A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

We introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

Noninvasive pressure difference mapping derived from 4D flow MRI in patients with unrepaired and repaired aortic coarctation.

PURPOSE To develop a method for computing and visualizing pressure differences derived from time-resolved velocity-encoded three-dimensional phase-contrast magnetic resonance imaging (4D flow MRI) and to compare pressure difference maps of patients with unrepaired and repaired aortic coarctation to young healthy volunteers. METHODS 4D flow MRI data of four patients with aortic coarctation either before or after repair (mean age 17 years, age range 3-28, one female, three males) and four young healthy volunteers without history of cardiovascular disease (mean age 24 years, age range 20-27, one female, three males) was acquired using a 1.5-T clinical MR scanner. Image analysis was performed with in-house developed image processing software. Relative pressures were computed based on the Navier-Stokes equation. RESULTS A standardized method for intuitive visualization of pressure difference maps was developed and successfully applied to all included patients and volunteers. Young healthy volunteers exhibited smooth and regular distribution of relative pressures in the thoracic aorta at mid systole with very similar distribution in all analyzed volunteers. Patients demonstrated disturbed pressures compared to volunteers. Changes included a pressure drop at the aortic isthmus in all patients, increased relative pressures in the aortic arch in patients with residual narrowing after repair, and increased relative pressures in the descending aorta in a patient after patch aortoplasty. CONCLUSIONS Pressure difference maps derived from 4D flow MRI can depict alterations of spatial pressure distribution in patients with repaired and unrepaired aortic coarctation. The technique might allow identifying pathophysiological conditions underlying complications after aortic coarctation repair.

FEM/FD Immersed Boundary FSI Simulations

Immersed boundary simulations have been under development for physiological flows, allowing for elegant handling of fluid-structure interaction modelling with large deformations due to retained domain-specific meshing. We couple a structural system in Lagrangian representation that is formulated in a weak form with a Navier-Stokes system discretized through a finite differences scheme. We build upon a proven highly scalable imcompressible flow solver that we extend to handle FSI. We aim at applying our method to investigating the hemodynamics of Aortic Valves. The code is going to be extended to conform to the new hybrid-node supercomputers.

Noninvasive 4D pressure difference mapping derived from 4D flow MRI in patients with repaired aortic coarctation: comparison with young healthy volunteers

To assess spatial and temporal pressure characteristics in patients with repaired aortic coarctation compared to young healthy volunteers using time-resolved velocity-encoded three-dimensional phase-contrast magnetic resonance imaging (4D flow MRI) and derived 4D pressure difference maps. After in vitro validation against invasive catheterization as gold standard, 4D flow MRI of the thoracic aorta was performed at 1.5T in 13 consecutive patients after aortic coarctation repair without recoarctation and 13 healthy volunteers. Using in-house developed processing software, 4D pressure difference maps were computed based on the Navier-Stokes equation. Pressure difference amplitudes, maximum slope of pressure amplitudes and spatial pressure range at mid systole were retrospectively measured by three readers, and twice by one reader to assess inter- and intraobserver agreement. In vitro, pressure differences derived from 4D flow MRI showed excellent agreement to invasive catheter measurements. In vivo, pressure difference amplitudes, maximum slope of pressure difference amplitudes and spatial pressure range at mid systole were significantly increased in patients compared to volunteers in the aortic arch, the proximal descending and the distal descending thoracic aorta (p < 0.05). Greatest differences occurred in the proximal descending aorta with values of the three parameters for patients versus volunteers being 19.7 ± 7.5 versus 10.0 ± 2.0 (p < 0.001), 10.9 ± 10.4 versus 1.9 ± 0.4 (p = 0.002), and 8.7 ± 6.3 versus 1.6 ± 0.9 (p < 0.001). Inter- and intraobserver agreements were excellent (p < 0.001). Noninvasive 4D pressure difference mapping derived from 4D flow MRI enables detection of altered intraluminal aortic pressures and showed significant spatial and temporal changes in patients with repaired aortic coarctation.

Advanced morphological 3D magnetic resonance observation of cartilage repair tissue (MOCART) scoring using a new isotropic 3D proton-density, turbo spin echo sequence with variable flip angle distribution (PD-SPACE) compared to an isotropic 3D steady-state free precession sequence (True-FISP) and standard 2D sequences

To evaluate a new isotropic 3D proton-density, turbo-spin-echo sequence with variable flip-angle distribution (PD-SPACE) sequence compared to an isotropic 3D true-fast-imaging with steady-state-precession (True-FISP) sequence and 2D standard MR sequences with regard to the new 3D magnetic resonance observation of cartilage repair tissue (MOCART) score.

Three-dimensional magnetic resonance observation of cartilage repair tissue (MOCART) score assessed with an isotropic three-dimensional true fast imaging with steady-state precession sequence at 3.0 Tesla

INTRODUCTION: Cartilage defects are common pathologies and surgical cartilage repair shows promising results. In its postoperative evaluation, the magnetic resonance observation of cartilage repair tissue (MOCART) score, using different variables to describe the constitution of the cartilage repair tissue and the surrounding structures, is widely used. High-field magnetic resonance imaging (MRI) and 3-dimensional (3D) isotropic sequences may combine ideal preconditions to enhance the diagnostic performance of cartilage imaging.Aim of this study was to introduce an improved 3D MOCART score using the possibilities of an isotropic 3D true fast imaging with steady-state precession (True-FISP) sequence in the postoperative evaluation of patients after matrix-associated autologous chondrocyte transplantation (MACT) as well as to compare the results to the conventional 2D MOCART score using standard MR sequences. MATERIAL AND METHODS: The study had approval by the local ethics commission. One hundred consecutive MR scans in 60 patients at standard follow-up intervals of 1, 3, 6, 12, 24, and 60 months after MACT of the knee joint were prospectively included. The mean follow-up interval of this cross-sectional evaluation was 21.4 +/- 20.6 months; the mean age of the patients was 35.8 +/- 9.4 years. MRI was performed at a 3.0 Tesla unit. All variables of the standard 2D MOCART score where part of the new 3D MOCART score. Furthermore, additional variables and options were included with the aims to use the capabilities of isotropic MRI, to include the results of recent studies, and to adapt to the needs of patients and physician in a clinical routine examination. A proton-density turbo spin-echo sequence, a T2-weighted dual fast spin-echo (dual-FSE) sequence, and a T1-weighted turbo inversion recovery magnitude (TIRM) sequence were used to assess the standard 2D MOCART score; an isotropic 3D-TrueFISP sequence was prepared to evaluate the new 3D MOCART score. All 9 variables of the 2D MOCART score were compared with the corresponding variables obtained by the 3D MOCART score using the Pearson correlation coefficient; additionally the subjective quality and possible artifacts of the MR sequences were analyzed. RESULTS: The correlation between the standard 2D MOCART score and the new 3D MOCART showed for the 8 variables "defect fill," "cartilage interface," "surface," "adhesions," "structure," "signal intensity," "subchondral lamina," and "effusion"-a highly significant (P < 0.001) correlation with a Pearson coefficient between 0.566 and 0.932. The variable "bone marrow edema" correlated significantly (P < 0.05; Pearson coefficient: 0.257). The subjective quality of the 3 standard MR sequences was comparable to the isotropic 3D-TrueFISP sequence. Artifacts were more frequently visible within the 3D-TrueFISP sequence. CONCLUSION: In the clinical routine follow-up after cartilage repair, the 3D MOCART score, assessed by only 1 high-resolution isotropic MR sequence, provides comparable information than the standard 2D MOCART score. Hence, the new 3D MOCART score has the potential to combine the information of the standard 2D MOCART score with the possible advantages of isotropic 3D MRI at high-field. A clear limitation of the 3D-TrueFISP sequence was the high number of artifacts. Future studies have to prove the clinical benefits of a 3D MOCART score.