Simulation of transient blood flow in models of arterial stenosis and aneurysm

Hye, Md. Abdul (2012) Simulation of transient blood flow in models of arterial stenosis and aneurysm. PhD thesis, University of Glasgow.

Abstract

The Large Eddy Simulation (LES) technique with the Smagorinsky-Lilly dynamic
subgrid model and two-equation Standard k-ω Transitional turbulence model are
applied to investigate non-spiral and spiral blood flow through three dimensional
models of arterial stenosis and aneurysm. A spiral pattern of blood flow is thought to
have many beneficial effects on hemodynamics. Previous computational studies on
spiral blood flow involve only steady spiral flow in a straight stenosed pipe without
considering an upstream curved section of the artery. But a spiral pattern in the
blood flow may exist due to the presence of an upstream curved section in the artery.
On the other hand, pressure is generally considered a constant quantity in studies on
pulsatile flow through either arterial stenosis or aneurysm; however, blood pressure
is a waveform in a physiological flow.
Although cosine-type or smooth regular stenoses are generally taken in investigations
of blood flow in a three-dimensional model of arterial stenosis, in reality,
stenoses are of irregular shape. Besides stenosis and aneurysm, another abnormal
condition of the artery is the presence of stenosis with an adjacent aneurysm in the
same arterial segment, especially in the posterior circulation. A study on (steady or
pulsatile) flow through such arterial stenosis with an adjacent aneurysm in the same
arterial segment is not available so far.
Therefore, taking above things into consideration, thorough investigations of
steady and unsteady pulsatile non-spiral and spiral blood flow in three-dimensional
models of stenosis and aneurysm are needed to give a sound understanding of the
transition-to-turbulence of blood flow due to stenosis and aneurysm and to study the
the effects of spiral velocity on the transition-to-turbulence.
The LES technique has mostly been used to investigate turbulent flow in engineering
fields other than bio-fluid mechanics. In the last decade, LES has seen its
excellent potential for studying the transition-to-turbulence of physiological flow in
bio-fluid mechanics. Though the k-ω Transitional model is used in few instances,
mainly LES is applied in this study.
Firstly, investigations of steady non-spiral and spiral blood flow through threedimensionalmodels
of cosine-type regular stenosed tube without and with upstream
curved segment of varying angles of curvature are performed by using the k-ω Transitional
model and LES. A fully developed Poiseuille velocity profile for blood is
introduced at the inlets of the models. To introduce a spiral effect at the inlet, onesixth
of the bulk velocity is taken as the tangential velocity at the inlet along with
the axial velocity profile there.
Secondly, physiological pulsatile non-spiral and spiral blood flow through a
three-dimensional model of a straight tube having cosine-type regular stenosis are
investigated by using mainly LES. A two-equation k-ω Transitional model is also
used in one non-spiral flow case. The first four harmonics of the Fourier series of
pressure pulse are used to generate physiological velocity profiles at the inlet. At the
outlet, a pressure waveform is introduced. The effects of percentage of area reduction
in the stenosis, length of the stenosis, amplitude of pulsation and Womersley
number are also examined.
Thirdly, transient pulsatile non-spiral and spiral blood flow through a threedimensional
model of irregular stenosis are investigated by applying LES and comparison
is drawn between non-spiral flow through a regular stenosis and that through
an irregular stenosis.
Lastly, pulsatile non-spiral and spiral blood flow through a three-dimensional
model of irregular stenosis with an adjacent post-stenotic irregular aneurysm in the
same arterial segment are studied by applying LES and the k-ω Transitional model.
The effects of variation in spiral velocity are also examined.
The results presented in this thesis are analysed with relevant pathophysioloical
consequences. In steady flow through the straight stenosed tube, excellent agreement
between LES results for Re = 1000 and 2000 and the corresponding experimental
results are found when the appropriate inlet perturbations are introduced.
In the models with an upstream curved segment, no significant effect of spiral flow
on any flow property is found for the investigated Reynolds numbers; spiral pattern
disappears before the stenosis – which may be due the rigid wall used in the models
and/or a steady flow at the inlet. The effects of the curved upstream model can be
seen mainly in the maximum turbulent kinetic energy (TKE), the maximum pressure
drop and the maximum wall shear stress (WSS), which in the curved upstream
models generally increase significantly compared with the corresponding results in
the straight stenosed tube.
The maximumcontributions of the SGS motion to the large-scale motion in both
non-spiral and spiral flow through a regular stenosis, an irregular stenosis and an irregular
stenosis with an adjacent post-stenotic irregular aneurysm are 50%, 55%and
25%, respectively, for the highest Reynolds number investigated in each model. Although
the wall pressure and shear stress obtained from the k-ω Transitional model
agree quite well with the corresponding LES results, the turbulent results obtained
from the k-ω Transitional model differ significantly from the corresponding LES
results – this shows unsuitability of the k-ω model for pulsatile flow simulation.
Large permanent recirculation regions are observed right after the stenosis throat in
both non-spiral and spiral flow, which in the model of a stenosis with an adjacent
post-stenotic aneurysm are stretched beyond the aneurysm and the length of the
recirculation regions increases with spiral velocity. This study shows that, in both
steady and unsteady pulsatile flow through the straight tube model having either a
stenosis (regular or irregular) or an irregular stenosis with an adjacent post-stenotic
irregular aneurysm, the TKE rises significantly at some locations and phases if a
spiral effect is introduced at the inlet of the model. However, the maximum value
of the TKE in a high spiral flow drops considerably compared with that in a low
spiral flow. The maximum wall pressure drop and shear stress occur around the
stenosis throat during all the phases of the pulsatile cycle. In the model of a stenosis
only, the wall pressure rises in the immediate post-stenotic region after its drop at
the stenosis throat. However, in the model of a stenosis with an adjacent aneurysm,
the wall pressure does not rise to regain its undisturbed value before the start of the
last quarter of the aneurysm. The effects of the spiral flow on the wall pressure and
WSS are visible only in the downstream region where they take oscillatory pattern.
The break frequencies of energy spectra for velocity and pressure fluctuations from
−5/3 power slope to −10/3 power slope and −7/3 power slope, respectively, are
observed in the downstream transition-to-turbulence region in both the non-spiral
and spiral flow. At some locations in the transition region, the velocity spectra
in the spiral flow has larger inertial subrange region than that in non-spiral flow.
The effects of the spiral flow on the pressure spectra is insignificant. Also, the
maximum wall pressure drop, the maximum WSS and the maximum TKE in the
non-spiral flow through the irregular stenosis rise significantly compared with the
corresponding results in the non-spiral flow through the regular stenosis.
When the area reduction in the stenosis is increased, the maximum pressure
drop, the maximumWSS and the TKE rise sharply. As for the effects of the length
of the stenosis, the maximum WSS falls significantly and the maximum TKE rises
sharply due to the increase in the length of the stenosis; but the maximum pressure
drop is almost unaffected by the increase in the stenosis length. The increase in
the amplitude of pulsation causes both the maximum pressure drop and the maximum
WSS to increase significantly under the inlet peak flow condition. While
the increased amplitude of pulsation decrease the maximum TKE, it is nonetheless
responsible for the sharp rise in the TKE found at some places in the transition-toturbulence
region. The decrease in the Womersley number causes the maximum
TKE to increase dramatically; however, the maximum pressure drop and the maximum
WSS decrease slightly under the inlet peak flow condition as a result of the
decrease in the Womersley number.
The author does believe that the present study makes a breakthrough in understanding
the non-spiral and spiral transient blood flows through arteries having a
stenosis and a stenosis with an adjacent post-stenotic aneurysm. The findings of the
thesis would, therefore, help the interested groups such as pathologists,medical surgeons
and researchers greatly in gaining better insight into the transient non-spiral
and spiral blood flow through models of arterial stenosis and aneurysm.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Non-spiral and spiral blood flow, physiological pulsatile non-spiral and spiral blood flow, pressure waveform, transtion-to-turbulence flow, arterial stenosis, stenosis with an upstream curved arterial segment, irregular stenosis, irregular stenosis with a post-stenotic adjacent irregular aneurysm, basilar artery, Large Eddy Simulation (LES), Standard k-ω Transitional turbulence model, Turbulent kinetic energy (TKE), Wall shear stress (WSS), wall pressure, energy spectra
• Subjects: Q Science > Q Science (General); Q Science > QA Mathematics; Q Science > QC Physics; R Medicine > RB Pathology; T Technology > TJ Mechanical engineering and machinery
• Colleges/Schools: College of Science and Engineering > School of Engineering > Systems Power and Energy
• Supervisor's Name: Paul, Dr. Manosh C.
• Date of Award: 2012
• Depositing User: Dr. Md. Abdul Hye
• Unique ID: glathesis:2012-3836
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 09 Jan 2013 13:36
• Last Modified: 09 Jan 2013 13:39
• URI: https://theses.gla.ac.uk/id/eprint/3836