Continuum mechanical modeling of developing epithelial tissues with anisotropic surface growth

A plant cell division algorithm based on cell biomechanics and ellipse-fitting.

In this paper, a three-dimensional numerical framework for modeling growth of swellable soft materials at large deformation is established based on the cell-based smooth finite element method, and the multiplicative decomposition scheme of deformation gradient is given. The second P-K stress and Green's strain tensor are selected as work conjugate pairs, and the corresponding mathematical expressions of stiffness matrix and geometric stiffness matrix are derived. The numerical method is implemented based on Matlab platform, and the isotropic and anisotropic growth behaviors of swellable soft materials are simulated respectively. The results show that anisotropic growth will inhibit the deformation of expandable soft materials compared with isotropic growth. The simulation results are compared with the calculation results in the existing literature. The comparison results show that the characteristics and the morphological mode are in good agreement, which proves the effectiveness of the numerical framework in simulating the growth behavior of expandable soft materials at large deformation, and is able to reveal the mechanical mechanism of the plant growth phenomenon in nature.

Anisotropic density growth of bone—A computational micro-sphere approach

Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the body. In contrast to bulk growth in the interior, the description of surface growth requires the addition of new continuum particles to the body. This is challenging for standard continuum formulations for solids that are meant for situations with a fixed amount of material. Recent approaches to handle this have used, for instance, higher-dimensional time-evolving reference configurations.In this work, an Eulerian approach to this problem is formulated, enabling the side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduces additional kinematic descriptors, namely the relaxed zero-stress deformation and the elastic deformation; in contrast to the deformation gradient, these have the important advantage that they are not required to satisfy kinematic compatibility. The zero-stress deformation and the elastic deformation are used to eliminate the deformation gradient from the formulation, with the evolution of the elastic deformation shown to be governed by a transport equation. The resulting model has only the density, velocity, and elastic deformation as variables in the Eulerian setting. The proposed method is applied to simplified examples that demonstrate non-normal growth and growth with boundary tractions.The introduction in this formulation of the relaxed deformation and the elastic deformation provides a description of surface growth whereby the added material can bring in its own kinematic information. Loosely, the added material “brings in its own reference configuration” through the specification of the relaxed deformation and the elastic deformation. This kinematic description enables, e.g., modeling of non-normal growth using a standard normal growth velocity and a simple approach to prescribing boundary conditions.

InP single crystal growth with controlled supercooling during the early stage by a modified LEC method

Computational modeling of cardiac growth in the post-natal rat with a strain-based growth law

Several polydactylous mutants affect the pattern of asymmetry along the anteroposterior axis of the vertebrate limb. In talpid2, diplopodia1, and diplopodia4 chick limb mutants, there is a preaxial extension that results in broader limb buds. Talpid2 shows reduction of the long bones and 9-10 syndactylous digits, none of which are specifically recognizable as members of the normal digit complement. In diplopodia1 and diplopodia4 extra digits are present preaxially in addition to the normal digits. This phenotype resembles the duplications obtained by grafting a polarizing region to the anterior margin of the limb bud. The abnormal skeletal pattern along the anteroposterior limb axis in both mutants suggests alterations in the signaling pathways that mediate growth and patterning of the limb. In situ hybridization studies reveal that whereas shh transcripts are restricted to the posterior limb margins, HoxD, Bmp-2, and Fgf-4 genes are ectopically expressed in the anterior region of the talpid2, diplopodia1, and diplopodia4 limb buds. The results obtained give insights into the molecular basis of talpid2 and diplopodia mutations and also into the possible roles of shh, Bmp-2, HoxD, and Fgf-4 genes in vertebrate limb morphogenesis.

We report the development of a computational model for the growth of multicellular tissues using a discrete approach based on cellular automata to study the tissue growth rates and population dynamics of two different populations of migrating and proliferating mammalian cells. Cell migration is modeled using a discrete-time Markov chain approach and each population of cells has its own division and motion characteristics that are based on experimental data. A large number of parameters allow for a detailed study of the population dynamics. This permits the exploration of the relative influence of various system parameters on the proliferation rate and some other aspects of cell behavior such as average speed of locomotion

Outgrowth and patterning of the vertebrate limb are controlled by reciprocal interactions between the posterior mesenchyme (polarizing region) and a specialized ectodermal structure, the apical ectodermal ridge (AER). Sonic hedgehog (SHH) signalling by the polarizing region modulates fibroblast growth factor (FGF)4 signalling by the posterior AER, which in turn maintains the polarizing region (SHH/FGF4 feedback loop). Here we report that the secreted bone-morphogenetic-protein (BMP) antagonist Gremlin relays the SHH signal from the polarizing region to the AER. Mesenchymal Gremlin expression is lost in limb buds of mouse embryos homozygous for the limb deformity (Id) mutation, which disrupts establishment of the SHH/FGF4 feedback loop. Grafting Gremlin-expressing cells into ld mutant limb buds rescues Fgf4 expression and restores the SHH/FGF4 feedback loop. Analysis of Shh-null mutant embryos reveals that SHH signalling is required for maintenance of Gremlin and Formin (the gene disrupted by the ld mutations). In contrast, Formin, Gremlin and Fgf4 activation are independent of SHH signalling. This study uncovers the cascade by which the SHH signal is relayed from the posterior mesenchyme to the AER and establishes that Formin-dependent activation of the BMP antagonist Gremlin is sufficient to induce Fgf4 and establish the SHH/FGF4 feedback loop.

This work presents the dynamic modeling and analysis of an electric field vulnerable morpho-elastic biological membranes. Such smart membranes combine electrical properties with active functionalities, creating flexible and responsive surfaces. A continuum physics-based electro-morpho-elastic model is developed to predict the dynamic response of the smart membrane and interrogate the impact of isotropic and anisotropic growth along with fiber orientations at different prestretches. The governing equation of motion for the membrane dynamics is derived by applying Newton’s second law. The findings of the model solutions offer an understanding of how the DC and AC dynamic actuation modes modify the nonlinear behavior of membranes. The free and forced vibrations are illustrated using the Poincaré map, phase diagrams, and time-history response. Notably, the steady oscillation around the stable equilibrium stretch, whose magnitude decreases with the enrichment in membrane anisotropy and fiber orientation, decreases with anisotropic growth. Additionally, the system energy rises with the anisotropy parameter and shifts from isotropic to anisotropic growth, decreasing with greater fiber orientation.

Skin expansion is the principal technique used in plastic surgery to repair large cutaneous defects, typically after tumour removal, burn care, craniofacial surgery and post-mastectomy breast reconstruction. It allows a gain of new tissue by means of gradual expansion of a prosthesis, surgically implanted beneath the patient's skin. Nevertheless, wide clinical use is not supported by a deep quantitative knowledge of the phenomena occurring during the expansion. A finite element model of the skin expansion was developed to evaluate the stresses and the strains of the skin due to the expander inflation and validated by proper in vitro experiments; furthermore, a growth model based on the mechanical stimulus was implemented to estimate the skin area gain. The developed computational approach, composed of the skin expansion model interaction and the growth law, proved its validity to investigate skin expansion phenomena: its use suggests a new predictive tool to optimize clinical procedures and the expander devices' design.

In this computational study, we used molecular dynamics and the embedded atom method to successfully reproduce the growth of gold nanorod morphologies from starting spherical seeds in the presence of model surfactants. The surfactant model was developed through extensive systematic attempts aimed at inducing nonisotropic nanoparticle growth in strictly isotropic computational growth environments. The aim of this study was to identify key properties of the surfactants which were most important for the successful anisotropic growth of nanorods. The observed surface and collective dynamics of surfactants shed light on the likely growth phenomena of real nanoprods. These phenomena include the initial thermodynamically driven selective adsorption, segregation, and orientation of the surfactant groups on specific crystallographic surfaces of spherical nanoparticle seeds and the kinetic elongation of unstable surfaces due to growth inhibiting surfactants on those surfaces. Interestingly, the model not only reproduced the growth of nearly all known nanorod morphologies when starting from an initial fcc or fivefold seed but also reproduced the experimentally observed failure of nanorod growth when starting from spherical nanoparticles such as the I(h) morphology or morphologies containing a single twinning plane. Nanorod morphologies observed in this work included fivefold nanorods, fcc crystalline nanorods in the [100] direction and [112] directions and the more exotic "dumbell-like" nanorods. Non-nanorod morphologies observed included the I(h) and the nanoprism morphology. Some of the key properties of the most successful surfactants seemed to be suggestive of the important but little understood role played by silver ions in the growth process of real nanorods.

Preparation and properties of (Y,Eu)-123 superconducting single crystals

Pharmacokinetics of topically applied recombinant human keratinocyte growth factor-2 in alkali-burned and intact rabbit eye

Anteroposterior polarity in the vertebrate limb is thought to be regulated in response to signals derived from a specialized region of distal posterior mesenchyme, the zone of polarizing activity. Sonic Hedgehog (Shh) is expressed in the zone of polarizing activity and appears to mediate the action of the zone of polarizing activity. Here we have manipulated Shh signal in the limb to assess whether it acts as a long-range signal to directly pattern all the digits. Firstly, we demonstrate that alterations in digit development are dependent upon the dose of Shh applied. DiI-labeling experiments indicate that cells giving rise to the extra digits lie within a 300 microm radius of a Shh bead and that the most posterior digits come from cells that lie very close to the bead. A response to Shh involves a 12-16 hour period in which no irreversible changes in digit pattern occur. Increasing the time of exposure to Shh leads to specification of additional digits, firstly digit 2, then 3, then 4. Cell marking experiments demonstrate that cells giving rise to posterior digits are first specified as anterior digits and later adopt a more posterior character. To monitor the direct range of Shh signalling, we developed sensitive assays for localizing Shh by attaching alkaline phosphatase to Shh and introducing cells expressing these forms into the limb bud. These experiments demonstrate that long-range diffusion across the anteroposterior axis of the limb is possible. However, despite a dramatic difference in their diffusibility in the limb mesenchyme, the two forms of alkaline phosphatase-tagged Shh proteins share similar polarizing activity. Moreover, Shh-N (aminoterminal peptide of Shh)-coated beads and Shh-expressing cells also exhibit similar patterning activity despite a significant difference in the diffusibility of Shh from these two sources. Finally, we demonstrate that when Shh-N is attached to an integral membrane protein, cells transfected with this anchored signal also induce mirror-image pattern duplications in a dose-dependent fashion similar to the zone of polarizing activity itself. These data suggest that it is unlikely that Shh itself signals digit formation at a distance. Beads soaked in Shh-N do not induce Shh in anterior limb mesenchyme ruling out direct propagation of a Shh signal. However, Shh induces dose-dependent expression of Bmp genes in anterior mesenchyme at the start of the promotion phase. Taken together, these results argue that the dose-dependent effects of Shh in the regulation of anteroposterior pattern in the limb may be mediated by some other signal(s). BMPs are plausible candidates.