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.

Gas transport in firn: multiple-tracer characterisation and model intercomparison for NEEM, Northern Greenland

Air was sampled from the porous firn layer at the NEEM site in Northern Greenland. We use an ensemble of ten reference tracers of known atmospheric history to characterise the transport properties of the site. By analysing uncertainties in both data and the reference gas atmospheric histories, we can objectively assign weights to each of the gases used for the depth-diffusivity reconstruction. We define an objective root mean square criterion that is minimised in the model tuning procedure. Each tracer constrains the firn profile differently through its unique atmospheric history and free air diffusivity, making our multiple-tracer characterisation method a clear improvement over the commonly used single-tracer tuning. Six firn air transport models are tuned to the NEEM site; all models successfully reproduce the data within a 1σ Gaussian distribution. A comparison between two replicate boreholes drilled 64 m apart shows differences in measured mixing ratio profiles that exceed the experimental error. We find evidence that diffusivity does not vanish completely in the lock-in zone, as is commonly assumed. The ice age- gas age difference (1 age) at the firn-ice transition is calculated to be 182+3−9 yr. We further present the first intercomparison study of firn air models, where we introduce diagnostic scenarios designed to probe specific aspects of the model physics. Our results show that there are major differences in the way the models handle advective transport. Furthermore, diffusive fractionation of isotopes in the firn is poorly constrained by the models, which has consequences for attempts to reconstruct the isotopic composition of trace gases back in time using firn air and ice core records.

IgG subclass distribution of anti-ADAMTS13 antibodies in patients with acquired thrombotic thrombocytopenic purpura

BACKGROUND: ADAMTS13-neutralizing IgG autoantibodies are the major cause of acquired thrombotic thrombocytopenic purpura (TTP). OBJECTIVE: To analyze the IgG subclass distribution of anti-ADAMTS13 antibodies and a potential relationship between subclass distribution and disease prognosis. METHODOLOGY: An enzyme-linked immunosorbent assay-based method was used to quantify the relative amounts of IgG subclasses of anti-ADAMTS13 antibodies in acquired TTP plasma. RESULTS: IgG(4) (52/58, 90%) was the most prevalent IgG subclass in patients with acquired TTP, followed by IgG(1) (52%), IgG(2) (50%), and IgG(3) (33%). IgG(4) was found either alone (17/52) or with other IgG subclasses (35/52). IgG(4) was not detected in 10% of the patients. There was an inverse correlation between the frequency and abundance of IgG(4) and IgG(1) antibodies (P < 0.01). Patients with high IgG(4) levels and undetectable IgG(1) are more prone to relapse than patients with low IgG(4) levels and detectable IgG(1). CONCLUSIONS: All IgG subclasses of anti-ADAMTS13 antibodies were detected in patients with acquired TTP, with IgG(4), followed by IgG(1), antibodies dominating the anti-ADAMTS13 immune response. Levels of IgG(4) could be useful for the identification of patients at risk of disease recurrence.

On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Search for new phenomena in photon+jet events collected in proton–proton collisions at √s = 8 TeV with the ATLAS detector

This Letter describes a model-independent search for the production of new resonances in photon + jet events using 20 inverse fb of proton--proton LHC data recorded with the ATLAS detector at a centre-of-mass energy of s√ = 8 TeV. The photon + jet mass distribution is compared to a background model fit from data; no significant deviation from the background-only hypothesis is found. Limits are set at 95% credibility level on generic Gaussian-shaped signals and two benchmark phenomena beyond the Standard Model: non-thermal quantum black holes and excited quarks. Non-thermal quantum black holes are excluded below masses of 4.6 TeV and excited quarks are excluded below masses of 3.5 TeV.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Bounding Standard Gaussian Tail Probabilities

We review various inequalities for Mills' ratio (1 - Φ)= Ø, where Ø and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.

The inverse problem for Schwinger pair production

The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

Validation of the Swiss methane emission inventory by atmospheric observations and inverse modelling

Atmospheric inverse modelling has the potential to provide observation-based estimates of greenhouse gas emissions at the country scale, thereby allowing for an independent validation of national emission inventories. Here, we present a regional-scale inverse modelling study to quantify the emissions of methane (CH₄) from Switzerland, making use of the newly established CarboCount-CH measurement network and a high-resolution Lagrangian transport model. In our reference inversion, prior emissions were taken from the "bottom-up" Swiss Greenhouse Gas Inventory (SGHGI) as published by the Swiss Federal Office for the Environment in 2014 for the year 2012. Overall we estimate national CH₄ emissions to be 196 ± 18 Gg yr⁻¹ for the year 2013 (1σ uncertainty). This result is in close agreement with the recently revised SGHGI estimate of 206 ± 33 Gg yr⁻¹ as reported in 2015 for the year 2012. Results from sensitivity inversions using alternative prior emissions, uncertainty covariance settings, large-scale background mole fractions, two different inverse algorithms (Bayesian and extended Kalman filter), and two different transport models confirm the robustness and independent character of our estimate. According to the latest SGHGI estimate the main CH₄ source categories in Switzerland are agriculture (78 %), waste handling (15 %) and natural gas distribution and combustion (6 %). The spatial distribution and seasonal variability of our posterior emissions suggest an overestimation of agricultural CH₄ emissions by 10 to 20 % in the most recent SGHGI, which is likely due to an overestimation of emissions from manure handling. Urban areas do not appear as emission hotspots in our posterior results, suggesting that leakages from natural gas distribution are only a minor source of CH₄ in Switzerland. This is consistent with rather low emissions of 8.4 Gg yr⁻¹ reported by the SGHGI but inconsistent with the much higher value of 32 Gg yr⁻¹ implied by the EDGARv4.2 inventory for this sector. Increased CH₄ emissions (up to 30 % compared to the prior) were deduced for the north-eastern parts of Switzerland. This feature was common to most sensitivity inversions, which is a strong indicator that it is a real feature and not an artefact of the transport model and the inversion system. However, it was not possible to assign an unambiguous source process to the region. The observations of the CarboCount-CH network provided invaluable and independent information for the validation of the national bottom-up inventory. Similar systems need to be sustained to provide independent monitoring of future climate agreements.