Homogenised models of nutrient transport in a fibrous bioreactor scaffold

Bioreactor scaffolds must be designed to facilitate adequate nutrient delivery to the growing tissue they support. For perfusion bioreactors, the dominant transport process is determined by the scale of fluid velocity relative to diffusion and the geometry of the scaffold. In this paper, models of n...

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Main Authors: Amy Kent, Sarah L. Waters, James M. Oliver, Stephen J. Chapman
Format: Article
Language:English
Published: Cambridge University Press
Series:European Journal of Applied Mathematics
Subjects:
Online Access:https://www.cambridge.org/core/product/identifier/S0956792525000129/type/journal_article
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author Amy Kent
Sarah L. Waters
James M. Oliver
Stephen J. Chapman
author_facet Amy Kent
Sarah L. Waters
James M. Oliver
Stephen J. Chapman
author_sort Amy Kent
collection DOAJ
description Bioreactor scaffolds must be designed to facilitate adequate nutrient delivery to the growing tissue they support. For perfusion bioreactors, the dominant transport process is determined by the scale of fluid velocity relative to diffusion and the geometry of the scaffold. In this paper, models of nutrient transport in a fibrous bioreactor scaffold are developed using homogenisation via multiscale asymptotics. The scaffold is modelled as an ensemble of aligned strings surrounded by viscous, slowly flowing fluid. Multiple scales analysis is carried out for various parameter regimes which give rise to macroscale transport models that incorporate the effects of advection, reaction and diffusion. Multiple scales in both space and time are employed when macroscale advection balances macroscale diffusion. The microscale model is solved to obtain the effective diffusion coefficient and simple solutions to the macroscale problem are presented for each regime.
format Article
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publisher Cambridge University Press
record_format Article
series European Journal of Applied Mathematics
spelling doaj-art-e7b5029ca39a410099997e7bab2357cc2025-08-20T03:18:37ZengCambridge University PressEuropean Journal of Applied Mathematics0956-79251469-442512810.1017/S0956792525000129Homogenised models of nutrient transport in a fibrous bioreactor scaffoldAmy Kent0https://orcid.org/0000-0001-5905-962XSarah L. Waters1James M. Oliver2Stephen J. Chapman3https://orcid.org/0000-0003-3347-6024Mathematical Institute, University of Oxford, Oxford, UKMathematical Institute, University of Oxford, Oxford, UKMathematical Institute, University of Oxford, Oxford, UKMathematical Institute, University of Oxford, Oxford, UKBioreactor scaffolds must be designed to facilitate adequate nutrient delivery to the growing tissue they support. For perfusion bioreactors, the dominant transport process is determined by the scale of fluid velocity relative to diffusion and the geometry of the scaffold. In this paper, models of nutrient transport in a fibrous bioreactor scaffold are developed using homogenisation via multiscale asymptotics. The scaffold is modelled as an ensemble of aligned strings surrounded by viscous, slowly flowing fluid. Multiple scales analysis is carried out for various parameter regimes which give rise to macroscale transport models that incorporate the effects of advection, reaction and diffusion. Multiple scales in both space and time are employed when macroscale advection balances macroscale diffusion. The microscale model is solved to obtain the effective diffusion coefficient and simple solutions to the macroscale problem are presented for each regime.https://www.cambridge.org/core/product/identifier/S0956792525000129/type/journal_articleHomogenisationdiffusionadvection35B2776S0535Q49
spellingShingle Amy Kent
Sarah L. Waters
James M. Oliver
Stephen J. Chapman
Homogenised models of nutrient transport in a fibrous bioreactor scaffold
European Journal of Applied Mathematics
Homogenisation
diffusion
advection
35B27
76S05
35Q49
title Homogenised models of nutrient transport in a fibrous bioreactor scaffold
title_full Homogenised models of nutrient transport in a fibrous bioreactor scaffold
title_fullStr Homogenised models of nutrient transport in a fibrous bioreactor scaffold
title_full_unstemmed Homogenised models of nutrient transport in a fibrous bioreactor scaffold
title_short Homogenised models of nutrient transport in a fibrous bioreactor scaffold
title_sort homogenised models of nutrient transport in a fibrous bioreactor scaffold
topic Homogenisation
diffusion
advection
35B27
76S05
35Q49
url https://www.cambridge.org/core/product/identifier/S0956792525000129/type/journal_article
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AT jamesmoliver homogenisedmodelsofnutrienttransportinafibrousbioreactorscaffold
AT stephenjchapman homogenisedmodelsofnutrienttransportinafibrousbioreactorscaffold