Application of Proper Orthogonal Decomposition to Study Coherent Flow Structures in a Saccular Aneurysm

Abstract

Aneurysms are localized expansions of weakened blood vessels that can be debilitating or fatal upon rupture. Previous studies have shown that flow in an aneurysm exhibits complex flow structures that are correlated with its inflow conditions. Therefore, the objective of this study was to demonstrate the application of Proper Orthogonal Decomposition (POD) to study the impact of different inflow conditions on energetic flow structures and their temporal behavior in an aneurysm. To achieve this objective, experiments were performed on an idealized rigid sidewall aneurysm model. A piston pump system was used for precise inflow control, i.e., peak Reynolds number ($Re_p$) and Womersley number ($\alpha$) were varied from 50-270 and 2-5, respectively. The velocity flow field measurements at the mid-plane location of the idealized aneurysm model were performed using Particle Image Velocimetry (PIV). The results demonstrate the efficacy of POD in decomposing complex data, and POD was able to capture the energetic flow structures unique to each studied inflow condition. Furthermore, the time-varying coefficient results highlighted the interplay between the coefficients and their corresponding POD modes, which in turn helped explain how POD modes impact certain flow features. The low-order reconstruction results were able to capture the flow evolution and provide information on complex flow in an aneurysm. The POD and low-order reconstruction results also indicated that vortex formation, evolution, and convection varied with an increase in $\alpha$, while vortex strength and formation of secondary structures were correlated with an increase in $Re_p$.

Aneurysmal Growth in Type-B Aortic Dissection: Assessing the Impact of Patient-Specific Inlet Conditions on Key Haemodynamic Indices

“…POD was performed using the velocity field from each IVP. Across all IVPs, the first four POD modes capture 96 − 97% of the total normalised KE, which matches observations in other cardiovascular POD analyses 48 . The normalised energy content of mode 1 varies between 79.4% and 84.2% for the different cases, as shown in Fig.…”

“…The energy-based ranking of modes is performed such that the flow can be accurately reconstructed using a discrete quantity of these modes 2 , thus reducing the order of the system. The flow is said to be accurately represented by the ensemble of modes containing 98% of the total KE which, in cardiovascular flows, has been widely reported to occur within the first 1-10 modes 17,29,8,48 .…”

Aneurysmal growth in type-B aortic dissection: assessing the impact of patient-specific inlet conditions on key haemodynamic indices

“…To compare cases, the energy captured within a given POD mode was normalized by the total energy across all 127 modes within that case. Across all IVPs, the first four POD modes capture 96-97% of the total normalized KE, matching observations in other cardiovascular POD analyses [33].…”

“…The energy-based ranking of modes is performed such that the flow can be accurately reconstructed using a reduced number of these modes [17], thus reducing the order of the system. The flow is said to be accurately represented by the ensemble of modes containing 98% of the total KE which, in cardiovascular flows, has been widely reported to occur within the first 1-10 modes [16,19,33].…”

Comparison of Flow Behavior in Saccular Aneurysm Models Using Proper Orthogonal Decomposition

“…The trend of vortical structure behavior was also observed with other experimental and numerical studies [12,[18][19][20][21][22]. Although the presence of these vortical structures has been studied extensively, understanding them better remains a challenge due to the complexity of flow patterns present inside the aneurysm sac that are dependent on incoming flow conditions [23,24].…”