Recovery and normalization of triple coincidences in PET

Purpose: Triple coincidences in positron emission tomography (PET) are events in which three γ-rays are detected simultaneously. These events, though potentially useful for enhancing the sensitivity of PET scanners, are discarded or processed without special consideration in current systems, because there is not a clear criterion for assigning them to a unique line-of-response (LOR). Methods proposed for recovering such events usually rely on the use of highly specialized detection systems, hampering general adoption, and/or are based on Compton-scatter kinematics and, consequently, are limited in accuracy by the energy resolution of standard PET detectors. In this work, the authors propose a simple and general solution for recovering triple coincidences, which does not require specialized detectors or additional energy resolution requirements.Methods: To recover triple coincidences, the authors’ method distributes such events among their possible LORs using the relative proportions of double coincidences in these LORs. The authors show analytically that this assignment scheme represents the maximum-likelihood solution for the triple-coincidence distribution problem. The PET component of a preclinical PET/CT scanner was adapted to enable the acquisition and processing of triple coincidences. Since the efficiencies for detecting double and triple events were found to be different throughout the scanner field-of-view, a normalization procedure specific for triple coincidences was also developed. The effect of including triple coincidences using their method was compared against the cases of equally weighting the triples among their possible LORs and discarding all the triple events. The authors used as figures of merit for this comparison sensitivity, noise-equivalent count (NEC) rates and image quality calculated as described in the NEMA NU-4 protocol for the assessment of preclinical PET scanners.Results: The addition of triple-coincidence events with the authors’ method increased peak NEC rates of the scanner by 26.6% and 32% for mouse- and rat-sized objects, respectively. This increase in NEC-rate performance was also reflected in the image-quality metrics. Images reconstructed using double and triple coincidences recovered using their method had better signal-to-noise ratio than those obtained using only double coincidences, while preserving spatial resolution and contrast. Distribution of triple coincidences using an equal-weighting scheme increased apparent system sensitivity but degraded image quality. The performance boost provided by the inclusion of triple coincidences using their method allowed to reduce the acquisition time of standard imaging procedures by up to ∼25%.Conclusions: Recovering triple coincidences with the proposed method can effectively increase the sensitivity of current clinical and preclinical PET systems without compromising other parameters like spatial resolution or contrast.This work was funded by Consejería de Educación, Juventud y Deporte de la Comunidad de Madrid (Spain) through the Madrid-MIT M + Visión Consortium. The authors also acknowledge the company Sedecal S.A. (Madrid, Spain) and the M + Visión Faculty for their support during this work.Publicad

Physical and psychophysical characterization of a GE senographe DS clinical system

Indirect-conversion FFDM systems usually present a lower spatial resolution, with respect to the direct-conversion one. This can put serious issues in mammography, since high resolution is required. Digital software has been developed for restoring the losses in spatial resolution caused by blurring in the scintillation phosphor. GE Senographe DS system gives users the possibility of using such restoration. Basically, a filtering can be performed on the acquired images, by activating the FineView software option. In this work we present a complete characterization of a clinical system, in terms of MTF, NPS, DQE, and contrast-detail analysis. Figures of merit have been calculated on images acquired with and without the FineView software. The effects of the restoration software are investigated, both on image quality parameters, and on contrast-detail visibility. The MTF of the FFDM system is improved when FineView is activated. On the other hand, NPS presents noticeably changes, especially at high frequencies. DQE is fairly independent from the exposure, when FineView filter is not activated, whereas it presents a clear spread over the exposures, when FineView is activated. CDMAM analysis does not show significant differences between images with or without the restoration filter. Besides, the Mo/Mo beam seems to provide slightly better results than the Rh/Rh one

Teaching mathematics in inclusive classrooms: a project integrating theory and practice for researchers, teachers and students

Supported by CNR. Supported by a grant from the National Science Foundation (award: TPE9153812)Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Interpretative Knowledge

Mathematics teacher knowledge has a central role in the research on mathematics teacher education. On the one hand, researchers investigate connections between practice and teacher knowledge within different theoretical perspectives. On the other hand, from a more theoretical point of view, the issue of identifying the scope and the nature of the mathematical knowledge needed for teaching is dominant in our field. Here we refer to a particular kind of mathematical knowledge, named Interpretative Knowledge (IK)