Amy Kent
Multiscale Mathematical Models for Tendon Tissue Engineering
Tendon tissue engineering aims to grow functional tendon in vitro. In bioreactor chambers, cells growing on a solid scaffold are fed with nutrient-rich media and stimulated by mechanical loads. The Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences is developing a Humanoid Robotic Bioreactor, where cells grow on a flexible fibrous scaffold actuated by a robotic shoulder. Tendon cells modulate their behaviour in response to shear stresses - experimentally, it is desirable to design robotic loading regimes that mimic physiological loads. The shear stresses are generated by flowing cell media; this flow induces deformation of the scaffold which in turn modulates the flow. Here, we capture this fluid-structure interaction using a homogenised model of fluid flow and scaffold deformation in a simplified bioreactor geometry. The homogenised model admits analytical solutions for a broad class of forces representing robotic loading. Given the solution to the microscale problem, we can determine microscale shear stresses at any point in the domain. In this presentation, we will outline the model derivation and discuss the experimental implications of model predictions.
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Michael Negus
High-Speed Droplet Impact Onto Deformable Substrates: Analysis And Simulations
The impact of a high-speed droplet onto a substrate is a highly non-linear, multiscale phenomenon and poses a formidable challenge to model. In addition, when the substrate is deformable, such as a spring-suspended plate or an elastic sheet, the fluid-structure interaction introduces an additional layer of complexity. We present two modeling approaches for droplet impact onto deformable substrates: matched asymptotics and direct numerical simulations. In the former, we use Wagner's theory of impact to derive analytical expressions which approximate the behaviour during the early stages of the impact. In the latter, we use the open source volume-of-fluid code Basilisk to conduct direct numerical simulations designed to both validate the analytical framework and provide insight into the later times of impact. Through both methods, we are able to observe how the properties of the substrate, such as elasticity, affect the behaviour of the flow. We conclude by showing how these methods are complementary, as a combination of both can lead to a thorough understanding of the droplet impact across timescales.
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Edwina Yeo
Modelling of Magnetically Targeted Stem Cell Delivery
Targeting delivery of stem cells to the site of an injury is a key challenge in regenerative medicine. One possible approach is to inject cells implanted withmagnetic nanoparticles into the blood stream. Cells can then be targeted to the delivery site by an external magnetic field. At the injury site, it is of criticalimportance that the cells do not form an aggregate which could significantly occlude the vessel.We develop a model for the transport of magnetically tagged cells in blood under the action of an external magnetic field. We consider a system of blood and stem cells in a single vessel. We exploit the small aspect ratio of the vessel to examine the system asymptotically. We consider the system for a range of magnetic field strengths and varying strengths of the diffusion coefficient of the stem cells. We explore the different regimes of the model and determine the optimal conditions for the effective delivery of stem cells while minimising vessel occlusion.
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Helen Zha
Mathematical model of a valve-controlled, gravity driven bioreactor for platelet production
Hospitals sometimes experience shortages of donor blood platelet supplies, motivating research into~\textit{in vitro}~production of platelets. We model a novel platelet bioreactor described in Shepherd et al [1]. The bioreactor consists of an upper channel, a lower channel, and a cell-seeded porous collagen scaffold situated between the two. Flow is driven by gravity, and controlled by valves on the four inlets and outlets. The bioreactor is long relative to its width, a feature which we exploit to derive a lubrication reduction of unsteady Stokes flow coupled to Darcy. As the shear stress experienced by cells influences platelet production, we use our model to quantify the effect of varying pressure head and valve dynamics on shear stress.
[1] Shepherd, J.H., Howard, D., Waller, A.K., Foster, H.R., Mueller, A., Moreau, T., Evans, A.L., Arumugam, M., Chalon, G.B., Vriend, E. and Davidenko, N., 2018. Structurally graduated collagen scaffolds applied to the ex vivo generation of platelets from human pluripotent stem cell-derived megakaryocytes: enhancing production and purity. Biomaterials.