Biomedical Engineering Reference
In-Depth Information
Fig. 7.22  Schematic of non-stented and stented aneurysmal artery
7.4.2
Modes of Aneurysmal Flow
Aneurysmal flows produce a force which propels blood into the aneurysmal sac.
This force is proportional to the difference in blood pressure from the vessel to the
aneurysm across its neck. The pressure gradient Δ P is influenced by the resistance
to that flow. Factors determining this resistance are the dimension of the aneurysmal
neck, and in the case of stenting, the effective orifice area of the neck that excludes
the stent strut areas.
For a steady, incompressible flow, the shear rate of strain of a fluid element is
defined as the rate of decrease of the angle formed by two mutually perpendicular
lines on the element. As such, the shear strain rate γ is defined as a function of τ and
is proportional to the velocity gradient in the perpendicular flow direction:
du
.
(7.11)
γ
=
f
()
τ
=−
dy
In general, the shear strain rate can be defined as a function of τ , and the linear re-
lationship between the shear stress and strain components with the viscosity as its
gradient. Mathematically, the model can be expressed as
τ µγ
=
,
(7.12)
where μ is the viscosity of the fluid.
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