Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: integrating viscous modeling and experimental approaches.

A major challenge in biology is to understand how mechanical interactions and cellular behavior affect the shapes of tissues and embryo morphology. The extension of the neural tube and paraxial mesoderm, which form the spinal cord and musculoskeletal system, respectively, results in the elongated shape of the vertebrate embryonic body. Despite our understanding of how each of these tissues elongates independently of the others, the morphogenetic consequences of their simultaneous growth and mechanical interactions are still unclear. Our study investigates how differential growth, tissue biophysical properties and mechanical interactions affect embryonic morphogenesis during axial extension using a 2D multi-tissue continuum-based mathematical model. Our model captures the dynamics observed in vivo by time-lapse imaging of bird embryos, and reveals the underestimated influence of differential tissue proliferation rates. We confirmed this prediction in quail embryos by showing that decreasing the rate of cell proliferation in the paraxial mesoderm affects long-term tissue dynamics, and shaping of both the paraxial mesoderm and the neighboring neural tube. Overall, our work provides a new theoretical platform upon which to consider the long-term consequences of tissue differential growth and mechanical interactions on morphogenesis.

Mechanistic framework for reduced-order models in soft materials: Application to three-dimensional granular intrusion.

Soft materials often display complex behaviors that transition through apparent solid- and fluid-like regimes. While a growing number of microscale simulation methods exist for these materials, reduced-order models that encapsulate the macroscale physics are often desired to predict how external bodies interact with soft media. Such an approach could provide direct insights in diverse situations from impact and penetration problems to locomotion over natural terrains. This work proposes a systematic program to develop three-dimensional (3D) reduced-order models for soft materials from a fundamental basis using continuum symmetries and rheological principles. In particular, we derive a reduced-order, 3D resistive force theory (3D-RFT), which is capable of accurately and quickly predicting the resistive stress distribution on arbitrary-shaped bodies intruding through granular media. Aided by a continuum description of the granular medium, a comprehensive set of spatial symmetry constraints, and a limited amount of reference data, we develop a self-consistent and accurate 3D-RFT. We verify the model capabilities in a wide range of cases and show that it can be quickly recalibrated to different media and intruder surface types. The premises leading to 3D-RFT anticipate application to other soft materials with strongly hyperlocalized intrusion behavior.

Phenotype-structured model of intra-clonal heterogeneity and drug resistance in multiple myeloma.

Multiple myeloma (MM) is a genetically complex hematological cancer characterized by the abnormal proliferation of malignant plasma cells in the bone marrow. This disease progresses from a premalignant condition known as monoclonal gammopathy of unknown significance (MGUS) through sequential genetic alterations involving various genes. These genetic changes contribute to the uncontrolled growth of multiple clones of plasma cells. In this study, we present a phenotype-structured model that captures the intra-clonal heterogeneity and drug resistance in multiple myeloma (MM). The model accurately reproduces the branching evolutionary pattern observed in MM progression, aligning with a previously developed multiscale model. Numerical simulations reveal that higher mutation rates enhance tumor phenotype diversity, while access to growth factors accelerates tumor evolution and increases its final size. Interestingly, the model suggests that further increasing growth factor access primarily amplifies tumor size rather than altering clonal dynamics. Additionally, the model emphasizes that higher mutation frequencies and growth factor availability elevate the chances of drug resistance and relapse. It indicates that the timing of the treatment could trajectory of tumor evolution and clonal emergence in the case of branching evolutionary pattern. Given its low computational cost, our model is well-suited for quantitative studies on MM clonal heterogeneity and its interaction with chemotherapeutic treatments.

Predictive Design and Analysis of Drug Transport by Multiscale Computational Models Under Uncertainty.

Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these drug carriers, dosages and treatment schemes will require advanced models that can simulate transport processes across multiple length and time scales from genomic to population levels. In order to address this problem, multiscale modeling efforts that integrate existing discrete and continuum modeling strategies have recently emerged. These multiscale approaches provide a promising direction for bottom-up in silico pipelines of drug design for delivery. However, there are remaining challenges in terms of model parametrization and validation in the presence of variability, introduced by multiple levels of heterogeneities in disease state. Parametrization based on physiologically relevant in vitro data from microphysiological systems as well as widespread adoption of uncertainty quantification and sensitivity analysis will help address these challenges.

Tailoring the Band Structure of Twisted Double Bilayer Graphene with Pressure.

Twisted two-dimensional structures open new possibilities in band structure engineering. At magic twist angles, flat bands emerge, which gave a new drive to the field of strongly correlated physics. In twisted double bilayer graphene dual gating allows changing of the Fermi level and hence the electron density and also allows tuning of the interlayer potential, giving further control over band gaps. Here, we demonstrate that by application of hydrostatic pressure, an additional control of the band structure becomes possible due to the change of tunnel couplings between the layers. We find that the flat bands and the gaps separating them can be drastically changed by pressures up to 2 GPa, in good agreement with our theoretical simulations. Furthermore, our measurements suggest that in finite magnetic field due to pressure a topologically nontrivial band gap opens at the charge neutrality point at zero displacement field.

A 3-variable PDE model for predicting fungal growth derived from microscopic mechanisms.

In this work, we present a new PDE model of the growth of Postia placenta, a species of brown rot fungus. The formulation was derived mainly from the biological mechanisms embedded in our discrete model, validated against experimental data. In order to mimic the growth mechanisms, we propose a new reaction-diffusion formulation, based on three variables: the concentration of tips, the branch density and the total hyphal density. The evolution of tips obeys a reaction-diffusion model, with constant diffusivity, while the evolution of the two other variables results from time integrals. The numerical solution is in excellent agreement with the averaged radial tip/hyphal densities of the mycelial network obtained by the discrete model. Thanks to the efficient exponential Euler method with Krylov subspace approximation, the solution needs only 3.5 s of CPU time to simulate 104-day of mycelium growth, in comparison with 8 hours for the discrete model. The great reduction of the RAM memory and computing time gives the possibility to upscale the simulation. The novelty of the PDE system is that the spatial colonization is formulated as a diffusion mechanism, which is self-standing, contrary to models based on an advection term. The continuous model can also reproduce the radial densities when the growth parameters in the discrete model are varied to adapt to different growth conditions. The correlation constructed between the two models provides us a tool for mutual insights between local biological mechanisms to the global biomass distribution, especially when analyzing experimental data.

Microvascular hemodynamics in the chick chorioallantoic membrane.

OBJECTIVE: The microvasculature of the CAM in the developing chick embryo is characterized by interdigitating arteriolar and venular trees, connected at multiple points along their lengths to a mesh-like capillary plexus. Theoretical modeling techniques were employed to investigate the resulting hemodynamic characteristics of the CAM. METHODS: Based on previously obtained anatomical data, a model was developed in which the capillary plexus was treated as a porous medium. Supply of blood from arterioles and drainage into venules were represented by distributions of flow sources and sinks. Predicted flow velocities were compared with measurements in arterioles and venules obtained via video microscopy. RESULTS: If it was assumed that blood flowed into and out of the capillary plexus only at the ends of terminal arterioles and venules, the predicted velocities increased with decreasing diameter in vessels below 50 µm in diameter, contrary to the observations. Distributing sources/sinks along arterioles/venules led to velocities consistent with the data. CONCLUSIONS: These results imply that connections to the capillary plexus distributed along the arterioles and venules strongly affect the hemodynamic characteristics of the CAM. The theoretical model provides a basis for quantitative simulations of structural adaptation in CAM networks in response to hemodynamic stimuli.

Mapping of Strain Fields in GaAs/GaAsP Core-Shell Nanowires with Nanometer Resolution.

We report the nanoscale quantification of strain in GaAs/GaAsP core-shell nanowires. By tracking the shifting of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction patterns, we observe unique variations in HOLZ line separation along different facets of the core-shell structure, demonstrating the nonuniform strain fields created by the heterointerface. Furthermore, through the use of continuum mechanical modeling and Bloch wave analysis we calculate expected HOLZ line shift behavior, which are directly matched to experimental results. This comparison demonstrates both the power of electron microscopy as a platform for nanoscale strain characterization and the reliability of continuum models to accurately calculate complex strain fields in nanoscale systems.

Microstructure-based modeling of primary cilia mechanics.

A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load-bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure-based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip-anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium-length-dependent, we found the mechanical properties of the cilium are also highly deformation-dependent. More important, we found that the cilium membrane near the base is not under pure in-plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure-based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging-informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base.

Controlling Electroosmosis in Nanopores Without Altering the Nanopore Sensing Region.

Nanopores are powerful tools for single-molecule sensing of biomolecules and nanoparticles. The signal coming from the molecule to be analyzed strongly depends on its interaction with the narrower section of the nanopore (constriction) that may be tailored to increase sensing accuracy. Modifications of nanopore constriction have also been commonly used to induce electroosmosis, that favors the capture of molecules in the nanopore under a voltage bias and independently of their charge. However, engineering nanopores for increasing both electroosmosis and sensing accuracy is challenging. Here it is shown that large electroosmotic flows can be achieved without altering the nanopore constriction. Using continuum electrohydrodynamic simulations, it is found that an external charged ring generates strong electroosmosis in cylindrical nanopores. Similarly, for conical nanopores it is shown that moving charges away from the cone tip still results in an electroosmotic flow (EOF), whose intensity reduces increasing the diameter of the nanopore section where charges are placed. This paradigm is applied to engineered biological nanopores showing, via atomistic simulations and experiments, that mutations outside the constriction induce a relatively intense electroosmosis. This strategy provides much more flexibility in nanopore design since electroosmosis can be controlled independently from the constriction, which can be optimized to improve sensing accuracy.

Setting up virgin stress conditions in discrete element models.

In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain.

Continuum interpretation of mechano-adaptation in micropatterned epithelia informed by in vitro experiments.

Epithelial tissues adapt their form and function following mechanical perturbations, or mechano-adapt, and these changes often result in reactive forces that oppose the direction of the applied change. Tissues subjected to ectopic tensions, for example, employ behaviors that lower tension, such as increasing proliferation or actomyosin turnover. This oppositional behavior suggests that the tissue has a mechanical homeostasis. Whether attributed to maintenance of cellular area, cell density, or cell and tissue tensions, epithelial mechanical homeostasis has been implicated in coordinating embryonic morphogenesis, wound healing, and maintenance of adult tissues. Despite advances toward understanding the feedback between mechanical state and tissue response in epithelia, more work remains to be done to examine how tissues regulate mechanical homeostasis using epithelial sheets with defined micropatterned shapes. Here, we used cellular microbiaxial stretching (CµBS) to investigate mechano-adaptation in micropatterned tissues of different shape consisting of Madin-Darby canine kidney cells. Using the CµBS platform, tissues were subjected to a 30% stretch that was held for 24 h. We found that, following stretch, tissue stresses immediately increased then slowly evolved over time, approaching their pre-stretch values by 24 h. Organization of the actin cytoskeletal was found to play a role in this process: anisotropic ally structured tissues exhibited anisotropic stress patterns, and the cytoskeletal became more aligned following stretch and reorganized over time. Interestingly, in unstretched tissues, stresses also decreased, which was found to be driven by proliferation-induced cellular confinement and change in tissue thickness. We modeled these behaviors with a continuum-based model of epithelial growth that accounted for stress-induced actin remodeling and proliferation, and found this model to strongly capture experimental behavior. Ultimately, this combined experimental-modeling approach suggests that epithelial mechano-adaptation depends on cellular architecture and proliferation, which can be modeled with a field-averaged approach applicable to more specific contexts in which change is driven by epithelial mechanical homeostasis. Insight box Epithelial tissues adapt their form and function following mechanical perturbation, and it is thought that this 'mechano-adaptation' plays an important role in driving processes like embryonic morphogenesis, wound healing, and adult tissue maintenance. Here, we use cellular microbiaxial stretching to probe this process in vitro in small epithelial tissues whose geometries were both controlled and varied. By using a highly precise stretching device and a continuum mechanics modeling framework, we revealed that tissue mechanical state changes following stretch and over time, and that this behavior can be explained by stress-dependent changes in actin fibers and proliferation. Integration of these approaches enabled a systematic approach to empirically and precisely measure these phenomena.

Electrostatic Potential Analysis in Polyelectrolyte Brush-Grafted Microchannels Filled with Polyelectrolyte Dispersion.

In this study, the model framework that includes almost all relevant parameters of interest has been developed to quantify the electrostatic potential and charge density occurring in microchannels grafted with polyelectrolyte brushes and simultaneously filled with polyelectrolyte dispersion. The brush layer is described by the Alexander-de Gennes model incorporated with the monomer distribution function accompanying the quadratic decay. Each ion concentration due to mobile charges in the bulk and fixed charges in the brush layer can be determined by multi-species ion balance. We solved 2-dimensional Poisson-Nernst-Planck equations adopted for simulating electric field with ion transport in the soft channel, by considering anionic polyelectrolyte of polyacrylic acid (PAA). Remarkable results were obtained regarding the brush height, ionization, electrostatic potential, and charge density profiles with conditions of brush, dispersion, and solution pH. The Donnan potential in the brush channel shows several times higher than the surface potential in the bare channel, whereas it becomes lower with increasing PAA concentration. Our framework is fruitful to provide comparative information regarding electrostatic interaction properties, serving as an important bridge between modeling and experiments, and is possible to couple with governing equations for flow field.

Solid-Electrolyte Interphase During Battery Cycling: Theory of Growth Regimes.

The capacity fade of modern lithium ion batteries is mainly caused by the formation and growth of the solid-electrolyte interphase (SEI). Numerous continuum models support its understanding and mitigation by studying SEI growth during battery storage. However, only a few electrochemical models discuss SEI growth during battery operation. In this article, a continuum model is developed that consistently captures the influence of open-circuit potential, current direction, current magnitude, and cycle number on the growth of the SEI. The model is based on the formation and diffusion of neutral lithium atoms, which carry electrons through the SEI. Recent short- and long-term experiments provide validation for our model. SEI growth is limited by either reaction, diffusion, or migration. For the first time, the transition between these mechanisms is modelled. Thereby, an explanation is provided for the fading of capacity with time t of the form tß with the scaling coefficent ß, 0≤ß≤1. Based on the model, critical operation conditions accelerating SEI growth are identified.

Liver Bioreactor Design Issues of Fluid Flow and Zonation, Fibrosis, and Mechanics: A Computational Perspective.

Tissue engineering, with the goal of repairing or replacing damaged tissue and organs, has continued to make dramatic science-based advances since its origins in the late 1980's and early 1990's. Such advances are always multi-disciplinary in nature, from basic biology and chemistry through physics and mathematics to various engineering and computer fields. This review will focus its attention on two topics critical for tissue engineering liver development: (a) fluid flow, zonation, and drug screening, and (b) biomechanics, tissue stiffness, and fibrosis, all within the context of 3D structures. First, a general overview of various bioreactor designs developed to investigate fluid transport and tissue biomechanics is given. This includes a mention of computational fluid dynamic methods used to optimize and validate these designs. Thereafter, the perspective provided by computer simulations of flow, reactive transport, and biomechanics responses at the scale of the liver lobule and liver tissue is outlined, in addition to how bioreactor-measured properties can be utilized in these models. Here, the fundamental issues of tortuosity and upscaling are highlighted, as well as the role of disease and fibrosis in these issues. Some idealized simulations of the effects of fibrosis on lobule drug transport and mechanics responses are provided to further illustrate these concepts. This review concludes with an outline of some practical applications of tissue engineering advances and how efficient computational upscaling techniques, such as dual continuum modeling, might be used to quantify the transition of bioreactor results to the full liver scale.

Modeling Segregation in Granular Flows.

Accurate continuum models of flow and segregation of dense granular flows are now possible. This is the result of extensive comparisons, over the last several years, of computer simulations of increasing accuracy and scale, experiments, and continuum models, in a variety of flows and for a variety of mixtures. Computer simulations-discrete element methods (DEM)-yield remarkably detailed views of granular flow and segregation. Conti-nuum models, however, offer the best possibility for parametric studies of outcomes in what could be a prohibitively large space resulting from the competition between three distinct driving mechanisms: advection, diffusion, and segregation. We present a continuum transport equation-based framework, informed by phenomenological constitutive equations, that accurately predicts segregation in many settings, both industrial and natural. Three-way comparisons among experiments, DEM, and theory are offered wherever possible to validate the approach. In addition to the flows and mixtures described here, many straightforward extensions of the framework appear possible.

A Continuum Model for the Effect of Dynamic Recrystallization on the Stress⁻Strain Response.

Austenitic Stainless Steels and High-Strength Low-Alloy (HSLA) steels show significant dynamic recovery and dynamic recrystallization (DRX) during hot forming. In order to design optimal and safe hot-formed products, a good understanding and constitutive description of the material behavior is vital. A new continuum model is presented and validated on a wide range of deformation conditions including high strain rate deformation. The model is presented in rate form to allow for the prediction of material behavior in transient process conditions. The proposed model is capable of accurately describing the stress⁻strain behavior of AISI 316LN in hot forming conditions, also the high strain rate DRX-induced softening observed during hot torsion of HSLA is accurately predicted. It is shown that the increase in recrystallization rate at high strain rates observed in experiments can be captured by including the elastic energy due to the dynamic stress in the driving pressure for recrystallization. Furthermore, the predicted resulting grain sizes follow the power-law dependence with steady state stress that is often reported in literature and the evolution during hot deformation shows the expected trend.

Rate-Dependent Morphology of Li2O2 Growth in Li-O2 Batteries.

Compact solid discharge products enable energy storage devices with high gravimetric and volumetric energy densities, but solid deposits on active surfaces can disturb charge transport and induce mechanical stress. In this Letter, we develop a nanoscale continuum model for the growth of Li2O2 crystals in lithium-oxygen batteries with organic electrolytes, based on a theory of electrochemical nonequilibrium thermodynamics originally applied to Li-ion batteries. As in the case of lithium insertion in phase-separating LiFePO4 nanoparticles, the theory predicts a transition from complex to uniform morphologies of Li2O2 with increasing current. Discrete particle growth at low discharge rates becomes suppressed at high rates, resulting in a film of electronically insulating Li2O2 that limits cell performance. We predict that the transition between these surface growth modes occurs at current densities close to the exchange current density of the cathode reaction, consistent with experimental observations.