revealed myelo-architectural abnormalities that explain the alterations observed through dMRI. The methods for dMRI acquisition and analysis used here are available in clinical settings and our work shows their clinical relevance to detect subtle cortical dysplasias through analysis of their microstructural properties.
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 clinicalb-
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 theb-value is typically lower (around 1000 s/mm2), 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.
This study developed a method to approximate the covariance matrix associated with the simulation of water molecular diffusion inside the brain tissue. The computation implements the Discontinuous ...Galerkin method of the diffusion equation. A physically consistent numerical flux is applied to model the interaction between the axon walls and extracellular regions. This numerical flux yields an efficient GPU-CUDA implementation. We consider the two-dimensional case of high axon pack density, valid, for instance, in the brain's corpus callosum region.
Diffusion-weighted magnetic resonance imaging (dMRI) is widely used to infer microstructural characteristics of tissue, particularly in cerebral white matter. Histological validation of the metrics ...derived from dMRI methods are needed to fully characterize their ability to capture biologically-relevant histological features non-invasively. The data described here were used to correlate metrics derived from dMRI and quantitative histology in an animal model of axonal degeneration (“Histological validation of per-bundle water diffusion metrics within a region of fiber crossing following axonal degeneration” 1). Unilateral retinal ischemia/reperfusion was induced in 10 rats, by the elevation of pressure of the anterior chamber of the eye for 90 min. Five rats were used as controls. After five weeks, injured animals were intracardially perfused to analyze the optic nerves and chiasm with dMRI and histology. This resulted in 15 brain scans, each with 80 diffusion-sensitizing gradient directions with b = 2000 and 2500 s/mm2 and 20 non-diffusion-weighted images (b = 0 s/mm2), with isometric voxel resolution of 125 μm3. Histological sections were obtained after dMRI. Optical microscopy photomicrographs of the optic nerves (stained with toluidine blue) are available, as well as their corresponding automatic segmentations of axons and myelin.
•We present an adaptive diffusion dictionary for estimating white matter structure.•Our proposal overcomes the limitations of the diffusion dictionary-based methods.•Our proposal re-estimates the ...parameters of the atoms independently in each voxel.•We improve the fitting of the Diffusion-Weighted Magnetic Resonance signal.•The improvements benefit brain research allowing to generate a better tractography.
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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.
Motion estimation in sequences with transparencies is an important problem in robotics and medical imaging applications. In this work we propose a variational approach for estimating multi-valued ...velocity fields in transparent sequences. Starting from existing local motion estimators, we derive a variational model for integrating in space and time such a local information in order to obtain a robust estimation of the multi-valued velocity field. With this approach, we can indeed estimate multi-valued velocity fields which are not necessarily piecewise constant on a layer—each layer can evolve according to a non-parametric optical flow. We show how our approach outperforms existing methods; and we illustrate its capabilities on challenging experiments on both synthetic and real sequences.
A flocking based method for brain tractography Aranda, Ramon; Rivera, Mariano; Ramirez-Manzanares, Alonso
Medical image analysis,
April 2014, 2014-Apr, 2014-04-00, 20140401, Letnik:
18, Številka:
3
Journal Article
Recenzirano
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•In our knowledge, no method for tractography shares information between particles.•We propose a probabilistic tractography method based on the flocking concept.•Improvements by using ...a collective information term on the particle motion are shown.•The gravitational force between particles gives that collective information.•Our proposal obtains the best performance on the Fiber Cup data.
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.
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.
•Robust phase-unwrapping algorithm.•3D and 2D phase unwrapping.•Phase unwrapping for magnetic resonance imaging.•Morphological dilating and erosion for phase unwrapping.
The accurate recovery of an ...n-Dimensional field from observations that are wrapped into a particular interval (e.g., −π,π) is a problematic step in many applications, such as holography, interferometry, optical metrology, magnetic resonance imaging and analog-to-digital conversion in digital photography. While methods designed for this purpose abound (mainly in the 2-Dimensional case), most fail if the original unwrapped field contains abrupt changes that become aliased. In this paper we present Maximum Smoothness Consistent Unwrapping (MSCU), a novel and general method that overcomes said limitation. The method operates in two stages: in the first, a region without aliased changes which is as large as possible (which we call the consistent region) is found, and in the second, the unwrapped phase in the consistent region is propagated to the inconsistent areas to get the final result. MSCU has the following advantages: it is well founded theoretically, which allows the assessment of the reliability of its results; it is directly applicable to fields in any number of dimensions and when the signal is wrapped module any real number P; it has no free parameters to adjust; and it is computationally efficient and easy to implement. We present a formal derivation of the method and illustrations of its performance, both in synthetic fields –where we compare it with that of other state-of-the-art methods– and in real data (2-D data from optical speckle interferometry and 3-D data from magnetic susceptibility images obtained by magnetic resonance acquisitions). In this paper we focus on phase unwrapping applications, but the presented method may be directly applied to the case of other wrapping intervals as well, as for instance in High Dynamic Range image processing.
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