Real-time image-guided treatment of mobile tumors in proton therapy by a library of treatment plans: a simulation study.

PURPOSE: To improve target coverage and reduce the dose in the surrounding organs-at-risks (OARs), we developed an image-guided treatment method based on a precomputed library of treatment plans controlled and delivered in real-time. METHODS: A library of treatment plans is constructed by optimizing a plan for each breathing phase of a four dimensional computed tomography (4DCT). Treatments are delivered by simulation on a continuous sequence of synthetic computed tomographies (CTs) generated from real magnetic resonance imaging (MRI) sequences. During treatment, the plans for which the tumor are at a close distance to the current tumor position are selected to deliver their spots. The study is conducted on five liver cases. RESULTS: We tested our approach under imperfect knowledge of the tumor positions with a 2 mm distance error. On average, compared to a 4D robustly optimized treatment plan, our approach led to a dose homogeneity increase of 5% (defined as 1 - D 5 - D 95 prescription $1-\frac{D_5-D_{95}}{\text{prescription}}$ ) in the target and a mean liver dose decrease of 23%. The treatment time was roughly increased by a factor of 2 but remained below 4 min on average. CONCLUSIONS: Our image-guided treatment framework outperforms state-of-the-art 4D-robust plans for all patients in this study on both target coverage and OARs sparing, with an acceptable increase in treatment time under the current accuracy of the tumor tracking technology.

Extended Formulations for Order Polytopes through Network Flows.

Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and convex polyhedral set, or polytope. Polyhedral combinatorics have thus played a key role in studying the mathematical structure of these models. However, standard methods for characterizing the polytopes of such models are subject to a combinatorial explosion in complexity as the number of choice alternatives increases. Specifically, this is the case for random preference models based on linear, weak, semi- and interval orders. For these, a complete, linear description of the polytope is currently known only for, at most, 5-8 choice alternatives. We leverage the method of extended formulations to break through those boundaries. For each of the four types of preferences, we build an appropriate network, and show that the associated network flow polytope provides an extended formulation of the polytope of the choice model. This extended formulation has a simple linear description that is more parsimonious than descriptions obtained by standard methods for large numbers of choice alternatives. The result is a computationally less demanding way of testing the probabilistic choice model on data. We sketch how the latter interfaces with recent developments in contemporary statistics.

Accelerated multiplicative updates and hierarchical ALS algorithms for nonnegative matrix factorization.

Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this letter, we consider two well-known algorithms designed to solve NMF problems: the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Cichocki et al. We propose a simple way to significantly accelerate these schemes, based on a careful analysis of the computational cost needed at each iteration, while preserving their convergence properties. This acceleration technique can also be applied to other algorithms, which we illustrate on the projected gradient method of Lin. The efficiency of the accelerated algorithms is empirically demonstrated on image and text data sets and compares favorably with a state-of-the-art alternating nonnegative least squares algorithm.