“To laugh in tragic joy” – a linguagem poética de W. B. Yeats em Lapis Lazuli

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Cyclotech - contribution to solve the Technetium shortage by using low energy medical cyclotrons

This paper presents work in progress, to develop an efficient and economic way to directly produce Technetium 99metastable (99mTc) using low-energy cyclotrons. Its importance is well established and relates with the increased global trouble in delivering 99mTc to Nuclear Medicine Departments relying on this radioisotope. Since the present delivery strategy has clearly demonstrated its intrinsic limits, our group decided to follow a distinct approach that uses the broad distribution of the low energy cyclotrons and the accessibility of Molybdenum 100 (100Mo) as the Target material. This is indeed an important issue to consider, since the system here presented, named CYCLOTECH, it is not based on the use of Highly Enriched (or even Low Enriched) Uranium 235 (235U), so entirely complying with the actual international trends and directives concerning the use of this potential highly critical material. The production technique is based on the nuclear reaction 100Mo (p,2n) 99mTc whose production yields have already been documented. Until this moment two Patent requests have already been submitted (the first at the INPI, in Portugal, and the second at the USPTO, in the USA); others are being prepared for submission on a near future. The object of the CYCLOTECH system is to present 99mTc to Nuclear Medicine radiopharmacists in a routine, reliable and efficient manner that, remaining always flexible, entirely blends with established protocols. To facilitate workflow and Radiation Protection measures, it has been developed a Target Station that can be installed on most of the existing PET cyclotrons and that will tolerate up to 400 μA of beam by allowing the beam to strike the Target material at an adequately oblique angle. The Target Station permits the remote and automatic loading and discharge of the Targets from a carriage of 10 Target bodies. On other hand, several methods of Target material deposition and Target substrates are presented. The object was to create a cost effective means of depositing and intermediate the target material thickness (25 - 100μm) with a minimum of loss on a substrate that is able to easily transport the heat associated with high beam currents. Finally, the separation techniques presented are a combination of both physical and column chemistry. The object was to extract and deliver 99mTc in the identical form now in use in radiopharmacies worldwide. In addition, the Target material is recovered and can be recycled.

Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.