The Study of the Function of AQP4 in Cerebral Ischaemia-Reperfusion Injury using Poroelastic Theory

Brain oedema is thought to form and to clear through the use of water-protein channels, aquaporin-4 (AQP4), which are found in the astrocyte endfeet. The model developed here is used to study the function of AQP4 in the formation and elimination of oedema fluid in ischaemia-reperfusion injury. The cerebral space is assumed to be made of four fluid compartments: astrocyte, neuron, ECS and blood microvessels, and a solid matrix for the tissue, and this is modelled using multiple-network poroelastic theory. AQP4 allows the movement of water between astrocyte and the ECS and the microvessels. It is found that the presence of AQP4 may help in reducing vasogenic oedema shown by a decrease in brain tissue extracellular pressure. However, the astrocyte pressure will increase to compensate for this decrease, which may lead to cytotoxic oedema. In addition, the swelling will also depend on the ionic concentrations in the astrocyte and extracellular space, which may change after ischaemic stroke. Understanding the role of AQP4 in oedema may thus help the development of a treatment plan in reducing brain swelling after ischaemia-reperfusion

Stokes flows in a 2D bifurcation

The flow network model is an established approach to approximate pressure-flow relationships in a network, which has been widely used in many contexts. However, little is known about the impact of bifurcation geometry on such approximations, so the existing models mostly rely on unidirectional flow assumption and Poiseuille's law, and thus neglect the flow details at each bifurcation. In this work, we address these limitations by computing Stokes flows in a 2D bifurcation using LARS (Lightning-AAA Rational Stokes), a novel mesh-free algorithm for solving 2D Stokes flow problems utilising an applied complex analysis approach based on rational approximation of the Goursat functions. Using our 2D bifurcation model, we show that the fluxes in two child branches depend on not only pressures and widths of inlet and outlet branches, as most previous studies have assumed, but also detailed bifurcation geometries (e.g. bifurcation angle), which were not considered in previous studies. The 2D Stokes flow simulations allow us to represent the relationship between pressures and fluxes of a bifurcation using an updated flow network, which considers the bifurcation geometry and can be easily incorporated into previous flow network approaches. The errors in the flow conductance of a channel in a bifurcation approximated using Poiseuille's law can be greater than 16%, when the centreline length is twice the inlet channel width and the bifurcation geometry is highly asymmetric. In addition, we present details of 2D Stokes flow features, such as flow separation in a bifurcation and flows around fixed objects at different locations, which previous flow network models cannot capture. These findings suggest the importance of incorporating detailed flow modelling techniques alongside existing flow network approaches when solving complex flow problems

Stokes flows in a two-dimensional bifurcation

The flow network model is an established approach to approximate pressure-flow relationships in a bifurcating network, and has been widely used in many contexts. Existing models typically assume unidirectional flow and exploit Poiseuille's law, and thus neglect the impact of bifurcation geometry and finite-sized objects on the flow. We determine the impact of bifurcation geometry and objects by computing Stokes flows in a two-dimensional (2D) bifurcation using the LARS (Lightning-AAA Rational Stokes) algorithm, a novel mesh-free algorithm for solving 2D Stokes flow problems utilising an applied complex analysis approach based on rational approximation of the Goursat functions. We compute the flow conductances of bifurcations with different channel widths, bifurcation angles, curved boundary geometries, and fixed circular objects. We quantify the difference between the computed conductances and their Poiseuille's law approximations to demonstrate the importance of incorporating detailed bifurcation geometry into existing flow network models. We parameterise the flow conductances of 2D bifurcation as functions of the dimensionless parameters of bifurcation geometry and a fixed object using a machine learning approach, which is simple to use and provides more accurate approximations than Poiseuille's law. Finally, the details of the 2D Stokes flows in bifurcations are presented

Contrasting the modelled sensitivity of the Amundsen Sea Embayment ice streams

Present-day mass loss from the West Antarctic ice sheet is centred on the Amundsen Sea Embayment (ASE), primarily through ice streams, including Pine Island, Thwaites and Smith glaciers. To understand the differences in response of these ice streams, we ran a perturbed parameter ensemble, using a vertically-integrated ice flow model with adaptive mesh refinement. We generated 71 sets of three physical parameters (basal traction coefficient, ice viscosity stiffening factor and sub-shelf melt rate), which we used to simulate the ASE for 50 years. We also explored the effects of different bed geometries and basal sliding laws. The mean rate of sea-level rise across the ensemble of simulations is comparable with current observed rates for the ASE. We found evidence that grounding line dynamics are sensitive to features in the bed geometry: simulations using BedMap2 geometry resulted in a higher rate of sea-level rise than simulations using a rougher geometry, created using mass conservation. Modelled grounding-line retreat of all the three ice streams was sensitive to viscosity and basal traction, while the melt rate was more important in Pine Island and Smith glaciers, which flow through more confined ice shelves than Thwaites, which has a relatively unconfined shelf