Clinical implementation of dynamic and step-and-shoot IMRT to treat prostate cancer with high risk of pelvic lymph node involvement

Clinical implementation of dynamic and step-and-shoot IMRT to treat prostate cancer with high risk of pelvic lymph node involvement Background and purpose: Two systems have been developed for treating patients with locally advanced prostate cancer using intensity-modulated radiotherapy (IMRT): one using dynamic multi-leaf collimator delivery and the other using step-and- shoot. This paper describes the clinical implementation of these two techniques, and presents results from the first 14 patients treated in a clinical setting (nine dynamic, five step-and-shoot). Patients and methods: Dynamic treatments were planned using Corvus, and step-and-shoot using Helax-TMS; all were delivered using Elekta accelerators. Prior to the first clinical treatments, validation measurements were carried out for each system, including measurements for a complete IMRT treatment. The reproducibility of dynamic delivery and the characteristics of the accelerator for low-monitor-unit (MU) deliveries were also assessed. An extensive quality assurance (QA) program was performed for each of the patients. Additionally, timing measurements were carried out to assess the practicalities of the technique. Results: The planning objectives were met in most cases. Absolute doses for complete IMRT treatments were within 2%, on average, with dose distributions generally showing agreement within 3% or 3 mm. Beam modulation measurements made throughout each patient's treatment indicated that both delivery methods were reproducible. The dynamic plans required an average of 765 MU per beam, with a treatment delivery time of 14 min; corresponding results for step-and-shoot plans were 105 MU and 10 min. Conclusions: Two IMRT techniques for this group of patients have been successfully implemented in the clinic. The more complex dynamic treatments showed no advantages over the step-and-shoot approach. QA results have shown accurate and reproducible delivery for both techniques, giving increased confidence in the techniques and allowing a reduction in the QA program. (C) 2003 Elsevier Ireland Ltd. All rights reserved

Global analysis of a Holling type II predator–prey model with a constant prey refuge

A global analysis of a Holling type II predator–prey model with a constant prey refuge is presented. Although this model has been much studied, the threshold condition for the global stability of the unique interior equilibrium and the uniqueness of its limit cycle have not been obtained to date, so far as we are aware. Here we provide a global qualitative analysis to determine the global dynamics of the model. In particular, a combination of the Bendixson–Dulac theorem and the Lyapunov function method was employed to judge the global stability of the equilibrium. The uniqueness theorem of a limit cycle for the Lineard system was used to show the existence and uniqueness of the limit cycle of the model. Further, the effects of prey refuges and parameter space on the threshold condition are discussed in the light of sensitivity analyses. Additional interesting topics based on the discontinuous (or Filippov) Gause predator–prey model are addressed in the discussion