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.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

An angiographic analysis of atherosclerosis progression in below-the-knee arteries after femoropopliteal angioplasty in claudicants

Purpose: To report an angiographic investigation of midterm atherosclerotic disease progression in below-the-knee (BTK) arteries of claudicants. Methods: Angiograms were performed in 58 consecutive claudicants (35 men; mean age 68.3±8.7 years) with endovascular treatment of femoropopliteal arteries in 58 limbs after a mean follow-up of 3.6±1.2 years. Angiograms were reviewed in consensus by 2 experienced readers blinded to clinical data. Progression of atherosclerosis in 4 BTK arterial segments (tibioperoneal trunk, anterior and posterior tibial arteries, and peroneal artery) was assessed according to the Bollinger score. The composite per calf Bollinger score represented the average of the 4 BTK arterial segment scores. The association of the Bollinger score with cardiovascular risk factors and gender was scrutinized. Results: A statistically significant increase in atherosclerotic burden was observed for the mean composite per calf Bollinger score (5.7±8.3 increase, 95% CI 3.5 to 7.9, p<0.0001), as well as for each single arterial segment analyzed. In multivariate linear regression analysis, diabetes mellitus was associated with a more pronounced progression of atherosclerotic burden in crural arteries (β: 5.6, p=0.035, 95% CI 0.398 to 10.806). Conclusion: Progression of infrapopliteal atherosclerotic lesions is common in claudicants during midterm follow-up. Presence of diabetes mellitus was confirmed as a major risk factor for more pronounced atherosclerotic BTK disease progression.

Analysis of the erosive effect of different dietary substances and medications

Excessive consumption of acidic drinks and foods contributes to tooth erosion. The aims of the present in vitro study were twofold: (1) to assess the erosive potential of different dietary substances and medications; (2) to determine the chemical properties with an impact on the erosive potential. We selected sixty agents: soft drinks, an energy drink, sports drinks, alcoholic drinks, juice, fruit, mineral water, yogurt, tea, coffee, salad dressing and medications. The erosive potential of the tested agents was quantified as the changes in surface hardness (ΔSH) of enamel specimens within the first 2 min (ΔSH2-0 = SH2 min - SHbaseline) and the second 2 min exposure (ΔSH4-2 = SH4 min - SH2 min). To characterise these agents, various chemical properties, e.g. pH, concentrations of Ca, Pi and F, titratable acidity to pH 7·0 and buffering capacity at the original pH value (β), as well as degree of saturation (pK - pI) with respect to hydroxyapatite (HAP) and fluorapatite (FAP), were determined. Erosive challenge caused a statistically significant reduction in SH for all agents except for coffee, some medications and alcoholic drinks, and non-flavoured mineral waters, teas and yogurts (P < 0·01). By multiple linear regression analysis, 52 % of the variation in ΔSH after 2 min and 61 % after 4 min immersion were explained by pH, β and concentrations of F and Ca (P < 0·05). pH was the variable with the highest impact in multiple regression and bivariate correlation analyses. Furthermore, a high bivariate correlation was also obtained between (pK - pI)HAP, (pK - pI)FAP and ΔSH.

Proteome analysis in cardiovascular pathophysiology using Dahl rat model

Dahl salt-sensitive (DS) and salt-resistant (DR) inbred rat strains represent a well established animal model for cardiovascular research. Upon prolonged administration of high-salt-containing diet, DS rats develop systemic hypertension, and as a consequence they develop left ventricular hypertrophy, followed by heart failure. The aim of this work was to explore whether this animal model is suitable to identify biomarkers that characterize defined stages of cardiac pathophysiological conditions. The work had to be performed in two stages: in the first part proteomic differences that are attributable to the two separate rat lines (DS and DR) had to be established, and in the second part the process of development of heart failure due to feeding the rats with high-salt-containing diet has to be monitored. This work describes the results of the first stage, with the outcome of protein expression profiles of left ventricular tissues of DS and DR rats kept under low salt diet. Substantial extent of quantitative and qualitative expression differences between both strains of Dahl rats in heart tissue was detected. Using Principal Component Analysis, Linear Discriminant Analysis and other statistical means we have established sets of differentially expressed proteins, candidates for further molecular analysis of the heart failure mechanisms.

Periodic breathing during ascent to extreme altitude quantified by spectral analysis of the respiratory volume signal

High altitude periodic breathing (PB) shares some common pathophysiologic aspects with sleep apnea, Cheyne-Stokes respiration and PB in heart failure patients. Methods that allow quantifying instabilities of respiratory control provide valuable insights in physiologic mechanisms and help to identify therapeutic targets. Under the hypothesis that high altitude PB appears even during physical activity and can be identified in comparison to visual analysis in conditions of low SNR, this study aims to identify PB by characterizing the respiratory pattern through the respiratory volume signal. A number of spectral parameters are extracted from the power spectral density (PSD) of the volume signal, derived from respiratory inductive plethysmography and evaluated through a linear discriminant analysis. A dataset of 34 healthy mountaineers ascending to Mt. Muztagh Ata, China (7,546 m) visually labeled as PB and non periodic breathing (nPB) is analyzed. All climbing periods within all the ascents are considered (total climbing periods: 371 nPB and 40 PB). The best crossvalidated result classifying PB and nPB is obtained with Pm (power of the modulation frequency band) and R (ratio between modulation and respiration power) with an accuracy of 80.3% and area under the receiver operating characteristic curve of 84.5%. Comparing the subjects from 1(st) and 2(nd) ascents (at the same altitudes but the latter more acclimatized) the effect of acclimatization is evaluated. SaO(2) and periodic breathing cycles significantly increased with acclimatization (p-value < 0.05). Higher Pm and higher respiratory frequencies are observed at lower SaO(2), through a significant negative correlation (p-value < 0.01). Higher Pm is observed at climbing periods visually labeled as PB with > 5 periodic breathing cycles through a significant positive correlation (p-value < 0.01). Our data demonstrate that quantification of the respiratory volume signal using spectral analysis is suitable to identify effects of hypobaric hypoxia on control of breathing.

Determination of histopathological tumor grade in neuroepithelial brain tumors by using spectral pattern analysis of in vivo spectroscopic data

OBJECT: In this study, 1H magnetic resonance (MR) spectroscopy was prospectively tested as a reliable method for presurgical grading of neuroepithelial brain tumors. METHODS: Using a database of tumor spectra obtained in patients with histologically confirmed diagnoses, 94 consecutive untreated patients were studied using single-voxel 1H spectroscopy (point-resolved spectroscopy; TE 135 msec, TE 135 msec, TR 1500 msec). A total of 90 tumor spectra obtained in patients with diagnostic 1H MR spectroscopy examinations were analyzed using commercially available software (MRUI/VARPRO) and classified using linear discriminant analysis as World Health Organization (WHO) Grade I/II, WHO Grade III, or WHO Grade IV lesions. In all cases, the classification results were matched with histopathological diagnoses that were made according to the WHO classification criteria after serial stereotactic biopsy procedures or open surgery. Histopathological studies revealed 30 Grade I/II tumors, 29 Grade III tumors, and 31 Grade IV tumors. The reliability of the histological diagnoses was validated considering a minimum postsurgical follow-up period of 12 months (range 12-37 months). Classifications based on spectroscopic data yielded 31 tumors in Grade I/II, 32 in Grade III, and 27 in Grade IV. Incorrect classifications included two Grade II tumors, one of which was identified as Grade III and one as Grade IV; two Grade III tumors identified as Grade II; two Grade III lesions identified as Grade IV; and six Grade IV tumors identified as Grade III. Furthermore, one glioblastoma (WHO Grade IV) was classified as WHO Grade I/II. This represents an overall success rate of 86%, and a 95% success rate in differentiating low-grade from high-grade tumors. CONCLUSIONS: The authors conclude that in vivo 1H MR spectroscopy is a reliable technique for grading neuroepithelial brain tumors.