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Rodriguez-Alvarez, M. J., Sanchez, F., Soriano, A., & Iborra, A. (2010). Sparse Givens resolution of large system of linear equations: Applications to image reconstruction. Math. Comput. Model., 52(7-8), 1258–1264.
Abstract: In medicine, computed tomographic images are reconstructed from a large number of measurements of X-ray transmission through the patient (projection data). The mathematical model used to describe a computed tomography device is a large system of linear equations of the form AX = B. In this paper we propose the QR decomposition as a direct method to solve the linear system. QR decomposition can be a large computational procedure. However, once it has been calculated for a specific system, matrices Q and R are stored and used for any acquired projection on that system. Implementation of the QR decomposition in order to take more advantage of the sparsity of the system matrix is discussed.
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Llosa, G., Barrio, J., Lacasta, C., Bisogni, M. G., Del Guerra, A., Marcatili, S., et al. (2010). Characterization of a PET detector head based on continuous LYSO crystals and monolithic, 64-pixel silicon photomultiplier matrices. Phys. Med. Biol., 55(23), 7299–7315.
Abstract: The characterization of a PET detector head based on continuous LYSO crystals and silicon photomultiplier (SiPM) arrays as photodetectors has been carried out for its use in the development of a small animal PET prototype. The detector heads are composed of a continuous crystal and a SiPM matrix with 64 pixels in a common substrate, fabricated specifically for this project. Three crystals of 12 mm x 12 mm x 5 mm size with different types of painting have been tested: white, black and black on the sides but white on the back of the crystal. The best energy resolution, obtained with the white crystal, is 16% FWHM. The detector response is linear up to 1275 keV. Tests with different position determination algorithms have been carried out with the three crystals. The spatial resolution obtained with the center of gravity algorithm is around 0.9 mm FWHM for the three crystals. As expected, the use of this algorithm results in the displacement of the reconstructed position toward the center of the crystal, more pronounced in the case of the white crystal. A maximum likelihood algorithm has been tested that can reconstruct correctly the interaction position of the photons also in the case of the white crystal.
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Oliver, J. F., & Rafecas, M. (2010). Improving the singles rate method for modeling accidental coincidences in high-resolution PET. Phys. Med. Biol., 55(22), 6951–6971.
Abstract: Random coincidences ('randoms') are one of the main sources of image degradation in PET imaging. In order to correct for this effect, an accurate method to estimate the contribution of random events is necessary. This aspect becomes especially relevant for high-resolution PET scanners where the highest image quality is sought and accurate quantitative analysis is undertaken. One common approach to estimate randoms is the so-called singles rate method (SR) widely used because of its good statistical properties. SR is based on the measurement of the singles rate in each detector element. However, recent studies suggest that SR systematically overestimates the correct random rate. This overestimation can be particularly marked for low energy thresholds, below 250 keV used in some applications and could entail a significant image degradation. In this work, we investigate the performance of SR as a function of the activity, geometry of the source and energy acceptance window used. We also investigate the performance of an alternative method, which we call 'singles trues' (ST) that improves SR by properly modeling the presence of true coincidences in the sample. Nevertheless, in any real data acquisition the knowledge of which singles are members of a true coincidence is lost. Therefore, we propose an iterative method, STi, that provides an estimation based on ST but which only requires the knowledge of measurable quantities: prompts and singles. Due to inter-crystal scatter, for wide energy windows ST only partially corrects SR overestimations. While SR deviations are in the range 86-300% (depending on the source geometry), the ST deviations are systematically smaller and contained in the range 4-60%. STi fails to reproduce the ST results, although for not too high activities the deviation with respect to ST is only a few percent. For conventional energy windows, i.e. those without inter-crystal scatter, the ST method corrects the SR overestimations, and deviations from the true random rate are of the order of 1% or less. In addition, in the case of conventional energy window STi results reproduce ST results and therefore the former can be used to obtain the true random rate.
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Cabello, J., & Wells, K. (2010). The spatial resolution of silicon-based electron detectors in beta-autoradiography. Phys. Med. Biol., 55(6), 1677–1699.
Abstract: Thin tissue autoradiography is an imaging modality where ex-vivo tissue sections are placed in direct contact with autoradiographic film. These tissue sections contain a radiolabelled ligand bound to a specific biomolecule under study. This radioligand emits beta- or beta+ particles ionizing silver halide crystals in the film. High spatial resolution autoradiograms are obtained using low energy radioisotopes, such as H-3 where an intrinsic 0.1-1 μm spatial resolution can be achieved. Several digital alternatives have been presented over the past few years to replace conventional film but their spatial resolution has yet to equal film, although silicon-based imaging technologies have demonstrated higher sensitivity compared to conventional film. It will be shown in this work how pixel size is a critical parameter for achieving high spatial resolution for low energy uncollimated beta imaging. In this work we also examine the confounding factors impeding silicon-based technologies with respect to spatial resolution. The study considers charge diffusion in silicon and detector noise, and this is applied to a range of radioisotopes typically used in autoradiography. Finally an optimal detector geometry to obtain the best possible spatial resolution for a specific technology and a specific radioisotope is suggested.
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Warnecke, S., Sevryuk, M. B., Ceperley, D. M., Toennies, J. P., Guardiola, R., & Navarro, J. (2010). The structure of para-hydrogen clusters. Eur. Phys. J. D, 56(3), 353–358.
Abstract: The path integral Monte Carlo calculated radial distributions of para-hydrogen clusters (p-H-2) N consisting of N = 4-40 molecules interacting via a Lennard-Jones potential at T = 1.5 K show evidence for additional peaks compared to radial distributions calculated by diffusion Monte Carlo (T = 0 K) and path integral Monte Carlo at T <= 0.5 K. The difference in structures is attributed to quantum delocalization at the lowest temperature. The new structures at finite temperatures appear to be consistent with classical structures calculated for an effective Morse potential, which in order to account for the large zero point energy, is substantially softer than the Lennard-Jones potential.
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