Migration Velocity Research Articles

A phase-field study on interaction process of moving grain boundary and spinodal decomposition

The grain boundary-directed spinodal decomposition has a substantial effect on the microstructure and properties of polycrystalline materials. However, due to the fact that the spinodal decomposition is usually too fast to be captured in experiments, our understanding of the grain boundary-directed spinodal decomposition process is still very limited. In this work, we simulate the spinodal decomposition process of a polycrystalline system by the phase-field model, check the influences of the curvature and the atom diffusion constant inside the grain boundary (<i>M</i><sub>t</sub>) on the phase decomposition patterns, and discuss the interaction between the moving grain boundaries and spinodal decomposition. The simulation results indicate that the velocity of spinodal decomposition near the grain boundary is faster, and the spinodal morphology at the grain boundary presents the anisotropic bicontinuous microstructures different from the isotropic continuous microstructures in the bulk phase. Further, we find that the spinodal pattern is parallel to the grain boundaries with larger curvatures, and it will perpendicular to the grain boundaries with smaller curvatures. We also find that the spinodal decomposition velocity increases with the augment of <i>M</i><sub>t</sub> , while the grain boundary migration velocity will first decrease and then increase with the augment of <i>M</i><sub>t</sub> under the effect of spinodal decomposition. Finally, we simulate the spinodal decomposition process of two-grain system in three dimensions, and we obtain the results consistent with the two-dimensional simulations.

Maintaining the PM Removal Efficiency of a Two-Stage ESP With External Ion-Injection Discharge via a Water Film on the Collection Plate and Cleaning of the Ionizer

A two-stage electrostatic precipitator (ESP) with a reduced footprint, external ion-injection discharge, and water film on the collection plate was developed for long-term operation. For optimal particulate matter (PM) removal efficiency, the ionizer of the external ion injection system was fixed at a distance of 5 mm from the bias plate. Under these operating conditions, the 0.3- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m PM (PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.3</sub> ) removal efficiency was reduced to approximately 70% due to low migration velocity. The application of an additional collection plate extended the residence time of the charged particles in the electric field, which resulted in a removal efficiency exceeding 95%. However, long-term operation (675 min) of the two-stage ESP with external ion-injected discharge resulted in spark generation due to contamination of the ionizer, and the PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> and PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> removal efficiencies decreased linearly from 80.4% to 62.2% and 87.7% to 68.2%, respectively. Changing the ionizer to a pin shape with electrical specifications similar to those of carbon fibers resulted in water film formation on the collection plate. The PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> and PM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> removal efficiencies remained at their initial levels for 120 min. The two-stage ESP with external ion-injected discharge operating with a water film is likely suitable for long-term operation in an industrial setting.

High-Resolution Velocity Model Building Based on Common-Source Migration Images and Convolutional Neural Networks

Building a reliable velocity model plays a vital role in seismic imaging and quantitative reservoir description. However, the current data-driven deep-learning-based velocity model building (VMB) approaches directly reconstruct the velocity model of the subsurface from prestack seismic recordings, which are very sensitive to the noise and amplitude mismatch in the data domain. In this letter, we propose a novel VMB approach based on common-source migration image gathers (CSMIGs) and convolutional neural networks (CNNs). The proposed CNN architecture uses the CSMIGs reconstructed by the reverse time migration approach and migration velocity model as the input data. It aims to capture the nonlinear relationship between the amplitude and phase information of CSMIGs and the optimal subsurface reflectivity model. Trained with realistic subsurface models, it can determine that the VMB approach is a computationally efficient solution for a high-resolution velocity reconstruction. In addition, the proposed approach has a better reconstruction performance, antinoise ability, and can be generalized much more easily than the data-driven VMB approach.

Short- and medium-chain chlorinated paraffins in green tea from 11 Chinese provinces and their migration from packaging

Chlorinated paraffins (CPs) have been found to occur ubiquitously in foodstuff of both animal and plant origin. However, limited information is available on the content of CPs in green tea, one of the most commonly consumed beverages worldwide. Herein, 107 commercial green tea samples originating from 11 provinces of China, were collected to study the occurrence of short- and medium-chain chlorinated paraffins (SCCPs and MCCPs, respectively). The concentration of SCCPs in all green tea samples ranged from 4.99 to 717 ng/g (mean: 55.7 ng/g), while MCCPs ranged from 2.55 to 543 ng/g (mean: 33.5 ng/g). CP profiles in green tea samples from different provinces exhibited no regional differences. To identify the potential sources of CPs in green tea, 19 tea packaging samples were collected and analyzed, showing that SCCPs and MCCPs existed at much higher concentrations in the tea packaging material than in the teas. Migration tests indicated that CPs could migrate from packaging into teas during storage, with the migration velocity and efficiency of SCCPs being higher than MCCPs.

Nanofiber curvature with Rho GTPase activity increases mouse embryonic fibroblast random migration velocity.

Mechanotransduction arises from information encoded in the shape of materials such as curvature. It induces activation of small GTPase signaling affecting cell phenotypes including differentiation. We carried out a set of preliminary experiments to test the hypothesis that curvature (1/radius) would also affect cell motility due to signal pathway crosstalk. High molecular weight poly (methyl methacrylate) straight nanofibers were electrospun with curvature ranging from 41 to 1μm-1 and collected on a passivated glass substrate. The fiber curvature increased mouse mesenchymal stem cell aspect ratio (P < 0.02) and decreased cell area (P < 0.01). Despite little effect on some motility patterns such as polarity and persistence, we found selected fiber curvatures can increase normalized random fibroblastic mouse embryonic cell (MEF) migration velocity close to 2.5 times compared with a flat surface (P < 0.001). A maximum in the velocity curve occurred near 2.5μm-1 and may vary with the time since initiation of attachment to the surface (range of 0-20h). In the middle range of fiber curvatures, the relative relationship to curvature was similar regardless of treatment with Rho-kinase inhibitor (Y27632) or cdc42 inhibitor (ML141), although it was decreased on most curvatures (P < 0.05). However, below a critical curvature threshold MEFs may not be able to distinguish shallow curvature from a flat surface, while still being affected by contact guidance. The preliminary data in this manuscript suggested the large low curvature fibers were interpreted in a manner similar to a non-curved surface. Thus, curvature is a biomaterial construct design parameter that should be considered when specific biological responses are desired. Statement of integration, innovation, and insight Replacement of damaged or diseased tissues that cannot otherwise regenerate is transforming modern medicine. However, the extent to which we can rationally design materials to affect cellular outcomes remains low. Knowing the effect of material stiffness and diameter on stem cell differentiation, we investigated cell migration and signaling on fibrous scaffolds. By investigating diameters across orders of magnitude (50-2000nm), we identified a velocity maximum of ~800nm. Furthermore, the results suggest large fibers may not be interpreted by single cells as a curved surface. This work presents insight into the design of constructs for engineering tissues.

Numerical analysis of velocity field and energy transformation, and prediction model for Taylor bubbles in annular slug flow of static power law fluid

Considering the rheological constitutive model and flow-control equation of the fluid around a Taylor bubble in an annulus, a prediction model of the flow field around the Taylor bubble is proposed. Combined with the flow-field distribution around a bubble, an energy-dissipation model for Taylor bubbles in an annulus is also established. Based on an analysis of the energy conservation, a unified prediction model for Taylor bubble migration in an annulus is developed by coupling the bubble-shape prediction model, flow-field prediction model around the bubble, and energy-dissipation model. Moreover, we independently develop a simulation program. Through a comparative analysis of the literature data, it was found that the prediction error of the migration velocity was less than 8%. The results of the energy dissipation demonstrate that the energy dissipation in the liquid-film region and fluid-viscosity dissipation are the key factors limiting the increase in bubble rising velocity.

Influence of MnS inclusions on dynamic recrystallization and annealing twins formation during thermal deformation

The existence of MnS inclusions during thermal deformation affects the dynamic recrystallization (DRX) behavior and twinning evolution of FCC matrix. In this study, we conducted thermal compression experiments on two sets of materials which are MnS-containing and non MnS-containing specimens, respectively. The mechanism of the influence of MnS inclusions on the dynamic recrystallization behavior of the matrix is revealed. The effect of MnS inclusions on the formation of annealed twins during dynamic recrystallization is clarified from the perspective of plastic deformation of MnS inclusions. The results show that the recrystallization behavior of MnS-containing materials are dominated by DDRX, but assisted by PSN and CDRX. Due to the severe plastic deformation and inhomogeneous deformation of MnS inclusions, the uncoordinated deformation between MnS inclusions and matrix cause the unevenly distributed stress and strain at the interface which provides a higher energy storage for the formation of the twin boundaries during DRX process. According to the growth accident model, the PSN mechanism induced by MnS inclusions produces new grains containing twin boundaries in the DRX nucleation stage, leading to the increase of nucleation rate of the twin boundaries. The faster grain boundary migration velocity promotes the nucleation and progression of twins adjacent to MnS inclusions in the DRX growth stage, thereby increasing the density of twin boundaries. Finally, the evolution of annealed twinning near the MnS inclusions during dynamic recrystallization is elucidated in detail.

Elastic depth trends for siliciclastic sequences

Elastic depth trends are an integral component of reservoir characterization whether explicitly or implicitly constructed. Applications to seismic data include migration velocity model building, pore-pressure prediction, inversion, and amplitude-variation-with-offset (AVO) analysis. In practice, workflows often involve fitting well logs with smooth curves, without reference to known lithology-dependent templates that could provide realistic constraints. We have constructed porosity-depth trends for shales and sandstones with reference to reliable measurements that span mechanical compaction and chemical diagenesis domains. These porosity trends are then used as inputs to well-established rock-physics models to estimate the median and bounding trends for acoustic and shear impedance. The resulting modeling has shown an important sensitivity to the pore-pressure regime (notably in shales) and the onset of cementation (in sands), among other variables. AVO predictions made from these trends provide a useful reference frame for anomaly prediction with depth, which is critical in frontier exploration.

Gα13 Mediates Transendothelial Migration of Neutrophils by Promoting Integrin-Dependent Motility without Affecting Directionality.

Neutrophil migration requires β2 integrins and chemoattractant receptor signaling for motility and directionality. G protein subunit Gα13 can facilitate cell migration by mediating RhoA activation induced by G protein-coupled receptors. However, the possible role of Gα13-integrin interaction in migration is unclear. In this study, we show that Gα13 -/- neutrophils are deficient in transendothelial migration and migration on β2 integrin ligand ICAM-1. However, unlike G protein-coupled receptors and integrin inside-out signaling pathways, Gα13 is important in migration velocity and neutrophil spreading but not in directionality nor cell adhesion. Importantly, neutrophil recruitment in vivo was also inhibited in Gα13 -/- mice, suggesting the importance of Gα13 in transendothelial migration of neutrophils in vitro and in vivo. Furthermore, a synthetic peptide (MB2mP6) derived from the Gα13 binding site of β2 inhibited Gα13-β2 interaction and Gα13-mediated transient RhoA inhibition in neutrophils, suggesting that this peptide inhibited integrin outside-in signaling. MB2mP6 inhibited migration of control neutrophils through endothelial cell monolayers or ICAM-1-coated filters, but was without further effect on Gα13 -/- neutrophils. It also inhibited integrin-dependent neutrophil migration velocity without affecting directionality. In vivo, MB2mP6 markedly inhibited neutrophil infiltration into the cardiac tissues induced by ischemia/reperfusion injury. Thus, Gα13-dependent outside-in signaling enables integrin-dependent neutrophil motility without affecting directionality and may be a new therapeutic target for inhibiting neutrophil trafficking but not adhesion.

Cell-Projection Pumping of Fibroblast Contents into Osteosarcoma SAOS-2 Cells Correlates with Increased SAOS-2 Proliferation and Migration, as well as Altered Morphology.

We earlier reported that cell-projection pumping transfers fibroblast contents to cancer cells and this alters the cancer cell phenotype. Here, we report on single-cell tracking of time lapse recordings from co-cultured fluorescent fibroblasts and SAOS-2 osteosarcoma cells, tracking 5201 cells across 7 experiments. The fluorescent lipophilic marker DiD was used to label fibroblast organelles and to trace the transfer of fibroblast cytoplasm into SAOS-2 cells. We related SAOS-2 phenotypic change to levels of fluorescence transfer from fibroblasts to SAOS-2 cells, as well as what we term ‘compensated fluorescence’, that numerically projects mother cell fluorescence post-mitosis into daughter cells. The comparison of absolute with compensated fluorescence allowed us to deduct if the phenotypic effects in mother SAOS-2 cells were inherited by their daughters. SAOS-2 receipt of fibroblast fluorescence correlated by Kendall’s tau with cell-profile area and without evidence of persistence in daughter cells (median tau = 0.51, p < 0.016); negatively and weakly with cell circularity and with evidence of persistence (median tau = −0.19, p < 0.05); and very weakly with cell migration velocity and without evidence of persistence (median tau = 0.01, p < 0.016). In addition, mitotic SAOS-2 cells had higher rates of prior fluorescence uptake (median = 64.9 units/day) than non-dividing cells (median = 35.6 units/day, p < 0.016) and there was no evidence of persistence post-mitosis. We conclude that there was an appreciable impact of cell-projection pumping on cancer cell phenotype relevant to cancer histopathological diagnosis, clinical spread and growth, with most effects being ‘reset’ by cancer cell mitosis.

Moment equations for partial filling capillary electrophoresis.

Moment equations were developed for partial filling CE systems, in which solute dissolution phenomena by spherical molecular assemblies or intermolecular interactions take place. Because experimental conditions of partial filling CE are divided into five categories on the basis of the magnitude relationship between the migration velocity of solute molecules and that of molecular assemblies or ligand molecules, the moment equations were systematically developed for each case by using the Einstein equation for diffusion and the random walk model. In order to demonstrate the effectiveness of the moment equations, they were applied to the analysis of partial filling CE behavior, which is correlated with dissolution phenomena of small solute molecules into spherical molecular assemblies as specific examples. Simulation results only in the case that the migration velocity of solute molecules is faster than that of molecular assemblies were represented in this paper. Detailed explanations about the derivation procedure of the moment equations and the simulation results in other cases can be found in the Supporting Information. The moment equations are theoretical bases for applying partial filling CE to the study on solute permeation kinetics at the interface of spherical molecular assemblies and on reaction kinetics of intermolecular interactions.

Retention and transport behavior of microplastic particles in water-saturated porous media

Microplastic (MP) pollution has become a global concern given its wide occurrence and potential ecological risks. The retention/transport features of MPs in porous media govern the fate and risks of MPs in subsurface environments. Polystyrene (PS) microspheres are employed as representative MPs to explore the migration behaviors in water-saturated quartz sand columns. The hydrodynamic size mainly determines the deposition and size exclusion straining of MPs in porous media, and further the attachment efficiency. PS50 (PS with 50 nm diameter) shows a total migration rate greater than 85% in each of the studied conditions. In contrast, PS500 commonly exhibits slower migration velocities and higher attachment efficiencies than those of PS50 and PS100. The ionic strength, pH, and dissolved organic matter content of the solution show obvious effects on the retention/transport of PS MPs. The influences of solution chemical properties are consistent with the prediction of Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The results in this study clarify the size-dependent migration characteristics of MPs in porous media and provide a basis for risk assessment of MPs in terrestrial environments.

Molecular dynamics study of the influence of uniaxial deformation on the migration velocity of tilt boundaries in nickel

The molecular dynamics method was used to study the influence of elastic uniaxial deformation on the migration velocity of tilt boundaries with misorientation axes [100] and [111] in nickel. The dependences of the migration velocity at a temperature of 1600 K on the misorientation angle were obtained. It is shown that the high-angle [100] and [111] tilt boundaries migrate at approximately the same velocity, while the low-angle [111] boundaries migrate approximately twice as fast as the [100] boundaries. The obtained dependences of the migration velocity of the boundaries on the value of uniaxial deformation in almost all cases turned out to be nonmonotonic and had a maximum at a tension value of about 1%. With a further increase in tension, migration slowed down, which is most likely explained by a decrease in the surface tension of the boundaries and, accordingly, in the driving force due to the finite sorption capacity of grain boundaries with respect to the free volume. Under elastic compression, in most cases, a monotonic decrease in the migration velocity was observed, which is due to a decrease in free space during compression and a decrease in the mobility of atoms at the boundary.

Thermocapillary effects on viscoelastic drops suspended in axisymmetric pressure driven flows

Dynamics and deformation of a viscoelastic drop in another immiscible viscoelastic medium in the presence of externally imposed pressure and temperature gradients are analyzed asymptotically in the present work. Both of the phases obey the linear Phan–Thien–Tanner constitutive model, capable of accounting for shear thinning behavior in polymeric fluids. The first two asymptotic corrections to the leading order Newtonian behavior are reported here, in the limit of small Deborah and Capillary numbers, which, respectively, characterize the extent of viscoelasticity and interfacial deformation. We establish that the viscoelastic properties of the inner phase strongly influence the migration velocity and the interfacial deformation of the drop. Our analysis reveals the possibility of realizing a maximum migration velocity for an intermediate viscosity of the interior phase, provided it has stronger viscoelastic characteristics than the suspending medium. We further compute the critical thermal gradient required to completely arrest the drop's motion and demonstrate that the same depends on the Deborah number as well as the viscosity of the inner phase. The viscoelastic stresses also dictate the deformation as the drop's shape changes from prolate to oblate when those stresses become significant. Our results may find potential applications in areas such as polymer processing and handling of biologically relevant media in medical diagnostics.

The ejection of large non-oscillating droplets from a hydrophobic wedge in microgravity

When confined within containers or conduits, drops and bubbles migrate to regions of minimum energy by the combined effects of surface tension, surface wetting, system geometry, and initial conditions. Such capillary phenomena are exploited for passive phase separation operations in micro-fluidic devices on earth and macro-fluidic devices aboard spacecraft. Our study focuses on the migration and ejection of large inertial-capillary drops confined between tilted planar hydrophobic substrates (a.k.a., wedges). In our experiments, the brief nearly weightless environment of a 2.1 s drop tower allows for the study of such capillary dominated behavior for up to 10 mL water drops with migration velocities up to 12 cm/s. We control ejection velocities as a function of drop volume, substrate tilt angle, initial confinement, and fluid properties. We then demonstrate how such geometries may be employed as passive no-moving-parts droplet generators for very large drop dynamics investigations. The method is ideal for hand-held non-oscillatory ‘droplet’ generation in low-gravity environments.

Exploring the interplay between cellular development and mechanics in the developing human brain

AbstractThe human brain has a complex structure on both cellular and organ scales. This structure is closely related to the brain's abilities and functions. Disruption of one of the biological processes occurring during brain development on the cellular scale may affect the cortical folding pattern of the brain on the organ scale. However, the link between disruptions in cellular brain development and associated cortical malformation remains largely unknown. From a mechanical perspective, the forces generated during development lead to mechanical instability and, eventually, the mergence of cortical folds. To fully understand mechanism underlying malformations of cortical development, it is key to consider both the events that occur on the cellular scale and the mechanical forces generated on the organ scale. Here we present a computational model describing cellular division and migration on the cellular scale, as well as growth and cortical folding on the tissue or organ scale, in a continuous way by a coupled finite growth and advection‐diffusion model. We introduce the cell density as an independent field controlling the volumetric growth. Furthermore, we formulate a positive relation between cell density and cortical layer stiffness. This allows us to study the influence of the migration velocity, the cell diffusivity, the local stiffness, and the local connectivity of cells on the cortical folding process and mechanical properties during normal and abnormal brain development numerically. We show how an increase in the density of the neurons increases the layer's mechanical stiffness. Moreover, weWe validate our simulation results through the comparison with histological sections of the fetal human brain. The current model aims to be a first step towards providing a reliable platform to systematically evaluate the role of different cellular events on the cortical folding process and vice versa.

The gravity-driven migration of a drop in an unsteady Stokes flow

The motion of a spherical droplet through a fluid driven by gravity is revisited theoretically. Analytical expressions for the translational velocity of the droplet as well as its internal and external flows coupled at their interface and described by the unsteady Stokes equations are derived combining two-point Padé and Padé-type approximants with the Laplace transform. These expressions, involving scaled complementary error functions, are fast and globally convergent to the exact solutions of the equations. The migration of the droplet depends on three non-dimensional parameters, two of which determine the flow patterns inside and outside, and the last is related to the timescale. The analytical solutions reveal that there is a diffusive shear layer of thickness O(t) on either side of the interface in the early stage. Several plots are made to compare migration velocities of the droplet for different parameter sets and changes in the flow field with time.

The Influence of Sediment Transport on Stationary and Mobile Knickpoints in River Profiles

AbstractThe analysis of stationary and mobile knickpoints has been one of the most powerful concepts in tectonic geomorphology for decades. While several models combining bedrock incision and sediment transport are available, the existing theory of knickpoints focuses on detachment‐limited erosion without consideration of sediment transport. On the other hand, fully transport‐limited systems do not maintain distinct knickpoints. This study addresses the existence and the properties of slope‐break knickpoints in fluvial systems between the two extremes with the help of the shared stream‐power model, which allows for a continuous shift between detachment‐limited and transport‐limited erosion. The most important result is that both stationary and mobile knickpoints remain sharp and are not smeared by sediment transport. The system responds to tectonic signals in two phases where the first phase is similar to the detachment‐limited model. Comparing rivers with the same equilibrium profile at a given uplift rate, the velocity of knickpoint migration increases toward transport‐limited conditions. The second phase of the response is dominated by changes in sediment flux and affects the entire river segment downstream of the mobile knickpoint including the fault where the tectonic signal was initiated. During this phase, the mobile knickpoint is flattened in the sense that the difference in steepness index across a slope‐break knickpoint decreases through time. It is also shown that large parts of the theory for the nonlinear model, in particular knickpoint sharpening and stretching, remain valid, but the effect of nonlinearity decreases with increasing contribution of sediment transport.

MigraR: An open-source, R-based application for analysis and quantification of cell migration parameters

Background and objective: Cell migration is essential for many biological phenomena with direct impact on human health and disease. One conventional approach to study cell migration involves the quantitative analysis of individual cell trajectories recorded by time-lapse video microscopy. Dedicated software tools exist to assist the automated or semi-automated tracking of cells and translate these into coordinate positions along time. However, cell biologists usually bump into the difficulty of plotting and computing these data sets into biologically meaningful figures and metrics. Methods: This report describes MigraR, an intuitive graphical user interface executed from the RStudioTM (via the R package Shiny), which greatly simplifies the task of translating coordinate positions of moving cells into measurable parameters of cell migration (velocity, straightness, and direction of movement), as well as of plotting cell trajectories and migration metrics. One innovative function of this interface is that it allows users to refine their data sets by setting limits based on time, velocity and straightness. Results: MigraR was tested on different data to assess its applicability. Intended users of MigraR are cell biologists with no prior knowledge of data analysis, seeking to accelerate the quantification and visualization of cell migration data sets delivered in the format of Excel files by available cell-tracking software. Conclusions: Through the graphics it provides, MigraR is an useful tool for the analysis of migration parameters and cellular trajectories. Since its source code is open, it can be subject of refinement by expert users to best suit the needs of other researchers. It is available at GitHub and can be easily reproduced.

Modeling and simulation of cell migration on the basis of force equilibrium.

To study cell behavior, we developed a cell model to simulate cell movements and the interacting forces among cells and between cells and obstacles. The developed model simulates several cells simultaneously and examines correlations among characteristic parameters between cells and substrates during migration. We modified Odde's model to develop fundamental model, applied Gillespie's stochastic algorithm to design time during in the migration simulation, and employed Keren's membrane theory to analyze the equilibrium at the leading edges. Thus, the proposed model can analyze stresses due to substrate, the intracellular body, and the external interaction between cells and obstacles. Simulation results indicate that cell-cell interaction depends on the equilibrium between the forces at the leading edge of the membrane, namely the cell-substrate interaction force, cell-cell interaction forces, and the cell membrane force. These results also indicate that the migration direction is dependent on the resultant forces. The membrane force and substrate force directions are "low correlation," and the polymerization rate exhibits "little correlative" with the migration direction. We propose a modified cell migration model for simulating allocation and interaction among multiple cells. This model helps indicate the weightings of characteristic parameters that affect the cell migration direction and velocity.