Quantitative assessment of 4D hemodynamics in cerebral aneurysms using proper orthogonal decomposition

Modal Decomposition Techniques: Application in Coherent Structures for a Saccular Aneurysm Model

Aneurysms are localized expansions of blood vessels which can be fatal upon rupture. Studies have shown that aneurysm flows exhibit complex flow phenomena which consist of single or multiple vortical structures that move within the flow cycle. Understanding the complex flow behaviors of aneurysms remain challenging. Thus, the goal of this study is to quantify the flow behavior and extract physical insights into aneurysm flows using advance data decomposition methods, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The velocity field data were obtained by performing 2D Particle Image Velocimetry (2D PIV) on the mid-plane of an idealized, rigid, saccular aneurysm model. The input flow conditions were set to Rep=50 and 150 for a fixed α=2 using a precisely controlled piston pump system. POD was used to quantify the spatial features of the flows, while DMD was used to obtain insight on the dynamics. The results obtained from POD and DMD showed the capability of both methods to quantify the flow field, with the modes obtained providing different insights into the flow evolution in the aneurysm. The curve-fitting step of the POD time-varying coefficients, and the appropriate selection of DMD modes based on their energy contribution, allowed the mathematical flow models from POD and DMD to reconstruct flow fields at any given time step. This can be used for validation of numerical or computational data.

Application of Dynamic Mode Decomposition to Study Temporal Flow Behavior in a Saccular Aneurysm

Aneurysms are abnormal expansion of weakened blood vessels which can cause mortality or long-term disability upon rupture. Several studies have shown that inflow conditions spatially and temporally influence aneurysm flow behavior. The objective of this investigation is to identify impact of inflow conditions on spatio-temporal flow behavior in an aneurysm using dynamic mode decomposition (DMD). For this purpose, low-frame rate velocity field measurements are performed in an idealized aneurysm model using particle image velocimetry (PIV). The inflow conditions are precisely controlled using a ViVitro SuperPump system where nondimensional fluid parameters such as peak Reynolds number (Rep) and Womersely number (α) are varied from 50-270 and 2-5, respectively. The results show the ability of DMD to identify the spatial flow structures and their frequency content. Furthermore, DMD captured the impact of inflow conditions, and change in mode shapes, amplitudes, frequency, and growth rate information is observed. The DMD low-order flow reconstruction also showed the complex interplay of flow features for each inflow scenario. Furthermore, the low-order reconstruction results provided a mathematical description of the flow behavior in the aneurysm which captured the vortex formation, evolution, and convection in detail. These results indicated that the vortical structure behavior varied with the change in α while its strength and presence of secondary structures are influenced by the change in Rep.

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

Aneurysms are abnormal ballooning of a blood vessel. Previous studies have shown presence of complex flow structures in aneurysms. The objective of this study was to quantify the flow features observed in two selected saccular aneurysm geometries over a range of inflow conditions using Proper Orthogonal Decomposition (POD). For this purpose, two rigid-wall saccular aneurysm models geometries were used (i.e., the bottleneck factor of 1 and 1.6), and the inflow conditions were varied using a peak Reynolds number (Rep) from 50 and 270 and Womersley number (α) from 2 and 5. The velocity flow field data for the studied aneurysm geometries were acquired using Particle Image Velocimetry (PIV). The average flow field from the PIV measurement showed that the model geometry and Rep have more significant impact on the average flow field than the variations in α. The POD results showed that the method was able to quantify the flow field characteristics between the two model geometries. The mode shapes obtained showed different spatial structures for each inflow scenarios and models. The POD energy results showed that more than 80% of the fluctuating kinetic energy were captured within five POD modes for BF=1.0 flow scenarios, while they were captured within ten modes for BF=1.6. The time varying coefficient results showed the complex interplay of POD modes at different inflow scenarios, highlighting important modes at different phases of the flow cycle. The low-order reconstruction results showed that the vortical structure either proceeded outward or stayed within the aneurysm, and this behavior was highly dependent on α, Rep, and model geometry that were not evident in average PIV results.

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

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 (Rep) and Womersley number (α) were varied from 50 to 270 and 2 to 5, respectively. The velocity flow field measurements at the midplane 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 α, while vortex strength and formation of secondary structures were correlated with an increase in Rep.

Spectral Decomposition of the Flow and Characterization of the Sound Signals through Stenoses with Different Levels of Severity

Treatments of atherosclerosis depend on the severity of the disease at the diagnosis time. Non-invasive diagnosis techniques, capable of detecting stenosis at early stages, are essential to reduce associated costs and mortality rates. We used computational fluid dynamics and acoustics analysis to extensively investigate the sound sources arising from high-turbulent fluctuating flow through stenosis. The frequency spectral analysis and proper orthogonal decomposition unveiled the frequency contents of the fluctuations for different severities and decomposed the flow into several frequency bandwidths. Results showed that high-intensity turbulent pressure fluctuations appeared inside the stenosis for severities above 70%, concentrated at plaque surface, and immediately in the post-stenotic region. Analysis of these fluctuations with the progression of the stenosis indicated that (a) there was a distinct break frequency for each severity level, ranging from 40 to 230 Hz, (b) acoustic spatial-frequency maps demonstrated the variation of the frequency content with respect to the distance from the stenosis, and (c) high-energy, high-frequency fluctuations existed inside the stenosis only for severe cases. This information can be essential for predicting the severity level of progressive stenosis, comprehending the nature of the sound sources, and determining the location of the stenosis with respect to the point of measurements.

Proper Orthogonal Decomposition Analysis of the Flow Downstream of a Dysfunctional Bileaflet Mechanical Aortic Valve

PURPOSE

Aortic valve replacement remains the only viable solution for symptomatic patients with severe aortic valve stenosis. Despite their improved design and long history of successful operation, bileaflet mechanical heart valves are still associated with post-operative complications leading to valve dysfunction. Thus, the flow dynamics can be highly disturbed downstream of the dysfunctional valve.

METHODS

In this in vitro study, the flow dynamics downstream of healthy and dysfunctional bileaflet mechanical heart valves have been investigated using particle image velocimetry measurements. Proper orthogonal decomposition of the velocity field has been performed in order to explore the coherent flow features in the ascending aorta in the presence of a dysfunctional bileaflet mechanical heart valve.

RESULTS

The ability of proper orthogonal decomposition derived metrics to differentiate between heathy and dysfunctional cases is reported. Moreover, reduced-order modeling using proper orthogonal decomposition is thoroughly investigated not only for the velocity field but also for higher order flow characteristics such as time average wall shear stress, oscillatory shear index and viscous energy dissipation.

CONCLUSION

Considering these results, proper orthogonal decomposition can provide a rapid binary classifier to evaluate if the bileaflet mechanical valve deviates from its normal operating conditions. Moreover, the study shows that the size of the reduced-order model depends on which flow parameter is required to be reconstructed.

A review on the reliability of hemodynamic modeling in intracranial aneurysms: why computational fluid dynamics alone cannot solve the equation

Computational blood flow modeling in intracranial aneurysms (IAs) has enormous potential for the assessment of highly resolved hemodynamics and derived wall stresses. This results in an improved knowledge in important research fields, such as rupture risk assessment and treatment optimization. However, due to the requirement of assumptions and simplifications, its applicability in a clinical context remains limited.This review article focuses on the main aspects along the interdisciplinary modeling chain and highlights the circumstance that computational fluid dynamics (CFD) simulations are embedded in a multiprocess workflow. These aspects include imaging-related steps, the setup of realistic hemodynamic simulations, and the analysis of multidimensional computational results. To condense the broad knowledge, specific recommendations are provided at the end of each subsection.Overall, various individual substudies exist in the literature that have evaluated relevant technical aspects. In this regard, the importance of precise vessel segmentations for the simulation outcome is emphasized. Furthermore, the accuracy of the computational model strongly depends on the specific research question. Additionally, standardization in the context of flow analysis is required to enable an objective comparison of research findings and to avoid confusion within the medical community. Finally, uncertainty quantification and validation studies should always accompany numerical investigations.In conclusion, this review aims for an improved awareness among physicians regarding potential sources of error in hemodynamic modeling for IAs. Although CFD is a powerful methodology, it cannot provide reliable information, if pre- and postsimulation steps are inaccurately carried out. From this, future studies can be critically evaluated and real benefits can be differentiated from results that have been acquired based on technically inaccurate procedures.