Dynamics of ranking processes in complex systems.

The world is addicted to ranking: everything, from the reputation of scientists, journals, and universities to purchasing decisions is driven by measured or perceived differences between them. Here, we analyze empirical data capturing real time ranking in a number of systems, helping to identify the universal characteristics of ranking dynamics. We develop a continuum theory that not only predicts the stability of the ranking process, but shows that a noise-induced phase transition is at the heart of the observed differences in ranking regimes. The key parameters of the continuum theory can be explicitly measured from data, allowing us to predict and experimentally document the existence of three phases that govern ranking stability.

Impact of synthetic elements on aortic root haemodynamics: computed fluid dynamics of aortic root reconstruction and valve reimplantation.

Objectives: The aim was to evaluate the impact of the aortic valve reimplantation (David) and of the aortic root (AoR) remodelling (Yacoub) on the AoR haemodynamics. Methods: In an experimental setup where the clinical scenario of Yacoub, ( n = 5, domestic pig) and of David ( n = 5, domestic pig) procedure was performed in each AoR, six high-fidelity (200 Hz) sonomicrometric crystals were implanted. Crystals were positioned at three commissures with their projection at the root base. In post-measurement processing 3D deformation of both AoR was determined and used for computed fluid dynamic modelling in order to evaluate pressure, velocity and shear stress profiles. Results: In David AoR: high pressure (> 150 mmHg) and low to moderate shear stress (0-30 Pa) were found from the period of isovolemic contraction to the closure of the aortic valve. At mid diastole pressure augmentation (> 120 mmHg) a low shear stress (0-10 Pa) was registered at the leaflets, three commissures, and intervalvular triangles. In Yacoub AoR: high pressure (110-130 mmHg) with moderate low shear stress (0-30 Pa) was only registered at isovolemic contraction. Conclusions: The results show that haemodynamic conditions following a David procedure have a less favourable pattern as compared to a Yacoub AoR. In David AoR, high pressure and low shear stress are present during 2/3 of the cardiac cycle, whereas in Yacoub root, these conditions are present only for a short period of isovolemic contraction.

Aortic root haemodynamics following David procedure: numerical analysis of 3-dimensional haemodynamics.

OBJECTIVES: The aim was to determine 3-dimensional (3D) geometrical deformation of the aortic root (AoR) following the David procedure in order to evaluate local haemodynamical conditions of individual AoR elements. METHODS: In the experimental set-up, the David procedure was performed on 10 domestic pigs. Data were compared with the measurements obtained in 10 native AoRs. In each AoR, six high-resolution ultrasonometric crystals (200 Hz) were implanted, being positioned at each commissure and at the AoR base. 3D geometrical deformation of the AoR, torsion and tilt angle was determined. Computed fluid dynamics (CFD) simulation analysis was used to evaluate local pressure, flow and shear stress. RESULTS: In David AoRs, the tilt angle was maximal at a peak ejection of 25.9 ± 1.49° and minimal at the end of isovolemic contraction at 23.5 ± 0.80°. David root rotation was maximal at a peak ejection of 27.93 ± 1.54° and minimal at the end of the isovolemic contraction at 25.7 ± 1.32°. In the native AoR, the opposite was observed. Here, the tilt and rotation angle were maximal at the end of isovolemic contraction (17.25 ± 0.68° and 19.71 ± 0.73°) and decreased to its minimal values at peak ejections (14.1 ± 0.62° and 16.33 ± 0.47°). In David AoR, high pressure (>140 mmHg) combined with low-to-moderate shear stress (0-40 Pa) was found at the leaflet body from the beginning of isovolemic contraction till the opening of the aortic valve. Similar high pressure (>140 mmHg) and shear stress (0-40 Pa) were found in the period from aortic valve closure till the beginning of the isovolemic contraction. In native AoRs, high pressure (>95 mmHg) was conjoined with low-to-moderate shear stress (0-30 Pa) at the leaflets and was registered at the end of isovolemic contraction. CONCLUSIONS: The David AoR is haemodynamically less favourable when compared with the native AoR. During almost two-thirds of the time period of the cardiac cycle, AoR elements are exposed to high pressure and low shear stress. In contrast, in native AoRs, similar conditions were present only during the short period of isovolemic contraction.

Numerical analysis of the 3-dimensional aortic root morphology during the cardiac cycle.

OBJECTIVES: The aim was to define the 3-dimensional (3D) geometrical changes of the aortic root and to determine the local shear stress profile of aortic root elements during the cardiac cycle. METHODS: Six sonomicrometric crystals (200 Hz) were implanted into the aortic root of five pigs at the commissures and at the aortic root base (AoB). 3D aortic root deformation including volume, torsion and tilt angle were determined. Geometrical data with measured local flow and pressure conditions was used for computed fluid dynamics modelling of the aortic root. RESULTS: Compared with end-diastole, the sinotubular junction and AoB have maximal expansion at peak ejection: 16.42 ± 6.36 and 7.60 ± 2.52%, and minimal at isovolaemic relaxation: 2.87 ± 1.62 and 1.85 ± 1.79%. Aortic root tilt and rotation angle were maximal at the end of diastole: 17.7 ± 8.8 and 21.2 ± 2.09°, and decreased to 15.24 ± 8.14 and 18.3 ± 0.1.94° at peak ejection. High shear stress >20 Pa was registered at peak ejection at coaptations, and during diastole at the superior two-thirds of the leaflets and intervalvular triangles (IVTs). The leaflet body, inferior one-third of the IVTs and valve nadir were exposed to moderate shear stress (8-16 Pa) during the cardiac cycle. CONCLUSIONS: Aortic root geometry demonstrates precise 3D changes of tilt and rotation angle. Reduction of angles during ejection results in a straight cylinder with low shear stress that facilitates the ejection; the increase during diastole results in a tilted frustum with elevated shear stress. Findings can be used for comparative analysis of native and synthetic structures with individual compliance.