On the visualization of universal degeneracy in the IMRT problem

BACKGROUND: In general, the IMRT optimisation problem possesses many equivalent solutions. This makes it difficult to decide whether a result produced by an IMRT planning algorithm can be further improved, e.g. by adding more beams, or whether it is close to the globally best solution. RESULTS: It is conjectured that the curvature properties of the objective function around any globally optimum dose distribution are universal. This allows an assessment of optimality of dose distributions that are generated by different beam arrangements in a complementary manner to the objective function value alone. A tool to visualize the curvature structure of the objective function is devised. CONCLUSION: In an example case, it is demonstrated how the assessment of the curvature space can indicate the equivalence of rival beam configurations and their proximity to the global optimum

Algorithms for flows over time with scheduling costs

Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering the arc; flows are time-varying. We consider a setting which is very standard within the transportation economic literature, but has received little attention from an algorithmic perspective. The flow consists of users who are able to choose their route but also their departure time, and who desire to arrive at their destination at a particular time, incurring a scheduling cost if they arrive earlier or later. The total cost of a user is then a combination of the time they spend commuting, and the scheduling cost they incur. We present a combinatorial algorithm for the natural optimization problem, that of minimizing the average total cost of all users (i.e., maximizing the social welfare). Based on this, we also show how to set tolls so that this optimal flow is induced as an equilibrium of the underlying game

A Spoonful of Math Helps the Medicine Go Down: An Illustration of How Healthcare can Benefit from Mathematical Modeling and Analysis

<p>Abstract</p> <p>Objectives</p> <p>A recent joint report from the Institute of Medicine and the National Academy of Engineering, highlights the benefits of--indeed, the need for--mathematical analysis of healthcare delivery. Tools for such analysis have been developed over decades by researchers in Operations Research (OR). An OR perspective typically frames a complex problem in terms of its essential mathematical structure. This article illustrates the use and value of the tools of operations research in healthcare. It reviews one OR tool, queueing theory, and provides an illustration involving a hypothetical drug treatment facility.</p> <p>Method</p> <p>Queueing Theory (QT) is the study of waiting lines. The theory is useful in that it provides solutions to problems of waiting and its relationship to key characteristics of healthcare systems. More generally, it illustrates the strengths of modeling in healthcare and service delivery.</p> <p>Queueing theory offers insights that initially may be hidden. For example, a queueing model allows one to incorporate randomness, which is inherent in the actual system, into the mathematical analysis. As a result of this randomness, these systems often perform much worse than one might have guessed based on deterministic conditions. Poor performance is reflected in longer lines, longer waits, and lower levels of server utilization.</p> <p>As an illustration, we specify a queueing model of a representative drug treatment facility. The analysis of this model provides mathematical expressions for some of the key performance measures, such as average waiting time for admission.</p> <p>Results</p> <p>We calculate average occupancy in the facility and its relationship to system characteristics. For example, when the facility has 28 beds, the average wait for admission is 4 days. We also explore the relationship between arrival rate at the facility, the capacity of the facility, and waiting times.</p> <p>Conclusions</p> <p>One key aspect of the healthcare system is its complexity, and policy makers want to design and reform the system in a way that affects competing goals. OR methodologies, particularly queueing theory, can be very useful in gaining deeper understanding of this complexity and exploring the potential effects of proposed changes on the system without making any actual changes.</p

A novel TOPSIS–CBR goal programming approach to sustainable healthcare treatment

Cancer is one of the most common diseases worldwide and its treatment is a complex and time-consuming process. Specifically, prostate cancer as the most common cancer among male population has received the attentions of many researchers. Oncologists and medical physicists usually rely on their past experience and expertise to prescribe the dose plan for cancer treatment. The main objective of dose planning process is to deliver high dose to the cancerous cells and simultaneously minimize the side effects of the treatment. In this article, a novel TOPSIS case based reasoning goal-programming approach has been proposed to optimize the dose plan for prostate cancer treatment. Firstly, a hybrid retrieval process TOPSIS–CBR [technique for order preference by similarity to ideal solution (TOPSIS) and case based reasoning (CBR)] is used to capture the expertise and experience of oncologists. Thereafter, the dose plans of retrieved cases are adjusted using goal-programming mathematical model. This approach will not only help oncologists to make a better trade-off between different conflicting decision making criteria but will also deliver a high dose to the cancerous cells with minimal and necessary effect on surrounding organs at risk. The efficacy of proposed method is tested on a real data set collected from Nottingham City Hospital using leave-one-out strategy. In most of the cases treatment plans generated by the proposed method is coherent with the dose plan prescribed by an experienced oncologist or even better. Developed decision support system can assist both new and experienced oncologists in the treatment planning process