Archetypal Analysis for neuronal clique detection in low-rate calcium fluorescence imaging.

Archetypal analysis (AA) is a versatile data analysis method to cluster distinct features within a data set. Here, we demonstrate a framework showing the power of AA to spatio-temporally resolve events in calcium imaging, an imaging modality commonly used in neurobiology and neuroscience to capture neuronal communication patterns. After validation of our AA-based approach on synthetic data sets, we were able to characterize neuronal communication patterns in recorded calcium waves. Clinical relevance- Transient calcium events play an essential role in brain cell communication, growth, and network formation, as well as in neurodegeneration. To reliably interpret calcium events from personalized medicine data, where patterns may differ from patient to patient, appropriate image processing and signal analysis methods need to be developed for optimal network characterization.

MNPmApp: An image analysis tool to quantify mononuclear phagocyte distribution in mucosal tissues.

Mononuclear phagocytes (MNPs) such as dendritic cells and macrophages perform key sentinel functions in mucosal tissues and are responsible for inducing and maintaining adaptive immune responses to mucosal pathogens. Positioning of MNPs at the epithelial interface facilitates their access to luminally-derived antigens and regulates MNP function through soluble mediators or surface receptor interactions. Therefore, accurately quantifying the distribution of MNPs within mucosal tissues as well as their spatial relationship with other cells is important to infer functional cellular interactions in health and disease. In this study, we developed and validated a MATLAB-based tissue cytometry platform, termed "MNP mapping application" (MNPmApp), that performs high throughput analyses of MNP density and distribution in the gastrointestinal mucosa based on digital multicolor fluorescence microscopy images and that integrates a Monte Carlo modeling feature to assess randomness of MNP distribution. MNPmApp identified MNPs in tissue sections of the human gastric mucosa with 98 ± 2% specificity and 76 ± 15% sensitivity for HLA-DR+ MNPs and 98 ± 1% specificity and 85 ± 12% sensitivity for CD11c+ MNPs. Monte Carlo modeling revealed that mean MNP-MNP distances for both HLA-DR+ and CD11c+ MNPs were significantly lower than anticipated based on random cell placement, whereas MNP-epithelial distances were similar to randomly placed cells. Surprisingly, H. pylori infection had no significant impact on the number of HLA-DR and CD11c MNPs or their distribution within the gastric lamina propria. However, our study demonstrated that MNPmApp is a reliable and user-friendly tool for unbiased quantitation of MNPs and their distribution at mucosal sites.

Data on the verification and validation of segmentation and registration methods for diffusion MRI.

The verification and validation of segmentation and registration methods is a necessary assessment in the development of new processing methods. However, verification and validation of diffusion MRI (dMRI) processing methods is challenging for the lack of gold-standard data. The data described here are related to the research article entitled "Surface-driven registration method for the structure-informed segmentation of diffusion MR images" [1], in which publicly available data are used to derive golden-standard reference-data to validate and evaluate segmentation and registration methods in dMRI.

Surface-driven registration method for the structure-informed segmentation of diffusion MR images.

Current methods for processing diffusion MRI (dMRI) to map the connectivity of the human brain require precise delineations of anatomical structures. This requirement has been approached by either segmenting the data in native dMRI space or mapping the structural information from T1-weighted (T1w) images. The characteristic features of diffusion data in terms of signal-to-noise ratio, resolution, as well as the geometrical distortions caused by the inhomogeneity of magnetic susceptibility across tissues hinder both solutions. Unifying the two approaches, we propose regseg, a surface-to-volume nonlinear registration method that segments homogeneous regions within multivariate images by mapping a set of nested reference-surfaces. Accurate surfaces are extracted from a T1w image of the subject, using as target image the bivariate volume comprehending the fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) maps derived from the dMRI dataset. We first verify the accuracy of regseg on a general context using digital phantoms distorted with synthetic and random deformations. Then we establish an evaluation framework using undistorted dMRI data from the Human Connectome Project (HCP) and realistic deformations derived from the inhomogeneity fieldmap corresponding to each subject. We analyze the performance of regseg computing the misregistration error of the surfaces estimated after being mapped with regseg onto 16 datasets from the HCP. The distribution of errors shows a 95% CI of 0.56-0.66mm, that is below the dMRI resolution (1.25mm, isotropic). Finally, we cross-compare the proposed tool against a nonlinear b0-to-T2w registration method, thereby obtaining a significantly lower misregistration error with regseg. The accurate mapping of structural information in dMRI space is fundamental to increase the reliability of network building in connectivity analyses, and to improve the performance of the emerging structure-informed techniques for dMRI data processing.

Mapping Buried Hydrogen-Bonding Networks.

We map buried hydrogen-bonding networks within self-assembled monolayers of 3-mercapto-N-nonylpropionamide on Au{111}. The contributing interactions include the buried S-Au bonds at the substrate surface and the buried plane of linear networks of hydrogen bonds. Both are simultaneously mapped with submolecular resolution, in addition to the exposed interface, to determine the orientations of molecular segments and directional bonding. Two-dimensional mode-decomposition techniques are used to elucidate the directionality of these networks. We find that amide-based hydrogen bonds cross molecular domain boundaries and areas of local disorder.

Fast Geodesic Active Fields for Image Registration Based on Splitting and Augmented Lagrangian Approaches.

In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.

Harmonic active contours.

We propose a segmentation method based on the geometric representation of images as 2-D manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set function and the objective functional corresponds to the surface of the image manifold. In this geometric framework, both data-fidelity and regularity terms of the segmentation are represented by a single functional that intrinsically aligns the gradients of the level set function with the gradients of the image and results in a segmentation criterion that exploits the directional information of image gradients to overcome image inhomogeneities and fragmented contours. The proposed formulation combines this robust alignment of gradients with attractive properties of previous methods developed in the same geometric framework: 1) the natural coupling of image channels proposed for anisotropic diffusion and 2) the ability of subjective surfaces to detect weak edges and close fragmented boundaries. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, which naturally generalizes existing segmentation methods (the geodesic active contours, the active contours without edges, and the robust edge integrator) to higher dimensional spaces, non-flat images, and feature spaces. Our experiments show that the proposed technique improves the segmentation of multi-channel images, images subject to inhomogeneities, and images characterized by geometric structures like ridges or valleys.

Efficient algorithm for level set method preserving distance function.

The level set method is a popular technique for tracking moving interfaces in several disciplines, including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issues. First, the level set method does not implicitly preserve the level set function as a distance function, which is necessary to estimate accurately geometric features, s.a. the curvature or the contour normal. Second, the level set algorithm is slow because the time step is limited by the standard Courant-Friedrichs-Lewy (CFL) condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast, accurate, and guaranteed to find the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the level set method. However, the binary function cannot provide the distance information, which can be essential for some applications, s.a. the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging. In this paper, we propose a fast algorithm to preserve distance functions in level set methods. Our algorithm is inspired by recent efficient l(1) optimization techniques, which will provide an efficient and easy to implement algorithm. It is interesting to note that our algorithm is not limited by the CFL condition and it naturally preserves the level set function as a distance function during the evolution, which avoids the classical re-distancing problem in level set methods. We apply the proposed algorithm to carry out image segmentation, where our methods prove to be 5-6 times faster than standard distance preserving level set techniques. We also present two applications where preserving a distance function is essential. Nonetheless, our method stays generic and can be applied to any level set methods that require the distance information.

Synergistic NGF/B27 gradients position synapses heterogeneously in 3D micropatterned neural cultures.

Native functional brain circuits show different numbers of synapses (synaptic densities) in the cerebral cortex. Until now, different synaptic densities could not be studied in vitro using current cell culture methods for primary neurons. Herein, we present a novel microfluidic based cell culture method that combines 3D micropatterning of hydrogel layers with linear chemical gradient formation. Micropatterned hydrogels were used to encapsulate dissociated cortical neurons in laminar cell layers and neurotrophic factors NGF and B27 were added to influence the formation of synapses. Neurotrophic gradients allowed for the positioning of distinguishable synaptic densities throughout a 3D micropatterned neural culture. NGF and B27 gradients were maintained in the microfluidic device for over two weeks without perfusion pumps by utilizing a refilling procedure. Spatial distribution of synapses was examined with a pre-synaptic marker to determine synaptic densities. From our experiments, we observed that (1) cortical neurons responded only to synergistic NGF/B27 gradients, (2) synaptic density increased proportionally to synergistic NGF/B27 gradients; (3) homogeneous distribution of B27 disturbed cortical neurons in sensing NGF gradients and (4) the cell layer position significantly impacted spatial distribution of synapses.

Geodesic active fields--a geometric framework for image registration.

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to the best of our knowledge, the first reparametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.