Geometric microcanonical theory of two-dimensional truncated Euler flows.

This paper presents a geometric microcanonical ensemble perspective on two-dimensional truncated Euler flows, which contain a finite number of (Fourier) modes and conserve energy and enstrophy. We explicitly perform phase space volume integrals over shells of constant energy and enstrophy. Two applications are considered. In the first part, we determine the average energy spectrum for highly condensed flow configurations and show that the result is consistent with Kraichnan's canonical ensemble description, despite the fact that no thermodynamic limit is invoked. In the second part, we compute the probability density for the largest-scale mode of a free-slip flow in a square, which displays reversals. We test the results against numerical simulations of a minimal model and find excellent agreement with the microcanonical theory, unlike the canonical theory, which fails to describe the bimodal statistics. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

Visualization of two-dimensional transverse blood flow direction using optical coherence tomography angiography.

SIGNIFICANCE: Evaluation of vessel patency and blood flow direction is important in various medical situations, including diagnosis and monitoring of ischemic diseases, and image-guided vascular surgeries. While optical coherence tomography angiography (OCTA) is the most widely used functional extension of optical coherence tomography that visualizes three-dimensional vasculature, inability to provide information of blood flow direction is one of its limitations. AIM: We demonstrate two-dimensional (2D) transverse blood flow direction imaging in en face OCTA. APPROACH: A series of triangular beam scans for the fast axis was implemented in the horizontal direction for the first volume scan and in the vertical direction for the following volume scan, and the inter A-line OCTA was performed for the blood flow direction imaging while the stepwise pattern was used for each slow axis scan. The decorrelation differences between the forward and the backward inter A-line OCTA were calculated for the horizontal and the vertical fast axis scans, and the ratio of the horizontal and the vertical decorrelation differences was utilized to show the 2D transverse flow direction information. RESULTS: OCTA flow direction imaging was verified using flow phantoms with various flow orientations and speeds, and we identified the flow speed range relative to the scan speed for reliable flow direction measurement. We demonstrated the visualization of 2D transverse blood flow orientations in mouse brain vascular networks in vivo. CONCLUSIONS: The proposed OCTA imaging technique that provides information of 2D transverse flow direction can be utilized in various clinical applications and preclinical studies.

Quantification of pulmonary regurgitation in patients with repaired Tetralogy of Fallot by 2D phase-contrast MRI: Differences between the standard method of velocity averaging and a pixel-wise analysis.

OBJECTIVES: To compare the values of pulmonary regurgitation in patients with repaired Tetralogy of Fallot quantified from two-dimensional phase-contrast data, by using a new pixel-wise analysis and the standard velocity-averaging method. DESIGN: Quantitative in silico and in vivo analysis. SETTING: Hospital Sótero del Río. The magnetic resonance images were acquired using a Philips Achieva 1.5T scanner. PARTICIPANTS: Twenty-five patients with repaired Tetralogy of Fallot who underwent cardiovascular magnetic resonance imaging requested by their referring physicians were included in this study. MAIN OUTCOME MEASURES: Using a computational fluid dynamics simulation, we validated our pixel-wise method, quantifying the error of our method in comparison with the standard method. The patients underwent a standard two-dimensional phase-contrast magnetic resonance imaging acquisition for quantifying pulmonary artery flow. Pulmonary regurgitation fraction was estimated by using our pixel-wise and the standard method. The two-dimensional flow profiles were inspected looking for simultaneous antegrade and retrograde flows in the same cardiac phase. Statistical analysis was performed with t-test for related samples, Bland-Altman plots, and Pearson correlation coefficient. RESULTS: Estimation of pulmonary regurgitation fraction using the pixel-wise analysis revealed higher values compared with the standard method (39 ± 16% vs. 30 ± 22%, p-value <0.01). Eight patients (32%) had a difference of more than 10% between methods. Analysis of two-dimensional flow profiles in these patients revealed simultaneous antegrade and retrograde flows through the pulmonary artery during systole-early diastole. CONCLUSION: Quantification of pulmonary regurgitation fraction in patients with repaired Tetralogy of Fallot through a pixel-wise analysis yields higher values of pulmonary regurgitation compared with the standard velocity-averaging method.