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Mathematik im ingenieurwissenschaftlichen Bachelorstudium : Lösung der Übungs- und Klausuraufgaben
(2010)
Purpose: Image analysis by the retinal vessel analyzer (RVA) observes retinal vessels in their dynamic state online noninvasively along a chosen vessel segment. It has been found that high-frequency diameter changes in the retinal artery blood column along the vessel increase significantly in anamnestically healthy volunteers with increasing age and in patients with glaucoma during vascular dilation. This study was undertaken to investigate whether longitudinal sections of the retinal artery blood column are altered in systemic hypertension.
Methods: Retinal arteries of 15 untreated patients with essential arterial hypertension (age, 50.9 ± 11.9 years) and of 15 age-matched anamnestically healthy volunteers were examined by RVA. After baseline assessment, a monochromatic luminance flicker (530–600 nm; 12.5 Hz; 20 s) was applied to evoke retinal vasodilation. Differences in amplitude and frequency of spatial artery blood column diameter change along segments (longitudinal arterial profiles) of 1 mm in length were measured and analyzed using Fourier transformation.
Results: In the control group, average reduced power spectra (ARPS) of longitudinal arterial profiles did not differ when arteries changed from constriction to dilation. In the systemic hypertension group, ARPS during constriction, baseline, and restoration were identical and differed from ARPS during dilation (P < 0.05). Longitudinal arterial profiles in both groups showed significant dissimilitude at baseline and restoration (P < 0.05).
Conclusions: The retinal artery blood column demonstrates microstructural alterations in systemic hypertension and is less irregular along the vessel axis during vessel dilation. These microstructural changes may be an indication of alterations in vessel wall rigidity, vascular endothelial function, and smooth muscle cells in this disease, leading to impaired perfusion and regulation.
Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.
The purpose of the current study in combination with our previous published data (Arampatzis et al., 2007) was to examine the effects of a controlled modulation of strain magnitude and strain frequency applied to the Achilles tendon on the plasticity of tendon mechanical and morphological properties. Eleven male adults (23.9±2.2 yr) participated in the study. The participants exercised one leg at low magnitude tendon strain (2.97±0.47%), and the other leg at high tendon strain magnitude (4.72±1.08%) of similar frequency (0.5 Hz, 1 s loading, 1 s relaxation) and exercise volume (integral of the plantar flexion moment over time) for 14 weeks, 4 days per week, 5 sets per session. The exercise volume was similar to the intervention of our earlier study (0.17 Hz frequency; 3 s loading, 3 s relaxation) allowing a direct comparison of the results. Before and after the intervention ankle joint moment has been measured by a dynamometer, tendon–aponeurosis elongation by ultrasound and cross-sectional area of the Achilles tendon by magnet resonance images (MRI). We found a decrease in strain at a given tendon force, an increase in tendon–aponeurosis stiffness and tendon elastic modulus of the Achilles tendon only in the leg exercised at high strain magnitude. The cross-sectional area (CSA) of the Achilles tendon did not show any statistically significant (P>0.05) differences to the pre-exercise values in both legs. The results indicate a superior improvement in tendon properties (stiffness, elastic modulus and CSA) at the low frequency (0.17 Hz) compared to the high strain frequency (0.5 Hz) protocol. These findings provide evidence that the strain magnitude applied to the Achilles tendon should exceed the value, which occurs during habitual activities to trigger adaptational effects and that higher tendon strain duration per contraction leads to superior tendon adaptational responses.
Ein 34-jähriger männlicher Patient stellte sich zur Abklärung einer seit dem 9. Lebensjahr bestehenden und im letzten Jahr rasch progredienten Visusminderung beider Augen bei uns vor. Er beschrieb eine subjektiv zunehmende, im Spiegel für ihn selbst sichtbare, weißliche Trübung in der Pupille beidseits und eine starke Blendempfindlichkeit. Nebenbefundlich gab er rezidivierende Konjunktivitiden und morgens verklebte Lider an. Eine Allergie auf Gräserpollen und eine Unverträglichkeit auf Alkohol sowie mehrere Lebensmittel seien ebenfalls bekannt.
Zusätzlich leidet der Patient an stark ausgeprägtem atopischem Ekzem. Dieses wurde nie systemisch, sondern nur bei Bedarf mit kortisonhaltiger Salbe therapiert.