A multiphase multiscale model for nutrient limited tissue growth

Abstract

In this work, an effective macroscale description is derived 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 to underlying Stokes-type cell problems that provide permeability tensors, with multiscale dependence incorporating active cell motion, with which to parameterise the macroscale flow. A subset of solutions are illustrated by numerical simulations.

Mathematical and computational models for bone tissue engineering in bioreactor systems

“…Increasingly, however, instead of focusing on one scale, multiscale models are developed which use homogenisation multiscale asymptotics or volume averaging approaches to derive averaged models determined by micro-scale features. 48–50 A good introduction into the theory can be found in the study of Davit et al 51 Such multiscale models can have either a discrete or continuous formulation at the micro-scale and are continuous at the macro-scale.…”