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.

Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory

2006 ◽  
Vol 52 (5) ◽  
pp. 571-594 ◽  
Author(s):  
Greg Lemon ◽  
John R. King ◽  
Helen M. Byrne ◽  
Oliver E. Jensen ◽  
Kevin M. Shakesheff
Keyword(s):  
Mathematical Modelling ◽  
Mixture Theory ◽  
Tissue Growth ◽  
Porous Flow ◽  
Engineered Tissue

A Hybrid Reactive Multiphasic Mixture with a Compressible Fluid Solvent

2021 ◽  
Author(s):  
Jay J. Shim ◽  
Gerard A. Ateshian
Keyword(s):  
Fluid Dynamics ◽  
Lagrange Multiplier ◽  
Deformation Gradient ◽  
Fluid Pressure ◽  
Volumetric Strain ◽  
Mixture Theory ◽  
Biological Tissues ◽  
Solid Matrix ◽  
State Function ◽  
Wide Range

Abstract Mixture theory is a general framework that has been used to model mixtures of solid, fluid, and solute constituents, leading to significant advances in modeling the mechanics of biological tissues and cells. Though versatile and applicable to a wide range of problems in biomechanics and biophysics, standard multiphasic mixture frameworks incorporate neither dynamics of viscous fluids nor fluid compressibility, both of which facilitate the finite element implementation of computational fluid dynamics solvers. This study formulates governing equations for reactive multiphasic mixtures where the interstitial fluid has a solvent which is viscous and compressible. This hybrid reactive multiphasic framework uses state variables that include the deformation gradient of the porous solid matrix, the volumetric strain and rate of deformation of the solvent, the solute concentrations, and the relative velocities between the various constituents. Unlike standard formulations which employ a Lagrange multiplier to model fluid pressure, this framework requires the formulation of a function of state for the pressure, which depends on solvent volumetric strain and solute concentrations. Under isothermal conditions the formulation shows that the solvent volumetric strain remains continuous across interfaces between hybrid multiphasic domains. Apart from the Lagrange multiplier-state function distinction for the fluid pressure, and the ability to accommodate viscous fluid dynamics, this hybrid multiphasic framework remains fully consistent with standard multiphasic formulations previously employed in biomechanics. With these additional features, the hybrid multiphasic mixture theory makes it possible to address a wider range of problems that are important in biomechanics and mechanobiology.

Modeling Compressive Reaction in Shock-Driven Secondary Granular Explosives

2011 ◽  
Author(s):  
Aaron L. Brundage
Keyword(s):  
Energetic Materials ◽  
Oil And Gas ◽  
Mixture Theory ◽  
Oil And Gas Industry ◽  
Department Of Energy ◽  
Multiphase Model ◽  
Gas Industry ◽  
The Us ◽  
Impact Experiments ◽  
Compaction Waves

Hexanitrostilbene (HNS) is a secondary, granular explosive with a wide usage in commercial and governmental sectors. For example, HNS is used in the aerospace industry as boosters in rockets, in the oil and gas industry in linear shaped charge designs in wellbore perforating guns, and in a number of applications in the US Department of Energy (DOE) and Department of Defense (DoD). In many of these applications, neat granules of HNS are pressed without binder and device performance is achieved with shock initiation of the powdered bed. Previous studies have demonstrated that powdered explosives do not transmit sharp shocks, but produce dispersive compaction waves. These compaction waves can induce combustion in the material, leading to a phenomenon termed Deflagration-to-Detonation Transition (DDT). The Baer-Nunziato (B-N) multiphase model was developed to predict compressive reaction in granular energetic materials due to shock and non-shock inputs using non-equilibrium multiphase mixture theory. The B-N model was fit to historical data of HNS, and this model was used to predict recent impact experiments where samples pressed to approximately 60% of theoretical maximum density (TMD) were shock loaded by high-velocity flyers [1]. Shock wave computations were performed using CTH, an Eulerian, multimaterial, multidimensional, finite-volume shock physics code developed at Sandia National Laboratories [2]. Predicted interface velocities using the B-N model were shown to be in good agreement with the measurements. Furthermore, an uncertainty quantification study was performed and the computational results are presented with best estimates of uncertainty.

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.

A Constitutive Model for Soft Tissue and its Application to a Boundary Value Problem

2013 ◽  
Author(s):  
P. Mythravaruni ◽  
Parag Ravindran
Keyword(s):  
Soft Tissue ◽  
Mixture Theory ◽  
Axial Loading ◽  
Tissue Growth ◽  
Theory Approach ◽  
Growth And Remodeling ◽  
Constrained Mixture ◽  
Set Up ◽  
And Function ◽  
Turn Over

Mechanical loading induces changes in the structure and function of soft tissue. Growth and remodeling results from the production and removal of constituents. We consider a tissue constituted of elastin and collagen. The collagen turns over at a much higher rate than elastin. In this work we propose a two-constituent, constrained mixture model for this soft tissue. One constituent is modeled as a viscoelastic material and the other as an elastic material. It is assumed that the collagen turns over depending on the stress applied and the elastin does not turn over. The standard mixture theory approach is followed and the balance equations are set-up. The model is studied in simple uni-axial loading to test its efficacy.

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.

Freeze-Fracture Replication in the Ultrastructure of Blue-Green Algae

1967 ◽  
Vol 25 ◽  
pp. 74-75
Author(s):  
L. V. Leak
Keyword(s):  
Cell Wall ◽  
Electron Microscope ◽  
Green Algae ◽  
Three Dimensional ◽  
Freeze Fracture ◽  
Electron Microscopic ◽  
Photosynthetic Membranes ◽  
Blue Green Algae ◽  
Cell Biol ◽  
Cellular Components

Electron microscopic observations of freeze-fracture replicas of Anabaena cells obtained by the procedures described by Bullivant and Ames (J. Cell Biol., 1966) indicate that the frozen cells are fractured in many different planes. This fracturing or cleaving along various planes allows one to gain a three dimensional relation of the cellular components as a result of such a manipulation. When replicas that are obtained by the freeze-fracture method are observed in the electron microscope, cross fractures of the cell wall and membranes that comprise the photosynthetic lamellae are apparent as demonstrated in Figures 1 & 2.A large portion of the Anabaena cell is composed of undulating layers of cytoplasm that are bounded by unit membranes that comprise the photosynthetic membranes. The adjoining layers of cytoplasm are closely apposed to each other to form the photosynthetic lamellae. Occassionally the adjacent layers of cytoplasm are separated by an interspace that may vary in widths of up to several 100 mu to form intralamellar vesicles.

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