P h a s e I I M u l t i c e n t e r S t u d y o f B r i e f S i n g l e -A g e n t M e t h o t r e x a t e F o l l o w e d b y I r r a d i a t i o n i n P r i m a r y C N S L y m p h o m aBy P. O'Brien, D. Roos, G. Pratt, K. Liew, M. Barton, M. Poulsen, I. Olver, and G. TrotterPurpose: To assess, in a multi-institutional setting, the impact on relapse, survival, and toxicity of adding two cycles of intravenous methotrexate to cranial irradiation for immunocompetent patients with primary CNS lymphoma.Patients and Methods: Forty-six patients with a median age of 58 years and Eastern Cooperative Oncology Group performance status 0 to 3 were entered onto this phase II study. The protocol consisted of methotrexate 1 g/m 2 on days 1 and 8 followed by cranial irradiation on day 15. A whole-brain dose of 45 Gy was followed by a boost of 5.4 Gy. Intrathecal chemotherapy and spinal irradiation were given only to patients for whom cytologic examination of CSF was positive for CNS lymphoma. The median follow-up time was 36 months, with a minimum potential follow-up of 12 months.Results: Median survival was 33 months, with 2-year probability of survival 62% ؎ 15% (95% confidence interval). Twenty patients have relapsed. The predominant site of relapse was the brain. Neither performance status nor age was found to influence survival. Six patients developed a dementing illness at a median of 16 months after treatment, and three of these died as a consequence.Conclusion: A brief course of intravenous methotrexate before cranial irradiation is associated with 2-year and median survival rates superior to those reported for radiotherapy alone and similar to more intensive combined-modality regimens. Neurotoxicity remains an important competing risk for these patients.

A new method for 5-axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ball-endmill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of an associated truncated cone along a general, doubly curved, free-form surface is explored. These lines serve as discrete positions of conical axes in 3D space. Spline surface fitting is used to generate a ruled surface that represents a single continuous sweep of a rigid conical milling tool. An optimization based approach is then applied to globally minimize the error between the design surface and the conical envelope. Our computer simulation are validated with physical experiments on two benchmark industrial datasets, reducing significantly the execution times while preserving or even reducing the milling error when compared to the state-of-the-art industrial software.

Randomized trials have shown that sucralfate is effective in the management of acute radiation reactions such as oesophagitis, mucositis and proctitis. However, at the time of commencement of the present trial, it had never been used in the management of moist desquamation of the skin. The purpose of the present study was to assess the value of sucralfate cream in the management of moist desquamation during radiotherapy. Patients who developed moist desquamation during radiation were eligible. Patients were stratified by site of radiotherapy into three groups: (i) the head and neck; (ii) the breast; and (iii) other sites. Patients were randomized to receive 10% sucralfate in sorbolene cream or sorbolene alone. Patients' pain and skin healing were assessed by using linear analogue self-assessment (LASA) scales and by serial measurement of the desquamated area. Due to poor patient accrual, the trial was terminated after 2 years and 39 patients. No statistically significant difference was found between the two arms in either time from randomization to healing or improvement in pain score. Twenty patients in the sucralfate arm took a geometric mean of 14.8 days to heal whereas 19 patients receiving sorbolene alone took a geometric mean of 14.2 days. The ratio of mean times of healing, 1.043, is not statistically different from 1 (P = 0.86; 95% CI = 0.65, 1.67). A total of 75% of the patients reported pain relief on application of either cream. Mean LASA scores for pain for each day after randomization were compared by treatment arm and there was no statistically significant difference (P = 0.32). The present trial was unable to show a difference in terms of time to healing or pain relief in the treatment of moist desquamation. The small number of patients in the trial gave a wide confidence interval for treatment difference, implying that an important effect of sucralfate has not been excluded. Given the poor accrual in the present, single-institution study, future studies may need to be multi-institutional and we encourage other centres to perform randomized trials in the management of moist desquamation.

We introduce a new concept for generating optimal quadrature rules for splines. Given a target spline space where we aim to generate an optimal quadrature rule, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by modifying the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C 1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C 2 cubic spline spaces where the rule was only conjectured heretofore. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.

We present an algorithm which is able to compute all roots of a given univariate polynomial within a given interval. In each step, we use degree reduction to generate a strip bounded by two quadratic polynomials which encloses the graph of the polynomial within the interval of interest. The new interval(s) containing the root(s) is (are) obtained by intersecting this strip with the abscissa axis. In the case of single roots, the sequence of the lengths of the intervals converging towards the root has the convergence rate 3. For double roots, the convergence rate is still superlinear ( 32 ). We show that the new technique compares favorably with the classical technique of Bézier clipping.

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user's intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.

We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature rules we recently derived [5] act on spaces of the smallest odd degrees and, therefore, are still slightly sub-optimal. In this work, we derive optimal rules directly for even-degree spaces and therefore further improve our recent result. We use optimal quadrature rules for spaces over two elements as elementary building blocks and use recursively the homotopy continuation concept described in [6] to derive optimal rules for arbitrary admissible number of elements. We demonstrate the proposed methodology on relevant examples, where we derive optimal rules for various even-degree spline spaces. We also discuss convergence of our rules to their asymptotic counterparts, these are the analogues of the midpoint rule of Hughes et al. [16], that are exact and optimal for infinite domains.

We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept [6] that transforms optimal quadrature rules from source spaces to target spaces, we derive optimal rules for splines defined on finite domains. Starting with the classical Gaussian quadrature for polynomials, which is an optimal rule for a discontinuous odd-degree space, we derive rules for target spaces of higher continuity. We further show how the homotopy methodology handles cases where the source and target rules require different numbers of optimal quadrature points. We demonstrate it by deriving optimal rules for various odd-degree spline spaces, particularly with non-uniform knot sequences and non-uniform multiplicities. We also discuss convergence of our rules to their asymptotic counterparts, that is, the analogues of the midpoint rule of Hughes et al. [34], that are exact and optimal for infinite domains. For spaces of low continuities, we numerically show that the derived rules quickly converge to their asymptotic counterparts as the weights and nodes of a few boundary elements differ from the asymptotic values.