Large Eddy Simulation (LES) is applied to study physiological pulsatile spiral and non-spiral blood flow through a model of an irregular stenosis with an adjacent post-stenotic fusiform irregular aneurysm in basilar artery. The stenosis and the aneurysm are of 75% area reduction and 126% area enlargement, respectively, at their centres [1]. Numerical results of various important physical quantities are presented to particularly investigate the transition-to-turbulence nature of the pulsatile flow with their relevant clinical implications

Hye, M.A.

Paul, M.C.

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       Hye, M.A., and Paul, M.C. (2013) LES of physiological blood flow in diseased basilar artery: semi-patient specific model. In: 1st UK National Conference on Patient-Specific Modelling & Translational Research, 9-10 Jan 2013, Cardiff, UK.    Copyright © 2013 Patient Specific Modelling Network       A copy can be downloaded for personal non-commercial research or study, without prior permission or charge   The content must not be changed in any way or reproduced in any format or medium without the formal permission of the copyright holder(s)   When referring to this work, full bibliographic details must be given       http://eprints.gla.ac.uk/74088     Deposited on: 22 January  2013             Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk 1st UK National Conference on Patient-Specific Modelling & Translational Research9-10 January 2013, Cardiff, Wales, UKLES of Physiological Blood Flow in Diseased Basilar Artery:Semi-Patient Specific ModelMd Abdul Hye and Manosh C. Paul?Systems, Power & Energy, School of Engineering, University of Glasgow, UK?E-mail: Manosh.Paul@glasgow.ac.ukSUMMARYLarge Eddy Simulation (LES) is applied to study physiological pulsatile spiral and non-spiralblood flow through a model of an irregular stenosis with an adjacent post-stenotic fusiform irreg-ular aneurysm in basilar artery. The stenosis and the aneurysm are of 75% area reduction and126% area enlargement, respectively, at their centres [1]. Numerical results of various importantphysical quantities are presented to particularly investigate the transition-to-turbulence nature ofthe pulsatile flow with their relevant clinical implications.Key Words: LES, arteriosclerosis, blood flow, turbulence, wall shear stress, aneurysm.1 INTRODUCTIONAtherosclerotic artery rarely has both stenosis and aneurysm in the same arterial segment. Untilrecently no reports on intracranial stenoses associated with adjacent aneurysms have been found[1]. In et al [1] reported the existence of a severe stenosis with an adjacent (pre-stenotic ‘saccular’or post-stenotic ‘fusiform’) aneurysm in basilar artery. They defined a ‘saccular’ aneurysm as ananeurysm which has a smooth berry-shaped body and a neck; and an ‘atherosclerotic fusiform’aneurysm as an aneurysm having a dilated arterial segment without definite neck formation.Aneurysm has the potential for rupture of the vessel wall, which may lead to haemorrhage, com-plications to local organ function, and even death as aneurysm ruptures have high mortality andmorbidity rates [2]. Hence, like severe stenosis, aneurysm could prove fatal if left without takingany therapeutic measures. The objective of this work is to study the transient blood flow througha semi-patient specific model of an arterial stenosis with an adjacent (post-stenotic) aneurysm inthe same arterial segment giving particular focus on the relevant pathophysiology associated withthe cardiovascular diseases.2 NUMERICAL MODELLING AND RESULTSFigure 1(a) depicts the model geometry resembling a section of basilar artery with stenosis andaneurysm. The diameter of the undiseased section of the model is taken as D = 8 mm [3]. Thestenosis is centred at z = 0 and of length 2D while the adjacent aneurysm is taken of length= 4D and centred at z = 3D. The cross-sections of both the stenosis and aneurysm are shifteda maximum of 0.25 mm randomly to either x or y-direction (positive or negative) to generate theirregular shape with a cosine function. Governing equations of flow are solved by LES [4] withphysiological and pressure pulses employed at the inlet and outlet, respectively. Spiral velocityFigure 1: Irregular model artery having stenosis with adjacent aneurysm (a); Instantaneous stream-wise velocity (b), streamlines (c) and rms of wall pressure fluctuations (d) at differentRe and spiralspeed. The Womersley number is fixed at 6.92.at the inlet is introduced by taking the magnitude (C) of the pulsatile bulk velocity as tangentialvelocity [5]. A no-slip condition is applied to the rigid wall and the results presented are almostmesh independent. The Reynolds numbers (Re) investigated, based on the bulk inlet velocity, are366 and 440 corresponding to the respective peak Re of ≈ 1000 and 1200. Due to the absence ofany experimental or ‘in-vivo’ data, the simulation for Re = 440 was run with the two-equationk-ω Transitional model to crudely assess the LES results.Fig. 1(b) shows that the flow reverses near the wall from the centre of the stenosis to the immediatedownstream region of the aneurysm. The stenotic jet becomes weaker at around the post-lip ofthe aneurysm, i.e. at z ≈ 5D, and starts to break down. The flow streamlines (c) towards thedownstream of aneurysm appear to be very chaotic due to the presence of turbulence. Where therms of the wall pressure fluctuations, 〈p′′〉rms (d), are found strongly oscillating with their peaksgenerally rising due to the spiral velocity which, associated with the extreme pressure fluctuations,usually causes arterial murmurs.3 CONCLUSIONSTransition process of the blood flow through a model of stenosis-aneurysm in basilar artery hasbeen studied by LES. Strong turbulence influenced by the spiral flow was predicted in the aneurysmdownstream and the turbulent energy spectra showed a large range of frequencies making up theinertial subrange region. Extremely large recirculation regions found are very harmful in the patho-logical context since they increase the blood residence time with potential risk of stroke and bloodclot or thrombosis inside the aneurysm. The turbulent wall shear stresses around the diseasedsection also reaches clinically dangerous level for both the Reynolds numbers.REFERENCES[1] In et al , Am J Neuroradiol, 31, 1895-1898, 2010.[2] Kassell et al , J. Neurosurgery, 73, 18-36, 1990.[3] Pico et al , Stroke, 37, 2342-2347, 2006.[4] Paul et al , Applied Mathematical Modelling, 36, 4393-4413, 2012.[5] Paul et al , Medical Engineering and Physics, 31, 1195-1203, 2009.

LES of physiological blood flow in diseased basilar artery:

semi-patient specific model

Enlighten: Publications

  
 
 
 
 
 
Hye, M.A., and Paul, M.C. (2013) LES of physiological blood flow in 
diseased basilar artery: semi-patient specific model. In: 1st UK National 
Conference on Patient-Specific Modelling & Translational Research, 9-10 
Jan 2013, Cardiff, UK. 
 
 
 
Copyright © 2013 Patient Specific Modelling Network 
 
 
 
   
A copy can be downloaded for personal non-commercial research or 
study, without prior permission or charge 
 
 
The content must not be changed in any way or reproduced in any format 
or medium without the formal permission of the copyright holder(s) 
 
 
When referring to this work, full bibliographic details must be given 
 
 
 
 
 
 
http://eprints.gla.ac.uk/74088 
 
 
 
 
Deposited on: 22 January  2013 
 
 
 
 
 
 
 
 
 
 
 
 
Enlighten – Research publications by members of the University of Glasgow 
http://eprints.gla.ac.uk 
1st UK National Conference on Patient-Specific Modelling & Translational Research
9-10 January 2013, Cardiff, Wales, UK
LES of Physiological Blood Flow in Diseased Basilar Artery:
Semi-Patient Specific Model
Md Abdul Hye and Manosh C. Paul?
Systems, Power & Energy, School of Engineering, University of Glasgow, UK
?E-mail: Manosh.Paul@glasgow.ac.uk
SUMMARY
Large Eddy Simulation (LES) is applied to study physiological pulsatile spiral and non-spiral
blood flow through a model of an irregular stenosis with an adjacent post-stenotic fusiform irreg-
ular aneurysm in basilar artery. The stenosis and the aneurysm are of 75% area reduction and
126% area enlargement, respectively, at their centres [1]. Numerical results of various important
physical quantities are presented to particularly investigate the transition-to-turbulence nature of
the pulsatile flow with their relevant clinical implications.
Key Words: LES, arteriosclerosis, blood flow, turbulence, wall shear stress, aneurysm.
1 INTRODUCTION
Atherosclerotic artery rarely has both stenosis and aneurysm in the same arterial segment. Until
recently no reports on intracranial stenoses associated with adjacent aneurysms have been found
[1]. In et al [1] reported the existence of a severe stenosis with an adjacent (pre-stenotic ‘saccular’
or post-stenotic ‘fusiform’) aneurysm in basilar artery. They defined a ‘saccular’ aneurysm as an
aneurysm which has a smooth berry-shaped body and a neck; and an ‘atherosclerotic fusiform’
aneurysm as an aneurysm having a dilated arterial segment without definite neck formation.
Aneurysm has the potential for rupture of the vessel wall, which may lead to haemorrhage, com-
plications to local organ function, and even death as aneurysm ruptures have high mortality and
morbidity rates [2]. Hence, like severe stenosis, aneurysm could prove fatal if left without taking
any therapeutic measures. The objective of this work is to study the transient blood flow through
a semi-patient specific model of an arterial stenosis with an adjacent (post-stenotic) aneurysm in
the same arterial segment giving particular focus on the relevant pathophysiology associated with
the cardiovascular diseases.
2 NUMERICAL MODELLING AND RESULTS
Figure 1(a) depicts the model geometry resembling a section of basilar artery with stenosis and
aneurysm. The diameter of the undiseased section of the model is taken as D = 8 mm [3]. The
stenosis is centred at z = 0 and of length 2D while the adjacent aneurysm is taken of length
= 4D and centred at z = 3D. The cross-sections of both the stenosis and aneurysm are shifted
a maximum of 0.25 mm randomly to either x or y-direction (positive or negative) to generate the
irregular shape with a cosine function. Governing equations of flow are solved by LES [4] with
physiological and pressure pulses employed at the inlet and outlet, respectively. Spiral velocity
Figure 1: Irregular model artery having stenosis with adjacent aneurysm (a); Instantaneous stream-
wise velocity (b), streamlines (c) and rms of wall pressure fluctuations (d) at differentRe and spiral
speed. The Womersley number is fixed at 6.92.
at the inlet is introduced by taking the magnitude (C) of the pulsatile bulk velocity as tangential
velocity [5]. A no-slip condition is applied to the rigid wall and the results presented are almost
mesh independent. The Reynolds numbers (Re) investigated, based on the bulk inlet velocity, are
366 and 440 corresponding to the respective peak Re of ≈ 1000 and 1200. Due to the absence of
any experimental or ‘in-vivo’ data, the simulation for Re = 440 was run with the two-equation
k-ω Transitional model to crudely assess the LES results.
Fig. 1(b) shows that the flow reverses near the wall from the centre of the stenosis to the immediate
downstream region of the aneurysm. The stenotic jet becomes weaker at around the post-lip of
the aneurysm, i.e. at z ≈ 5D, and starts to break down. The flow streamlines (c) towards the
downstream of aneurysm appear to be very chaotic due to the presence of turbulence. Where the
rms of the wall pressure fluctuations, 〈p′′〉rms (d), are found strongly oscillating with their peaks
generally rising due to the spiral velocity which, associated with the extreme pressure fluctuations,
usually causes arterial murmurs.
3 CONCLUSIONS
Transition process of the blood flow through a model of stenosis-aneurysm in basilar artery has
been studied by LES. Strong turbulence influenced by the spiral flow was predicted in the aneurysm
downstream and the turbulent energy spectra showed a large range of frequencies making up the
inertial subrange region. Extremely large recirculation regions found are very harmful in the patho-
logical context since they increase the blood residence time with potential risk of stroke and blood
clot or thrombosis inside the aneurysm. The turbulent wall shear stresses around the diseased
section also reaches clinically dangerous level for both the Reynolds numbers.
REFERENCES
[1] In et al , Am J Neuroradiol, 31, 1895-1898, 2010.
[2] Kassell et al , J. Neurosurgery, 73, 18-36, 1990.
[3] Pico et al , Stroke, 37, 2342-2347, 2006.
[4] Paul et al , Applied Mathematical Modelling, 36, 4393-4413, 2012.
[5] Paul et al , Medical Engineering and Physics, 31, 1195-1203, 2009.


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LES of physiological blood flow in diseased basilar artery: semi-patient specific model

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