Abstract: Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and, therefore, observers with arbitrary motions should be able to provide a complete physical description of the world. This suggests that in a regular spacetime, all physically acceptable observers should have complete paths. In this work we explore this idea by studying the motion of accelerated observers in spherically symmetric spacetimes and illustrate it by considering two geodesically complete black hole spacetimes recently described in the literature. We show that for bound and locally unbound accelerations, the paths of accelerated test particles are complete, providing further support to the regularity of such spacetimes.

Abstract: Sensitivity and spatial resolution are the main parameters to maximize in the performance of a PET scanner. For this purpose, detectors consisting of a combination of continuous crystals optically coupled to segmented photodetectors have been employed. With the use of continuous crystals the sensitivity is increased with respect to the pixelated crystals. In addition, spatial resolution is no longer limited to the crystal size. The main drawback is the difficulty in determining the interaction position. In this work, we present the characterization of the performance of a full ring based on cuboid continuous crystals coupled to SiPMs. To this end, we have employed the simulations developed in a previous work for our experimental detector head. Sensitivity could be further enhanced by using tapered crystals. This enhancement is obtained by increasing the solid angle coverage, reducing the wedge-shaped gaps between contiguous detectors. The performance of the scanners based on both crystal geometries was characterized following NEMA NU 4-2008 standardized protocol in order to compare them. An average sensitivity gain over the entire axial field of view of 13.63% has been obtained with tapered geometry while similar performance of the spatial resolution has been proven with both scanners. The activity at which NECR and true peak occur is smaller and the peak value is greater for tapered crystals than for cuboid crystals. Moreover, a higher degree of homogeneity was obtained in the sensitivity map due to the tighter packing of the crystals, which reduces the gaps and results in a better recovery of homogeneous regions than for the cuboid configuration. Some of the results obtained, such as spatial resolution, depend on the interaction position estimation and may vary if other method is employed.

Abstract: One factor limiting the current applicability extent of hadron therapy is the lack of a reliable method for real time treatment monitoring. The use of Compton imaging systems as monitors requires the correct reconstruction of the distribution of prompt gamma productions during patient irradiation. In order to extract the maximum information from all the measurable events, we implemented a spectral reconstruction method that assigns to all events a probability of being either partial or total energy depositions. The method, implemented in a list-mode maximum likelihood expectation maximization algorithm, generates a four dimensional image in the joint spatial-spectral domain, in which the voxels containing the emission positions and energies are obtained. The analytical model used for the system response function is also employed to derive an analytical expression for the sensitivity, which is calculated via Monte Carlo integration. The performance of the method is evaluated through reconstruction of various experimental and simulated sources with different spatial and energy distributions. The results show that the proposed method can recover the spectral and spatial information simultaneously, but only under the assumption of ideal measurements. The analysis of the Monte Carlo simulations has led to the identification of two important degradation sources: the mispositioning of the gamma interaction point and the missing energy recorded in the interaction. Both factors are related to the high energy transferred to the recoil electrons, which can travel far from the interaction point and even escape the detector. These effects prevent the direct application of the current method in more realistic scenarios. Nevertheless, experimental point-like sources have been accurately reconstructed and the spatial distributions and spectral emission of complex simulated phantoms can be identified.

Abstract: Purpose: In skin high-dose-rate (HDR) brachytherapy, sources are located outside, in contact with, or implanted at some depth below the skin surface. Most treatment planning systems use the TG-43 formalism, which is based on single-source dose superposition within an infinite water medium without accounting for the true geometry in which conditions for scattered radiation are altered by the presence of air. The purpose of this study is to evaluate the dosimetric limitations of the TG-43 formalism in HDR skin brachytherapy and the potential clinical impact. Methods: Dose rate distributions of typical configurations used in skin brachytherapy were obtained: a 5 cm x 5 cm superficial mould; a source inside a catheter located at the skin surface with and without backscatter bolus; and a typical interstitial implant consisting of an HDR source in a catheter located at a depth of 0.5 cm. Commercially available HDR Co-60 and Ir-192 sources and a hypothetical Yb-169 source were considered. The Geant4Monte Carlo radiation transport code was used to estimate dose rate distributions for the configurations considered. These results were then compared to those obtained with the TG-43 dose calculation formalism. In particular, the influence of adding bolus material over the implant was studied. Results: For a 5 cm x 5 cm Ir-192 superficial mould and 0.5 cm prescription depth, dose differences in comparison to the TG-43 method were about -3%. When the source was positioned at the skin surface, dose differences were smaller than -1% for Co-60 and Ir-192, yet -3% for Yb-169. For the interstitial implant, dose differences at the skin surface were -7% for Co-60, -0.6% for Ir-192, and -2.5% for Yb-169. Conclusions: This study indicates the following: (i) for the superficial mould, no bolus is needed; (ii) when the source is in contact with the skin surface, no bolus is needed for either Co-60 and Ir-192. For lower energy radionuclides like Yb-169, bolus may be needed; and (iii) for the interstitial case, at least a 0.1 cm bolus is advised for Co-60 to avoid underdosing superficial target layers. For Ir-192 and Yb-169, no bolus is needed. For those cases where no bolus is needed, its use might be detrimental as the lack of radiation scatter may be beneficial to the patient, although the 2% tolerance for dose calculation accuracy recommended in the AAPM TG-56 report is not fulfilled.

Abstract: We present the technical/physical foundations of a new imaging technique that combines ordinary radiographic information (generated by conventional X-ray settings) with the patient's volume to derive densitometric images. Traditionally, these images provide quantitative information about tissues densities. In our approach, they graphically enhance either soft or bony regions. After measuring the patient's volume with contour recognition devices, the physical traversed lengths within it (as the Roentgen beam intersects the patient) are calculated and pixel-wise associated with the original radiograph (X). In order to derive this map of lengths (L), the camera equations of the X-ray system and the contour sensor are determined. The patient's surface is also translated to the point-of-view of the X-ray beam and all its entrance/exit points are sought with the help of ray-casting methods. The derived L is applied to X as a physical operation (subtraction), obtaining soft tissue-(D-S) or bone-enhanced (D'(B)) figures. In the D-S type, the contained graphical information can be linearly mapped to the average electronic density (traversed by the X-ray beam). This feature represents an interesting proof-of-concept of associating density data to radiographs, but most important, their intensity histogram is objectively compressed, i.e., the dynamic range is more shrunk (compared against the corresponding X). This leads to other advantages: improvement in the visibility of border/edge areas (high gradient), extended manual window level/width manipulations during screening, and immediate correction of underexposed X instances. In the D-B' type, high-density elements are highlighted and easier to discern. All these results can be achieved with low-energy beam exposures, saving costs and dose. Future work will deepen this clinical side of our research. In contrast with other image-based modifiers, the proposed method is grounded on the measurement of a physical entity: the span of the X-ray beam within a body while undertaking a radiographic examination.