No abstract

The quantitative and systematic analysis of embryonic cell dynamics from in vivo 3D+time image data sets is a major challenge at the forefront of developmental biology. Despite recent breakthroughs in the microscopy imaging of living systems, producing an accurate cell lineage tree for any developing organism remains a difficult task. We present here the BioEmergences workflow integrating all reconstruction steps from image acquisition and processing to the interactive visualization of reconstructed data. Original mathematical methods and algorithms underlie image filtering, nucleus centre detection, nucleus and membrane segmentation, and cell tracking. They are demonstrated on zebrafish, ascidian and sea urchin embryos with stained nuclei and membranes. Subsequent validation and annotations are carried out using Mov-IT, a custom-made graphical interface. Compared with eight other software tools, our workflow achieved the best lineage score. Delivered in standalone or web service mode, BioEmergences and Mov-IT offer a unique set of tools for in silico experimental embryology.

SUMMARYA new method for solution of the evolution of plane curves satisfying the geometric equation v=ÿ(x; k; ), where v is the normal velocity, k and are the curvature and tangential angle of a plane curve ⊂ R 2 at the point x ∈ , is proposed. We derive a governing system of partial di erential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves and prove local in time existence of a classical solution. These equations include a non-trivial tangential velocity functional governing a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system of equations in order to ÿnd a numerical solution for 2D anisotropic interface motions and image segmentation problems.

No abstract

We designed a strategy for extracting the shapes of cell membranes and nuclei from time lapse confocal images taken throughout early zebrafish embryogenesis using a partial-differential-equation-based segmentation. This segmentation step is a prerequisite for an accurate quantitative analysis of cell morphodynamics during embryogenesis and it is the basis for an integrated understanding of biological processes. The segmentation of embryonic cells requires live zebrafish embryos fluorescently labeled to highlight sub-cellular structures and designing specific algorithms by adapting classical methods to image features. Our strategy includes the following steps: the signal-to-noise ratio is first improved by an edge-preserving filtering, then the cell shape is reconstructed applying a fully automated algorithm based on a generalized version of the Subjective Surfaces technique. Finally we present a procedure for the algorithm validation either from the accuracy and the robustness perspective.

We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], [30]) is also included in the study. We prove L ∞ and W 1,1 estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution.

No abstract

Due to the relative transparency of its embryos and larvae, the zebrafish is an ideal model organism for bioimaging approaches in vertebrates. Novel microscope technologies allow the imaging of developmental processes in unprecedented detail, and they enable the use of complex image-based read-outs for highthroughput/high-content screening. Such applications can easily generate Terabytes of image data, the handling and analysis of which becomes a major bottleneck in extracting the targeted information. Here, we describe the current state of the art in computational image analysis in the zebrafish system. We discuss the challenges encountered when handling high-content image data, especially with regard to data quality, annotation, and storage. We survey methods for preprocessing image data for further analysis, and describe selected examples of automated image analysis, including the tracking of cells during embryogenesis, heartbeat detection, identification of dead embryos, recognition of tissues and anatomical landmarks, and quantification of behavioral patterns of adult fish. We review recent examples for applications using such methods, such as the comprehensive analysis of cell lineages during early development, the generation of a three-dimensional brain atlas of zebrafish larvae, and high-throughput drug screens based on movement patterns. Finally, we identify future challenges for the zebrafish image analysis community, notably those concerning the compatibility of algorithms and data formats for the assembly of modular analysis pipelines.