Mathematical modelling for tendon tissue engineering in a humanoid robotic bioreactor

Thesis

Tendon tissue engineering aims to grow functional tissue in vitro. Tissue is grown in bioreactors which regulate the biochemical and mechanical environment of the growing cells. This thesis develops mathematical models motivated by the Humanoid Robotic Bioreactor under development at the Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences. Cells grow on a scaffold consisting of many aligned, flexible strings, surrounded by cell media. The focus of this work is modelling fluid-induced shear stresses and metabolite transport within this fluid-fibre composite.

We begin in chapter 1 by providing background on tissue engineering and introducing the humanoid robotic bioreactor. In chapter 2, we develop methods required in later chapters, identifying the correct way to treat integral constraints in multiple scales problems with a slowly varying domain. We consider a simple example from electrostatics, using a particular limit of the problem treated with standard multiple scales to identify the correct method to treat integral constraints directly. We apply this method in chapter 3, where we use homogenisation theory to obtain an effective model for the fluid-string interaction in the bioreactor scaffold. We solve the model in simple cases to explore how the cell shear stress depends on the imposed forcing. In chapter 4, we homogenise the metabolite transport problem, outlining the different effective models that arise for various regimes. We consider simple solutions to each case and identify the most relevant regime to the humanoid robotic bioreactor. We draw conclusions and outline directions for future work in chapter 5.

Authors: Kent, A

• DOI: 10.5287/bodleian:aVV8bNkdG
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: integral constraints; mathematical modelling; homogenisation via multiscale asymptotics
• Subjects: Applied mathematics