Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging.

We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med. 48(6):1358–1372, 2004) of the brain. The goal is to reveal the architecture of the neural fibers in brain white matter. To the variety of existing techniques, we wish to add novel approaches that exploit differential geometry and tensor calculus. In Diffusion Tensor Imaging (DTI), the diffusion of water is modeled by a symmetric positive definite second order tensor, leading naturally to a Riemannian geometric framework. A limitation is that it is based on the assumption that there exists a single dominant direction of fibers restricting the thermal motion of water molecules. Using HARDI data and higher order tensor models, we can extract multiple relevant directions, and Finsler geometry provides the natural geometric generalization appropriate for multi-fiber analysis. In this paper we provide an exact criterion to determine whether a spherical function satisfies the strong convexity criterion essential for a Finsler norm. We also show a novel fiber tracking method in Finsler setting. Our model incorporates a scale parameter, which can be beneficial in view of the noisy nature of the data. We demonstrate our methods on analytic as well as simulated and real HARDI data

Assessment of SAR Image Filtering using Adaptive Stack Filters

Stack filters are a special case of non-linear filters. They have a good performance for filtering images with different types of noise while preserving edges and details. A stack filter decomposes an input image into several binary images according to a set of thresholds. Each binary image is then filtered by a Boolean function, which characterizes the filter. Adaptive stack filters can be designed to be optimal; they are computed from a pair of images consisting of an ideal noiseless image and its noisy version. In this work we study the performance of adaptive stack filters when they are applied to Synthetic Aperture Radar (SAR) images. This is done by evaluating the quality of the filtered images through the use of suitable image quality indexes and by measuring the classification accuracy of the resulting images

A simplified algorithm for inverting higher order diffusion tensors

In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann-Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI). An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI) data, one can estimate the diffusion orientation distribution function (dODF), which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor) to directly generalize the (second order) diffusion tensor approach. To enable efficient computation of Riemann-Finslerian quantities on diffusion weighted (DW)-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.</p

Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean function

Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function. The so called selection probabilities can be computed along the way.Comment: This is the version published in Journal of Mathematical Imaging and Vision, online first, 1 august 201

A Strategy For Identifying Putative Causes Of Gene Expression Variation In Human Cancer

There is often a need to predict the impact of alterations in one variable on another variable. This is especially the case in cancer research, where much effort has been made to carry out large-scale gene expression screening by microarray techniques. However, the causes of this variability from one cancer to another and from one gene to another often remain unknown. In this study we present a systematic procedure for finding genes whose expression is altered by an intrinsic or extrinsic explanatory phenomenon. The procedure has three stages: preprocessing, data integration and statistical analysis. We tested and verified the utility of this approach in a study, where expression and copy number of 13,824 genes were determined in 14 breast cancer samples. The expression of 270 genes could be explained by the variability of gene copy number. These genes may represent an important set of primary, genetically &quot;damaged&quot; genes that drive cancer progression

Inferring the Genes Underlying Flavonoid Production in Tomato

Flavonoids are plant secondary metabolites that are extensively studied for their proposed positive effects on human health. They are the end products of a cascade of enzymatic reactions that convert initially toxic substances to glycosylated forms. To determine which enzymes are precisely responsible for which conversions is by far not trivial, since hundreds of candidate genes are in principle capable of performing the transformation of interest. In this paper we propose a method to solve this problem for the glycosylation of flavonoids by coupling gene expression data to the metabolic pathway underlying glycosylation. The core of the method is to estimate time dependent coefficients in a highly efficient way. To show how this approach performs, we apply this method to study the flavonoid glycosylation pathway in tomato (Solanum lycopersicum) seedlings

Effect of amino acid supplementation and stress on expression of molecular markers in meagre (Argyrosomus regius)

The objectives of this work were: 1) develop of molecular stress biomarkers obtaining sequence data of different transcripts, 2) study the molecular stress response through the expression quantification of key gene involved in it, and 3) assess the effects of dietary amino acid additives on stress response in meagre meagres (Argyrososmus regius). Fish batches were fed two experimental diets with tryptophan (Trp) or aspartate (Asp) added for seven days. Before sampling fish were submitted to confinement/netting stress during 1 h, except control fish. Therefore fish were sampled before and after stress (1 h and 6 h post-stress). The sampling consisted of blood and tissues (brain, hypophysis and liver). Several gene expressions related to the stress response were measured in those tissues, and the cloning of corticotropin-releasing hormone (crh), corticotropin-releasing hormone binding protein (crh-bp), and thyrotropin-releasing hormone (trh) has been reported in meagre for the first time. In fact, fish fed an additional Asp diet did not present any sl, prl and gh expression changes, as for the control group. Contrarily, the Trp diet altered the prl and gh expressions after stress. For crh and crh-bp expressions, no significant differences were detected within the Asp diet hence that amino acid improved the stress response. However, Asp feeding, but not Trp, enhanced pomc-a expression after stress. Hsp70 expression varied for every treatment, including the control feeding, indicating a late response at 6 h post-stress sampling, where both Asp and Trp treatments increased these expressions significantly. Concluding, the response of molecular stress markers to amino acid enriched diets was diverse. The stressor did not change significantly the relative expression of most analyzed genes for control feeding groups, though the Asp supplemented diet was more effective for attenuating molecular markers than the Trp one.info:eu-repo/semantics/publishedVersio

Inferring the Gene Network Underlying the Branching of Tomato Inflorescence

The architecture of tomato inflorescence strongly affects flower production and subsequent crop yield. To understand the genetic activities involved, insight into the underlying network of genes that initiate and control the sympodial growth in the tomato is essential. In this paper, we show how the structure of this network can be derived from available data of the expressions of the involved genes. Our approach starts from employing biological expert knowledge to select the most probable gene candidates behind branching behavior. To find how these genes interact, we develop a stepwise procedure for computational inference of the network structure. Our data consists of expression levels from primary shoot meristems, measured at different developmental stages on three different genotypes of tomato. With the network inferred by our algorithm, we can explain the dynamics corresponding to all three genotypes simultaneously, despite their apparent dissimilarities. We also correctly predict the chronological order of expression peaks for the main hubs in the network. Based on the inferred network, using optimal experimental design criteria, we are able to suggest an informative set of experiments for further investigation of the mechanisms underlying branching behavio

Smooth muscle cells in human atherosclerosis: proteomic profiling reveals differences in expression of Annexin A1 and mitochondrial proteins in carotid disease.

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The Flavonoid Pathway in Tomato Seedlings: Transcript Abundance and the Modeling of Metabolite Dynamics

Flavonoids are secondary metabolites present in all terrestrial plants. The flavonoid pathway has been extensively studied, and many of the involved genes and metabolites have been described in the literature. Despite this extensive knowledge, the functioning of the pathway in vivo is still poorly understood. Here, we study the flavonoid pathway using both experiments and mathematical models. We measured flavonoid metabolite dynamics in two tissues, hypocotyls and cotyledons, during tomato seedling development. Interestingly, the same backbone of interactions leads to very different accumulation patterns in the different tissues. Initially, we developed a mathematical model with constant enzyme concentrations that described the metabolic networks separately in both tissues. This model was unable to fit the measured flavonoid dynamics in the hypocotyls, even if we allowed unrealistic parameter values. This suggested us to investigate the effect of transcript abundance on flavonoid accumulation. We found that the expression of candidate flavonoid genes varies considerably with time. Variation in transcript abundance results in enzymatic variation, which could have a large effect on metabolite accumulation. Candidate transcript abundance was included in the mathematical model as representative for enzyme concentration. We fitted the resulting model to the flavonoid dynamics in the cotyledons, and tested it by applying it to the data from hypocotyls. When transcript abundance is included, we are indeed able to explain flavonoid dynamics in both tissues. Importantly, this is possible under the biologically relevant restriction that the enzymatic properties estimated by the model are conserved between the tissues