Mathematical model and numerical simulation of the cell growth in scaffolds

Abstract

A scaffold is a three-dimensional matrix that provides a structural base to fill tissue lesion and provides cells with a suitable environment for proliferation and differentiation. Cell-seeded scaffolds can be implanted immediately or be cultured in vitro for a period of time before implantation. To obtain uniform cell growth throughout the entire volume of the scaffolds, an optimal strategy on cell seeding into scaffolds is important. We propose an efficient and accurate numerical scheme for a mathematical model to predict the growth and distribution of cells in scaffolds. The proposed numerical algorithm is a hybrid method which uses both finite difference approximations and analytic closed-form solutions. The effects of each parameter in the mathematical model are numerically investigated. Moreover, we propose an optimization algorithm which finds the best set of model parameters that minimize a discrete l(2) error between numerical and experimental data. Using the mathematical model and its efficient and accurate numerical simulations, we could interpret experimental results and identify dominating mechanisms.

Design, Materials, and Mechanobiology of Biodegradable Scaffolds for Bone Tissue Engineering

“… Proliferation: it is growth of cell population due to mitosis. Exponential or logistic law is usually considered here [ 153 , 155 ]. Nutrient transport and consumption: they are nutrient concentrations gradients due to cell population location and generation and disposal of waste substances.…”

“… Nutrient transport and consumption: they are nutrient concentrations gradients due to cell population location and generation and disposal of waste substances. Regarding the interaction of nutrient availability and cell proliferation reaction diffusion equations is employed as seen in [ 153 , 155 ]. Senescence: it is decrease of cell population due to apoptosis [ 184 , 208 ].…”

Application of computational fluid dynamics in tissue engineering

“…Many studies are performed using suboptimal substrates which may not have mechanical properties similar to the native tissue. There is a need to perform cell growth kinetic studies using matrices applied to tissue regeneration applications and determine corresponding rate constants (83). However, the challenge is to accurately measure the rate constants in 3D constructs.…”

Sensitivity Analysis for Model Comparison and Selection in Tissue Engineering

“…The properties considered in these works include porosity (Coletti et al, 2006;Yan et al, 2012), permeability (Coletti et al, 2006;Santamaría et al, 2013;Truscello et al, 2012), mean pore size (McCoy et al, 2012;Truscello et al, 2012), surface energy (Decuzzi and Ferrari, 2010), roughness (Decuzzi and Ferrari, 2010) and effective Young's modulus (Gómez-Pachón et al, 2013). Besides this, modeling techniques have also been used in the comparison of different bioreactor designs (Devarapalli et al, 2009;Hidalgo-Bastida et al, 2012;Pathi et al, 2005) and seeding techniques (Chung et al, 2010;Doagǎ et al, 2008;Jeong et al, 2012). The processes most studied in tissue development are nutrient diffusion and convection (Chung et al, 2008(Chung et al, , 2007(Chung et al, , 2006Coletti et al, 2006;Locke, 1999a, 1999b;Lin et al, 2011;Shakeel, 2011;Yan et al, 2012), cell growth (Chung et al, 2008(Chung et al, , 2007(Chung et al, , 2006Coletti et al, 2006;Locke, 1999a, 1999b;Lin et al, 2011;Shakeel, 2011;Truscello et al, 2012;Yan et al, 2012), cell adhesion strength (Decuzzi and Ferrari, 2010), morphology (McCoy et al, 2012), and cell deformation and detachment (McCoy et al, 2012).…”