Cluster Analysis of Diffusion Tensor Fields with Application to the Segmentation of the Corpus Callosum

AbstractAccurate segmentation of the Corpus Callosum (CC) is an important aspect of clinical medicine and is used in the diagnosis of various brain disorders. In this paper, we propose an automated method for two and three dimensional segmentation of the CC using diffusion tensor imaging. It has been demonstrated that Hartigan's K-means is more efficient than the traditional Lloyd algorithm for clustering. We adapt Hartigan's K-means to be applicable for use with the metrics that have a f -mean (e.g. Cholesky, root Euclidean and log Euclidean). Then we applied the adapted Hartigan's K-means, using Euclidean, Cholesky, root Euclidean and log Euclidean metrics along with Procrustes and Riemannian metrics (which need numerical solutions for mean computation), to diffusion tensor images of the brain to provide a segmentation of the CC. The log Euclidean and Riemannian metrics provide more accurate segmentations of the CC than the other metrics as they present the least variation of the shape and size of the tensors in the CC for 2D segmentation. They also yield a full shape of the splenium for the 3D segmentation

The effect of realistic geometries on the susceptibility-weighted MR signal in white matter

Purpose: To investigate the effect of realistic microstructural geometry on the susceptibility-weighted magnetic resonance (MR) signal in white matter (WM), with application to demyelination. Methods: Previous work has modeled susceptibility-weighted signals under the assumption that axons are cylindrical. In this work, we explore the implications of this assumption by considering the effect of more realistic geometries. A three-compartment WM model incorporating relevant properties based on literature was used to predict the MR signal. Myelinated axons were modeled with several cross-sectional geometries of increasing realism: nested circles, warped/elliptical circles and measured axonal geometries from electron micrographs. Signal simulations from the different microstructural geometries were compared to measured signals from a Cuprizone mouse model with varying degrees of demyelination. Results: Results from simulation suggest that axonal geometry affects the MR signal. Predictions with realistic models were significantly different compared to circular models under the same microstructural tissue properties, for simulations with and without diffusion. Conclusion: The geometry of axons affects the MR signal significantly. Literature estimates of myelin susceptibility, which are based on fitting biophysical models to the MR signal, are likely to be biased by the assumed geometry, as will any derived microstructural properties.Comment: Accepted March 4 2017, in publication at Magnetic Resonance in Medicin

Modeling diffusion directions of Corpus Callosum

Diffusion Tensor Imaging (DTI) has been used to study the characteristics of Multiple Sclerosis (MS) in the brain. The von Mises- Fisher distribution (vmf) is a probability distribution for modeling directional data on the unit hypersphere. In this paper we modeled the diffusion directions of the Corpus Callosum (CC) as a mixture of vmf distributions for both MS subjects and healthy controls. Higher diffusion concentration around the mean directions and smaller sum of angles between the mean directions are observed on the normal-appearing CC of the MS subjects as compared to the healthy controls

Exploiting Spatial Information to Enhance DTI Segmentations via Spatial Fuzzy c-Means with Covariance Matrix Data and Non-Euclidean Metrics

A diffusion tensor models the covariance of the Brownian motion of water at a voxel and is required to be symmetric and positive semi-definite. Therefore, image processing approaches, designed for linear entities, are not effective for diffusion tensor data manipulation, and the existence of artefacts in diffusion tensor imaging acquisition makes diffusion tensor data segmentation even more challenging. In this study, we develop a spatial fuzzy c-means clustering method for diffusion tensor data that effectively segments diffusion tensor images by accounting for the noise, partial voluming, magnetic field inhomogeneity, and other imaging artefacts. To retain the symmetry and positive semi-definiteness of diffusion tensors, the log and root Euclidean metrics are used to estimate the mean diffusion tensor for each cluster. The method exploits spatial contextual information and provides uncertainty information in segmentation decisions by calculating the membership values for assigning a diffusion tensor at one voxel to different clusters. A regularisation model that allows the user to integrate their prior knowledge into the segmentation scheme or to highlight and segment local structures is also proposed. Experiments on simulated images and real brain datasets from healthy and Spinocerebellar ataxia 2 subjects showed that the new method was more effective than conventional segmentation methods

Data-driven corpus callosum parcellation method through diffusion tensor imaging

The corpus callosum (CC) is a set of neural fibers in the cerebral cortex, responsible for facilitating inter-hemispheric communication. The CC structural characteristics appear as an essential element for studying healthy subjects and patients diagnosed with neurodegenerative diseases. Due to its size, the CC is usually divided into smaller regions, also known as parcellation. Since there are no visible landmarks inside the structure indicating its division, CC parcellation is a challenging task and methods proposed in the literature are geometric or atlas-based. This paper proposed an automatic data-driven CC parcellation method, based on diffusion data extracted from diffusion tensor imaging that uses the Watershed transform. Experiments compared parcellation results of the proposed method with results of three other parcellation methods on a data set containing 150 images. Quantitative comparison using the Dice coefficient showed that the CC parcels given by the proposed method has a mean overlap higher than 0,9 for some parcels and lower than 0,6 for other parcels. Poor overlap results were confirmed by the statistically significant differences obtained for diffusion metrics values in each parcel, when using different parcellation methods. The proposed method was also validated by using the CC tractography and was the only study that proposed a non-geometric approach for the CC parcellation, based only on the diffusion data of each subject analyzed59Advanced signal processing methods in medical imaging2242122432COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPESFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPnão tem2013/07559-

Statistical Medial Model dor Cardiac Segmentation and Morphometry

In biomedical image analysis, shape information can be utilized for many purposes. For example, irregular shape features can help identify diseases; shape features can help match different instances of anatomical structures for statistical comparison; and prior knowledge of the mean and possible variation of an anatomical structure\u27s shape can help segment a new example of this structure in noisy, low-contrast images. A good shape representation helps to improve the performance of the above techniques. The overall goal of the proposed research is to develop and evaluate methods for representing shapes of anatomical structures. The medial model is a shape representation method that models a 3D object by explicitly defining its skeleton (medial axis) and deriving the object\u27s boundary via inverse-skeletonization . This model represents shape compactly, and naturally expresses descriptive global shape features like thickening , bending , and elongation . However, its application in biomedical image analysis has been limited, and it has not yet been applied to the heart, which has a complex shape. In this thesis, I focus on developing efficient methods to construct the medial model, and apply it to solve biomedical image analysis problems. I propose a new 3D medial model which can be efficiently applied to complex shapes. The proposed medial model closely approximates the medial geometry along medial edge curves and medial branching curves by soft-penalty optimization and local correction. I further develop a scheme to perform model-based segmentation using a statistical medial model which incorporates prior shape and appearance information. The proposed medial models are applied to a series of image analysis tasks. The 2D medial model is applied to the corpus callosum which results in an improved alignment of the patterns of commissural connectivity compared to a volumetric registration method. The 3D medial model is used to describe the myocardium of the left and right ventricles, which provides detailed thickness maps characterizing different disease states. The model-based myocardium segmentation scheme is tested in a heterogeneous adult MRI dataset. Our segmentation experiments demonstrate that the statistical medial model can accurately segment the ventricular myocardium and provide useful parameters to characterize heart function

Spectral Clustering en IRM de diffusion pour Retrouver les Faisceaux de la Matière Blanche

White matter fiber clustering allows to get insight about anatomical structures in order to generate atlases, perform clear visualizations and compute statistics across subjects, all important and current neuroimaging problems. In this work, we present a Diffusion Maps clustering method applied to diffusion MRI in order to cluster and segment complex white matter fiber bundles. It is well-known that Diffusion Tensor Imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent High Angular Resolution Diffusion Imaging (HARDI) such has Q-Ball Imaging (QBI) have been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima agreeing with the underlying fiber populations. In this paper, we introduce the usage of the Diffusion Maps technique and show how it can be used to directly cluster set of fiber tracts, that could be obtained through a streamline tractography for instance, and how it can also help in segmenting fields of ODF images, obtained through a linear and regularized ODF estimation algorithm based on a spherical harmonics representation of the Q-Ball data. We first show the advantage of using Diffusion Maps clustering over classical methods such as N-Cuts and Laplacian Eigenmaps in both cases. In particular, our Diffusion Maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in fiber tract clustering and ODF image segmentation and automatically exhibits the number of clusters in both cases by using an adaptive scale-space parameter. We also show that our ODF Diffusion Maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our ODF-based method succeeds to separate fiber bundles and crossing regions whereas the DT-based methods generate artifacts and exhibit wrong number of clusters. Finally, we illustrate the potential of our approach on a real brain dataset where we successfully segment well-known fiber bundles

Magnetic resonance imaging evidence for presymptomatic change in thalamus and caudate in familial Alzheimer’s disease

Amyloid imaging studies of presymptomatic familial Alzheimer’s disease have revealed the striatum and thalamus to be the earliest sites of amyloid deposition. This study aimed to investigate whether there are associated volume and diffusivity changes in these subcortical structures during the presymptomatic and symptomatic stages of familial Alzheimer’s disease. As the thalamus and striatum are involved in neural networks subserving complex cognitive and behavioural functions, we also examined the diffusion characteristics in connecting white matter tracts. A cohort of 20 presenilin 1 mutation carriers underwent volumetric and diffusion tensor magnetic resonance imaging, neuropsychological and clinical assessments; 10 were symptomatic, 10 were presymptomatic and on average 5.6 years younger than their expected age at onset; 20 healthy control subjects were also studied. We conducted region of interest analyses of volume and diffusivity changes in the thalamus, caudate, putamen and hippocampus and examined diffusion behaviour in the white matter tracts of interest (fornix, cingulum and corpus callosum). Voxel-based morphometry and tract-based spatial statistics were also used to provide unbiased whole-brain analyses of group differences in volume and diffusion indices, respectively. We found that reduced volumes of the left thalamus and bilateral caudate were evident at a presymptomatic stage, together with increased fractional anisotropy of bilateral thalamus and left caudate. Although no significant hippocampal volume loss was evident presymptomatically, reduced mean diffusivity was observed in the right hippocampus and reduced mean and axial diffusivity in the right cingulum. In contrast, symptomatic mutation carriers showed increased mean, axial and in particular radial diffusivity, with reduced fractional anisotropy, in all of the white matter tracts of interest. The symptomatic group also showed atrophy and increased mean diffusivity in all of the subcortical grey matter regions of interest, with increased fractional anisotropy in bilateral putamen. We propose that axonal injury may be an early event in presymptomatic Alzheimer’s disease, causing an initial fall in axial and mean diffusivity, which then increases with loss of axonal density. The selective degeneration of long-coursing white matter tracts, with relative preservation of short interneurons, may account for the increase in fractional anisotropy that is seen in the thalamus and caudate presymptomatically. It may be owing to their dense connectivity that imaging changes are seen first in the thalamus and striatum, which then progress to involve other regions in a vulnerable neuronal network