Simple Cell Model Research Articles

Effect of micro-structure on yield strength of porous solid: A comparative study of two simple cell models

An objective of this paper is to estimate an extent to which the yield strength of a powder compact is affected by its micro-structure. For this purpose, two opposite idealized structures of porous solid were investigated numerically. The first of them is a continuous matrix with isolated spherical pores simulating micro-geometry of the products obtained by the free sintering technology. The second one, being an array of spherical particles with isolated finite-sized contact spots, is typical for the powder compacts produced by cold pressing or intensive electro sintering. Their comparative study shows that the yield strength of porous solid is rather structure-sensitive and, therefore, the micro-structure parameters (and their evolution during consolidation) should be incorporated in the model in order to provide adequate description of their elastic–plastic behavior. It is found that behavior of both the considered materials can be described satisfactory by the Gurson–Tvergaard–Needleman (GTN) model. Numerical study shows that the coefficients entering the GTN-model are structure-dependent and, hence, can be effectively used as the internal state variables of porous solid. It opens a way of utilizing the available GTN-model based finite element software in computer simulation of the powder metallurgy technologies, with adequate account for micro-structure evolution of the consolidated powder compacts.

Cell-field interaction arising from tissue inhomogeneity determines electric stimulation efficiency

Background Electrical stimulation of neuronal tissue has been widely used in laboratory research and in the treatment of neurological diseases such as Parkinson's disease, essential tremor and dystonia. During stimulation, cells are polarized by the electrically-induced transmembrane potential, and the electric field is re-distributed by the presence of the cell. Previous studies have separately studied each aspect of this interaction. The electrically-induced transmembrane potential has been computed by various modeling works with various cell shapes, cell-field orientations, and field designs. The electrical field distribution has also been extensively studied. How do cellfield interactions influence the efficiency of electrical stimulation? To answer this question, we have developed a simple spherical cell model under uniform DC electrical field stimulation.

Learning in a geometric model of place cell firing

Following Hartley et al. (Hartley et al. (2000) Hippocampus 10:369-379), we present a simple feed-forward model of place cell (PC) firing predicated on neocortical information regarding the environmental geometry surrounding the animal. Incorporating the idea of boundaries with distinct sensory qualities, we show that synaptic plasticity mediated by a BCM-like rule (Bienenstock et al. (1982) J Neurosci 2:32-48) produces PCs that encode position relative to specific extended landmarks. In an unchanging environment the model is shown to undergo an initial phase of learning, resulting in the formation of stable place fields. In familiar environments, perturbation of environmental cues produces graded changes in the firing rate and position of place fields. Model simulations are compared favorably with three sets of experimental data: (1) Results published by Barry et al. (Barry et al. (2006) Rev Neurosci 17:71-97) showing the slow disappearance of duplicate place fields produced when a barrier is placed into a familiar environment. (2) Rivard et al.'s (Rivard et al. (2004) J Gen Physiol 124:9-25) study showing a graded response in PC firing such that fields near to a centrally placed object encode space relative to the object, whereas more distant fields respond to the surrounding environment. (3) Fenton et al.'s (Fenton et al. (2000a) J Gen Physiol 116:191-209) observation that inconsistent rotation of cue cards produces parametric changes in place field positions. The merits of the model are discussed in terms of its extensibility and biological plausibility.

Numerical modeling of the thermo-mechanical behavior of particle reinforced metal matrix composites in laser forming by using a multi-particle cell model

In this paper, a three-dimensional finite element method integrated with a multi-particle cell (MPC) model is developed to examine the effect of particle distribution on deformation behavior of a particle reinforced metal matrix composite Al6092/25%SiC p in laser forming. Thirty identical elastic spheres are generated to be embedded in an elasto-plastic matrix and the interface between the particle and matrix is assumed perfect. The thermo-mechanical properties of the particle reinforced metal matrix composite (PMMCs), including the thermal conductivity, the coefficient of thermal expansion and the mechanical properties are determined by MPC model. Based on the predicted properties, the deformation behavior involving temperature/structural fields and final bending angles of the composite under different spatial arrangements of reinforcements is examined during laser forming. A comparison between the MPC and the simple cubic cell (SCC) models is made, and the significance of the findings will be discussed in the paper.

Effect of reinforcement morphology on deformation behavior of particle reinforced metal matrix composites in laser forming

In this paper, the effect of reinforcement morphology on deformation behavior of the Al6092/SiCp metal matrix composite in laser forming was examined by a microstructure integrated finite element method. With the assumptions that the reinforcement performs elastically in the elasto-plastic matrix and the interface between them is perfect, a simple cubic cell (SCC) model was developed to investigate the effect of reinforcement morphology on the temperature dependent thermo-mechanical properties of the composite including thermal conductivity, coefficient of thermal expansion (CTE) and mechanical properties for different reinforcement shapes (spherical, cubic and cylindrical) and aspect ratios. Based on the predicted properties, the deformation behavior of the composite in laser forming was examined. It was found that the numerical results with unity aspect ratio were in good agreement with the published experimental data. The influence of aspect ratio of rectangular reinforcement was also examined and discussed in the paper.

On Compatible Condition for Morphogenetic Diversity and Recursive Production of Multicellular Organisms

The development of a multicellular organism is a dynamic process. With the increase of the cell number, starting from one or a few cells, cells are differentiated with different compositions. These differet types of cells form an ordered pattern. It is rather surprising that differentiation in cell types and formation of controlled patterns are compatible, because the former gives morphogenetic diversification whereas the latter implies recursive production of a cell ensemble, reducing individual differences. We studied this problem by taking a simple cell model with intracellular reaction dynamics of chemical concentrations, cell-cell interactions, and increase in cell numbers. We show that, by starting from an initial object consisting of both the cell type with diverse chemicals and the differentiated cell type, the recursive production of a multicellular organism with morphogenetic diversity is possible.

Mass Transfer from Ensembles of Newtonian Fluid Spheres at Moderate Reynolds and Peclet Numbers

In this work, the rate of mass transfer from an ensemble of mono-size spherical Newtonian droplets (free from surfactants) to a Newtonian continuous phase has been numerically studied at moderate Reynolds and Peclet numbers. A simple spherical cell model (so-called free surface cell model) has been used to account for inter-drop hydrodynamic interactions. Extensive numerical results have been obtained to elucidate the effects of the Reynolds number ( Re o), the ratio of internal to external fluid viscosity ( k), the volume fraction of the dispersed phase ( ɛ) and the Schmidt number ( Sc) on the local and average Sherwood number ( Sh) over the ranges of conditions: 1 ≤ Re o ≤ 200, 0.2 ≤ ɛ ≤ 0.6, 0.1 ≤ k≤ 50 and 1 ≤ Sc ≤ 10 000. It has been observed that the effects of viscosity ratio on the local and average Sherwood number is less significant for small values of the Peclet number ( Pe) for all values of dispersed phase concentration. As the value of the viscosity ratio increases, the average Sherwood number decreases for all values of the droplet concentration and the Reynolds number. Based on the present numerical results, a simple predictive correlation is proposed which can be used to estimate the rate of inter-phase mass transfer in a liquid–liquid system in a new application. However, it is also appropriate to add here that at higher concentrations, fluid spheres interact significantly, deform and coalesce. All these effects are neglected in this study. Therefore, the present results are valid only for dilute to moderate concentration of the dispersed phase.

Sedimentation in Emulsions of Mono-size Droplets at Moderate Reynolds Numbers

The steady incompressible flow of a Newtonian fluid through an ensemble of Newtonian fluid spheres has been numerically investigated using a finite difference method based SMAC algorithm. For both, dispersed and continuous phases, the convective terms have been discretized using the QUICK scheme, and diffussive terms with the second-order central differencing scheme. A simple concentric sphere cell model has been employed to account for inter-particle hydrodynamic interactions. Extensive numerical results on pressure drag ( C dp ), friction drag ( C df ) and total drag ( C D ) coefficients have been presented as functions of the Reynolds number ( Re o ) for the continuous phase, the volume fraction of the dispersed phase (∈), and the ratio of internal to external fluid viscosity ( k ) over the ranges of conditions: 1 ≤ Re o ≤ 500, 0.2 ≤ ∈ ≤ 0.6 and 0.1 ≤ k ≤ 50. Based on the numerical values of the total drag coefficients obtained in this work, a simple correlation has been proposed which can be used to predict the rate of sedimentation in liquid–liquid systems.

The Osmotic Behavior of Short Stiff Polyelectrolytes

AbstractWe report our recent advances in understanding when a simple cell model of a single, short polyelectrolyte is able to correctly reproduce the osmotic coefficient of a bulk solution. To this end we proposed a self‐consistent geometry optimized cell model. In contrast to the usual monotonic Poisson‐Boltzmann prediction, the cell model predicts the correct non‐monotonic dependence of the osmotic coefficient on concentration. A lower degree of polymerization is found to reduce significantly the counterion condensation for a typical dilute strong polyelectrolyte solution, thus increasing the osmotic coefficient. The results agree quantitatively with simulations of a corresponding many‐body bulk system up to a dense semi‐dilute regime. We investigate the effect of chain flexibility and on residual salt on the osmotic properties, and give a short overview about other effects which might be responsible for the observed discrepancy to recent experimental results on a PPP polyelectrolyte system.

What simple and complex cells compute

Visual neuroscientists seek to answer two related questions. First, what does the visual system do? Second, how does it do it? While an answer to the second question is a description based on anatomy and biophysics, an answer to the first question is a description of computations performed on images. Important steps in providing this description were made with the publication of two classical studies on primary visual cortex by Movshon et al. (1978a,b). These studies have not aged in their readability, and do not require an interpretive key to be enjoyed by the contemporary reader. As an introduction, however, this Perspectives article briefly reviews the state of the art at the time of their appearance, their main findings, and their influence on three decades of subsequent investigations.

Numerical Calculation for Fuel Depletion State of SOFCs

Fuel depletion states under cell operations of SOFCs were simulated. Three dimensional calculations for the cell operations were carried out using a commercial computational fluid dynamics code. Using a simple geometry model of an anode-supported cell, effects of a gas diffusion in a porous anode, a current density, and a fuel utilization on the fuel depletion state were studied. A local fuel depletion resulting in a large concentration overpotential and thus a steep drop of the electromotive force was figured out and discussed. The study made clear that the planar SOFC is robust against the fuel depletion state.

On the Computational Complexity of the Bidomain and the Monodomain Models of Electrophysiology

The bidomain model, coupled with accurate models of cell membrane kinetics, is generally believed to provide a reasonable basis for numerical simulations of cardiac electrophysiology. Because of changes occurring in very short time intervals and over small spatial domains, discretized versions of these models must be solved on fine computational grids, and small time-steps must be applied. This leads to huge computational challenges that have been addressed by several authors. One popular way of reducing the CPU demands is to approximate the bidomain model by the monodomain model, and thus reducing a two by two set of partial differential equations to one scalar partial differential equation; both of which are coupled to a set of ordinary differential equations modeling the cell membrane kinetics. A reduction in CPU time of two orders of magnitude has been reported. It is the purpose of the present paper to provide arguments that such a reduction is not present when order-optimal numerical methods are applied. Theoretical considerations and numerical experiments indicate that the reduction factor of the CPU requirements from bidomain to monodomain computations, using order-optimal methods, typically is about 10 for simple cell models and less than two for more complex cell models.

Actin filament branching and protrusion velocity in a simple 1D model of a motile cell

We formulate and analyse a 1D model for the spatial distribution of actin density at the leading edge of a motile cell. The model incorporates nucleation, capping, growth and decay of actin filaments, as well as retrograde flow of the actin meshwork and known parameter values based on the literature. Using a simplified geometry, and reasonable assumptions about the biochemical processes, we derive PDEs for the density of actin filaments and their tips. Analytic travelling wave solutions are used to predict how the speed of the cell depends on rates of nucleation, capping, polymerization and membrane resistance. Analysis and simulations agree with experimental profiles for measured actin distributions. Extended versions of the model are studied numerically. We find that our model produces stable travelling wave solutions with reasonable cell speeds. Increasing the rate of nucleation of filaments (by the actin related protein Arp2/3) or the rate of actin polymerization leads to faster cell speed, whereas increasing the rate of capping or the membrane resistance reduces cell speed. We consider several variants of nucleation (spontaneous, tip, and side branching) and find best agreement with experimentally measured spatial profiles of filament and tip density in the side branching case.

Slow slip events controlled by the slab dip and its lateral change along a trench

Several slow slip events (SSEs) have recently been globally detected at subduction zones by analyses of high precision GPS data. They occur at the transition zone from seismogenic to stable sliding ones, but seem to occur at restricted areas. Though researchers have proposed some generation mechanisms of SSE, they made no mention of such restricted occurrence areas of SSE. To explain why SSEs occur in some restricted area, we compile the features of globally detected SSEs and we find that the slab dip and its lateral change are important factors for controlling their occurrences. Through simulations of earthquake cycle including SSEs using a simplified cell model, we examine the effect of dip angle at the transition zone on the interseismic SSEs. The remarkable SSEs occur several times in a seismic cycle at the cell with a smaller dip, while at the cell with a larger dip, few small SSEs occur and attenuate in the interseismic term. Actually, SSEs occur only at the area with the smallest dip at the transition zone. Moreover in the case where cells are placed at the neighbor of the existing cell in the lateral direction, SSEs are restrained to become smaller if the dips of cells are the same. To the contrary, the cells with different dips do not restrain SSEs. This result well explains the observed feature that SSEs occur at the area where the dip of the plate is laterally changing. In addition, it is also reproduced that a cell with a smaller dip angle has SSEs with a longer interval and longer duration. These simulation results are understood in terms of the frictional condition related to the dip-dependent stiffness of plate interface, that is, the stress accumulation due to the plate subduction, relative to the critical stiffness determined by frictional parameters and the stress interaction which is also dependent on the dip angle.

Cell modeling with reusable agent-based formalisms

Biologists are building increasingly complex models and simulations of cells and other biological entities, and are looking at alternatives to traditional representations. Making use of the object-oriented (OO) paradigm, the Unified Modeling Language (UML) and Real-time Object-Oriented Modeling (ROOM) visual formalisms, and the Rational Rose RealTime (RRT) visual modeling tool, we summarize a previously-described multi-step process for constructing top-down models of cells. We first construct a simple model of a cell using an architecture in which all objects are containers, agents, or passive objects. We then reuse these architectural principles and components to extend our simple cell model into a more complex cell, the goal being to demonstrate that encapsulation familiar to artificial intelligence researchers can be employed by systems biologists in their models. A red blood cell is embedded in a straight-forward manner within a larger system, which is in turn iteratively embedded within still larger systems, including a blood vessel, a circulatory system, a human being, and a simple ecology. Each complexity increment reuses the same architectural principles, including the use of agents, each of which continuously either moves passive small molecules between containers, or transforms these passive objects from one type into another. We show how it is possible to start with a direct diagrammatic representation of a biological structure such as a cell, using terminology familiar to biologists, and by following a process of gradually adding more and more detail, arrive at a system with structure and behavior of arbitrary complexity that can run and be observed on a computer.

Integrate-and-Fire Model for Electrically Stimulated Nerve Cell

A commonly used simple spiking cell model is modified for extracellular current activation. It is proposed to simplify the simulation of a myelinated fiber nerve cell at the electrode-tissue interface by substituting for the activation site(s) identified with a more complex neuron model.

The influence of particle distribution and volume fraction on the post-necking behaviour of aluminium alloys

Experimental observations show that the continuous cast (CC) Al–Mg alloy with 0.21 wt% Fe has a considerably lower fracture strain than that of a CC alloy with 0.08 wt% Fe and a direct chill cast (DC) alloy with 0.21% Fe. However, the forming limit strains are almost the same for the three alloys. The similarities and differences are thought to relate with the distribution of hard second-phase particles. In the present paper, the influence of particle distribution characteristics (random vs. stringer pattern) and volume fraction (1.2% vs. 3.5%) is examined in detail with the use of a simple plane stress finite element unit cell model. The model permits extension of the composite stress–strain curve beyond the diffuse necking condition so that the nominally uniform response is followed directly by localized necking. The model results agree very well with tensile tests with respect to the differing behaviour of the three materials in the deformation range between the onset of diffuse necking and that for localized necking.

A Theoretical Analysis of the Influence of Fixational Instability on the Development of Thalamocortical Connectivity

Under natural viewing conditions, the physiological instability of visual fixation keeps the projection of the stimulus on the retina in constant motion. After eye opening, chronic exposure to a constantly moving retinal image might influence the experience-dependent refinement of cell response characteristics. The results of previous modeling studies have suggested a contribution of fixational instability to the Hebbian maturation of the receptive fields of V1 simple cells (Rucci, Edelman, & Wray, 2000; Rucci & Casile, 2004). This letter examines the origins of such a contribution. Using quasilinear models of lateral geniculate nucleus units and V1 simple cells, we derive analytical expressions for the second-order statistics of thalamocortical activity before and after eye opening. We show that in the presence of natural stimulation, fixational instability introduces a spatially uncorrelated signal in the retinal input, which strongly influences the structure of correlated activity in the model. This input signal produces a regime of thalamocortical activity similar to that present before eye opening and compatible with the Hebbian maturation of cortical receptive fields.

A Theoretical Analysis of the Influence of Fixational Instability on the Development of Thalamocortical Connectivity

Under natural viewing conditions, the physiological instability of visual fixation keeps the projection of the stimulus on the retina in constant motion. After eye opening, chronic exposure to a constantly moving retinal image might influence the experience-dependent refinement of cell response characteristics. The results of previous modeling studies have suggested a contribution of fixational instability to the Hebbian maturation of the receptive fields of V1 simple cells (Rucci, Edelman, & Wray, 2000; Rucci & Casile, 2004). This letter examines the origins of such a contribution. Using quasilinear models of lateral geniculate nucleus units and V1 simple cells, we derive analytical expressions for the second- order statistics of thalamocortical activity before and after eye opening. We show that in the presence of natural stimulation, fixational instability introduces a spatially uncorrelated signal in the retinal input, which strongly influences the structure of correlated activity in the model. This input signal produces a regime of thalamocortical activity similar to that present before eye opening and compatible with the Hebbian maturation of cortical receptive fields.

Nonlinear Viscoelastic Analysis of Composites using Competing Micromechanical Models

Micromechanical models for a study of nonlinear viscoelastic (NVE) response of composite laminae are developed and their performance compared. A single integral constitutive law proposed by Schapery and subsequently generalized to multiaxial states of stress is utilized in the study for the matrix material. This is used in conjunction with a computationally facile scheme in which hereditary strains are computed using a recursive relation suggested by Henriksen. Composite response is studied using two competing micromodels, a simplified square cell model (SSCM) and a finite element based self-consistent cylindrical model (FECM). The algorithm is developed assuming that the material response computations are carried out in a module attached to a general purpose finite element program used for composite structural analysis. It is shown that the SSCM as used in investigations of material nonlinearity can involve significant errors in the prediction of transverse Young’s modulus and shear modulus. The errors in the elastic strains thus predicted are of the same order of magnitude as the creep strains accruing due to viscoelasticity. The FECM on the other hand does appear to perform better both in the prediction of elastic constants and the study of creep response.