11,097 research outputs found
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
Particle Density Estimation with Grid-Projected Adaptive Kernels
The reconstruction of smooth density fields from scattered data points is a
procedure that has multiple applications in a variety of disciplines, including
Lagrangian (particle-based) models of solute transport in fluids. In random
walk particle tracking (RWPT) simulations, particle density is directly linked
to solute concentrations, which is normally the main variable of interest, not
just for visualization and post-processing of the results, but also for the
computation of non-linear processes, such as chemical reactions. Previous works
have shown the superiority of kernel density estimation (KDE) over other
methods such as binning, in terms of its ability to accurately estimate the
"true" particle density relying on a limited amount of information. Here, we
develop a grid-projected KDE methodology to determine particle densities by
applying kernel smoothing on a pilot binning; this may be seen as a "hybrid"
approach between binning and KDE. The kernel bandwidth is optimized locally.
Through simple implementation examples, we elucidate several appealing aspects
of the proposed approach, including its computational efficiency and the
possibility to account for typical boundary conditions, which would otherwise
be cumbersome in conventional KDE
On Median Filters for Motion by Mean Curvature
The median filter scheme is an elegant, monotone discretization of the level
set formulation of motion by mean curvature. It turns out to evolve every level
set of the initial condition precisely by another class of methods known as
threshold dynamics. Median filters are, in other words, the natural level set
versions of threshold dynamics algorithms. Exploiting this connection, we
revisit median filters in light of recent progress on the threshold dynamics
method. In particular, we give a variational formulation of, and exhibit a
Lyapunov function for, median filters, resulting in energy based unconditional
stability properties. The connection also yields analogues of median filters in
the multiphase setting of mean curvature flow of networks. These new multiphase
level set methods do not require frequent redistancing, and can accommodate a
wide range of surface tensions.Comment: 41 pages, 8 figure
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