We argue that registration should be thought of as a means to an end, and not as a goal by itself. In particular, we consider the problem of predicting the locations of hidden labels of a test image using observable features, given a training set with both the hidden labels and observable features. For example, the hidden labels could be segmentation labels or activation regions in fMRI, while the observable features could be sulcal geometry or MR intensity. We analyze a probabilistic framework for computing an optimal atlas, and the subsequent registration of a new subject using only the observable features to optimize the hidden label alignment to the training set. We compare two approaches for co-registering training images for the atlas construction: the traditional approach of only using observable features and a novel approach of only using hidden labels. We argue that the alternative approach is superior particularly when the relationship between the hidden labels and observable features is complex and unknown. As an application, we consider the task of registering cortical folds to optimize Brodmann area localization. We show that the alignment of the Brodmann areas improves by up to 25% when using the alternative atlas compared with the traditional atlas. To the best of our knowledge, these are the most accurate Brodmann area localization results (achieved via cortical fold registration) reported to date.

A novel framework for joint clustering and point-by-point mapping of white matter fiber pathways is presented. Accurate clustering of the trajectories into fiber bundles requires point correspondence determined along the fiber pathways. This knowledge is also crucial for any tract-oriented quantitative analysis. We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster, an estimate of the cluster parameters, and point correspondences along the trajectories. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center. Probabilistic assignment of the trajectories to clusters is controlled by imposing a minimum threshold on the membership probabilities, to remove outliers in a principled way. The presented results confirm the efficiency and effectiveness of the proposed framework for quantitative analysis of diffusion tensor MRI.

BACKGROUND: Mapping functional areas of the brain is important for planning tumour resections. With the increased use of functional magnetic resonance imaging (fMRI) for presurgical planning, there is a need to validate that fMRI activation mapping is consistent with the mapping obtained during surgery using direct electrocortical stimulation (DECS). METHODS: A quantitative comparison of DECS and fMRI mapping techniques was performed, using a patient-specific conductivity model to find the current distribution resulting from each stimulation site. The resulting DECS stimulation map was compared to the fMRI activation map, using the maximal Dice similarity coefficient (MDSC). RESULTS: Our results show some agreement between these two mapping techniques—the stimulation site with the largest MOSC was the only site that demonstrated intra-operative effect. CONCLUSIONS: There is a substantial effort to improve the techniques used to map functional areas, particularly using fMRI. It seems likely that fMRI will eventually provide a valid non-invasive means for functional mapping.

The logarithm of the odds ratio (LogOdds) is frequently used in areas such as artificial neural networks, economics, and biology, as an alternative representation of probabilities. Here, we use LogOdds to place probabilistic atlases in a linear vector space. This representation has several useful properties for medical imaging. For example, it not only encodes the shape of multiple anatomical structures but also captures some information concerning uncertainty. We demonstrate that the resulting vector space operations of addition and scalar multiplication have natural probabilistic interpretations. We discuss several examples for placing label maps into the space of LogOdds. First, we relate signed distance maps, a widely used implicit shape representation, to LogOdds and compare it to an alternative that is based on smoothing by spatial Gaussians. We find that the LogOdds approach better preserves shapes in a complex multiple object setting. In the second example, we capture the uncertainty of boundary locations by mapping multiple label maps of the same object into the LogOdds space. Third, we define a framework for non-convex interpolations among atlases that capture different time points in the aging process of a population. We evaluate the accuracy of our representation by generating a deformable shape atlas that captures the variations of anatomical shapes across a population. The deformable atlas is the result of a principal component analysis within the LogOdds space. This atlas is integrated into an existing segmentation approach for MR images. We compare the performance of the resulting implementation in segmenting 20 test cases to a similar approach that uses a more standard shape model that is based on signed distance maps. On this data set, the Bayesian classification model with our new representation outperformed the other approaches in segmenting subcortical structures.

In this article, we have developed a simple model that describes the adsorption of polymer chains from a solution having a good solvent onto a reactive surface of varying curvatures. In order to evaluate the impact of particle size on the adsorption process, we have probed the adsorption of poly(methyl methacrylate) (PMMA) on aluminum oxide (Al2O3) surfaces belonging to particles of different sizes. The basic approach assumed that the details of the chemisorption mechanism of PMMA on aluminum oxide surfaces are independent of surface curvature. The combination of the experimental results with the theoretical approach that we have developed show the existence of three different regimes of adsorption of polymer chains onto the surfaces of metal nanoparticles.