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

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## 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 |

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