  In this paper, we derive an effective macroscale description suitable to
describe the growth of biological tissue within a porous tissue-engineering
scaffold. As in our recent work (Holden \textit{et al.} "A multiphase
multiscale model for nutrient limited tissue growth", The ANZIAM Journal, 2018,
doi:10.1017/S1446181118000044) the underlying tissue dynamics is described as a
multiphase mixture, thereby naturally accommodating features such as
interstitial growth and active cell motion. Via a linearisation of the
underlying multiphase model (whose nonlinearity poses significant challenge for
such analyses), we obtain, by means of multiple-scales homogenisation, a
simplified macroscale model that nevertheless retains explicit dependence on
both the microscale scaffold structure and the tissue dynamics. The model we
obtain 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 to parameterise the macroscale description. In Holden
\textit{et al.}, the cell problems retain macroscale dependence, posing
significant computational challenges; here, we obtain a decoupled system
whereby the quasi-steady cell-problems may be solved separately from the
macroscale description, thereby greatly reducing the complexity associated with
fully-coupled multiscale descriptions. Moreover, we indicate how the
formulation is influenced by a set of alternative microscale boundary
conditions.S
