SMRI Seminar: Ismail -- Mathematical Modelling of Physiological Fluid Flows

’Mathematical Modelling of Physiological Fluid Flows’ Zuhaila Ismail (Universiti
Teknologi Malaysia) 

Date & Time: Friday 14 Feb, 9.30am - 10.30am Location: Quad S227 

The study of physiological fluid flows provides a great challenge in both fields of
mathematical medicine and engineering.  Two different physiological fluid flows problems
regarding blood flow in stenosed bifurcated artery and flow in the human eye are
considered, showing how changes in fluid mechanics of the problems contribute to the
development of the arterial and human eye diseases.  Modelling of blood as non-Newtonian
fluids are necessary especially in a diseased vessel with smaller diameter.  In this
paper, generalized power law model is selected to represent the rheological behaviour of
blood.  The shear-thinning, Newtonian as well as shear -thickening effects of blood are
presented with combine effects from different Reynolds number and severity of stenosis.
To overcome several difficulties exists from the classical Galerkin method, a stabilized
finite element technique known as Galerkin Least-squares method is employed to a viscous
flow of generalized power law fluid.  GLS allows the Babuska-Brezzi condition to be
neglected for velocity and pressure subspaces.  Due to that, the computational domain of
the proposed vessel is discretized as a linear triangular element with three corner
nodes representing the degree of freedoms for velocities and pressure components.
Whereas, to deals with the non-linearity appears in momentum equations, the
Newton-Raphson method is implemented to linearize them.  The vessel is modelled as a
bifurcated channel with the presence of an overlapping stenosis in parent’s arterial
lumen, having a rigid wall with non-slip condition.  Descemet membrane detachment (DMD)
is a tear or break on the Descement membrane (DM) which is a part of the cornea
membrane.  DMD is occurred when DM separate from stroma.  The separation is due to the
aqueous humour (AH) flows into the subspaces between the stroma and DM.  Modelling of
buoyancy driven AH flow is developed to analyse the behaviour of the fluid flows through
the pupil aperture in anterior chamber (AC) during DMD.  Finite element method using
COMSOL Multiphysics 5.2 is implemented to simulate the buoyancy driven flow of AH enters
the AC across pupil aperture and leaves through Trabecular meshwork (TM) during DMD.
The expected results on the two different physiological fluid flows characteristics such
as velocity, streamlines and wall shear stress are analysed.