scholarly journals A MULTIPHASE MULTISCALE MODEL FOR NUTRIENT-LIMITED TISSUE GROWTH, PART II: A SIMPLIFIED DESCRIPTION

2019 ◽  
Vol 61 (4) ◽  
pp. 368-381
Author(s):  
E. C. HOLDEN ◽  
S. J. CHAPMAN ◽  
B. S. BROOK ◽  
R. 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.

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 Classification and stability of global inhomogeneous solutions of a macroscopic model of cell motion

2012 ◽  
Vol 238 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Richard Gejji ◽  
Bogdan Kazmierczak ◽  
Mark Alber
Keyword(s):  
Macroscopic Model ◽  
Cell Motion

A Multiscale Model of Composite Failure Under Impact

2006 ◽  
Author(s):  
Caglar Oskay ◽  
Jacob Fish
Keyword(s):  
Mesoscale Model ◽  
Computational Cost ◽  
Expansion Method ◽  
Multiple Scale ◽  
Multiscale Model ◽  
Field Analysis ◽  
Computationally Efficient ◽  
Composite Failure ◽  
Homogenization Approach ◽  
Transformation Field Analysis

We present a new computationally efficient mesoscale model aimed at predicting the dominant characteristics of failure at the microstructural level. This method combines the multiple scale asymptotic expansion method with the generalized transformation field analysis (GTFA) to reduce the computational cost of the direct homogenization approach. A computational validation methodology was devised for the validation of the proposed mesoscale model against experimental data. The proposed validation methodology permits incorporation of various types of experiments to the validation process by employing an experiment simulator repository.

Spatially resolved modelling of immune responses following a multiscale approach: from computational implementation to quantitative predictions

2019 ◽  
Vol 34 (5) ◽  
pp. 253-260 ◽  
Author(s):  
Dmitry S. Grebennikov ◽  
Gennady A. Bocharov
Keyword(s):  
Cell Migration ◽  
Hiv Infection ◽  
Initial Boundary ◽  
Multiscale Model ◽  
Euler Method ◽  
Reaction Diffusion Equations ◽  
Target Cells ◽  
Multiscale Approach ◽  
Type I ◽  
Computational Implementation

Abstract In this work we formulate a hybrid multiscale model for describing the fundamental immune processes in human immunodeficiency type 1 (HIV) infection. These include (i) the T cell migration in the lymphoid tissue, (ii) the replication cycle of HIV within an infected cell, (iii) the type I interferon (IFN) response of the target cells, and (iv) the spatiotemporal dynamics of the HIV and type I IFN fields. Computational implementation of the hybrid multiscale model is presented. It is based on the use of semi-implicit first-order symplectic Euler method for solving the equations of the second Newton’s law for cell migration and the alternating direction method for the initial-boundary value problem for reaction–diffusion equations governing the spatial evolution of the virus and IFN fields in 2D domain representing the lymph node (LN) tissue. Both, the stochastic and deterministic descriptions of the intracellular HIV infection and the IFN reaction are developed. The potential of the calibrated multiscale hybrid model is illustrated by predicting the dynamics of the local HIV infection bursts in LN tissue.

scholarly journals Modelling cell guidance and curvature control in evolving biological tissues

2020 ◽  
Author(s):  
Solene G.D. Hegarty-Cremer ◽  
Matthew J. Simpson ◽  
Thomas L. Andersen ◽  
Pascal R. Buenzli
Keyword(s):  
Mathematical Model ◽  
Moving Boundary ◽  
Particle Method ◽  
Biological Tissues ◽  
Tissue Growth ◽  
Tissue Properties ◽  
Front Tracking Method ◽  
Cell Guidance ◽  
Cell Motion ◽  
Curvature Control

AbstractTissue geometry is an important influence on the evolution of many biological tissues. The local curvature of an evolving tissue induces tissue crowding or spreading, which leads to differential tissue growth rates, and to changes in cellular tension, which can influence cell behaviour. Here, we investigate how directed cell motion interacts with curvature control in evolving biological tissues. Directed cell motion is involved in the generation of angled tissue growth and anisotropic tissue material properties, such as tissue fibre orientation. We develop a new cell-based mathematical model of tissue growth that includes both curvature control and cell guidance mechanisms to investigate their interplay. The model is based on conservation principles applied to the density of tissue synthesising cells at or near the tissue’s moving boundary. The resulting mathematical model is a partial differential equation for cell density on a moving boundary, which is solved numerically using a hybrid front-tracking method called the cell-based particle method. The inclusion of directed cell motion allows us to model new types of biological growth, where tangential cell motion is important for the evolution of the interface, or for the generation of anisotropic tissue properties. We illustrate such situations by applying the model to simulate both the resorption and infilling components of the bone remodelling process, and provide user-friendly MATLAB code to implement the algorithms.

scholarly journals A MULTIPHASE MODEL OF TUMOR AND TISSUE GROWTH INCLUDING CELL ADHESION AND PLASTIC REORGANIZATION

2011 ◽  
Vol 21 (09) ◽  
pp. 1901-1932 ◽  
Author(s):  
LUIGI PREZIOSI ◽  
GUIDO VITALE
Keyword(s):  
Chemical Cues ◽  
Deformation Gradient ◽  
Mixture Theory ◽  
Tissue Growth ◽  
Bond Rupture ◽  
Multiphase Model ◽  
Interaction Forces ◽  
Pde Model ◽  
Cellular Components ◽  
Cellular Constituent

The main aim of the paper is to embed the experimental results recently obtained studying the detachment force of single adhesion bonds in a multiphase model developed in the framework of mixture theory. In order to do that the microscopic information is upscaled to the macroscopic level to describe the dependence of some crucial terms appearing in the PDE model on the sub-cellular dynamics involving, for instance, the density of bonds on the membrane, the probability of bond rupture and the rate of bond formation. In fact, adhesion phenomena influence both the interaction forces among the constituents of the mixtures and the constitutive equation for the stress of the cellular components. Studying the former terms a relationship between interaction forces and relative velocity is found. The dynamics presents a behavior resembling the transition from epithelial to mesenchymal cells or from mesenchymal to ameboid motion, though the chemical cues triggering such transitions are not considered here. The latter terms are dealt with using the concept of evolving natural configurations consisting in decomposing in a multiplicative way the deformation gradient of the cellular constituent distinguishing the contributions due to growth, to cell rearrangement and to elastic deformation. This allows the description of situations in which if in some points the ensemble of cells is subject to a stress above a threshold, then locally some bonds may break and some others may form, giving rise to an internal reorganization of the tissue that allows to relax exceedingly high stresses.

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