The influence of model order reduction on the computed fractional flow reserve using parameterized coronary geometries

\u3cp\u3eComputational fluid dynamics (CFD) models combined with patient-specific imaging data are used to non-invasively predict functional significance of coronary lesions. This approach to predict the fractional flow reserve (FFR) is shown to have a high diagnostic accuracy when comparing against invasively measured FFR. However, one of the main drawbacks is the high computational effort needed for preprocessing and computations. Hence, uncertainty quantification may become unfeasible. Reduction of complexity is desirable, computationally inexpensive models with high diagnostic accuracy are preferred. We present a parametric comparison study for three types of CFD models (2D axisymmetric, Semi-3D and 3D) in which we study the impact of model reduction on three models on the predicted FFR. In total 200 coronary geometries were generated for seven geometrical characteristics e.g. stenosis severity, stenosis length and vessel curvature. The effect of time-averaged flow was investigated using unsteady, mean steady and a root mean square (RMS) steady flow. The 3D unsteady model was regarded as reference model. Results show that when using an unsteady or RMS flow, predicted FFR hardly varies between models contrary to using average flows. The 2D model with RMS flow has a high diagnostic accuracy (0.99), reduces computational time by a factor 162,000 and the introduced model error is well below the clinical relevant differences. Stenosis severity, length, curvature and tapering cause most discrepancies when using a lower order model. An uncertainty analysis showed that this can be explained by the low variability that is caused by variations in stenosis asymmetry.\u3c/p\u3

A metamodeling approach for instant severity assessment and uncertainty quantification of iliac artery stenoses

\u3cp\u3eTwo-dimensional (2D) or three-dimensional (3D) models of blood flow in stenosed arteries can be used to patient-specifically predict outcome metrics, thereby supporting the physicians in decision making processes. However, these models are time consuming which limits the feasibility of output uncertainty quantification (UQ). Accurate surrogates (metamodels) might be the solution. In this study, we aim to demonstrate the feasibility of a generalized polynomial chaos expansion-based metamodel to predict a clinically relevant output metric and to quantify the output uncertainty. As an example, a metamodel was constructed from a recently developed 2D model that was shown to be able to estimate translesional pressure drops in iliac artery stenoses (-0.9 ± 12.7 mmHg, R2 = 0.81). The metamodel was constructed from a virtual database using the adaptive generalized polynomial chaos expansion (agPCE) method. The constructed metamodel was then applied to 25 stenosed iliac arteries to predict the patient-specific pressure drop and to perform UQ. Comparing predicted pressure drops of the metamodel and in vivo measured pressure drops, the mean bias (-0.2 ± 13.7 mmHg) and the coefficient of determination (R2 = 0.80) were as good as of the original 2D computational fluid dynamics (CFD) model. UQ results of the 2D and metamodel were comparable. Estimation of the uncertainty interval using the original 2D model took 14 days, whereas the result of the metamodel was instantly available. In conclusion, it is feasible to quantify the uncertainty of the output metric and perform sensitivity analysis (SA) instantly using a metamodel. Future studies should investigate the possibility to construct a metamodel of more complex problems.\u3c/p\u3

Application of an adaptive polynomial chaos expansion on computationally expensive three-dimensional cardiovascular models for uncertainty quantification and sensitivity analysis

When applying models to patient-specific situations, the impact of model input uncertainty on the model output uncertainty has to be assessed. Proper uncertainty quantification (UQ) and sensitivity analysis (SA) techniques are indispensable for this purpose. An efficient approach for UQ and SA is the generalized polynomial chaos expansion (gPCE) method, where model response is expanded into a finite series of polynomials that depend on the model input (i.e., a meta-model). However, because of the intrinsic high computational cost of three-dimensional (3D) cardiovascular models, performing the number of model evaluations required for the gPCE is often computationally prohibitively expensive. Recently, Blatman and Sudret (2010, “An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis,” Probab. Eng. Mech., 25(2), pp. 183–197) introduced the adaptive sparse gPCE (agPCE) in the field of structural engineering. This approach reduces the computational cost with respect to the gPCE, by only including polynomials that significantly increase the meta-model’s quality. In this study, we demonstrate the agPCE by applying it to a 3D abdominal aortic aneurysm (AAA) wall mechanics model and a 3D model of flow through an arteriovenous fistula (AVF). The agPCE method was indeed able to perform UQ and SA at a significantly lower computational cost than the gPCE, while still retaining accurate results. Cost reductions ranged between 70–80% and 50–90% for the AAA and AVF model, respectively

Decoupling the effect of shear stress and stretch on tissue growth and remodeling in a vascular graft

\u3cp\u3eThe success of cardiovascular tissue engineering (TE) strategies largely depends on the mechanical environment in which cells develop a neotissue through growth and remodeling processes. This mechanical environment is defined by the local scaffold architecture to which cells adhere, that is, the microenvironment, and by external mechanical cues to which cells respond, that is, hemodynamic loading. The hemodynamic environment of early developing blood vessels consists of both shear stress (due to blood flow) and circumferential stretch (due to blood pressure). Experimental platforms that recapitulate this mechanical environment in a controlled and tunable manner are thus critical for investigating cardiovascular TE. In traditional perfusion bioreactors, however, shear stress and stretch are coupled, hampering a clear delineation of their effects on cell and tissue response. In this study, we uniquely designed a bioreactor that independently combines these two types of mechanical cues in eight parallel vascular grafts. The system is computationally and experimentally validated, through finite element analysis and culture of tissue constructs, respectively, to distinguish various levels of shear stress (up to 5 Pa) and cyclic stretch (up to 1.10). To illustrate the usefulness of the system, we investigated the relative contribution of cyclic stretch (1.05 at 0.5 Hz) and shear stress (1 Pa) to tissue development. Both types of hemodynamic loading contributed to cell alignment, but the contribution of shear stress overruled stretch-induced cell proliferation and matrix (i.e., collagen and glycosaminoglycan) production. At a macroscopic level, cyclic stretching led to the most linear stress-stretch response, which was not related to the presence of shear stress. In conclusion, we have developed a bioreactor that is particularly suited to further unravel the interplay between hemodynamics and in situ TE processes. Using the new system, this work highlights the importance of hemodynamic loading to the study of developing vascular tissues.\u3c/p\u3