MultisegPipeline: Automatic tissue segmentation of brain MR images with subject-specific atlases

Automated segmentation and labeling of individual brain anatomical regions is challenging due to individual structural variability. Although, atlas-based segmentation has shown its potential for both tissue and structure segmentation, the inherent natural variability as well as disease-related changes in MR appearance is often inappropriately represented by a single atlas image. In order to have a more accurate representation, several atlases may be used for the segmentation task in a given neuroimaging study. In this paper, we present the MultisegPipeline, it uses multiple atlases that have been visually inspected and capture the expected variability in a neonatal population. The MultisegPipeline transfers the labeled regions from each atlas to the target image using deformable registration (ANTs or QuickSilver is available for this task). Additionally, the set of labels are merged using a label fusion technique that reduces the errors produced by the registration. The final output is a single label map that combines the results produced by all atlases into a consensus solution. In our study, the MultisegPipeline is used to segment brain MR images from 31 infants, a leave-one-out strategy was used to test our framework. The average dice score coefficient was 0.89

On thermodynamically consistent Stefan problems with variable surface energy

A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities, it is proved that it exists globally in time and converges towards an equilibrium of the problem. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable if surface heat capacity is small; however, if kinetic undercooling is absent, they are stable if surface heat capacity is sufficiently large.Comment: To appear in Arch. Ration. Mech. Anal. The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0938-y. arXiv admin note: substantial text overlap with arXiv:1101.376

Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells. This convergence has been proved in Peletier, Savar\'e, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system. The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents. A consequence of these results is that solutions of the {\epsilon}-problem converge to a solution of the limiting problem.Comment: Added two sections, corrected minor typos, updated reference

The visual perception of natural motion: abnormal task-related neural activity in DYT1 dystonia

Although primary dystonia is defined by its characteristic motor manifestations, non-motor signs and symptoms have increasingly been recognized in this disorder. Recent neuroimaging studies have related the motor features of primary dystonia to connectivity changes in cerebello-thalamo-cortical pathways. It is not known, however, whether the non-motor manifestations of the disorder are associated with similar circuit abnormalities. To explore this possibility, we used functional magnetic resonance imaging to study primary dystonia and healthy volunteer subjects while they performed a motion perception task in which elliptical target trajectories were visually tracked on a computer screen. Prior functional magnetic resonance imaging studies of healthy subjects performing this task have revealed selective activation of motor regions during the perception of \u27natural\u27 versus \u27unnatural\u27 motion (defined respectively as trajectories with kinematic properties that either comply with or violate the two-thirds power law of motion). Several regions with significant connectivity changes in primary dystonia were situated in proximity to normal motion perception pathways, suggesting that abnormalities of these circuits may also be present in this disorder. To determine whether activation responses to natural versus unnatural motion in primary dystonia differ from normal, we used functional magnetic resonance imaging to study 10 DYT1 dystonia and 10 healthy control subjects at rest and during the perception of \u27natural\u27 and \u27unnatural\u27 motion. Both groups exhibited significant activation changes across perceptual conditions in the cerebellum, pons, and subthalamic nucleus. The two groups differed, however, in their responses to \u27natural\u27 versus \u27unnatural\u27 motion in these regions. In healthy subjects, regional activation was greater during the perception of natural (versus unnatural) motion (P \u3c 0.05). By contrast, in DYT1 dystonia subjects, activation was relatively greater during the perception of unnatural (versus natural) motion (P \u3c 0.01). To explore the microstructural basis for these functional changes, the regions with significant interaction effects (i.e. those with group differences in activation across perceptual conditions) were used as seeds for tractographic analysis of diffusion tensor imaging scans acquired in the same subjects. Fibre pathways specifically connecting each of the significant functional magnetic resonance imaging clusters to the cerebellum were reconstructed. Of the various reconstructed pathways that were analysed, the ponto-cerebellar projection alone differed between groups, with reduced fibre integrity in dystonia (P \u3c 0.001). In aggregate, the findings suggest that the normal pattern of brain activation in response to motion perception is disrupted in DYT1 dystonia. Thus, it is unlikely that the circuit changes that underlie this disorder are limited to primary sensorimotor pathways

Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension

The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities in a sense made precise below, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable, reminiscent of the onset of Ostwald ripening.Comment: 56 pages. Expanded introduction, added references. This revised version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-66

Pedestrians moving in dark: Balancing measures and playing games on lattices

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-D\"{o}ring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures

Deep Modeling of Growth Trajectories for Longitudinal Prediction of Missing Infant Cortical Surfaces

Charting cortical growth trajectories is of paramount importance for understanding brain development. However, such analysis necessitates the collection of longitudinal data, which can be challenging due to subject dropouts and failed scans. In this paper, we will introduce a method for longitudinal prediction of cortical surfaces using a spatial graph convolutional neural network (GCNN), which extends conventional CNNs from Euclidean to curved manifolds. The proposed method is designed to model the cortical growth trajectories and jointly predict inner and outer cortical surfaces at multiple time points. Adopting a binary flag in loss calculation to deal with missing data, we fully utilize all available cortical surfaces for training our deep learning model, without requiring a complete collection of longitudinal data. Predicting the surfaces directly allows cortical attributes such as cortical thickness, curvature, and convexity to be computed for subsequent analysis. We will demonstrate with experimental results that our method is capable of capturing the nonlinearity of spatiotemporal cortical growth patterns and can predict cortical surfaces with improved accuracy.Comment: Accepted as oral presentation at IPMI 201

Self-similar Solutions to a Kinetic Model for Grain Growth

We prove the existence of self-similar solutions to the Fradkov model for two-dimensional grain growth, which consists of an infinite number of nonlocally coupled transport equations for the number densities of grains with given area and number of neighbours (topological class). For the proof we introduce a finite maximal topological class and study an appropriate upwind-discretization of the time dependent problem in self-similar variables. We first show that the resulting finite dimensional differential system has nontrivial steady states. Afterwards we let the discretization parameter tend to zero and prove that the steady states converge to a compactly supported self-similar solution for a Fradkov model with finitely many equations. In a third step we let the maximal topology class tend to infinity and obtain self-similar solutions to the original system that decay exponentially. Finally, we use the upwind discretization to compute self-similar solutions numerically.Comment: 25 pages, several figure