21 research outputs found
A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth
Mollusk shells are an ideal model system for understanding the morpho-elastic
basis of morphological evolution of invertebrates' exoskeletons. During the
formation of the shell, the mantle tissue secretes proteins and minerals that
calcify to form a new incremental layer of the exoskeleton. Most of the
existing literature on the morphology of mollusks is descriptive. The
mathematical understanding of the underlying coupling between pre-existing
shell morphology, de novo surface deposition and morpho-elastic volume growth
is at a nascent stage, primarily limited to reduced geometric representations.
Here, we propose a general, three-dimensional computational framework coupling
pre-existing morphology, incremental surface growth by accretion, and
morpho-elastic volume growth. We exercise this framework by applying it to
explain the stepwise morphogenesis of seashells during growth: new material
surfaces are laid down by accretive growth on the mantle whose form is
determined by its morpho-elastic growth. Calcification of the newest surfaces
extends the shell as well as creates a new scaffold that constrains the next
growth step. We study the effects of surface and volumetric growth rates, and
of previously deposited shell geometries on the resulting modes of mantle
deformation, and therefore of the developing shell's morphology. Connections
are made to a range of complex shells ornamentations.Comment: Main article is 20 pages long with 15 figures. Supplementary material
is 4 pages long with 6 figures and 6 attached movies. To be published in PLOS
Computational Biolog
Elastic free energy drives the shape of prevascular solid tumors
It is well established that the mechanical environment influences cell
functions in health and disease. Here, we address how the mechanical
environment influences tumor growth, in particular, the shape of solid tumors.
In an in vitro tumor model, which isolates mechanical interactions between
tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling
the same, oft-reported observation of in vivo tumors. Specifically, an oblate
ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that
are stiffer than the tumors, but when they grow in more compliant hydrogels
they remain closer to spherical in shape. Using large scale, nonlinear
elasticity computations we show that the oblate ellipsoidal shape minimizes the
elastic free energy of the tumor-hydrogel system. Having eliminated a number of
other candidate explanations, we hypothesize that minimization of the elastic
free energy is the reason for predominance of the experimentally observed
ellipsoidal shape. This result may hold significance for explaining the shape
progression of early solid tumors in vivo and is an important step in
understanding the processes underlying solid tumor growth.Comment: Six figures in main text. Supporting Information with 6 additional
figure
A Numerical Investigation of Dimensionless Numbers Characterizing Meltpool Morphology of the Laser Powder Bed Fusion Process
Microstructure evolution in metal additive manufacturing (AM) is a complex multi-physics and multi-scale problem. Understanding the impact of AM process conditions on the microstructure evolution and the resulting mechanical properties of the printed component remains an active area of research. At the meltpool scale, the thermo-fluidic governing equations have been extensively modeled in the literature to understand the meltpool conditions and the thermal gradients in its vicinity. In many phenomena governed by partial differential equations, dimensional analysis and identification of important dimensionless numbers can provide significant insights into the process dynamics. In this context, we present a novel strategy using dimensional analysis and the linear least-squares regression method to numerically investigate the thermo-fluidic governing equations of the Laser Powder Bed Fusion AM process. First, the governing equations are solved using the Finite Element Method, and the model predictions are validated by comparing with experimentally estimated cooling rates, and with numerical results from the literature. Then, through dimensional analysis, an important dimensionless quantity interpreted as a measure of heat absorbed by the powdered material and the meltpool, is identified. This dimensionless measure of absorbed heat, along with classical dimensionless quantities such as Péclet, Marangoni, and Stefan numbers, are employed to investigate advective transport in the meltpool for different alloys. Further, the framework is used to study variations in the thermal gradients and the solidification cooling rate. Important correlations linking meltpool morphology and microstructure-evolution-related variables with classical dimensionless numbers are the key contribution of this work
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematics and revealed by a three dimensional computational framework
Biomembranes play a central role in various phenomena like locomotion of
cells, cell-cell interactions, packaging of nutrients, and in maintaining
organelle morphology and functionality. During these processes, the membranes
undergo significant morphological changes through deformation, scission, and
fusion. Modeling the underlying mechanics of such morphological changes has
traditionally relied on reduced order axisymmetric representations of membrane
geometry and deformation. Axisymmetric representations, while robust and
extensively deployed, suffer from their inability to model symmetry breaking
deformations and structural bifurcations. To address this limitation, a 3D
computational mechanics framework for high fidelity modeling of biomembrane
deformation is presented. The proposed framework brings together Kirchhoff-Love
thin-shell kinematics, Helfrich-energy based mechanics, and state-of-the-art
numerical techniques for modeling deformation of surface geometries. Lipid
bilayers are represented as spline-based surfaces immersed in a 3D space; this
enables modeling of a wide spectrum of membrane geometries, boundary
conditions, and deformations that are physically admissible in a 3D space. The
mathematical basis of the framework and its numerical machinery are presented,
and their utility is demonstrated by modeling 3 classical, yet non-trivial,
membrane problems: formation of tubular shapes and their lateral constriction,
Piezo1-induced membrane footprint generation and gating response, and the
budding of membranes by protein coats during endocytosis. For each problem, the
full 3D membrane deformation is captured, potential symmetry-breaking
deformation paths identified, and various case studies of boundary and load
conditions are presented. Using the endocytic vesicle budding as a case study,
we also present a "phase diagram" for its symmetric and broken-symmetry states
Elastic Free Energy Drives the Shape of Prevascular Solid Tumors
<div><p>It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an <i>in vitro</i> tumor model, which isolates mechanical interactions between cancer tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of <i>in vivo</i> tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors <i>in vivo</i> and is an important step in understanding the processes underlying solid tumor growth.</p></div