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The paper discusses a stabilization of a finite element method for the equations of fluid motion in a time-dependent domain. After experimental convergence analysis, the method is applied to simulate a blood flow in the right ventricle of a post-surgery patient with the transposition of the great arteries disorder. The flow domain is reconstructed from a sequence of 4D CT images. The corresponding segmentation and triangulation algorithms are also addressed in brief.

In this work we analyze the impact of left ventricular assist devices on the systemic circulation in subjects with heart failure associated with left ventricular dilated cardiomyopathy. We use an integrated model of the left heart and blood flow in the systemic arteries with a left ventricular assist device. We study the impact of the rotation speed of the pump on haemodynamic characteristics of distal arteries. We identify the rotation speed for simultaneous recovery of the healthy average values in all systemic arteries, the heart and the aorta. Our numerical experiments show that blood distribution over the graph of systemic vessels does not depend on flow regimes in ascending aorta. We also observe that the optimal pump rotation speed changes in the atherosclerotic vascular network and depends on stenoses localization.

While coronary revascularization strategies guided by instantaneous wave-free ratio (iFR) are, in general, noninferior to those guided by fractional flow reserve (FFR) with respect to the rate of major adverse cardiac events at one-year follow-up in patients with stable angina or an acute coronary syndrome, the overall accuracy of diagnosis with iFR in large patient cohorts is about 80% compared with the diagnosis with FFR. So far, it remains incompletely understood what factors contribute to the discordant diagnosis between iFR and FFR. In this study, a computational method was used to systemically investigate the respective effects of various cardiovascular factors on FFR and iFR. The results showed that deterioration in aortic valve disease (e.g., regurgitation or stenosis) led to a marked decrease in iFR and a mild increase in FFR given fixed severity of coronary artery stenosis and that increasing coronary microvascular resistance caused a considerable increase in both iFR and FFR, but the degree of increase in iFR was lower than that in FFR. These findings suggest that there is a high probability of discordant diagnosis between iFR and FFR in patients with severe aortic valve disease or coronary microcirculation dysfunction.

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. These preconditioners are analyzed on the fine scale and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.