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

Q Science (General);QA Mathematics;QC Physics;RB Pathology;TJ Mechanical engineering and machinery

Hye, Md. Abdul ; Paul, Manosh C.

University:University of Glasgow

Department:School of Engineering

关键词: 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;   

Others  :  http://theses.gla.ac.uk/3836/1/2012hyephd.pdf

来源: University of Glasgow

【 摘 要 】

The Large Eddy Simulation (LES) technique with the Smagorinsky-Lilly dynamicsubgrid model and two-equation Standard k-ω Transitional turbulence model areapplied to investigate non-spiral and spiral blood flow through three dimensionalmodels of arterial stenosis and aneurysm. A spiral pattern of blood flow is thought tohave many beneficial effects on hemodynamics. Previous computational studies onspiral blood flow involve only steady spiral flow in a straight stenosed pipe withoutconsidering an upstream curved section of the artery. But a spiral pattern in theblood 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 onpulsatile flow through either arterial stenosis or aneurysm; however, blood pressureis a waveform in a physiological flow.Although cosine-type or smooth regular stenoses are generally taken in investigationsof blood flow in a three-dimensional model of arterial stenosis, in reality,stenoses are of irregular shape. Besides stenosis and aneurysm, another abnormalcondition of the artery is the presence of stenosis with an adjacent aneurysm in thesame arterial segment, especially in the posterior circulation. A study on (steady orpulsatile) flow through such arterial stenosis with an adjacent aneurysm in the samearterial segment is not available so far.Therefore, taking above things into consideration, thorough investigations ofsteady and unsteady pulsatile non-spiral and spiral blood flow in three-dimensionalmodels of stenosis and aneurysm are needed to give a sound understanding of thetransition-to-turbulence of blood flow due to stenosis and aneurysm and to study thethe effects of spiral velocity on the transition-to-turbulence.The LES technique has mostly been used to investigate turbulent flow in engineeringfields other than bio-fluid mechanics. In the last decade, LES has seen itsexcellent potential for studying the transition-to-turbulence of physiological flow inbio-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 threedimensionalmodelsof cosine-type regular stenosed tube without and with upstreamcurved segment of varying angles of curvature are performed by using the k-ω Transitionalmodel and LES. A fully developed Poiseuille velocity profile for blood isintroduced at the inlets of the models. To introduce a spiral effect at the inlet, onesixthof the bulk velocity is taken as the tangential velocity at the inlet along withthe axial velocity profile there.Secondly, physiological pulsatile non-spiral and spiral blood flow through athree-dimensional model of a straight tube having cosine-type regular stenosis areinvestigated by using mainly LES. A two-equation k-ω Transitional model is alsoused in one non-spiral flow case. The first four harmonics of the Fourier series ofpressure pulse are used to generate physiological velocity profiles at the inlet. At theoutlet, a pressure waveform is introduced. The effects of percentage of area reductionin the stenosis, length of the stenosis, amplitude of pulsation and Womersleynumber are also examined.Thirdly, transient pulsatile non-spiral and spiral blood flow through a threedimensionalmodel of irregular stenosis are investigated by applying LES and comparisonis drawn between non-spiral flow through a regular stenosis and that throughan irregular stenosis.Lastly, pulsatile non-spiral and spiral blood flow through a three-dimensionalmodel of irregular stenosis with an adjacent post-stenotic irregular aneurysm in thesame 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 pathophysioloicalconsequences. In steady flow through the straight stenosed tube, excellent agreementbetween LES results for Re = 1000 and 2000 and the corresponding experimentalresults are found when the appropriate inlet perturbations are introduced.In the models with an upstream curved segment, no significant effect of spiral flowon any flow property is found for the investigated Reynolds numbers; spiral patterndisappears before the stenosis – which may be due the rigid wall used in the modelsand/or a steady flow at the inlet. The effects of the curved upstream model can beseen mainly in the maximum turbulent kinetic energy (TKE), the maximum pressuredrop and the maximum wall shear stress (WSS), which in the curved upstreammodels generally increase significantly compared with the corresponding results inthe straight stenosed tube.The maximumcontributions of the SGS motion to the large-scale motion in bothnon-spiral and spiral flow through a regular stenosis, an irregular stenosis and an irregularstenosis with an adjacent post-stenotic irregular aneurysm are 50%, 55%and25%, respectively, for the highest Reynolds number investigated in each model. Althoughthe wall pressure and shear stress obtained from the k-ω Transitional modelagree quite well with the corresponding LES results, the turbulent results obtainedfrom the k-ω Transitional model differ significantly from the corresponding LESresults – this shows unsuitability of the k-ω model for pulsatile flow simulation.Large permanent recirculation regions are observed right after the stenosis throat inboth non-spiral and spiral flow, which in the model of a stenosis with an adjacentpost-stenotic aneurysm are stretched beyond the aneurysm and the length of therecirculation regions increases with spiral velocity. This study shows that, in bothsteady and unsteady pulsatile flow through the straight tube model having either astenosis (regular or irregular) or an irregular stenosis with an adjacent post-stenoticirregular aneurysm, the TKE rises significantly at some locations and phases if aspiral effect is introduced at the inlet of the model. However, the maximum valueof the TKE in a high spiral flow drops considerably compared with that in a lowspiral flow. The maximum wall pressure drop and shear stress occur around thestenosis throat during all the phases of the pulsatile cycle. In the model of a stenosisonly, the wall pressure rises in the immediate post-stenotic region after its drop atthe 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 thelast quarter of the aneurysm. The effects of the spiral flow on the wall pressure andWSS 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, areobserved in the downstream transition-to-turbulence region in both the non-spiraland spiral flow. At some locations in the transition region, the velocity spectrain 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, themaximum wall pressure drop, the maximum WSS and the maximum TKE in thenon-spiral flow through the irregular stenosis rise significantly compared with thecorresponding results in the non-spiral flow through the regular stenosis.When the area reduction in the stenosis is increased, the maximum pressuredrop, the maximumWSS and the TKE rise sharply. As for the effects of the lengthof the stenosis, the maximum WSS falls significantly and the maximum TKE risessharply due to the increase in the length of the stenosis; but the maximum pressuredrop is almost unaffected by the increase in the stenosis length. The increase inthe amplitude of pulsation causes both the maximum pressure drop and the maximumWSS to increase significantly under the inlet peak flow condition. Whilethe increased amplitude of pulsation decrease the maximum TKE, it is nonethelessresponsible for the sharp rise in the TKE found at some places in the transition-toturbulenceregion. The decrease in the Womersley number causes the maximumTKE to increase dramatically; however, the maximum pressure drop and the maximumWSS decrease slightly under the inlet peak flow condition as a result of thedecrease in the Womersley number.The author does believe that the present study makes a breakthrough in understandingthe non-spiral and spiral transient blood flows through arteries having astenosis and a stenosis with an adjacent post-stenotic aneurysm. The findings of thethesis would, therefore, help the interested groups such as pathologists,medical surgeonsand researchers greatly in gaining better insight into the transient non-spiraland spiral blood flow through models of arterial stenosis and aneurysm.