Two-dimensional Multiscale Model of Cell Motion in a Chemotactic Field

2007 ◽  
pp. 53-76 ◽  
Author(s):  
Mark Alber ◽  
Nan Chen ◽  
Tilmann Glimm ◽  
Pavel Lushnikov
Keyword(s):  
Multiscale Model ◽  
Two Dimensional ◽  
Cell Motion

scholarly journals Simulated Two-dimensional Red Blood Cell Motion, Deformation, and Partitioning in Microvessel Bifurcations

2008 ◽  
Vol 36 (10) ◽  
pp. 1690-1698 ◽  
Author(s):  
Jared O. Barber ◽  
Jonathan P. Alberding ◽  
Juan M. Restrepo ◽  
Timothy W. Secomb
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Two Dimensional ◽  
Cell Motion

scholarly journals A multiphase multiscale model for nutrient-limited tissue growth, Part II: a simplified description

2020 ◽  
Vol 61 ◽  
pp. 368-381
Author(s):  
Elizabeth C. Holden ◽  
S. Jonathan Chapman ◽  
Bindi S. Brook ◽  
Reuben D. O'Dea
Keyword(s):  
Multiple Scale ◽  
Multiscale Model ◽  
Tissue Growth ◽  
Macroscopic Model ◽  
Multiphase Model ◽  
Multiphase Mixture ◽  
Computational Implementation ◽  
Scaffold Structure ◽  
Interstitial Growth ◽  
Cell Motion

In this paper, we revisit our previous work in which we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearization of the underlying multiphase model (whose nonlinearity poses a significant challenge for such analyses), we obtain, by means of multiple-scale homogenization, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics, via so-called unit-cell problems that provide permeability tensors to parameterize the macroscale description. In our previous work, the cell problems retain macroscale dependence, posing significant challenges for computational implementation of the eventual macroscopic model; here, we obtain a decoupled system whereby the quasi-steady cell problems may be solved separately from the macroscale description. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions. doi:10.1017/S1446181119000130

scholarly journals A MULTIPHASE MULTISCALE MODEL FOR NUTRIENT LIMITED TISSUE GROWTH

2018 ◽  
Vol 59 (4) ◽  
pp. 499-532
Author(s):  
E. C. HOLDEN ◽  
J. COLLIS ◽  
B. S. BROOK ◽  
R. D. O’DEA
Keyword(s):  
Volume Fraction ◽  
Porous Scaffold ◽  
Multiple Scale ◽  
Multiscale Model ◽  
Tissue Growth ◽  
Active Cell ◽  
Multiphase Model ◽  
Structure And Dynamics ◽  
Interstitial Growth ◽  
Cell Motion

We derive an effective macroscale description for the growth of tissue on a porous scaffold. A multiphase model is employed to describe the tissue dynamics; linearisation to facilitate a multiple-scale homogenisation provides an effective macroscale description, which incorporates dependence on the microscale structure and dynamics. In particular, the resulting description admits both interstitial growth and active cell motion. This model comprises Darcy flow, and differential equations for the volume fraction of cells within the scaffold and the concentration of nutrient, required for growth. These are coupled with Stokes-type cell problems on the microscale, incorporating dependence on active cell motion and pore scale structure. The cell problems provide the permeability tensors with which the macroscale flow is parameterised. A subset of solutions is illustrated by numerical simulations.

scholarly journals Multiscale reactor modelling of total pressure effects on complete methane oxidation over Pd/Al2O3

2019 ◽  
Vol 9 (12) ◽  
pp. 3055-3065 ◽  
Author(s):  
Carl-Robert Florén ◽  
Per-Anders Carlsson ◽  
Derek Creaser ◽  
Henrik Grönbeck ◽  
Magnus Skoglundh
Keyword(s):  
Methane Oxidation ◽  
Total Pressure ◽  
Oxidation Reaction ◽  
Multiscale Model ◽  
Pressure Effects ◽  
Exhaust Gas ◽  
Two Dimensional

A two-dimensional multiscale model is developed to describe the complete methane oxidation reaction for simulated exhaust gas conditions.

Upscale Impact of Mesoscale Disturbances of Tropical Convection on Synoptic-Scale Equatorial Waves in Two-Dimensional Flows

2017 ◽  
Vol 74 (9) ◽  
pp. 3099-3120 ◽  
Author(s):  
Qiu Yang ◽  
Andrew J. Majda
Keyword(s):  
Potential Temperature ◽  
Leading Edge ◽  
Multiscale Model ◽  
Tropical Convection ◽  
Equatorial Waves ◽  
Two Dimensional ◽  
Shallow Convection ◽  
Synoptic Scale ◽  
Cloud Resolving Model ◽  
Moist Environment

Abstract Superclusters on the synoptic scale containing mesoscale systems are frequently organized by convectively coupled equatorial waves (CCEWs). Present-day global models struggle to simulate multiscale tropical convection, and the upscale effects of mesoscale systems are not well understood. A simple two-dimensional multiscale model with prescribed two-scale heating and eddy transfer of momentum and temperature drives the synoptic-scale circulation, successfully reproduces key features of flow fields with a front-to-rear tilt, and compares well with results from a cloud-resolving model (CRM). In the scenario with an elevated upright mean heating, the tilted vertical structure of synoptic-scale circulation is still induced by the upscale impact of mesoscale disturbances. In a faster propagation scenario, the upscale impact becomes less important as a result of competing effects of eddy transfer of momentum and temperature, while the synoptic-scale circulation response to mean heating dominates, in agreement with cloud-resolving models. In the unrealistic scenario with upward–westward-tilted mesoscale heating, positive potential temperature anomalies are induced in the leading edge, which will suppress shallow convection in a moist environment.

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