A multiphase multiscale model for nutrient limited tissue growth
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 dep...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Published: |
Cambridge University Press
2018
|
| Online Access: | https://eprints.nottingham.ac.uk/49326/ |
| _version_ | 1848797973803171840 |
|---|---|
| author | Holden, Elizabeth Collis, Joe Brook, Bindi S. O'Dea, Reuben D. |
| author_facet | Holden, Elizabeth Collis, Joe Brook, Bindi S. O'Dea, Reuben D. |
| author_sort | Holden, Elizabeth |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:12:23Z |
| format | Article |
| id | nottingham-49326 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:12:23Z |
| publishDate | 2018 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-493262020-05-04T19:37:29Z https://eprints.nottingham.ac.uk/49326/ A multiphase multiscale model for nutrient limited tissue growth Holden, Elizabeth Collis, Joe Brook, Bindi S. O'Dea, Reuben D. 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. Cambridge University Press 2018-05-23 Article PeerReviewed Holden, Elizabeth, Collis, Joe, Brook, Bindi S. and O'Dea, Reuben D. (2018) A multiphase multiscale model for nutrient limited tissue growth. ANZIAM Journal, 59 (4). pp. 499-532. ISSN 1446-8735 https://www.cambridge.org/core/journals/anziam-journal/article/multiphase-multiscale-model-for-nutrient-limited-tissue-growth/30C4ACA604627DED7FE469DEEBF01E85 doi:10.1017/S1446181118000044 doi:10.1017/S1446181118000044 |
| spellingShingle | Holden, Elizabeth Collis, Joe Brook, Bindi S. O'Dea, Reuben D. A multiphase multiscale model for nutrient limited tissue growth |
| title | A multiphase multiscale model for nutrient limited tissue growth |
| title_full | A multiphase multiscale model for nutrient limited tissue growth |
| title_fullStr | A multiphase multiscale model for nutrient limited tissue growth |
| title_full_unstemmed | A multiphase multiscale model for nutrient limited tissue growth |
| title_short | A multiphase multiscale model for nutrient limited tissue growth |
| title_sort | multiphase multiscale model for nutrient limited tissue growth |
| url | https://eprints.nottingham.ac.uk/49326/ https://eprints.nottingham.ac.uk/49326/ https://eprints.nottingham.ac.uk/49326/ |