Peter R. Johnston

No matter the fluid dynamics solver, it can be difficult to simulate oscillatory flow in axisymmetric tubes where the tube radius varies along its length in a periodic and longitudinally asymmetric manner. To reduce the complexity of implementing such simulations, we first derive approximations for pulsatile flow in a tube of constant radius, valid for low Womersley numbers, from the analytic velocity profile. We then extend this approximation to more complicated tube profiles by appropriately scaling steady-state velocity fields, obtained from lattice Boltzmann methods, according to the low Womersley number approximations. Errors and velocity profiles are investigated in order to confirm the validity of our approximations. While we primarily consider lattice Boltzmann methods throughout, it should be noted that the low Womersley number approximations given are applicable to any oscillatory flows within axisymmetric geometries, irrespective of solution technique used to obtain the steady-state flow field.

A numerical investigation concerning the effect of arterial constriction on the flow behaviour of blood in a porous bifurcated artery under the influence of a transverse magnetic field has been carried out. The equations of motion governing the flow are derived in the Cartesian coordinate system by treating the fluid as an electrically conducting, Newtonian, incompressible and fully developed blood flow. The blood is considered to flow through a constricted bifurcated artery with overlapping stenosis located at the mother artery. This developed model is consistent with the principles of magnetohydrodynamics. A stabilized form of finite element method, known as the Galerkin least-squares method is employed in solving the governing equation with suitably prescribed boundary conditions. Then, the non-linear systems resulting from the developed model are linearized by an iterative technique called the Newton-Raphson method. The effects of various parameters particularly the severity of stenosis, magnetohydrodynamics constant and permeability parameter on blood flow characteristics are analysed graphically for the velocity profile and streamline pattern. The findings obtained show that the presence of a magnetic field caused a significant alteration in the blood flow behaviour. Slight changes occurred in the flow pattern with the porous medium consideration. The application of a magnetic field could be utilized in controlling the hemodynamic flow of blood by decelerating the flow velocity and reducing the vortex sizes with rising in Hartmann number. While the pathological state of arterial disease as a porous structure reveals that a more porous fluid medium could have slightly promoted the growth in vortex size.

Accurate values for the six cardiac conductivities of the bidomain model are crucial for meaningful electrophysiological simulations of cardiac tissue and are yet to be achieved. A two-stage optimisation process is used to retrieve the cardiac conductivities from cardiac potentials measured on a multi-electrode array—the first stage simultaneously fits all six conductivities, and the second stage fits a subset of the conductivities (intracellular conductivities), while holding the remainder of the conductivities (extracellular conductivities) constant. Previous studies have shown that the intracellular conductivities are retrieved to a lesser degree of accuracy than extracellular conductivities. This study tests the proposition that there exists a relationship between the extracellular and intracellular conductivities during the second stage of the optimisation that affects the accuracy of the retrieved intracellular conductivities. A measure to quantify this relationship is developed using polynomial chaos. The results show that a significant relationship does exist, and thus any errors in the extracellular conductivities are magnified in the retrieved intracellular conductivities. Thus, it is suggested that future protocols for retrieving conductivities incorporate the uncertainty in the extracellular conductivities. References

A stabilized form of finite element formulation known as the Galerkin least-squares (GLS) method is implemented here for solving the two-dimensional incompressible non-Newtonian fluid model of blood flow in a diseased artery. The modelling for this type of flow is based on the conservation of mass and momentum equations, coupled with the generalised Newtonian liquid (GNL) constitutive equation characterized by the generalised power law (GPL) model. The flow of blood in this present study are assumed as steady, laminar and fully developed. The finite element algorithms considered herein are first solved for the Newtonian fluid in a straight artery with a bell shaped stenosis for validation purposes. As the efficiency and validity of the proposed algorithms are obtained through comparison with the findings from existing literature and COMSOL Multiphysics 5.2 software. Then, the algorithms are being implemented to the generalised power law fluid model of blood flow in a bifurcated artery with overlapping stenosis located at the parent's arterial lumen. The numerical results illustrate the arising of distinct sizes of vortex shedding downstream of the stenotic region for each generalised power law index.

This study aimed to adapt the Get Set2 quiz and design a diagnostic quiz for implementation under assumed knowledge admissions into university science degrees. The GetReady Quiz that was designed, comprised five modules benchmarked against the high school curriculum in Mathematics, Chemistry and Biology. The significance of this study stems from the development of an alternate approach to support students, with deficiencies in mathematical skills, who enter university STEM programmes with recommended foundational knowledge in mathematics and science. A mixed-mode research methodology was employed in which quiz design was coupled with implementation and evaluation with a pilot study. The GetReady Quiz design featured five discipline modules in Mathematics, Chemistry and Biology, with progression of question difficulty. Knowledge gaps and apparent difficulties for some students with conceptual understanding were evident. Students displayed a realization of their lack of knowledge by reporting that completion of the GetReady Quiz helped them identify areas for revision. The findings indicated that the GetReady quiz was appropriate for assumed knowledge self-diagnosis for commencing students. Approaches to diagnostic testing, such as the GetReady Quiz, should be recommended, if not compulsory, for university students who commence study with STEM assumed knowledge admission.

A number of areas of difficulty in basic numeracy and mathematical skills were identified, which hinder students’ success in a foundational biochemistry course. Many students have difficulty with the concepts of pH and buffers (requiring proficiency with logarithms) and enzyme kinetics (requiring algebraic manipulations and graphing). The voluntary use by students of an ‘in house’ online support site, the Maths Skills Site, to address these difficulties was varied and seemed to be motivated by assessment deadlines, as well as deliberate instructions to refer to the relevant Maths Skills Site modules when completing assessment. The majority of the users of the online support site were those who performed poorly on a diagnostic test administered at the beginning of the course. There was a small but significant effect of Maths Support Site usage with users achieving improved grades for graphing functions compared to non-users. The combination of mathematical backgrounds and prior academic performance also correlated with success in first-year university biochemistry.