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Dynamics and stability of flow through abdominal aortic aneurysms

Abstract : The main objective of this thesis is to characterise the flow fields observed in an ab- dominal aortic aneurysm (AAA) under different physiological conditions during its progressive enlargement. An axisymmetric AAA, modeled as an inflation of gaus- sian shape on a vessel of circular cross-section, is considered in the present study. This means that the results are more significant for the early stages of growth of an AAA. The model AAA is characterized by a maximum height H and width W , made dimensionless by the upstream vessel diameter. To begin with, the flow char- acteristics in AAAs are investigated using steady flows. The global linear stability of the base flows is analysed by determining the eigenfrequencies and eigenfunctions of small-amplitude perturbations. In order to understand the instability mechanisms, the energy transfer between the base flow and the perturbations is computed. The flow in relatively shallow aneurysms (of relatively large width) become unstable by the lift-up mechanism and have a perturbation flow which is characterized by sta- tionary, growing modes. More localized aneurysms (with relatively small width) become unstable at larger Reynolds numbers, presumably by an elliptic instability mechanism; in this case the perturbation flow is characterized by oscillatory modes. For the case of pulsatile flows, two types of physiological flowrate waveforms are considered in our study, corresponding to rest and exercise conditions. The flows are observed to remain attached to the walls during the systolic phase, with flow separation generally observed during the deceleration after the peak systole. Dur- ing this phase, the vorticity is found to roll-up into a vortex at the proximal end. This vortex enlarges with time and impinges at the downstream end of the AAA, resulting in large spatial gradients of wall shear stress (WSS) along the wall, which are not found in the healthy case. The flow conditions are observed to vary signifi- cantly with Womersley (Wo) and Reynolds (Re) numbers, with the flow remaining attached to the walls for longer times, as the Womersley number Wo increases. The principal effect of increasing Re is that the primary vortex formed after peak systole is stronger. Clinically relevant flow characteristics of aneurysmal flow, i.e. detache- ment of flow and impingement on the distal end, the presence of low oscillatory WSS within the AAA, are observed even for very shallow aneurysms. For deep aneurysms, multiple vortices are observed throughout the cycle within the AAA cavity. Stability analysis of pulsatile base flows reveals that the maximum values of the perturbations are observed near the distal end of the AAA. However, they are not entirely confined to the AAA cavity and extend downstream, implying that once an AAA is formed, the disturbed flow conditions spread even to the unde- formed arterial walls downstream of the AAA. Finally, by considering two equiva- lent AAA shapes modeled by a sinusoidal and a gaussian function, the sensitivity of these results with respect to the details of the geometry has been established.
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Submitted on : Friday, February 28, 2014 - 4:47:54 PM
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  • HAL Id : tel-00954202, version 1


Shyam Sunder Gopalakrishnan. Dynamics and stability of flow through abdominal aortic aneurysms. Fluids mechanics [physics.class-ph]. Université Claude Bernard - Lyon I, 2014. English. ⟨NNT : ⟩. ⟨tel-00954202⟩



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