Complex-Grid Spectral Algorithms For Inviscid Linear Instability of Boundary-Layer Flows

We present a suite of algorithms designed to obtain accurate numerical solutions of the generalised eigenvalue problem governing inviscid linear instability of boundary-layer type of flow in both the incompressible and compressible regimes on planar and axisymmetric curved geometries. The large gradient problems which occur in the governing equations at critical layers are treated by diverting the integration path into the complex plane, making use of complex mappings. The need for expansion of the basic flow profiles in truncated Taylor series is circumvented by solving the boundary-layer equations directly on the same (complex) grid used for the instability calculations. Iterative and direct solution algorithms are employed and the performance of the resulting algorithms using nonlinear radiation or homogeneous Dirichlet far-field boundary conditions is examined. The dependence of the solution on the parameters of the complex mappings is discussed. Results of incompressible and supersonic flow examples are presented; their excellent agreement with established works demonstrates the accuracy and robustness of the new methods presented. Means of improving the efficiency of the proposed spectral algorithms are suggested

Robust evolutionary bi-objective optimization for prostate cancer treatment with high-dose-rate brachytherapy

We address the real-world problem of automating the design of high-quality prostate cancer treatment plans in case of high-dose-rate brachytherapy, a form of internal radiotherapy. For this, recently a bi-objective real-valued problem formulation was introduced. With a GPU parallelization of the Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA), good treatment plans were found in clinically acceptable running times. However, optimizing a treatment plan and delivering it to the patient in practice is a two-stage decision process and involves a number of uncertainties. Firstly, there is uncertainty in the identified organ boundaries due to the limited resolution of the medical images. Secondly, the treatment involves placing catheters inside the patient, which always end up (slightly) different from what was optimized. An important factor is therefore the robustness of the final treatment plan to these uncertainties. In this work, we show how we can extend the evolutionary optimization approach to find robust plans using multiple scenarios without linearly increasing the amount of required computation effort, as well as how to deal with these uncertainties efficiently when taking into account the sequential decision-making moments. The performance is tested on three real-world patient cases. We find that MO-RV-GOMEA is equally well capable of solving the more complex robust problem formulation, resulting in a more realistic reflection of the treatment plan qual

Consistent improvement in health-related quality of life with tiotropium in patients with chronic obstructive pulmonary disease: Novel and conventional responder analyses.

INTRODUCTION: Improving health-related quality of life (HRQoL) in COPD patients is an important pharmacotherapeutic objective. This study investigated the extent, consistency, and durability of tiotropium maintenance therapy impact on HRQoL in moderate-to-very severe COPD. METHODS: Patients received once-daily tiotropium 18 μg (n = 5244) or placebo (n = 4799) via HandiHaler(®) (10 trials), or once-daily tiotropium 5 μg (n = 2622) or placebo (n = 2618) via Respimat(®) inhaler (3 trials). St George's Respiratory Questionnaire (SGRQ) total scores were measured at baseline, and 6 months (13 trials) and 1 year (9 trials) from treatment start. Adjusted mean differences between treatments for change from baseline in total scores were calculated at each time-point for each trial. Responder and deteriorator rates (decrease or increase in score ≥4 units from baseline, respectively), net benefit (responder rate increase plus deteriorator rate decrease), and cumulative improvement and deterioration were determined. RESULTS: Adjusted mean total score differences between treatments for change from baseline were significant (p < 0.05) in favor of tiotropium in 10/13 trials at 6 months and in 8/9 trials at 1 year. In all trials, estimated differences in responder rates between treatments favored tiotropium (significant [p < 0.05]: 5/13 trials at 6 months; 8/9 trials at 1 year). Net benefit favored tiotropium and cumulative improvement rates were consistently greater and deterioration rates consistently lower for tiotropium versus placebo. CONCLUSIONS: Tiotropium maintenance therapy significantly and consistently improved HRQoL in moderate-to-very severe COPD patients in a durable manner. These results may provide a benchmark for assessing benefits on HRQoL of other COPD treatments