Integral Equation Methods for Ocean Acoustics with Depth-Dependent Background Sound Speed

Time-harmonic acoustic wave propagation in an ocean with depth-dependent background sound speed can be described by the Helmholtz equation in an infinite, two- or three-dimensional waveguide of finite height. A crucial subproblem for the anayltic and numeric treatment of associated wave propagation problems is a Liouville eigenvalue problem that involves the depth-dependent contrast. For different types of background sound speed profiles, we discuss discretization schemes for the Liouville eigenvalue problem arising in the vertical variable. Due to variational theory in Sobolev spaces, we then show well-posedness of weak solutions to the corresponding scattering problem from a bounded inhomogeneity inside such an ocean: We introduce an exterior Dirichlet-to-Neumann operator for depth-dependent sound speed and prove boundedness, coercivity, and holomorphic dependence of this operator in suitable function spaces adapted to our weak solution theory. Analytic Fredholm theory then implies existence and uniqueness of solution for the scattering problem for all but a countable sequence of frequencies. Introducing the Green's function of the waveguide, we prove equivalence of the source problem for the Helmholtz equation with depth-dependent sound speed profile, Neumann boundary condition on the bottom and Dirichlet boundary condition on the top surface, to the Lippmann-Schwinger integral equation in dimensions two and three. Next, we periodize the Lippmann-Schwinger integral equation in dimensions two and three. The periodized version of the Lippmann-Schwinger integral equation and an interpolation projection onto a space spanned by finitely many eigenfunctions in the vertical variable and trigonometric polynomials in the horizontal variables, two different collocation schemes are derived. A result of Sloan [J.Approx Theory, 39:97-117,1983] on non-polynomial interpolation yields both converge and algebraic convergence rates depending on the smoothness of the inhomogeneity and the source of both schemes. Using one collocation scheme we present numerical results in dimension two. We further present an optimization technique of the vertical transform process, when the height of the obstacle is small compared to the finite height of the ocean, which makes computation in dimension three possible. If several scatters are present in the waveguide, this discretization technique leads to one computational domain containing all scatterers. For a three dimensional waveguide, we reformulate the Lippmann-Schwinger integral equation as a coupled system in an union of several boxes, each containing one part of the scatter

Propionibacterium prosthetic joint infection: experience from a retrospective database analysis.

With improved diagnostic methods and longer prosthesis indwelling time, the frequency of diagnosed Propionibacterium prosthetic joint infections (PJI) is increasing. Data on clinical, microbiological, radiological and surgical treatment are limited, and importance of this organism in PJI is probably underestimated. We retrospectively analyzed patients with PJI caused by Propionibacterium spp. diagnosed at our institution between 2000 and 2012. Patient data were retrieved through chart review, and the outcome was evaluated at patient follow-up visits. Of 15 included patients (median age 65 years, range 44-87), 8 hip, 4 shoulder, 2 knee and 1 ankle PJI were recorded. The median time from implantation to diagnosis of PJI was 44.2 months (range 2-180 months). Most PJI (8 patients, 53 %) were diagnosed late (>24 months after arthroplasty). Persistent pain was present in 13, local joint symptoms in 8, fever in 4 and sinus tract in 3 patients. Radiological signs of loosening were present in 11 patients (73 %). Organisms were detected in intraoperative biopsy (n = 5), sonication (n = 4) or preoperative joint puncture (n = 4). In three cases coinfection with a coagulase-negative staphylococcus was diagnosed. Revision surgery was performed in all cases. After a mean follow-up of 16 months after revision surgery (range 4-37 months), 14 patients (93 %) showed no signs or symptoms of infection and had a functional prosthesis; one patient experienced a new infection with another organism (Staphylococcus epidermidis). Patients with persistent postoperative pain and/or loosening of implants should be screened for PJI with low-virulent organisms such as Propionibacterium, including

Zusammenhang zwischen präoperativer Angst und dem subjektiven Unterstützungsbedarf vor elektiven Eingriffen in Allgemeinanästhesie beim Erwachsenen

Eine Vielzahl an Untersuchungen zeigt, dass eine hohe Prävalenz für präoperative Angst unter Erwachsenen besteht, die sich elektiven Eingriffen in Allgemeinanästhesie unterziehen. So gaben bspw. in einer im Vorfeld im Universitäts-Klinikum Gießen-Marburg (UKGM, Standort Marburg) durchgeführten Studie mit mehr als 3.000 eingeschlossenen Patienten gemäß numerischer Rating Skala (NRS, 0-10) lediglich weniger als 10% keine präoperative Angst (NRS = 0) an. Bisher jedoch ungeklärt geblieben ist, inwieweit diese präoperative Angst durch Patienten als belastend bzw. störend wahrgenommen wird und inwiefern daraus ein Unterstützungsbedarf zur Bewältigung von präoperativer Angst seitens Patienten resultiert. Für die vorliegende Arbeit wurden über den Zeitraum eines knappen Jahres (November 2017 – Oktober 2018) 1.082 erwachsene Patienten im UKGM (Standort Marburg) befragt, bei denen eine elektive Operation in Allgemeinanästhesie geplant war. Der dafür erstellte achtseitige Fragebogen wurden von geeigneten und einwilligungsfähigen Patienten vor dem anästhesiologischen Prämedikationsgespräch ausgefüllt. Vorhandene Angst, deren empfinden als belastend und/oder störend (emotionale Bürde) sowie der Unterstützungsbedarf wurden jeweils dichotom (ja/nein) erfasst. Das Angstniveau wurde gemäß der validierten Amsterdam Preoperative Anxiety and Information Scale (APAIS) erhoben. Hierbei war die Gesamtangst APAIS-A-T mit Werten von 4 (keine Angst) bis 20 (maximale Angst) von besonderem Interesse. Deskriptiv ausgewertet wurden Patientencharakteristika, sowie die Häufigkeit und die Intensität von präoperativer Angst, emotionaler Bürde und individuellem Unterstützungsbedarf. Die Auswertung der Zusammenhänge des Angstniveaus mit empfundener Bürde und dem Unterstützungsbedarf erfolgte mittels logistischer Regression. Mittels Kreuztabellen und ROC-Analyse sowie der Berechnung des Youden-Index‘ wurden APAIS-A-T-Schwellenwerte hinsichtlich der emotionalen Bürde durch präoperative Angst und den daraus resultierenden Unterstützungsbedarf untersucht. Von den 1.082 befragten Patienten konnten 1000 in die Studie eingeschlossen werden (537 Frauen, 459 Männer, 4 keine Angabe; Alter: M = 57 Jahre bei SD = 18). Von diesen 1000 bejahten 493 Patienten präoperative Angst (318 Frauen, 64,5% vs. 171 Männer, 34,7%). Von diesen 493 Patienten mit präoperativer Angst gaben 320 Patienten (64,9%) an, die Angst als belastend zu empfinden. Außerdem bejahten 291 Patienten (59%) der Gruppe mit präoperativer Angst das Vorhandensein von Unterstützungsbedarf. Mit steigendem Gesamtangstniveau (APAIS-A-T) stiegen sowohl die emotionale Bürde (β = 0,407; OR = 1,50 bei 95% KI: 1,37 – 1,64, p < 0,001) als auch der Unterstützungsbedarf an (β = 0,270; OR = 1,31 bei 95% KI: 1,22 – 1,41, p < 0,001), was einen statistisch signifikanten Zusammenhang zwischen steigender Angst und sowohl empfundener emotionaler Bürde als auch Unterstützungsbedarf zeigt. Selbst bei niedrigstem Angstniveau (APAIS-A-T = 5) sind aus präoperativer Angst resultierende emotionale Bürde und daraus entstehender Unterstützungsbedarf nicht ausgeschlossen. Bei gleicher Gewichtung von Sensitivität und Spezifität ist zur Vorhersage von emotionaler Bürde sowie von bestehendem Unterstützungsbedarf jeweils ein APAIS-A-T > 9 (Sensitivität 0,899; Spezifität 0,755 bzw. Sensitivität 0,861; Spezifität 0,724) am günstigsten geeignet. Da kein APAIS-A-T zur eindeutigen Identifizierung von Patienten mit präoperativer Angst, deren Angst nicht als emotionale Bürde wahrgenommen wird und nicht mit Unterstützungsbedarf einhergeht, genutzt werden kann, scheint die alleinige Erhebung des Angstniveaus (z.B. mittels APAIS) im klinischen Alltag nicht sinnvoll zu sein, um jene Patienten zu identifizieren, die präoperative Angst haben und bei denen daraus eine emotionale Bürde sowie der Wunsch nach Unterstützung resultiert. Sinnvoller scheint es zu sein, allen Patienten die dichotome Frage nach präoperativer Angst zu stellen und bei jenen, die sie bejahen, ebenfalls mit dichotomen Fragen eine evtl. aus präoperativer Angst resultierende emotionale Bürde sowie bestehenden Unterstützungsbedarfs zu erfassen. Um zusätzlich Rückschlüsse auf Coping-Verhalten der Patienten ziehen zu können, sollte ebenfalls dichotom der Informationsbedarf eines Patienten mit präoperativer Angst erhoben werden

The effect of femoral component rotation on the five-year outcome of cemented mobile bearing total knee arthroplasty

Purpose: Performing total knee replacement, accurate alignment and neutral rotation of the femoral component are widely believed to be crucial for the ultimate success. Contrary to absolute bone referenced alignment, using a ligament balancing technique does not automatically rotate the femoral component parallel to the transepicondylar axis. In this context we established the hypothesis that rotational alignment of the femoral component parallel to the transepicondylar axis (0° ± 3°) results in better outcome than alignment outside of this range. Methods: We analysed 204 primary cemented mobile bearing total knee replacements fiveyears postoperatively. Femoral component rotation was measured on axial radiographs using the condylar twist angle (CTA). Knee society score, range of motion as well as subjective rating documented outcome. Results: In 96 knees the femoral component rotation was within the range 0 ± 3° (neutral rotation group), and in 108 knees the five-year postoperative rotational alignment of the femoral component was outside of this range (outlier group). Postoperative CTA showed a mean of 2.8° (±3.4°) internal rotation (IR) with a range between 6° external rotation (ER) and 15° IR (CI 95). No difference with regard to subjective and objective outcome could be detected. Conclusion: The present work shows that there is a large given natural variability in optimal rotational orientation, in this study between 6° ER and 15° IR, with numerous co-factors determining correct positioning of the femoral component. Further studies substantiating pre- and postoperative determinants are required to complete the understanding of resulting biomechanics in primary TK

Fractional quantum conductance plateaus in mosaic-like conductors and their similarities to the fractional quantum hall effect

A simple route to generate magnetotransport data is reported that results in fractional quantum Hall plateaus in the conductance without invoking strongly correlated physics. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that the occurrence of fractional conductance values, in particular in two‐terminal measurements, does not necessarily indicate interaction‐driven physics. The importance of an independent determination of charge densities is underscored and similarities with and differences to the fractional quantum Hall effect are critically discussed

Ion Channel Modeling beyond State of the Art: A Comparison with a System Theory-Based Model of the Shaker-Related Voltage-Gated Potassium Channel Kv 1.1

The mathematical modeling of ion channel kinetics is an important tool for studying the electrophysiological mechanisms of the nerves, heart, or cancer, from a single cell to an organ. Common approaches use either a Hodgkin–Huxley (HH) or a hidden Markov model (HMM) description, depending on the level of detail of the functionality and structural changes of the underlying channel gating, and taking into account the computational effort for model simulations. Here, we introduce for the first time a novel system theory-based approach for ion channel modeling based on the concept of transfer function characterization, without a priori knowledge of the biological system, using patch clamp measurements. Using the shaker-related voltage-gated potassium channel Kv1.1 (KCNA1) as an example, we compare the established approaches, HH and HMM, with the system theory-based concept in terms of model accuracy, computational effort, the degree of electrophysiological interpretability, and methodological limitations. This highly data-driven modeling concept offers a new opportunity for the phenomenological kinetic modeling of ion channels, exhibiting exceptional accuracy and computational efficiency compared to the conventional methods. The method has a high potential to further improve the quality and computational performance of complex cell and organ model simulations, and could provide a valuable new tool in the field of next-generation in silico electrophysiology

Guard Cell-Specific Calcium Sensitivity of High Density and Activity SV/TPC1 Channels

The slow vacuolar (SV) channel, a Ca2+-regulated vacuolar cation conductance channel, in Arabidopsis thaliana is encoded by the single-copy gene AtTPC1. Although loss-of-function tpc1 mutants were reported to exhibit a stoma phenotype, knowledge about the underlying guard cell-specific features of SV/TPC1 channels is still lacking. Here we demonstrate that TPC1 transcripts and SV current density in guard cells were much more pronounced than in mesophyll cells. Furthermore, the SV channel in motor cells exhibited a higher cytosolic Ca2+ sensitivity than in mesophyll cells. These distinct features of the guard cell SV channel therefore probably account for the published stomatal phenotype of tpc1-