Impact of measurement errors on the determination of the linear modulus of human meniscal attachments

For the development of meniscal substitutes and related finite element models it is necessary to know the mechanical properties of the meniscus and its attachments. Measurement errors can falsify the determination of material properties. Therefore the impact of metrological and geometrical measurement errors on the determination of the linear modulus of human meniscal attachments was investigated. After total differentiation the error of the force (+0.10%), attachment deformation (−0.16%), and fibre length (+0.11%) measurements almost annulled each other. The error of the cross-sectional area determination ranged from 0.00%, gathered from histological slides, up to 14.22%, obtained from digital calliper measurements. Hence, total measurement error ranged from +0.05% to −14.17%, predominantly affected by the cross-sectional area determination error. Further investigations revealed that the entire cross-section was significantly larger compared to the load-carrying collagen fibre area. This overestimation of the cross-section area led to an underestimation of the linear modulus of up to −36.7%. Additionally, the cross-sections of the collagen-fibre area of the attachments significantly varied up to +90% along their longitudinal axis. The resultant ratio between the collagen fibre area and the histologically determined cross-sectional area ranged between 0.61 for the posterolateral and 0.69 for the posteromedial ligament. The linear modulus of human meniscal attachments can be significantly underestimated due to the use of different methods and locations of cross-sectional area determination. Hence, it is suggested to assess the load carrying collagen fibre area histologically, or, alternatively, to use the correction factors proposed in this study.

VMC++ versus BEAMnrc: a comparison of simulated linear accelerator heads for photon beams

BEAMnrc, a code for simulating medical linear accelerators based on EGSnrc, has been bench-marked and used extensively in the scientific literature and is therefore often considered to be the gold standard for Monte Carlo simulations for radiotherapy applications. However, its long computation times make it too slow for the clinical routine and often even for research purposes without a large investment in computing resources. VMC++ is a much faster code thanks to the intensive use of variance reduction techniques and a much faster implementation of the condensed history technique for charged particle transport. A research version of this code is also capable of simulating the full head of linear accelerators operated in photon mode (excluding multileaf collimators, hard and dynamic wedges). In this work, a validation of the full head simulation at 6 and 18 MV is performed, simulating with VMC++ and BEAMnrc the addition of one head component at a time and comparing the resulting phase space files. For the comparison, photon and electron fluence, photon energy fluence, mean energy, and photon spectra are considered. The largest absolute differences are found in the energy fluences. For all the simulations of the different head components, a very good agreement (differences in energy fluences between VMC++ and BEAMnrc <1%) is obtained. Only a particular case at 6 MV shows a somewhat larger energy fluence difference of 1.4%. Dosimetrically, these phase space differences imply an agreement between both codes at the <1% level, making VMC++ head module suitable for full head simulations with considerable gain in efficiency and without loss of accuracy.

Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

Grazing response patterns indicate isolation of semi-natural European grasslands

Identifying drivers of species diversity is a major challenge in understanding and predicting the dynamics of species-rich semi-natural grasslands. In particular in temperate grasslands changes in land use and its consequences, i.e. increasing fragmentation, the on-going loss of habitat and the declining importance of regional processes such as seed dispersal by livestock, are considered key drivers of the diversity loss witnessed within the last decades. It is a largely unresolved question to what degree current temperate grassland communities already reflect a decline of regional processes such as longer distance seed dispersal. Answering this question is challenging since it requires both a mechanistic approach to community dynamics and a sufficient data basis that allows identifying general patterns. Here, we present results of a local individual- and trait-based community model that was initialized with plant functional types (PFTs) derived from an extensive empirical data set of species-rich grasslands within the `Biodiversity Exploratories' in Germany. Driving model processes included above- and belowground competition, dynamic resource allocation to shoots and roots, clonal growth, grazing, and local seed dispersal. To test for the impact of regional processes we also simulated seed input from a regional species pool. Model output, with and without regional seed input, was compared with empirical community response patterns along a grazing gradient. Simulated response patterns of changes in PFT richness, Shannon diversity, and biomass production matched observed grazing response patterns surprisingly well if only local processes were considered. Already low levels of additional regional seed input led to stronger deviations from empirical community pattern. While these findings cannot rule out that regional processes other than those considered in the modeling study potentially play a role in shaping the local grassland communities, our comparison indicates that European grasslands are largely isolated, i.e. local mechanisms explain observed community patterns to a large extent.

The dominant role of semi-arid ecosystems in the trend and variability of the land CO2 sink

The growth rate of atmospheric carbondioxide(CO2) concentrations since industrialization is characterized by large interannual variability, mostly resulting from variability in CO 2 uptake by terrestrial ecosystems (typically termed carbon sink). However, the contributions of regional ecosystems to that variability are not well known. Using an ensemble of ecosystem and land-surface models and an empirical observation-based product of global gross primary production, we show that the mean sink, trend, and interannual variability in CO2 uptake by terrestrial ecosystems are dominated by distinct biogeographic regions. Whereas the mean sink is dominated by highly productive lands (mainly tropical forests), the trend and interannual variability of the sink are dominated by semi-arid ecosystems whose carbon balance is strongly associated with circulation-driven variations in both precipitation and temperature.

The coupling of non-linear supersymmetry to supergravity

We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R−λ)2=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.

Synthesis of Semi-Natural Grassland Vegetation of a Biogeographically Heterogeneous Area: Mesophilous Species-Rich Meadows in Switzerland

For a hundred years semi-natural species-rich meadow vegetation has been described from various areas of Switzerland. The first description dates from 1892 by Stebler and Schröter. In the present study, relevés of 65 semi-natural mesophilous meadow associations and communities reported by 26 authors, which were collected throughout the century, are summarized. An increasing number of descriptions dating from the 1980s and 1990s is included. A numerical classification of these 65 types resulted in four main groups of meadow-types. When compared with the existing literature of alliances a high correlation is found with the Polygono-Trisetion Br.-Bl. et R. Tx. ex Marshall 1947, the Arrhenatherion W. Koch 1926, the Agrostio-Festucion Puscaru et al. 1956, the Mesobromion Br.-Bl. et Moor 1938 em. Oberdorfer 1957, and with the Chrysopogonetum W. Koch 1943. The Agrostio-Festucion is characteristic for the montane belt in southern Switzerland and was until recently poorly known. This alliance is discussed in detail. Some classifications of meadow types by the original authors had to be rearranged for the present purpose. The present classification coincides well with the one Stebler and Schröter gave in 1892. Today, after a century of intensive changes in land use, their four main types are still valid.

Detection of urinary stones at reduced radiation exposure: a phantom study comparing computed radiography and a low-dose digital radiography linear slit scanning system

OBJECTIVE: In this experimental study we assessed the diagnostic performance of digital linear slit scanning radiography compared with computed radiography (CR) for the detection of urinary calculi in an anthropomorphic phantom imitating patients weighing approximately 58-88 kg. CONCLUSION: Compared with CR, linear slit scanning radiography is superior for the detection of urinary stones and may be used for pretreatment localization and follow-up at a lower patient exposure.

A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere

Background and Aims Ongoing global warming has been implicated in shifting phenological patterns such as the timing and duration of the growing season across a wide variety of ecosystems. Linear models are routinely used to extrapolate these observed shifts in phenology into the future and to estimate changes in associated ecosystem properties such as net primary productivity. Yet, in nature, linear relationships may be special cases. Biological processes frequently follow more complex, non-linear patterns according to limiting factors that generate shifts and discontinuities, or contain thresholds beyond which responses change abruptly. This study investigates to what extent cambium phenology is associated with xylem growth and differentiation across conifer species of the northern hemisphere. Methods Xylem cell production is compared with the periods of cambial activity and cell differentiation assessed on a weekly time scale on histological sections of cambium and wood tissue collected from the stems of nine species in Canada and Europe over 1–9 years per site from 1998 to 2011. Key Results The dynamics of xylogenesis were surprisingly homogeneous among conifer species, although dispersions from the average were obviously observed. Within the range analysed, the relationships between the phenological timings were linear, with several slopes showing values close to or not statistically different from 1. The relationships between the phenological timings and cell production were distinctly non-linear, and involved an exponential pattern. Conclusions The trees adjust their phenological timings according to linear patterns. Thus, shifts of one phenological phase are associated with synchronous and comparable shifts of the successive phases. However, small increases in the duration of xylogenesis could correspond to a substantial increase in cell production. The findings suggest that the length of the growing season and the resulting amount of growth could respond differently to changes in environmental conditions.

A Parallel Solver for the Time-Periodic Navier–Stokes Equations

We investigate parallel algorithms for the solution of the Navier–Stokes equations in space-time. For periodic solutions, the discretized problem can be written as a large non-linear system of equations. This system of equations is solved by a Newton iteration. The Newton correction is computed using a preconditioned GMRES solver. The parallel performance of the algorithm is illustrated.