Combining statistical shape modeling, CFD, and meta‐modeling to approximate the patient‐specific pressure‐drop across the aortic valve in real‐time

Abstract

Background: Advances in medical imaging, segmentation techniques, and high performance computing have stimulated the use of complex, patient-specific, three-dimensional Computational Fluid Dynamics (CFD) simulations. Patient-specific, CFD-compatible geometries of the aortic valve are readily obtained. CFD can then be used to obtain the patient-specific pressure-flow relationship of the aortic valve. However, such CFD simulations are computationally expensive, and real-time alternatives are desired. Aim: The aim of this work is to evaluate the performance of a meta-model with respect to high-fidelity, three-dimensional CFD simulations of the aortic valve. Methods: Principal component analysis was used to build a statistical shape model (SSM) from a population of 74 iso-topological meshes of the aortic valve. Synthetic meshes were created with the SSM, and steady-state CFD simulations at flow-rates between 50 and 650 mL/s were performed to build a metamodel. The meta-model related the statistical shape variance, and flow-rate to the pressure-drop. Results: Even though the first three shape modes account for only 46% of shape variance, the features relevant for the pressure-drop seem to be captured. The three-mode shape-model approximates the pressure-drop with an average error of 8.8% to 10.6% for aortic valves with a geometric orifice area below 150 mm 2. The proposed methodology was least accurate for aortic valve areas above 150 mm 2. Further reduction to a meta-model introduces an additional 3% error.

The impact of shape uncertainty on aortic‐valve pressure‐drop computations

“…Density based methods which characterize the output distribution by the cumulative density function, may in those cases be more appropriate, and should be considered in future work. 62 In line with Hoeijmakers et al, 4 the transvalvular pressure-drop at peak systole was approximated by CFD simulations, and expressed as an uncertain scalar parameter Y . In-vivo however, the transvalvular pressure-drop would strongly vary throughout the cardiac cycle due to flow pulsatility.…”

“…However, 3D patient‐specific computational models are generally of complex shape, difficult to parameterize, and the influence of shape variation is therefore mostly neglected. Instead of using physically meaningful parameters, this work used statistical shape modeling to parameterize the shape of the valve 4 . The statistical shape modes provided a parameterization of the geometry, and facilitated the training of a meta‐model (Figure 1(A)).…”

“…The shape coefficients can be regarded as a patient‐specific parameterization of the aortic valve and surrounding structures, and values for the 74 original valve segmentations were found by Equation (6). Besides approximating the surface meshes in the training set, Equation (5) was used to generate a population of “virtual” aortic valve geometries that were within three times the square root of the eigenvalue () of its respective shape mode, also see Hoeijmakers et al 4 or Heimann and Meinzer 33 . Figure 2 illustrates the shape variation that was contained in the first five shape modes, and showed that the first shape mode (), weighted by , controlled the opening and closing behavior of the aortic valve.…”

“…This weighting factor was empirically established, and helped to reduce the approximation error of vertices that were part of, or close to the free cusp edges. For a more detailed description on the performance (e.g., compactness and generalizability) of the statistical shape model and for a comparison between CFD results on the original segmentation and the approximated shape by the SSM we would like to refer to the work of Hoeijmakers et al 4 The shape coefficients α p,m can be regarded as a patient-specific parameterization of the aortic valve and surrounding structures, and values for the 74 original valve segmentations were found by Equation ( 6). Besides approximating the surface meshes in the training set, Equation ( 5) was used to generate a population of "virtual" aortic valve geometries that were within three times the square root of the eigenvalue ( À3 ffiffiffiffiffi ffi…”

Data-driven cardiovascular flow modelling: examples and opportunities

“…PCA has been used in predicting cerebral aneurysm rupture based on morphology and haemodynamics [43]. Statistical shape modelling with PCA could facilitate geometric characterization of the vasculature [44][45][46][47] and the heart [48,49]. One challenge in using PCA is that the rows need to be consistently placed in different snapshots.…”