BackgroundIncreased aortic stiffness is an independent predictor of cardiovascular disease. Optimal measurement is highly beneficial for the detection of atherosclerosis and the management of patients at risk. Thus, it was our purpose to selectively measure aortic stiffness using a novel imaging method and to provide reference values from a population-based study.MethodsOne hundred twenty six inhabitants of Freiburg, Germany, between 20 and 80 years prospectively underwent 3 Tesla cardiovascular magnetic resonance (CMR) of the thoracic aorta. 4D flow CMR (spatial/temporal resolution 2mm3/20ms) was executed to calculate aortic pulse wave velocity (PWV) in m/s using dedicated software. In addition, we calculated distensibility coefficients (DC) using 2D CINE CMR imaging of the ascending (AAo) and descending aorta (DAo). Segmental aortic diameter and thickness of aortic plaques were determined by 3D T1 weighted CMR (spatial resolution 1mm3).ResultsPWV increased from 4.93 ± 0.54 m/s in 20–30 year-old to 8.06 ± 1.03 m/s in 70–80 year-old subjects. PWV was significantly lower in women compared to men (p < 0.0001). Increased blood pressure (systolic r = 0.36, p < 0.0001; diastolic r = 0.33, p = 0.0001; mean arterial pressure r = 0.37, p < 0.0001) correlated with PWV after adjustment for age and gender. Finally, PWV increased with increasing diameter of the aorta (ascending aorta r = 0.20, p = 0.026; aortic arch r = 0.24, p = 0.009; descending aorta r = 0.26, p = 0.004). Correlation of PWV and DC of the AAo and DAo or the mean of both was high (r = 0.69, r = 0.68, r = 0.73; p < 0.001).Conclusions4D flow CMR was successfully applied to calculate aortic PWV and thus aortic stiffness. Findings showed a high correlation with distensibility coefficients representing local compliance of the aorta. Our novel method and reference data for PWV may provide a reliable biomarker for the identification of patients with underlying cardiovascular disease and optimal guidance of future treatment in studies or clinical routine.

Abstract. Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order k+1 to 2k+1 through the use of smoothness-increasing accuracy-conserving (SIAC) filtering. However, it is a computationally complex task to perform this in an efficient manner, which becomes an even greater issue considering nonquadrilateral mesh structures. In this paper, we present an extension of this SIAC filter to structured triangular meshes. The basic theoretical assumption in the previous implementations of the postprocessor limits the use to numerical solutions solved over a quadrilateral mesh. However, this assumption is restrictive, which in turn complicates the application of this postprocessing technique to general tessellations. Additionally, moving from quadrilateral meshes to triangulated ones introduces more complexity in the calculations as the number of integrations required increases. In this paper, we extend the current theoretical results to variable coefficient hyperbolic equations over structured triangular meshes and demonstrate the effectiveness of the application of this postprocessor to structured triangular meshes as well as exploring the effect of using inexact quadrature. We show that there is a direct theoretical extension to structured triangular meshes for hyperbolic equations with bounded variable coefficients. This is a challenging first step toward implementing SIAC filters for unstructured tessellations. We show that by using the usual B-spline implementation, we are able to improve on the order of accuracy as well as decrease the magnitude of the errors. These results are valid regardless of whether exact or inexact integration is used. The results here demonstrate that it is still possible, both theoretically and computationally, to improve to 2k+1 over the DG solution itself for structured triangular meshes.

2 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2018.

Abstract. The discontinuous Galerkin (DG) method has very quickly found utility in such diverse applications as computational solid mechanics, fluid mechanics, acoustics, and electromagnetics. The DG methodology merely requires weak constraints on the fluxes between elements. This feature provides a flexibility which is difficult to match with conventional continuous Galerkin methods. However, allowing discontinuity between element interfaces can in turn be problematic during simulation postprocessing, such as in visualization. Consequently, smoothness-increasing accuracyconserving (SIAC) filters were proposed in [M. Steffen et al., IEEE Trans. Vis. Comput. Graph., 14 (2008), pp. 680-692, D. Walfisch et al., J. Sci. Comput., 38 (2009 as a means of introducing continuity at element interfaces while maintaining the order of accuracy of the original input DG solution. Although the DG methodology can be applied to arbitrary triangulations, the typical application of SIAC filters has been to DG solutions obtained over translation invariant meshes such as structured quadrilaterals and triangles. As the assumption of any sort of regularity including the translation invariance of the mesh is a hindrance towards making the SIAC filter applicable to real life simulations, we demonstrate in this paper for the first time the behavior and complexity of the computational extension of this filtering technique to fully unstructured tessellations. We consider different types of unstructured triangulations and show that it is indeed possible to get reduced errors and improved smoothness through a proper choice of kernel scaling. These results are promising, as they pave the way towards a more generalized SIAC filtering technique.

The discontinuous Galerkin (DG) methods provide a high-order extension of the finite volume method in much the same way as high-order or spectral/hp elements extend standard finite elements. However, lack of inter-element continuity is often contrary to the smoothness assumptions upon which many post-processing algorithms such as those used in visualization are based. Smoothness-increasing accuracy-conserving (SIAC) filters were proposed as a means of ameliorating the challenges introduced by the lack of regularity at element interfaces by eliminating the discontinuity between elements in a way that is consistent with the DG methodology; in particular, high-order accuracy is preserved and in many cases increased. The goal of this paper is to explicitly define the steps to efficient computation of this filtering technique as applied to both structured triangular and quadrilateral meshes. Furthermore, as the SIAC filter is a good candidate for parallelization, we provide, for the first time, results that confirm anticipated performance scaling when parallelized on a shared-memory multi-processor machine.