Three-dimensional Multiscale Model Research Articles

A three-dimensional multiscale model for gas exchange in fruit.

Respiration of bulky plant organs such as roots, tubers, stems, seeds, and fruit depends very much on oxygen (O2) availability and often follows a Michaelis-Menten-like response. A multiscale model is presented to calculate gas exchange in plants using the microscale geometry of the tissue, or vice versa, local concentrations in the cells from macroscopic gas concentration profiles. This approach provides a computationally feasible and accurate analysis of cell metabolism in any plant organ during hypoxia and anoxia. The predicted O2 and carbon dioxide (CO2) partial pressure profiles compared very well with experimental data, thereby validating the multiscale model. The important microscale geometrical features are the shape, size, and three-dimensional connectivity of cells and air spaces. It was demonstrated that the gas-exchange properties of the cell wall and cell membrane have little effect on the cellular gas exchange of apple (Malus×domestica) parenchyma tissue. The analysis clearly confirmed that cells are an additional route for CO2 transport, while for O2 the intercellular spaces are the main diffusion route. The simulation results also showed that the local gas concentration gradients were steeper in the cells than in the surrounding air spaces. Therefore, to analyze the cellular metabolism under hypoxic and anoxic conditions, the microscale model is required to calculate the correct intracellular concentrations. Understanding the O2 response of plants and plant organs thus not only requires knowledge of external conditions, dimensions, gas-exchange properties of the tissues, and cellular respiration kinetics but also of microstructure.

A three-dimensional multiscale model of intergranular hydrogen-assisted cracking

We present a three-dimensional model of intergranular hydrogen-embrittlement (HE) that accounts for: (i) the degradation of grain-boundary strength that arises from hydrogen coverage; (ii) grain-boundary diffusion of hydrogen; and (iii) a continuum model of plastic deformation that explicitly resolves the three-dimensional polycrystalline structure of the material. The polycrystalline structure of the specimen along the crack propagation path is resolved explicitly by the computational mesh. The texture of the polycrystal is assumed to be random and the grains are elastically anisotropic and deform plastically by crystallographic slip. We use the impurity-dependent cohesive model in order to account for the embrittling of grain boundaries due to hydrogen coverage. We have carried out three-dimensional finite-element calculations of crack-growth initiation and propagation in AISI 4340 steel double-cantilever specimens in contact with an aggressive environment and compared the predicted initiation times and crack-growth curves with the experimental data. The calculated crack-growth curves exhibit a number of qualitative features that are in keeping with observation, including: an incubation time followed by a well-defined crack-growth initiation transition for sufficiently large loading; the existence of a threshold intensity factor K Iscc below which there is no crack propagation; a subsequent steeply rising part of the curve known as stage I; a plateau, or stage II, characterized by a load-insensitive crack-growth rate; and a limiting stress-intensity factor K Ic , or toughness, at which pure mechanical failure occurs. The calculated dependence of the crack-growth initiation time on applied stress-intensity factor exhibits power-law behavior and the corresponding characteristic exponents are in the ball-park of experimental observation. The stage-II calculated crack-growth rates are in good overall agreement with experimental measurements.

Platelet Adhesive Dynamics. Part II: High Shear-Induced Transient Aggregation via GPIb α-vWF-GPIb α Bridging

A three-dimensional multiscale computational model, platelet adhesive dynamics (PAD), is developed and applied in Part I and Part II articles to characterize and quantify key biophysical aspects of GPIb α-von-Willebrand-factor (vWF)-mediated interplatelet binding at high shear rates, a necessary and enabling step that initiates shear-induced platelet aggregation. In this article, an adhesive dynamics model of the transient aggregation of two unactivated platelets via GPIb α-vWF-GPIb α bridging is developed and integrated with the three-dimensional hydrodynamic flow model discussed in Part I. Platelet binding efficiencies predicted by PAD are in good agreement with platelet aggregation behavior observed experimentally, as documented in the literature. Deviations from average vWF ligand size or healthy GPIb α-vWF-A1 binding kinetics are observed in simulations to have significant effects on the dynamics of transient platelet aggregation, i.e., the efficiency of platelet aggregation and characteristics of bond failure, in ways that typify diseased conditions. The GPIb α-vWF-A1 bond formation rate is predicted to have piecewise linear dependence on the prevailing fluid shear rate, with a sharp transition in fluid shear dependency at 7200 s −1. Interplatelet bond force-loading is found to be complex and highly nonlinear. These results demonstrate PAD as a powerful predictive modeling tool for elucidating platelet adhesive phenomena under flow.

Platelet Adhesive Dynamics. Part I: Characterization of Platelet Hydrodynamic Collisions and Wall Effects

Abnormally high shear stresses encountered in vivo induce spontaneous activation of blood platelets and formation of aggregates, even in the absence of vascular injury. A three-dimensional multiscale computational model—platelet adhesive dynamics—is developed and applied in Part I and Part II articles to elucidate key biophysical aspects of GPIb α-von-Willebrand-factor-mediated interplatelet binding that characterizes the onset of shear-induced platelet aggregation. In this article, the hydrodynamic effects of the oblate spheroidal shape of platelets and proximity of a plane wall on the nature of cell-cell collisions are systematically investigated. Physical quantities characterizing the adhesion probabilities between colliding platelet surfaces for the entire range of near-wall encounters between two platelets are obtained for application in platelet adhesive dynamics simulations of platelet aggregation explored in a companion article. The technique for matching simulation predictions of interplatelet binding efficiency to experimentally determined efficiencies is also described. Platelet collision behavior is found to be strikingly different from that of spheres, both close to and far from a bounding wall. Our results convey the significant effects that particle shape and presence of a bounding wall have on the particle trajectories and collision mechanisms, collision characteristics such as collision time and contact area, and collision frequency.

Development of a three-dimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer

Experimental evidence suggests that epidermal growth factor receptor (EGFR)-mediated activation of the signaling protein phospholipase C γ plays a critical role in a cancer cell's phenotypic decision to either proliferate or to migrate at a given point in time. Here, we present a novel three-dimensional multiscale agent-based model to simulate this cellular decision process in the context of a virtual brain tumor. Each tumor cell is equipped with an EGFR gene-protein interaction network module that also connects to a simplified cell cycle description. The simulation results show that over time proliferative and migratory cell populations not only oscillate but also directly impact the spatio-temporal expansion patterns of the entire cancer system. The percentage change in the concentration of the sub-cellular interaction network's molecular components fluctuates, and, for the ‘proliferation-to-migration’ switch we find that the phenotype triggering molecular profile to some degree varies as the tumor system grows and the microenvironment changes. We discuss potential implications of these findings for experimental and clinical cancer research.

Observed and modelled “chemical weather” during ESCOMPTE

The new MOdèle de Chimie Atmosphérique à Grande Echelle (MOCAGE) three-dimensional multiscale chemistry and transport model (CTM) has been applied to study heavy pollution episodes observed during the ESCOMPTE experiment. The model considers the troposphere and lower stratosphere, and allows the possibility of zooming from the planetary scale down to the regional scale over limited area subdomains. Like this, it generates its own time-dependent chemical boundary conditions in the vertical and in the horizontal. This paper focuses on the evaluation and quantification of uncertainties related to chemical and transport modelling during two intensive observing periods, IOP2 and IOP4 (June 20–26 and July 10–14, 2001, respectively). Simulations are compared to the database of four-dimensional observations, which includes ground-based sites and aircraft measurements, radiosoundings, and quasi-continuous measurements of ozone by LIDARs. Thereby, the observed and modelled day-to-day variabilities in air composition both at the surface and in the vertical have been assessed. Then, three sensitivity studies are conducted concerning boundary conditions, accuracy of the emission dataset, and representation of chemistry. Firstly, to go further in the analysis of chemical boundary conditions, results from the standard grid nesting set-up and altered configurations, relying on climatologies, are compared. Along with other recent studies, this work advocates the systematic coupling of limited-area models with global CTMs, even for regional air quality studies or forecasts. Next, we evaluate the benefits of using the detailed high-resolution emissions inventory of ESCOMPTE: improvements are noticeable both on ozone reactivity and on the concentrations of various species of the ozone photochemical cycle especially primary ones. Finally, we provide some insights on the comparison of two simulations differing only by the parameterisation of chemistry and using two state-of-the-art chemical schemes for regional photochemical modelling. Regional air quality modelling is found to be highly sensitive to the emission inventory dataset and also to the vertical and horizontal boundary conditions and detailed representation of chemistry. Interestingly enough, they infer the same range of errors compared to total model errors.

Effect of lateral resolution on topographical images and three-dimensional functional parameters

The influence of the analysis scale on the characterisation of surface roughness is set out in this work. First the effect of lateral resolution on the local morphology of a random engineered surface is shown. The effect of the geometry of a tactile profilometer tip is studied by the variation of the tip radius of curvature. The incidence of the scale observation is analysed from micro- to nano-scale with three microscopes: a tactile, laser and atomic force microscope. The lateral resolution influences not only the roughness amplitude parameters, but also spectral range, slopes, local radius of curvature of the summits, bearing area, developed surface, the void or material volume. In the second half of this work the contribution of fractal geometry is examined. This is because, through its roughness index, called the Hölder index, it may be independent of the measurement. By using the Weierstrass-Mandelbrot function as a three-dimensional multi-scale model of the topography, the evolution of the bearing area, the developed surface and the volume as a function of the Hölder roughness index can be shown.

Plasma flow in the cometosheath of comet Halley

Plasma parameters are investigated in the regions upstream and downstream of the bow shock of comet Halley based on the ion spectra measured by the Plasmag-1 instrument aboard the Vega-2 spacecraft. Proton velocities observed by the Solar Direction Analyser and by the Cometary Ram Analyser are compared with the simulated bulk velocity profile provided by a three-dimensional multiscale MHD model (Gombosi et al., 1996). Disregarding the effects of presumably interplanetary disturbances, the simulated and measured values are in good agreement at cometocentric distances larger than about 0.5 million km.