3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Dynamical system approach for edge detection using coupled FitzHugh–Nagumo neurons

The prospect of emulating the impressive computational capabilities of biological systems has led to considerable interest in the design of analog circuits that are potentially implementable in very large scale integration CMOS technology and are guided by biologically motivated models. For example, simple image processing tasks, such as the detection of edges in binary and grayscale images, have been performed by networks of FitzHugh-Nagumo-type neurons using the reaction-diffusion models. However, in these studies, the one-to-one mapping of image pixels to component neurons makes the size of the network a critical factor in any such implementation. In this paper, we develop a simplified version of the employed reaction-diffusion model in three steps. In the first step, we perform a detailed study to locate this threshold using continuous Lyapunov exponents from dynamical system theory. Furthermore, we render the diffusion in the system to be anisotropic, with the degree of anisotropy being set by the gradients of grayscale values in each image. The final step involves a simplification of the model that is achieved by eliminating the terms that couple the membrane potentials of adjacent neurons. We apply our technique to detect edges in data sets of artificially generated and real images, and we demonstrate that the performance is as good if not better than that of the previous methods without increasing the size of the network

Monitoring Galvanic Replacement Through Three-Dimensional Morphological and Chemical Mapping

Galvanic replacement reactions on metal nanoparticles are often used for the preparation of hollow nanostructures with tunable porosity and chemical composition, leading to tailored optical and catalytic properties. However, the precise interplay between the three-dimensional (3D) morphology and chemical composition of nanostructures during Galvanic replacement is not always well understood as the 3D chemical imaging of nanoscale materials is still challenging. It is especially far from straightforward to obtain detailed information from the inside of hollow nanostructures using electron microscopy techniques such as SEM or TEM. We demonstrate here that a combination of state-of-the-art EDX mapping with electron tomography results in the unambiguous determination of both morphology transformation and elemental composition of nanostructures in 3D, during Galvanic replacement of Ag nanocubes. This work provides direct and unambiguous experimental evidence leading to new insights in the understanding of the galvanic replacement reaction. In addition, the powerful approach presented here can be applied to a wide range of nanoscale transformation processes, which will undoubtedly guide the development of novel nanostructures

Image Segmentation with Eigenfunctions of an Anisotropic Diffusion Operator

We propose the eigenvalue problem of an anisotropic diffusion operator for image segmentation. The diffusion matrix is defined based on the input image. The eigenfunctions and the projection of the input image in some eigenspace capture key features of the input image. An important property of the model is that for many input images, the first few eigenfunctions are close to being piecewise constant, which makes them useful as the basis for a variety of applications such as image segmentation and edge detection. The eigenvalue problem is shown to be related to the algebraic eigenvalue problems resulting from several commonly used discrete spectral clustering models. The relation provides a better understanding and helps developing more efficient numerical implementation and rigorous numerical analysis for discrete spectral segmentation methods. The new continuous model is also different from energy-minimization methods such as geodesic active contour in that no initial guess is required for in the current model. The multi-scale feature is a natural consequence of the anisotropic diffusion operator so there is no need to solve the eigenvalue problem at multiple levels. A numerical implementation based on a finite element method with an anisotropic mesh adaptation strategy is presented. It is shown that the numerical scheme gives much more accurate results on eigenfunctions than uniform meshes. Several interesting features of the model are examined in numerical examples and possible applications are discussed

Contribution of X-ray CMT and image processing to the modelling of pyrocarbon Chemical Vapour Infiltration

International audienceThe Chemical Vapour Infiltration (CVI) process is used to fabricate the pyrocarbon matrices of C/C composites. This process involves complex physico-chemical phenomena such as the transport of precursor, carrier, and by-product gases in the reactor and inside a fibrous preform, heat transfer, chemical reactions (pyrolysis and deposition), and the structural evolution of the preform. It is able to provide high-quality materials because the processing conditions are rather mild with respect to the fibres; however it is expensive and sometimes difficult to optimize. This process has been the object of extensive modelling efforts, because of imperative optimization needs. The present work presents an approach suited to the exploitation of computerized microtomographs of C/C composites, which features image acquisition, computation of geometrical and transport properties, and infiltration modelling, as applied to the infiltration of needled carbon fibre fabrics. Another application to the reinforcement of carbon foams is also presented, as an example of inserting this approach in a global modelling strategy