Validation of the Swiss Monte Carlo Plan for a static and dynamic 6 MV photon beam

Monte Carlo (MC) based dose calculations can compute dose distributions with an accuracy surpassing that of conventional algorithms used in radiotherapy, especially in regions of tissue inhomogeneities and surface discontinuities. The Swiss Monte Carlo Plan (SMCP) is a GUI-based framework for photon MC treatment planning (MCTP) interfaced to the Eclipse treatment planning system (TPS). As for any dose calculation algorithm, also the MCTP needs to be commissioned and validated before using the algorithm for clinical cases. Aim of this study is the investigation of a 6 MV beam for clinical situations within the framework of the SMCP. In this respect, all parts i.e. open fields and all the clinically available beam modifiers have to be configured so that the calculated dose distributions match the corresponding measurements. Dose distributions for the 6 MV beam were simulated in a water phantom using a phase space source above the beam modifiers. The VMC++ code was used for the radiation transport through the beam modifiers (jaws, wedges, block and multileaf collimator (MLC)) as well as for the calculation of the dose distributions within the phantom. The voxel size of the dose distributions was 2mm in all directions. The statistical uncertainty of the calculated dose distributions was below 0.4%. Simulated depth dose curves and dose profiles in terms of [Gy/MU] for static and dynamic fields were compared with the corresponding measurements using dose difference and γ analysis. For the dose difference criterion of ±1% of D(max) and the distance to agreement criterion of ±1 mm, the γ analysis showed an excellent agreement between measurements and simulations for all static open and MLC fields. The tuning of the density and the thickness for all hard wedges lead to an agreement with the corresponding measurements within 1% or 1mm. Similar results have been achieved for the block. For the validation of the tuned hard wedges, a very good agreement between calculated and measured dose distributions was achieved using a 1%/1mm criteria for the γ analysis. The calculated dose distributions of the enhanced dynamic wedges (10°, 15°, 20°, 25°, 30°, 45° and 60°) met the criteria of 1%/1mm when compared with the measurements for all situations considered. For the IMRT fields all compared measured dose values agreed with the calculated dose values within a 2% dose difference or within 1 mm distance. The SMCP has been successfully validated for a static and dynamic 6 MV photon beam, thus resulting in accurate dose calculations suitable for applications in clinical cases.

A multiple source model for 6 MV photon beam dose calculations using Monte Carlo

A multiple source model (MSM) for the 6 MV beam of a Varian Clinac 2300 C/D was developed by simulating radiation transport through the accelerator head for a set of square fields using the GEANT Monte Carlo (MC) code. The corresponding phase space (PS) data enabled the characterization of 12 sources representing the main components of the beam defining system. By parametrizing the source characteristics and by evaluating the dependence of the parameters on field size, it was possible to extend the validity of the model to arbitrary rectangular fields which include the central 3 x 3 cm2 field without additional precalculated PS data. Finally, a sampling procedure was developed in order to reproduce the PS data. To validate the MSM, the fluence, energy fluence and mean energy distributions determined from the original and the reproduced PS data were compared and showed very good agreement. In addition, the MC calculated primary energy spectrum was verified by an energy spectrum derived from transmission measurements. Comparisons of MC calculated depth dose curves and profiles, using original and PS data reproduced by the MSM, agree within 1% and 1 mm. Deviations from measured dose distributions are within 1.5% and 1 mm. However, the real beam leads to some larger deviations outside the geometrical beam area for large fields. Calculated output factors in 10 cm water depth agree within 1.5% with experimentally determined data. In conclusion, the MSM produces accurate PS data for MC photon dose calculations for the rectangular fields specified.

Computer algebra for x-ray spectral reconstruction between 6 and 25 MV

A previously presented algorithm for the reconstruction of bremsstrahlung spectra from transmission data has been implemented into MATHEMATICA. Spectra vectorial algebra has been used to solve the matrix system A * F = T. The new implementation has been tested by reconstructing photon spectra from transmission data acquired in narrow beam conditions, for nominal energies of 6, 15, and 25 MV. The results were in excellent agreement with the original calculations. Our implementation has the advantage to be based on a well-tested mathematical kernel. Furthermore it offers a comfortable user interface.

Simple beam models for Monte Carlo photon beam dose calculations in radiotherapy

Monte Carlo (code GEANT) produced 6 and 15 MV phase space (PS) data were used to define several simple photon beam models. For creating the PS data the energy of starting electrons hitting the target was tuned to get correct depth dose data compared to measurements. The modeling process used the full PS information within the geometrical boundaries of the beam including all scattered radiation of the accelerator head. Scattered radiation outside the boundaries was neglected. Photons and electrons were assumed to be radiated from point sources. Four different models were investigated which involved different ways to determine the energies and locations of beam particles in the output plane. Depth dose curves, profiles, and relative output factors were calculated with these models for six field sizes from 5x5 to 40x40cm2 and compared to measurements. Model 1 uses a photon energy spectrum independent of location in the PS plane and a constant photon fluence in this plane. Model 2 takes into account the spatial particle fluence distribution in the PS plane. A constant fluence is used again in model 3, but the photon energy spectrum depends upon the off axis position. Model 4, finally uses the spatial particle fluence distribution and off axis dependent photon energy spectra in the PS plane. Depth dose curves and profiles for field sizes up to 10x10cm2 were not model sensitive. Good agreement between measured and calculated depth dose curves and profiles for all field sizes was reached for model 4. However, increasing deviations were found for increasing field sizes for models 1-3. Large deviations resulted for the profiles of models 2 and 3. This is due to the fact that these models overestimate and underestimate the energy fluence at large off axis distances. Relative output factors consistent with measurements resulted only for model 4.

Search for supersymmetry in events with photons, bottom quarks, and missing transverse momentum in proton-proton collisions at a centre-of-mass energy of 7 TeV with the ATLAS detector

A search has been performed for the experimental signature of an isolated photon with high transverse momentum, at least one jet identified as originating from a bottom quark, and high missing transverse momentum. Such a final state may originate from supersymmetric models with gauge-mediated supersymmetry breaking in events in which one of a pair of higgsino-like neutralinos decays into a photon and a gravitino while the other decays into a Higgs boson and a gravitino. The search is performed using the full dataset of 7 TeV proton-proton collisions recorded with the ATLAS detector at the LHC in 2011, corresponding to an integrated luminosity of 4.7 fb(-1). A total of 7 candidate events are observed while 7.5 +/- 2.2 events are expected from the Standard Model background. The results of the search are interpreted in the context of general gauge mediation to exclude certain regions of a benchmark plane for higgsino-like neutralino production.

Search for non-pointing photons in the diphoton and ETmiss final state in sqrt(s) = 7 TeV proton-proton collisions using the ATLAS detector

A search has been performed for photons originating in the decay of a neutral long-lived particle, exploiting the capabilities of the ATLAS electromagnetic calorimeter to make precise measurements of the flight direction of photons, as well as the calorimeter's excellent time resolution. The search has been made in the diphoton plus missing transverse energy final state, using the full data sample of 4.8 fb(-1) of 7 TeV proton-proton collisions collected in 2011 with the ATLAS detector at the LHC. No excess is observed above the background expected from Standard Model processes. The results are used to set exclusion limits in the context of gauge mediated supersymmetry breaking models, with the lightest neutralino being the next-to-lightest supersymmetric particle and decaying with a lifetime in excess of 0.25 ns into a photon and a gravitino.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Search for nonpointing and delayed photons in the diphoton and missing transverse momentum final state in 8 TeV pp collisions at the LHC using the ATLAS detector

A search has been performed, using the full 20.3  fb −1 data sample of 8 TeV proton-proton collisions collected in 2012 with the ATLAS detector at the LHC, for photons originating from a displaced vertex due to the decay of a neutral long-lived particle into a photon and an invisible particle. The analysis investigates the diphoton plus missing transverse momentum final state, and is therefore most sensitive to pair production of long-lived particles. The analysis technique exploits the capabilities of the ATLAS electromagnetic calorimeter to make precise measurements of the flight direction, as well as the time of flight, of photons. No excess is observed over the Standard Model predictions for background. Exclusion limits are set within the context of gauge mediated supersymmetry breaking models, with the lightest neutralino being the next-to-lightest supersymmetric particle and decaying into a photon and gravitino with a lifetime in the range from 250 ps to about 100 ns.

Measurement of the inclusive isolated prompt photons cross section in pp collisions at s √ =7 TeV with the ATLAS detector using 4.6 fb −1

A measurement of the cross section for the production of isolated prompt photons in pp collisions at a center-of-mass energy s √ =7  TeV is presented. The results are based on an integrated luminosity of 4.6  fb −1 collected with the ATLAS detector at the LHC. The cross section is measured as a function of photon pseudorapidity η γ and transverse energy E γ T in the kinematic range 100≤E γ T <1000  GeV and in the regions |η γ |<1.37 and 1.52≤|η γ |<2.37 . The results are compared to leading-order parton-shower Monte Carlo models and next-to-leading-order perturbative QCD calculations. Next-to-leading-order perturbative QCD calculations agree well with the measured cross sections as a function of E γ T and η γ .