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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.

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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.

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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.

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Micro-architectural characteristics of white matter can be inferred through analysis of diffusion-weighted magnetic resonance imaging (dMRI). The diffusion-dependent signal can be analyzed through several methods, with the tensor model being the most frequently used due to its straightforward interpretation and low requirements for acquisition parameters. While valuable information can be gained from the tensor-derived metrics in regions of homogeneous tissue organization, this model does not provide reliable microstructural information at crossing fiber regions, which are pervasive throughout human white matter. Several multiple fiber models have been proposed that seem to overcome the limitations of the tensor, with few providing per-bundle dMRI-derived metrics. However, biological interpretations of such metrics are limited by the lack of histological confirmation. To this end, we developed a straightforward biological validation framework. Unilateral retinal ischemia was induced in ten rats, which resulted in axonal (Wallerian) degeneration of the corresponding optic nerve, while the contralateral was left intact; the intact and injured axonal populations meet at the optic chiasm as they cross the midline, generating a fiber crossing region in which each population has different diffusion properties. Five rats served as controls. High-resolution ex vivo dMRI was acquired five weeks after experimental procedures. We correlated and compared histology to per-bundle descriptors derived from three methodologies for dMRI analysis (constrained spherical deconvolution and two multi-tensor representations). We found a tight correlation between axonal density (as evaluated through automatic segmentation of histological sections) with per-bundle apparent fiber density and fractional anisotropy (derived from dMRI). The multi-fiber methods explored were able to correctly identify the damaged fiber populations in a region of fiber crossings (chiasm). Our results provide validation of metrics that bring substantial and clinically useful information about white-matter tissue at crossing fiber regions. Our proposed framework is useful to validate other current and future dMRI methods.

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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.

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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.

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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.

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