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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
Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types regulated b
A continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model can include finite deformation, and
We propose a multiscale chemo-mechanical model of cancer tumour development in an epithelial tissue. The model is based on transformation of normal cells into the cancerous state triggered by a local failure of spatial synchronisation of the circadia
The electrical coupling between myocytes and fibroblasts and the spacial distribution of fibroblasts within myocardial tissues are significant factors in triggering and sustaining cardiac arrhythmias but their roles are poorly understood. This articl
The analytical theory of our earlier study (Mortensen et al. (2021), Mathematical Medicine and Biology, 38(1), pp. 106-131) is extended to address the outstanding cases of fibroblast barrier distribution and myocyte strait distribution. In particular