Transconvolution and the virtual positron emission tomograph--a new method for cross calibration in quantitative PET∕CT imaging

PURPOSE Positron emission tomography (PET)∕computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET∕CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET∕CT in the context of multicenter trials. METHODS To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET∕CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET∕CT systems, a dedicated solid-state phantom incorporating (68)Ge∕(68)Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET∕CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system. RESULTS The proposed Transconvolution method matched different PET∕CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs. CONCLUSIONS By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.

Stakeholder analysis combined with social network analysis provides fine-grained insights into water infrastructure planning processes

Environmental policy and decision-making are characterized by complex interactions between different actors and sectors. As a rule, a stakeholder analysis is performed to understand those involved, but it has been criticized for lacking quality and consistency. This lack is remedied here by a formal social network analysis that investigates collaborative and multi-level governance settings in a rigorous way. We examine the added value of combining both elements. Our case study examines infrastructure planning in the Swiss water sector. Water supply and wastewater infrastructures are planned far into the future, usually on the basis of projections of past boundary conditions. They affect many actors, including the population, and are expensive. In view of increasing future dynamics and climate change, a more participatory and long-term planning approach is required. Our specific aims are to investigate fragmentation in water infrastructure planning, to understand how actors from different decision levels and sectors are represented, and which interests they follow. We conducted 27 semi-structured interviews with local stakeholders, but also cantonal and national actors. The network analysis confirmed our hypothesis of strong fragmentation: we found little collaboration between the water supply and wastewater sector (confirming horizontal fragmentation), and few ties between local, cantonal, and national actors (confirming vertical fragmentation). Infrastructure planning is clearly dominated by engineers and local authorities. Little importance is placed on longer-term strategic objectives and integrated catchment planning, but this was perceived as more important in a second analysis going beyond typical questions of stakeholder analysis. We conclude that linking a stakeholder analysis, comprising rarely asked questions, with a rigorous social network analysis is very fruitful and generates complementary results. This combination gave us deeper insight into the socio-political-engineering world of water infrastructure planning that is of vital importance to our well-being.

West Antarctic Ice Streams

Solar heat is the acknowledged driving force for climatic change. However, ice sheets are also capable of causing climatic change. This property of ice sheets derives from the facts that ice and rock are crystalline whereas the oceans and atmosphere are fluids and that ice sheets are massive enough to depress the earth's crust well below sea level. These features allow time constants for glacial flow and isostatic compensation to be much larger than those for ocean and atmospheric circulation and therefore somewhat independent of the solar variations that control this circulation. This review examines the nature of dynamic processes in ice streams that give ice sheets their degree of independent behavior and emphasizes the consequences of viscoplastic instability inherent in anisotropic polycrystalline solids such as glacial ice. Viscoplastic instability and subglacial topography are responsible for the formation of ice streams near ice sheet margins grounded below sea level. As a result the West Antarctic marine ice sheet is inherently unstable and can be rapidly carved away by calving bays which migrate up surging ice streams. Analyses of tidal flexure along floating ice stream margins, stress and velocity fields in ice streams, and ice stream boundary conditions are presented and used to interpret ERTS 1 photomosaics for West Antarctica in terms of characteristic ice sheet crevasse patterns that can be used to monitor ice stream surges and to study calving bay dynamics.

On the Pulling Power of Ice Streams

Gravity wants to pull an ice sheet to the center of the Earth, but cannot because the Earth's crust is in the way, so ice is pushed out sideways instead. Or is it? The ice sheet "sees" nothing preventing it from spreading out except air, which is much less massive than ice. Therefore, does not ice rush forward to fill this relative vacuum; does not the relative vacuum suck ice into it, because Nature abhors a vacuum? If so, the ice sheet is not only pulled downward by gravity, it is also pulled outward by the relative vacuum. This pulling outward will be most rapid where the ice sheet encounters least resistance. The least resistance exists along the bed of ice streams, where ice-bed coupling is reduced by a basal water layer, especially if the ice stream becomes afloat and the floating part is relatively unconfined around its perimeter and unpinned to the sea floor. Ice streams are therefore fast currents of ice that develop near the margins of an ice sheet where these conditions exist. Because of these conditions, ice streams pull ice out of ice sheets and have pulling power equal to the longitudinal gravitational pulling force multiplied by the ice-stream velocity. These boundary conditions beneath and beyond ice streams can be quantified by a basal buoyancy factor that provides a life-cycle classification of ice streams into inception, growth, mature, declining and terminal stages, during which ice streams disintegrate the ice sheet. Surface profiles of ice streams are diagnostic of the stage in a life cycle and, hence, of the vitality of the ice sheet.

LGM Summer Climate on the Southern Margin of the Laurentide Ice Sheet: Wet Or Dry?

Regional climate simulations are conducted using the Polar fifth-generation Pennsylvania State University (PSU)-NCAR Mesoscale Model (MM5) with a 60-km horizontal resolution domain over North America to explore the summer climate of the Last Glacial Maximum (LGM: 21 000 calendar years ago), when much of the continent was covered by the Laurentide Ice Sheet (LIS). Output from a tailored NCAR Community Climate Model version 3 (CCM3) simulation of the LGM climate is used to provide the initial and lateral boundary conditions for Polar MM5. LGM boundary conditions include continental ice sheets, appropriate orbital forcing, reduced CO2 concentration, paleovegetation, modified sea surface temperatures, and lowered sea level. The simulated LGM summer climate is characterized by a pronounced low-level thermal gradient along the southern margin of the LIS resulting from the juxtaposition of the cold ice sheet and adjacent warm ice-free land surface. This sharp thermal gradient anchors the midtropospheric jet stream and facilitates the development of synoptic cyclones that track over the ice sheet, some of which produce copious liquid precipitation along and south of the LIS terminus. Precipitation on the southern margin is orographically enhanced as moist southerly low-level flow (resembling a contemporary, Great Plains low-level jet configuration) in advance of the cyclone is drawn up the ice sheet slope. Composites of wet and dry periods on the LIS southern margin illustrate two distinctly different atmospheric flow regimes. Given the episodic nature of the summer rain events, it may be possible to reconcile the model depiction of wet conditions on the LIS southern margin during the LGM summer with the widely accepted interpretation of aridity across the Great Plains based on geological proxy evidence.

Polar MM5 Simulations of the Winter Climate of the Laurentide Ice Sheet at the LGM

Optimized regional climate simulations are conducted using the Polar MM5, a version of the fifth-generation Pennsylvania State University-NCAR Mesoscale Model (MM5), with a 60-km horizontal resolution domain over North America during the Last Glacial Maximum (LGM, 21 000 calendar years ago), when much of the continent was covered by the Laurentide Ice Sheet (LIS). The objective is to describe the LGM annual cycle at high spatial resolution with an emphasis on the winter atmospheric circulation. Output from a tailored NCAR Community Climate Model version 3 (CCM3) simulation of the LGM climate is used to provide the initial and lateral boundary conditions for Polar MM5. LGM boundary conditions include continental ice sheets, appropriate orbital forcing, reduced CO2 concentration, paleovegetation, modified sea surface temperatures, and lowered sea level. Polar MM5 produces a substantially different atmospheric response to the LGM boundary conditions than CCM3 and other recent GCM simulations. In particular, from November to April the upper-level flow is split around a blocking anticyclone over the LIS, with a northern branch over the Canadian Arctic and a southern branch impacting southern North America. The split flow pattern is most pronounced in January and transitions into a single, consolidated jet stream that migrates northward over the LIS during summer. Sensitivity experiments indicate that the winter split flow in Polar MM5 is primarily due to mechanical forcing by LIS, although model physics and resolution also contribute to the simulated flow configuration. Polar MM5 LGM results are generally consistent with proxy climate estimates in the western United States, Alaska, and the Canadian Arctic and may help resolve some long-standing discrepancies between proxy data and previous simulations of the LGM climate.

Influence of microphysical schemes on atmospheric water in the Weather Research and Forecasting model

This study examines how different microphysical parameterization schemes influence orographically induced precipitation and the distributions of hydrometeors and water vapour for midlatitude summer conditions in the Weather Research and Forecasting (WRF) model. A high-resolution two-dimensional idealized simulation is used to assess the differences between the schemes in which a moist air flow is interacting with a bell-shaped 2 km high mountain. Periodic lateral boundary conditions are chosen to recirculate atmospheric water in the domain. It is found that the 13 selected microphysical schemes conserve the water in the model domain. The gain or loss of water is less than 0.81% over a simulation time interval of 61 days. The differences of the microphysical schemes in terms of the distributions of water vapour, hydrometeors and accumulated precipitation are presented and discussed. The Kessler scheme, the only scheme without ice-phase processes, shows final values of cloud liquid water 14 times greater than the other schemes. The differences among the other schemes are not as extreme, but still they differ up to 79% in water vapour, up to 10 times in hydrometeors and up to 64% in accumulated precipitation at the end of the simulation. The microphysical schemes also differ in the surface evaporation rate. The WRF single-moment 3-class scheme has the highest surface evaporation rate compensated by the highest precipitation rate. The different distributions of hydrometeors and water vapour of the microphysical schemes induce differences up to 49 W m−2 in the downwelling shortwave radiation and up to 33 W m−2 in the downwelling longwave radiation.

Next-to-Minimal SOFTSUSY

We describe an extension to the SOFTSUSY program that provides for the calculation of the sparticle spectrum in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), where a chiral superfield that is a singlet of the Standard Model gauge group is added to the Minimal Supersymmetric Standard Model (MSSM) fields. Often, a Z3 symmetry is imposed upon the model. SOFTSUSY can calculate the spectrum in this case as well as the case where general Z3 violating (denoted as ) terms are added to the soft supersymmetry breaking terms and the superpotential. The user provides a theoretical boundary condition for the couplings and mass terms of the singlet. Radiative electroweak symmetry breaking data along with electroweak and CKM matrix data are used as weak-scale boundary conditions. The renormalisation group equations are solved numerically between the weak scale and a high energy scale using a nested iterative algorithm. This paper serves as a manual to the NMSSM mode of the program, detailing the approximations and conventions used.

Image-based biomechanical assessment of vertebral body and intervertebral disc in the human lumbar spine

Life expectancy continuously increases but our society faces age-related conditions. Among musculoskeletal diseases, osteoporosis associated with risk of vertebral fracture and degenerative intervertebral disc (IVD) are painful pathologies responsible for tremendous healthcare costs. Hence, reliable diagnostic tools are necessary to plan a treatment or follow up its efficacy. Yet, radiographic and MRI techniques, respectively clinical standards for evaluation of bone strength and IVD degeneration, are unspecific and not objective. Increasingly used in biomedical engineering, CT-based finite element (FE) models constitute the state-of-art for vertebral strength prediction. However, as non-invasive biomechanical evaluation and personalised FE models of the IVD are not available, rigid boundary conditions (BCs) are applied on the FE models to avoid uncertainties of disc degeneration that might bias the predictions. Moreover, considering the impact of low back pain, the biomechanical status of the IVD is needed as a criterion for early disc degeneration. Thus, the first FE study focuses on two rigid BCs applied on the vertebral bodies during compression test of cadaver vertebral bodies, vertebral sections and PMMA embedding. The second FE study highlights the large influence of the intervertebral disc’s compliance on the vertebral strength, damage distribution and its initiation. The third study introduces a new protocol for normalisation of the IVD stiffness in compression, torsion and bending using MRI-based data to account for its morphology. In the last study, a new criterion (Otsu threshold) for disc degeneration based on quantitative MRI data (axial T2 map) is proposed. The results show that vertebral strength and damage distribution computed with rigid BCs are identical. Yet, large discrepancies in strength and damage localisation were observed when the vertebral bodies were loaded via IVDs. The normalisation protocol attenuated the effect of geometry on the IVD stiffnesses without complete suppression. Finally, the Otsu threshold computed in the posterior part of annulus fibrosus was related to the disc biomechanics and meet objectivity and simplicity required for a clinical application. In conclusion, the stiffness normalisation protocol necessary for consistent IVD comparisons and the relation found between degeneration, mechanical response of the IVD and Otsu threshold lead the way for non-invasive evaluation biomechanical status of the IVD. As the FE prediction of vertebral strength is largely influenced by the IVD conditions, this data could also improve the future FE models of osteoporotic vertebra.

Relating in situ gas measurements to the surface outgassing properties of cometary nuclei

The sensitivity of the gas flow field to changes in different initial conditions has been studied for the case of a highly simplified cometary nucleus model. The nucleus model simulated a homogeneously outgassing sphere with a more active ring around an axis of symmetry. The varied initial conditions were the number density of the homogeneous region, the surface temperature, and the composition of the flow (varying amounts of H2O and CO2) from the active ring. The sensitivity analysis was performed using the Polynomial Chaos Expansion (PCE) method. Direct Simulation Monte Carlo (DSMC) was used for the flow, thereby allowing strong deviations from local thermal equilibrium. The PCE approach can be used to produce a sensitivity analysis with only four runs per modified input parameter and allows one to study and quantify non-linear responses of measurable parameters to linear changes in the input over a wide range. Hence the PCE allows one to obtain a functional relationship between the flow field properties at every point in the inner coma and the input conditions. It is for example shown that the velocity and the temperature of the background gas are not simply linear functions of the initial number density at the source. As probably expected, the main influence on the resulting flow field parameter is the corresponding initial parameter (i.e. the initial number density determines the background number density, the temperature of the surface determines the flow field temperature, etc.). However, the velocity of the flow field is also influenced by the surface temperature while the number density is not sensitive to the surface temperature at all in our model set-up. Another example is the change in the composition of the flow over the active area. Such changes can be seen in the velocity but again not in the number density. Although this study uses only a simple test case, we suggest that the approach, when applied to a real case in 3D, should assist in identifying the sensitivity of gas parameters measured in situ by, for example, the Rosetta spacecraft to the surface boundary conditions and vice versa.

Brand Authenticity: An Integrative Framework and Measurement Scale

This article develops an integrative framework of the concept of perceived brand authenticity (PBA) and sheds light on PBA’s (1) measurement, (2) drivers, (3) consequences, as well as (4) an underlying process of its effects and (5) boundary conditions. A multi-phase scale development process resulted in a 15-item PBA scale to measure its four dimensions of credibility, integrity, symbolism, and continuity. PBA is influenced by indexical, existential, and iconic cues, whereby the latter’s influence is moderated by consumers’ level of marketing skepticism. Results also suggest that PBA drives brand choice likelihood through self-congruence for consumers high in self-authenticity.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

North Atlantic Eddy-Driven Jet in interglacial and glacial winter climates

The atmospheric westerly flow in the North Atlantic (NA) sector is dominated by atmospheric waves or eddies generating via momentum flux convergence, the so-called eddy-driven jet. The position of this jet is variable and shows for the present-day winter climate three preferred latitudinal states: a northern, central, and southernposition in the NA. Here, the authors analyze the behavior of the eddy-driven jet under different glacial and interglacial boundary conditions using atmosphere–land-only simulations with the CCSM4 climate model. As state-of-the-art climate models tend to underestimate the trimodality of the jet latitude, the authors apply a bias correction and successfully extract the trimodal behavior of the jet within CCSM4. The analysis shows that during interglacial times (i.e., the early Holocene and the Eemian) the preferred jet positions are rather stable and the observed multimodality is the typical interglacial character of the jet. During glacial times, the jet is strongly enhanced, its position is shifted southward, and the trimodal behavior vanishes. This is mainly due to the presence of the Laurentide ice sheet (LIS). The LIS enhances stationary waves downstream, thereby accelerating and displacing the NA eddy-driven jet by anomalous stationary momentum flux convergence. Additionally, changes in the transient eddy activity caused by topography changes as well as other glacial boundary conditions lead to an acceleration of the westerly winds over the southern NA at the expenseof more northernareas. Consequently, bothstationaryand transient eddiesfoster the southward shift of the NA eddy-driven jet during glacial winter times.

Compactified N = 1 supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition

Fermion boundary conditions play a relevant role in revealing the confinement mechanism of N=1 supersymmetric Yang-Mills theory with one compactified space-time dimension. A deconfinement phase transition occurs for a sufficiently small compactification radius, equivalent to a high temperature in the thermal theory where antiperiodic fermion boundary conditions are applied. Periodic fermion boundary conditions, on the other hand, are related to the Witten index and confinement is expected to persist independently of the length of the compactified dimension. We study this aspect with lattice Monte Carlo simulations for different values of the fermion mass parameter that breaks supersymmetry softly. We find a deconfined region that shrinks when the fermion mass is lowered. Deconfinement takes place between two confined regions at large and small compactification radii, that would correspond to low and high temperatures in the thermal theory. At the smallest fermion masses we find no indication of a deconfinement transition. These results are a first signal for the predicted continuity in the compactification of supersymmetric Yang-Mills theory.

Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.