Applications of Computational Modelling and Simulation of Porous Medium in Tissue Engineering

German, Carrie; Madihally, Sundararajan V.

doi:10.3390/computation4010007

Cited by 12 publications

(4 citation statements)

References 35 publications

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“…These approaches are computationally much cheaper than a full simulation of flow within the pores and do not require detailed knowledge of the microstructure. Due to the complexity of growing tissue in vitro, and the wealth of biochemical and biophysical processes involved over a range of spatial and temporal scales, many different theoretical models exist in the literature (German and Madihally, 2016). These models result in partial differential equations for the dependent variables, such as cell density and fluid velocity, with constitutive assumptions describing the interactions between these variables.…”

Section: Introductionmentioning

confidence: 99%

Lattice and continuum modelling of a bioactive porous tissue scaffold

Krause

Beliaev

Gorder

et al. 2018

Mathematical Medicine and Biology: A Journal of the IMA

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A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

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Section: Introductionmentioning

confidence: 99%

Lattice and continuum modelling of a bioactive porous tissue scaffold

Krause

Beliaev

Gorder

et al. 2018

Mathematical Medicine and Biology: A Journal of the IMA

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“…Permeability of collagens and other porous scaffolds reduces at compressive stresses [ 74 ] and is reasonably expected to increase when tensile forces are applied to the scaffold volume. The case of compression is well studied for diffusion of fluids through porous scaffold in tissue engineering and study biomechanics of biomaterials in Orthopedics [ 74 ], [ 75 ]. The data obtained by these researchers can be used as an indication of ECM permeability for cells, as function of stress.…”

Section: In Silico Modelmentioning

confidence: 99%

Cell – extracellular matrix interaction in glioma growth. In silico model

Kalinin¹

2020

Journal of Integrative Bioinformatics

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The study aims to investigate the role of viscoelastic interactions between cells and extracellular matrix (ECM) in avascular tumor growth. Computer simulations of glioma multicellular tumor spheroid (MTS) growth are being carried out for various conditions. The calculations are based on a continuous model, which simulates oxygen transport into MTS; transitions between three cell phenotypes, cell transport, conditioned by hydrostatic forces in cell–ECM composite system, cell motility and cell adhesion. Visco-elastic cell aggregation and elastic ECM scaffold represent two compressible constituents of the composite. Cell–ECM interactions form a Transition Layer on the spheroid surface, where mechanical characteristics of tumor undergo rapid transition. This layer facilitates tumor progression to a great extent. The study demonstrates strong effects of ECM stiffness, mechanical deformations of the matrix and cell–cell adhesion on tumor progression. The simulations show in particular that at certain, rather high degrees of matrix stiffness a formation of distant multicellular clusters takes place, while at further increase of ECM stiffness subtumors do not form. The model also illustrates to what extent mere mechanical properties of cell–ECM system may contribute into variations of glioma invasion scenarios.

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“…Free convection in permeable enclosure has gained major attention in past years due to its numerous applications in medical, engineering, geophysics and industries such as circulatory system, biomass transport, cooling of electronic equipment, combustion technology, thermal insulation of buildings, solar energy systems, petroleum reservoir, energy storage, deep bed filtration, solar air heater, reduction of aerodynamic noise, greenhouses and geothermal reservoirs [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Many researchers have adopted experimental, numerical and theoretical approaches to explore fluid flow and thermal distribution in several porous cavity.…”

Section: Introductionmentioning

confidence: 99%

Impact of uniform and non-uniform heated rods on free convective flow inside a porous enclosure: finite element analysis

et al. 2021

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A numerical study of laminar natural convective flow in a porous rectangular cavity having two heated rods is performed in this article. Both heated rods are placed in the middle of the cavity. Further, it is assumed that the flow and isothermal contours are influenced by permeable medium. Physical laws transform this physical setup into the mathematical form, which is expressed as partial differential equation. Finite element method is adopted to get the solution of these partial differential equations, the results against various flow controlling variables are presented in contour plots and line graphs. Results illustrate that in the case of non-uniform heating, the heat transfer rate is suppressed with the enhancement Rayleigh parameter as compared to uniform heating. In addition, with the increase in heated length of rods, flow field gets stronger due to stronger buoyancy effects. Moreover, the velocity distribution and Nusselt number are enhanced with the rise of permeability of porous medium.

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Applications of Computational Modelling and Simulation of Porous Medium in Tissue Engineering

Cited by 12 publications

References 35 publications

Lattice and continuum modelling of a bioactive porous tissue scaffold

Lattice and continuum modelling of a bioactive porous tissue scaffold

Cell – extracellular matrix interaction in glioma growth. In silico model

Impact of uniform and non-uniform heated rods on free convective flow inside a porous enclosure: finite element analysis

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