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

Differentiable Surface Triangulation

Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation. Unfortunately, the combinatorial nature of the triangulation prevents taking derivatives over the space of possible meshings of any given surface. As a result, to date, mesh processing and optimization techniques have been unable to truly take advantage of modular gradient descent components of modern optimization frameworks. In this work, we present a differentiable surface triangulation that enables optimization for any per-vertex or per-face differentiable objective function over the space of underlying surface triangulations. Our method builds on the result that any 2D triangulation can be achieved by a suitably perturbed weighted Delaunay triangulation. We translate this result into a computational algorithm by proposing a soft relaxation of the classical weighted Delaunay triangulation and optimizing over vertex weights and vertex locations. We extend the algorithm to 3D by decomposing shapes into developable sets and differentiably meshing each set with suitable boundary constraints. We demonstrate the efficacy of our method on various planar and surface meshes on a range of difficult-to-optimize objective functions. Our code can be found online: https://github.com/mrakotosaon/diff-surface-triangulation

Repairing triangle meshes built from scanned point cloud

The Reverse Engineering process consists of a succession of operations that aim at creating a digital representation of a physical model. The reconstructed geometric model is often a triangle mesh built from a point cloud acquired with a scanner. Depending on both the object complexity and the scanning process, some areas of the object outer surface may never be accessible, thus inducing some deficiencies in the point cloud and, as a consequence, some holes in the resulting mesh. This is simply not acceptable in an integrated design process where the geometric models are often shared between the various applications (e.g. design, simulation, manufacturing). In this paper, we propose a complete toolbox to fill in these undesirable holes. The hole contour is first cleaned to remove badly-shaped triangles that are due to the scanner noise. A topological grid is then inserted and deformed to satisfy blending conditions with the surrounding mesh. In our approach, the shape of the inserted mesh results from the minimization of a quadratic function based on a linear mechanical model that is used to approximate the curvature variation between the inner and surrounding meshes. Additional geometric constraints can also be specified to further shape the inserted mesh. The proposed approach is illustrated with some examples coming from our prototype software

3D Radiative Transfer in η\eta Carinae: Application of the SimpleX Algorithm to 3D SPH Simulations of Binary Colliding Winds

Eta Carinae is an ideal astrophysical laboratory for studying massive binary interactions and evolution, and stellar wind-wind collisions. Recent three-dimensional (3D) simulations set the stage for understanding the highly complex 3D flows in $\eta$ Car. Observations of different broad high- and low-ionization forbidden emission lines provide an excellent tool to constrain the orientation of the system, the primary's mass-loss rate, and the ionizing flux of the hot secondary. In this work we present the first steps towards generating synthetic observations to compare with available and future HST/STIS data. We present initial results from full 3D radiative transfer simulations of the interacting winds in $\eta$ Car. We use the SimpleX algorithm to post-process the output from 3D SPH simulations and obtain the ionization fractions of hydrogen and helium assuming three different mass-loss rates for the primary star. The resultant ionization maps of both species constrain the regions where the observed forbidden emission lines can form. Including collisional ionization is necessary to achieve a better description of the ionization states, especially in the areas shielded from the secondary's radiation. We find that reducing the primary's mass-loss rate increases the volume of ionized gas, creating larger areas where the forbidden emission lines can form. We conclude that post processing 3D SPH data with SimpleX is a viable tool to create ionization maps for $\eta$ Car.Comment: 18 pages, 11 figures, accepted for publication in MNRA

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Modelo computacional de remodelamiento óseo mediante estructuras discretas

Libro de tesis, algunas figuras en color, mayoría en blanco y negro.ilustraciones, tablasIn-silico models applied to bone remodeling are widely used to investigate bone mechanics, bone diseases, bone-implant interactions, and also the effect of treatments in bone pathologies. This work proposes a new methodology to solve the bone remodeling problem using one-dimensional (1D) elements to discretize trabecular structures more efficiently. First a concept review on the bone remodelling process and mathematical approaches, such as homogenization for its modelling are revised along with famous previous works on this field, later, in chapter two, the discrete modelling approach is validated by comparing FE simulations with experimental results for a cellular like material created using additive manufacturing and following a tessellation algorithm, and later, applying an optimization scheme based on maximum stiffness for a given porosity. In chapter three, an Euler integration scheme for a bone remodelling problem is coupled with the momentum equations to obtain the evolution of material density at each step. For the simulations, the equations were solved by using the finite element method and a direct formulation, and two benchmark tests were solved varying mesh parameters in two dimensions, an additional three-dimensional benchmark was addressed with the same methodology. Proximal femur and calcaneus bone were selected as study cases given the vast research available on the topology of these bones, and compared with the anatomical features of trabecular bone reported in the literature, the study cases were examined mainly in two dimensions, but the main trabecular groups for the femur were also obtained in three dimensions. The presented methodology has proven to be efficient in optimizing topologies of lattice structures; It can predict the trend in formation patterns of the main trabecular groups from two different cancellous bones (femur and calcaneus) using domains set up by discrete elements as a starting point. Preliminary results confirm that the proposed approach is suitable and useful in bone remodeling problems in 2D and 3D leading to a considerable computational cost reduction. Characteristics similar to those encountered in topological optimization algorithms were identified in the benchmark tests as well, showing the viability of the proposed approach in other applications such as bio-inspired design. Finally, in the last part of this work, the discrete approach developed in chapter two and three is coupled with two classic bone remodelling models, forming a new model that takes into account a variety of biological parameters such as paracrine and autocrine regulators and is able to predict different periodical responses in the bone remodelling process within a 2D domain with mechanical field variables. (Text taken from source)Los modelos in-silico aplicados a la remodelación ósea son ampliamente utilizados para investigar la mecánica del hueso, las enfermedades óseas, las interacciones hueso-implante y también el efecto de los tratamientos en las patologías óseas. Este trabajo propone una nueva metodología para resolver el problema de la remodelación ósea utilizando elementos unidimensionales (1D) para discretizar las estructuras trabeculares de forma más eficiente. En primer lugar se revisa una revisión conceptual sobre el proceso de remodelación ósea y las aproximaciones matemáticas, como el método de homogeneización para su modelización, junto con famosos trabajos previos en este campo, posteriormente, en el capítulo dos, se valida la modelación discreta comparando las simulaciones de FE (elementos finitos) con los resultados experimentales para un material similar al celular creado mediante fabricación aditiva y siguiendo un algoritmo de teselación, y posteriormente, aplicando un esquema de optimización basado en la máxima rigidez para una determinada porosidad. En el capítulo tres, se acopla un esquema de integración de Euler para un problema de remodelación ósea con las ecuaciones de momento para obtener la evolución de la densidad del material en cada paso de tiempo. Para las simulaciones, las ecuaciones se resolvieron utilizando el método de los elementos finitos y una formulación directa, y se resolvieron dos pruebas de referencia variando los parámetros de la malla en dos dimensiones, adicionalmente, se abordó una prueba de referencia tridimensional adicional con la misma metodología. Se seleccionaron el fémur proximal y el hueso calcáneo como casos de estudio, dada la amplia investigación disponible sobre la topología de estos huesos, y se compararon con las características anatómicas del hueso trabecular reportadas en la literatura, los casos de estudio se examinaron principalmente en dos dimensiones, pero los principales grupos trabeculares para el fémur también se obtuvieron en tres dimensiones. La metodología presentada ha demostrado ser eficaz en la optimización de las topologías de estructuras reticulares; puede predecir la tendencia de los patrones de formación de los principales grupos trabeculares de dos huesos esponjosos diferentes (fémur y calcáneo) utilizando dominios establecidos por elementos discretos como punto de partida. Los resultados preliminares confirmaron que el enfoque propuesto es adecuado y útil en problemas de remodelación ósea en 2D y 3D, lo que conlleva una considerable reducción del coste computacional. En las pruebas de referencia también se identificaron características similares a las encontradas en los algoritmos de optimización topológica, lo que demuestra la viabilidad del enfoque propuesto en otras aplicaciones como el diseño bioinspirado. Finalmente, en la última parte de este trabajo, el enfoque discreto desarrollado en los capítulos dos y tres se acopla con dos modelos clásicos de remodelación ósea, formando un nuevo modelo que tiene en cuenta una variedad de parámetros biológicos como los reguladores paracrinos y autocrinos, y es capaz de predecir diferentes respuestas periódicas en el proceso de remodelación ósea dentro de un dominio 2D con variables de campo mecánico. (Texto tomado de la fuente)MaestríaMagíster en Ingeniería BiomédicaMecánica computaciona

Restoration of paintings on domes with non-developable geometry (Los Santos Juanes Church in Valencia)

[EN] The restoration of paintings on elements in cultural heritage buildings (fundamentally, churches) involves two structural problems: capturing the geometry of the construction element and its development. In many cases, the geometries are regular (e.g., cylinders, spheres, elliptical domes). However, there are cases in which the elements cannot be adapted to any known geometry, much less one that can be mathematically developed. The development of surfaces becomes essential for the restoration of paintings over "flat elements" (over which work is performed on the ground) that are subsequently transferred to the real surface (ceilings). The mathematical transformations that allow regular geometries to be developed are widely known (cartographic projections). However, when the geometry is irregular, there is no development. This study presents a new methodology based on differential rectification and its application for the development of oculi in the Los Santos Juanes Church (Valencia), whose geometry is completely irregular both in shape and as a result of construction defects (and damage caused by fire). The present study focuses on the restoration of paintings damaged by fire.Navarro Esteve, PJ.; Yudici Oliver, SA.; Herráez Boquera, J.; Denia Rios, JL.; Martín Sánchez, MT.; Rodríguez Pereña, J. (2018). Restoration of paintings on domes with non-developable geometry (Los Santos Juanes Church in Valencia). International Journal of Architectural Heritage. 12(2):169-177. https://doi.org/10.1080/15583058.2017.1356946S16917712