A Geant4 simulation code for simulating optical photons in SPECT scintillation detectors

Geant4 is an object oriented toolkit created for the simulation of High-Energy Physics detectors. Geant4 allows an accurate modeling of radiation sources and detector devices, with easy configuration and friendly interface and at the same time with great accuracy in the simulation of physical processes. While most Monte Carlo codes do not allow the simulation of the transport and boundary characteristics for optical photons transport generated by scintillating crystal, Geant4 allows the simulation of the optical photons. In this paper we present an application of the Geant4 program for simulating optical photons in SPECT cameras. We aim to study the light transport within scintillators, photomultiplier tubes and coupling devices. To this end, we simulated a detector based on a scintillator, coupled to a photomultiplier tube through a glass window. We compared simulated results with experimental data and theoretical models, in order to verify the good matching with our simulations. We simulated a pencil beam of 140 keV photons impinging the crystal at different locations. For each condition, we calculated the value of the Pulse Height Centroid and the spread of the charge distribution, as read out by the anode array of the photomultiplier. Finally, the spatial and the energy resolutions of the camera have been estimated by simulated data. In all cases, we found that simulations agree very well with experimental data

In silico validation of MCID tool for voxel dosimetry applied to 90Y radioembolization of liver malignancies

The aim of this work is validating the Monte Carlo Internal Dosimetry (MCID) tool for internal dosimetry, which allows personalized treatment planning starting from patient-specific images and direct Monte Carlo (MC) simulations. The absorbed dose for different computational phantoms, calculated with MC and with conventional MIRD methods at both organ and voxel level, were compared, obtaining differences of about 0.3% and within 3%, respectively, whereas differences increased (up to 14%) introducing tissue heterogeneities in phantoms. The absorbed dose of spheres with different radius (10 mm ≤ r ≤ 30 mm), calculated from MC code and from OLINDA/EXM was also compared, obtaining differences varying in the range 2–9% after correcting for partial volume effects (PVEs) from imaging. This work validated the MCID tool which allows the fast generation of input macros for MC simulations, starting from patient-specific images. It also shows the impact of tissue inhomogeneities on dosimetric results and their relevance for an accurate dosimetric plan

Comparison of different calculation techniques for absorbed dose assessment in patient specific peptide receptor radionuclide therapy

Aim: The present work concerns the comparison of the performances of three systems for dosimetry in RPT that use different techniques for absorbed dose calculation (organ-level dosimetry, voxel-level dose kernel convolution and Monte Carlo simulations). The aim was to assess the importance of the choice of the most adequate calculation modality, providing recommendations about the choice of the computation tool. Methods: The performances were evaluated both on phantoms and patients in a multi-level approach. Different phantoms filled with a 177Lu-radioactive solution were used: a homogeneous cylindrical phantom, a phantom with organ-shaped inserts and two cylindrical phantoms with inserts different for shape and volume. A total of 70 patients with NETs treated by PRRT with 177Lu-DOTATOC were retrospectively analysed. Results: The comparisons were performed mainly between the mean values of the absorbed dose in the regions of interest. A general better agreement was obtained between Dose kernel convolution and Monte Carlo simulations results rather than between either of these two and organ-level dosimetry, both for phantoms and patients. Phantoms measurements also showed the discrepancies mainly depend on the geometry of the inserts (e.g. shape and volume). For patients, differences were more pronounced than phantoms and higher inter/intra patient variability was observed. Conclusion: This study suggests that voxel-level techniques for dosimetry calculation are potentially more accurate and personalized than organ-level methods. In particular, a voxel-convolution method provides good results in a short time of calculation, while Monte Carlo based computation should be conducted with very fast calculation systems for a possible use in clinics, despite its intrinsic higher accuracy. Attention to the calculation modality is recommended in case of clinical regions of interest with irregular shape and far from spherical geometry, in which Monte Carlo seems to be more accurate than voxel-convolution methods

Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields

We consider a family of vector fields and we assume a horizontal regularity on their derivatives. We discuss the notion of commutator showing that different definitions agree. We apply our results to the proof of a ball-box theorem and Poincar\'e inequality for nonsmooth H\"ormander vector fields.Comment: arXiv admin note: material from arXiv:1106.2410v1, now three separate articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520

Evaluation of Sentinel-3A and Sentinel-3B ocean land colour instrument green instantaneous fraction of absorbed photosynthetically active radiation

This article presents the evaluation of the Copernicus Sentinel-3 Ocean Land Colour Instrument (OLCI) operational terrestrial products corresponding to the green instantaneous Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) and its associated rectified channels. These products are estimated using OLCI spectral measurements acquired at the top of the atmosphere by a physically-based approach and are available operationally at full (300 m) and reduced (1.2 km) spatial resolution daily. The evaluation of the quality of the FAPAR OLCI values was based on the availability of data acquired over several years by Sentinel-3A (S3A) and Sentinel-3B (S3B). The evaluation exercise consisted of several stages: first, an overall comparison of the two S3 platform products was carried out during the tandem phase; second, comparison with an FAPAR climatology derived from the Medium Resolution Imaging Spectrometer (MERIS) provided information on the seasonality of various types of land cover. Then, direct comparisons were made with the same type of FAPAR products retrieved from two sensors, the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Sentinel-2 (S2) Multispectral Instrument (MSI), and with several ground-based estimates. In addition, an analysis of the efficiency of the retrieval algorithm with 3D radiative transfer simulations was performed. The results indicated that the consistency between daily and monthly S3A and S3B on a global scale was very good during the tandem phase (RMSD = 0.01 and a correlation R2 of 0.99 with a bias of 0.003); we found an agreement with a correlation of 0.95 and 0.93 (RMSD = 0.07 and 0.09) with JRC FAPAR S2 and JRC FAPAR MODIS, respectively. Compatibility with the ground-based data was between 0.056 and 0.24 in term of RMSD depending on the type of vegetation with an overall R2 of 0.89. Immler diagrams demonstrate that their variances were lower than the total uncertainties. The quality assurance using 3D radiative transfer model has shown that the apparent performance of the algorithm depends strongly on the type of in-situ measurement and canopy type

The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE

In this survey we consider a general Hormander type operator, represented as a sum of squares of vector fields plus a drift and we outline the central role of the fundamental solution in developing Potential and Regularity Theory for solutions of related PDEs. After recalling the Gaussian behavior at infinity of the kernel, we show some mean value formulas on the level sets of the fundamental solution, which are the starting point to obtain a comprehensive parallel of the classical Potential Theory. Then we show that a precise knowledge of the fundamental solution leads to global regularity results, namely estimates at the boundary or on the whole space. Finally in the problem of regularity of non linear differential equations we need an ad hoc modification of the parametrix method, based on the properties of the fundamental solution of an approximating problem