A radiotherapy technique to improve dose homogeneity around bone prostheses.

Purpose. Following limb conserving surgery for bone or soft tissue sarcoma, patients may require post-operative radiotherapy to minimise the risk of local recurrence. In such circumstances the metal prosthesis reduces the dose in its shadow by approximately 10% when using opposed fields. We describe a technique to boost the underdosed area to overcome this problem.Patients or subjects. Seven sequential patients presenting between 1995 and 2001 had their treatment individualised because they had metal prosthesis in the treatment volume.Methods. To improve the target dose homogeneity we used a custom-made keyhole cutout to boost the area in the shadow of the prosthesis. The degree of attenuation caused by the metal prosthesis was estimated and a boost dose calculated. Exit thermoluminescent dosimetry (TLD) was used to confirm the estimates made.Results and discussion. Variation between patients was seen, demonstrating the need for exit TLD to individualise the treatment plan. The use of a boost field provides a method to overcome under-dosage in the shadow of a metal prosthesis. It improves dose homogeneity throughout the target volume and ensures adequate dose intensity around the prosthesis, the site most at risk of local recurrence.Peer Reviewe

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Remarks on the Cauchy functional equation and variations of it

This paper examines various aspects related to the Cauchy functional equation $f(x+y)=f(x)+f(y)$, a fundamental equation in the theory of functional equations. In particular, it considers its solvability and its stability relative to subsets of multi-dimensional Euclidean spaces and tori. Several new types of regularity conditions are introduced, such as a one in which a complex exponent of the unknown function is locally measurable. An initial value approach to analyzing this equation is considered too and it yields a few by-products, such as the existence of a non-constant real function having an uncountable set of periods which are linearly independent over the rationals. The analysis is extended to related equations such as the Jensen equation, the multiplicative Cauchy equation, and the Pexider equation. The paper also includes a rather comprehensive survey of the history of the Cauchy equation.Comment: To appear in Aequationes Mathematicae (important remark: the acknowledgments section in the official paper exists, but it appears before the appendix and not before the references as in the arXiv version); correction of a minor inaccuracy in Lemma 3.2 and the initial value proof of Theorem 2.1; a few small improvements in various sections; added thank

A Radiotherapy Technique to Improve Dose Homogeneity Around Bone Prostheses

Purpose. Following limb conserving surgery for bone or soft tissue sarcoma, patients may require post-operative radiotherapy to minimise the risk of local recurrence. In such circumstances the metal prosthesis reduces the dose in its shadow by approximately 10% when using opposed fields. We describe a technique to boost the underdosed area to overcome this problem

Flow Electrification of a Corona-Charged Polyethylene Terephthalate Film

Corona charging a free-standing polymer film can produce a quasi-permanent potential difference across the film thickness, while the absolute amplitude of surface voltage may be highly sensitive to the free charges. To precisely control the voltage distribution, we investigated the flow electrification technology, by exposing corona-charged polyethylene terephthalate films to a variety of sodium salt solutions. The surface voltage and the free charge density were adjusted by the salt concentration, the anion size, and the flow rate. The dipolar component of electric potential remained unchanged. This result has significant scientific interest and technological importance to surface treatment, filtration, energy harvesting, bio-actuation and bio-sensing, among others

Correlação radiológica e histológica de lesões mamárias não-palpáveis em pacientes submetidas a marcação pré-cirúrgica, utilizando-se o sistema BI-RADS Radiological and histological correlation of non-palpable breast lesions in patients submitted to preoperative marking according to BI-RADS classification

OBJETIVO: Avaliar as categorias 3, 4 e 5 da classificação BI-RADS (Breast Imaging Reporting and Data System) como fator preditivo para malignidade, correlacionando os achados mamográficos e histológicos em lesões não-palpáveis da mama. MATERIAIS E MÉTODOS: Estudo analítico descritivo de 169 mulheres submetidas a biópsia cirúrgica, após localização estereotáxica de lesões mamárias não-palpáveis. As mamografias dessas pacientes foram classificadas de acordo com a quarta edição do BI-RADS, avaliando-se as categorias 3, 4 (A, B e C) e 5. Correlacionaram-se os achados mamográficos com os exames histológicos das lesões, avaliando-se o valor preditivo positivo em cada categoria. RESULTADOS: No total de 169 casos, foram diagnosticados 42 casos de câncer (24,8%). Destes, houve apenas um caso na categoria 3, 19 casos na categoria 4 e 22 casos na categoria 5. Os valores preditivos positivos para as categorias 3, 4A, 4B, 4C e 5 foram, respectivamente, de 3,4%, 10,3%, 11,3%, 36% e 91,7%. As microcalcificações foram o achado mais freqüente relacionado à doença maligna, ocorrendo em 61,5% do total. CONCLUSÃO: Este estudo demonstrou que a classificação BI-RADS permite predizer com segurança que há alta suspeição de malignidade para achados classificados na categoria 5 e diminuta chance para os achados da categoria 3. Quanto à categoria 4, foi constatada elevação progressiva dos valores preditivos positivos nas subcategorias A, B e C, mostrando que esta subdivisão contribui de forma mais detalhada e precisa na indicação de lesões suspeitas para malignidade.<br>OBJECTIVE: To evaluate the positive predictive value for BI-RADS (Breast Imaging Reporting and Data System) categories 3, 4 and 5, correlating mammographic and histological diagnosis in non-palpable breast lesions. MATERIALS AND METHODS: Analytical-descriptive study of 169 women submitted to stereotactic localization for surgical biopsy of non-palpable breast lesions. Mammographic and histological findings were correlated, analyzing the predictive positive value for each category. RESULTS: Forty-two (24.8%) cases were diagnosed with breast cancer - only one in category 3, 19 in category 4, and 22 in category 5. The positive predictive value for categories 3, 4A, 4B, 4C and 5 were, respectively, 3.4%, 10.3%, 11.3%, 36% and 91.7%. Microcalcifications were the most frequent finding related to malignancy, present in 61.5% of these cases. CONCLUSION: The present study has demonstrated that BI-RADS allows a safe prediction of high suspicion of malignancy in lesions category 5 and low suspicion for category 3. As regards the category 4, the positive predictive value has shown a progressive increase in subcategories A, B and C, demonstrating that this subclassification represents an invaluable contribution for a more detailed and accurate assessment of lesions suspicious for malignancy