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In this study we develop an efficient computational procedure that generates medically acceptable treatment plans for volumetric modulated arc therapy with constant gantry speed. Our proposed method is a column generation heuristic based on a mixed integer linear programming model, where the objective function contains minimization of total monitor unit of the treatment plan and dose-volume requirements are included as conditional value-at-risk constraints. Our heuristic generates a full treatment arc for the restricted master problem and calibrates the right hand side parameters of the conditional value-at-risk constraints in the first phase. In the second phase, this initial solution is improved by performing column generation. This is a fully automated procedure and produces treatment plans in a single call without any human intervention. We evaluate its performance on real prostate cancer data by comparing the quality of the generated plans with those obtained by a widely used commercial treatment planning system. Our analysis shows that the results are promising, and the generated plans satisfy the prescription restrictions and require fewer monitor units on average compared to the ones obtained using Eclipse.

This study analyzes two decision levels in appointment system design in the context of clinics that face seasonal demand for scheduled and walk-in patients. The macro-level problem addresses access rules dealing with capacity allocation decisions in terms of how many slots to reserve for walk-ins and scheduled patients given fixed daily capacity for the clinic session. The micro-level problem addresses scheduling rules determining the specific time slots for scheduled arrivals. A fully-integrated simulation model is developed where daily demand actualized at the macro level becomes an input to the micro model that simulates the in-clinic dynamics, such as the arrivals of walk-ins and scheduled patients, as well as stochastic service times. The proposed integrated approach is shown to improve decision-making by considering patient lead times (i.e., indirect wait), direct wait times, and clinic overtime as relevant measures of performance. The traditional methods for evaluating appointment system performance are extended to incorporate multiple trade-offs. This allows combining both direct wait and indirect wait that are generally addressed separately due to time scale differences (minutes vs. days). The results confirm the benefits of addressing both decision levels in appointment system design simultaneously. We investigate how environmental factors affect the performance and the choice of appointment systems. The most critical environmental factors emerge as the demand load, seasonality level, and percentage of walk-ins, listed in the decreasing order of importance.

The volumetric modulated arc therapy (VMAT) problem is highly non-convex and much more difficult than the fixed-field intensity modulated radiotherapy optimization problem. To solve it efficiently, we propose a sequential convex programming algorithm that solves a sequence of convex optimization problems. Beginning by optimizing the aperture weights of many (72) evenly distributed beams using the beam’s eye view of the target from each direction as the initial aperture shape, the search space is constrained to allowing the leaves to move within a pre-defined step-size. A convex approximation problem is introduced and solved to optimize the leaf positions and the aperture weights within the search space. The algorithm is equipped with both local and global search strategies, whereby a global search is followed by a local search: a large step-size results in a global search with a less accurate convex approximation, followed by a small step-size local search with an accurate convex approximation. The performance of the proposed algorithm is tested on three patients with three different disease sites (paraspinal, prostate and oligometastasis). The algorithm generates VMAT plans comparable to the ideal 72-beam fluence map optimized plans (i.e. IMRT plans before leaf sequencing) in 14 iterations and 36 mins on average. The algorithm is also tested on a small down-sampled prostate case for which we could computationally afford to obtain the ground-truth by solving the non-convex mixed-integer optimization problem exactly. This general algorithm is able to produce results essentially equivalent to the ground-truth but 12 times faster. The algorithm is also scalable and can handle real clinical cases, whereas the ground-truth solution using mixed-integer optimization can only be obtained for highly down-sampled cases.

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