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International audience; BackgroundThe improvement of in vitro assessment of targeted alpha therapy (reproducibility, comparability of experiments horizontal ellipsis ) requires precise evaluation of the dose delivered to the cells. To answer this need, a previous study proposed an innovative dosimetry method based on alpha-spectroscopy and a specific deconvolution process to recover the spatial distribution of Pb-212 isotopes inside in vitro culture wells. Nevertheless, although promising, the deconvolution method was time consuming and only tested for a simple isotope decay chain. PurposeThe purpose of this work is to propose a new matrix deconvolution method of alpha spectra based on a constrained-non-negative-maximum-likelihood decomposition, both faster and offering a greater modelling flexibility, allowing to study independently the kinetics of each of the daughter nuclides of complex decay chains (illustrated here with Ra-223) in in vitro culture wells. MethodsFirstly, the performance of the new method was fully evaluated through Monte Carlo simulations of in vitro irradiations. Different spatial distributions of Pb-212 and Ra-223, the corresponding alpha spectra measured by a silicon detector and the doses delivered to the cells were simulated with Geant4. The deconvolution results were then compared to the simulation results. Secondly, measurements were carried out in culture wells without cells containing 15 kBq of Pb-212 or 9.3 kBq of Ra-223, placed above silicon detectors recording alpha spectra in real time. The matrix deconvolution was then applied to determine the spatial and temporal distribution of all alpha-emitting daughters of studied isotopes. ResultsThe matrix deconvolution was proved to recover the simulated distribution gradients, ensuring simulated doses within 3 % for both tested radionuclides, with errors on dose normally distributed around the reference value (consequently not exhibiting any bias), even in the case of complex decay chains as Ra-223. The experimental study of Pb-212 and Ra-223 showed highly inhomogeneous distributions and time evolution of the concentration gradients, consistent with the previous study. Furthermore, it highlighted the complex kinetics of Ra-223 with different distributions of its alpha-emitting daughters (Rn-219, Po-215, At-215, Bi-211, Po-211). ConclusionsThis study validates a new deconvolution method, fast and flexible, that proved to be accurate and reliable. This method allowed to reveal the complexity of isotopes kinetics in in vitro experiments, especially with complex decay chains. Experimental dosimetry, necessary to improve reliability of in vitro studies in targeted alpha therapy, is demonstrated to be feasible with the proposed method.

International audience; Purpose: Respiratory motion is a source of artifacts that reduces image quality in PET. Four dimensional (4D) PET/CT is one approach to overcome this problem. Ex- isting techniques to limiting the eects of respiratory motions are based on prospec- tive phase binning which requires a long acquisition duration (15-25 min). This time is uncomfortable for the patients and limits the clinical exploitation of 4D PET/CT. In this work, we evaluated an existing and an alternative retrospective binning meth- ods to reduce the acquisition duration of 4D PET/CT. Methods: We studied an existing mixed-amplitude binning (MAB) and an alterna- tive binning method by mixed-phases binning (MPhB). Before implementing MPhB, we analyzed the regularity of the breathing patterns in patients. We studied the breathing signal drift and missing CT slices that could be challenging for implement- ing MAB. We compared the performance of MAB and MPhB with current binning methods to measure the maximum uptake, internal volume and maximal range of tumour motion. Results: MPhB can be implemented depending on an optimal phase (in average the exhalation peak phase - 4:1% of the entire breathing cycle duration). Signal drift of patients was in average 35% relatively to the breathing amplitude. Even after correcting this drift, MAB was feasible in 4D CT for only 64% of patients. No sig- nicant dierences appeared between the dierent binning methods to measure the maximum uptake, internal volume and maximal range of tumour motion. We also determined the inaccuracies of MAB and MPhB to measure the maximum amplitude of tumour motion with 3 bins (less than 3 mm for movement inferior to 12 mm, up to 6:4 mm for a 21 mm movement). Conclusions: We proposed an alternative binning method by mixed-phase binning that halves the acquisition duration of 4D PET/CT. Mixed-amplitude binning was challenging because of signal drift and missing CT slices. We showed that more than 3 bins were necessary for a more accurate measurement of the maximum amplitude of the tumour motion. However, the current 4D-CT technology limits the increase of the number of bins in 4D PET/CT because of missing CT slices. One can reconstruct 4D PET images with more bins but without attenuation/scatter correction.

Motivated by the observation of inhomogeneous patterns in some high-Tc cuprate compounds, several variational Gutzwiller-projected wave functions with built-in charge and bond-order parameters are proposed for the extended t−J−V model on the square lattice at low doping. First, following a recent Gutzwiller-projected mean-field approach by one of us [D. Poilblanc, Phys. Rev. B 72, 060508(R) (2005)], we investigate, as a function of doping and Coulomb repulsion the relative stability of a wide variety of modulated structures with square unit cells of size 2×2, √8×√8, 4×4, and √32×√32. It is found that the 4×4 bond-order wave function with staggered-flux pattern (and small charge and spin current density wave) is a remarkable competitive candidate for hole doping around 1∕8 in agreement with scanning tunneling microscopy observations in the underdoped regime of some cuprates. This wave function is then optimized accurately and its properties studied extensively using a variational Monte Carlo scheme. Moreover, we find that under increasing the Coulomb repulsion, the d-wave superconducting RVB wave function is rapidly destabilized with respect to the 4×4 bond-order wave function. The stability of the bond-modulated wave function is connected to a gain of Coulomb and exchange energies. We suggest that such ordering patterns could be dynamical or could spontaneously appear in the vicinity of an impurity or a vortex in the mixed phase of the cuprates. Finally, we consider also a commensurate flux phase, but this wave function turns out not to be competitive because of its rather poor kinetic energy. However, we find it has very competitive exchange and Coulomb energies.