A coupled column generation,mixed integer approach to optimal planning of intensity modulated radiation therapy for cancer

Approximately 40% of all U.S. cancer cases are treated with radiation therapy. In Intensity-Modulated Radiation Therapy (IMRT) the treatment planning problem is to choose external beam angles and their corresponding intensity maps (showing how the intensity varies across a given beam) to maximize tumor dose subject to the tolerances of surrounding healthy tissues. Dose, like temperature, is a quantity defined at each point in the body, and the distribution of dose is determined by the choice of treatment parameters available to the planner. In addition to absolute dose limits in healthy tissues, some tissues have at least one dose-volume restriction that requires a fraction of its volume to not exceed a specified tighter threshold level for damage. There may also be a homogeneity limit for the tumor that restricts the allowed spread of dose across its volume. We formulate this planning problem as a mixed integer program over a coupled pair of column generation processes -- one designed to produce intensity maps, and a second specifying protected area choices for tissues under dose-volume restrictions. The combined procedure is shown to strike a balance between computing an approximately optimal solution and bounding its maximum possible suboptimality that we believe holds promise for implementations able to offer the power and flexibility of mixed-integer linear programming models on instances of practical scale.A portion of the work of Dr. Langer, Mr. Thai and Dr. Preciado-Walters was supported by National Science Foundation grant ECS-0120145 and National Cancer Institute 1R41CA91688-01. Dr. Rardin is participated while on rotation as Program Director for Operations Research and Service Enterprise Engineering at the National Science Foundation.     

Electroanalytical voltammetry in flowing solutions

A review is given of the principles, key developments and representative applications of small electrodes in flow-through electrochemical (ec) detectors having very low effective dead volume (<10 μl) for voltammetric and amperometric detection in flowing solutions. Emphasis is placed on factors contributing to high sensitivity, reliability and selectivity of ec detection as an integral part of larger analytical systems utilizing continuously flowing, unsegmented streams, e.g., flow-injection and liquid chromatographic analyses. Solid and mercury electrodes are considered under potentiostatic and potentiodynamic control. A review is given also of auxiliary chemical and photolytic derivatizations coupled to ec detection. The majority of the literature on the subject relates to liquid chromatography with electrochemical detection (l.c./ec); however, applications to these concepts to specific examples in flow-injection systems, as well as for on-line process control, should be obvious. Details of chromatographic separations and design of total analytical systems are not reviewed.     

Technique for Importing Greater Evolution Resolution in Multidimensional NMR Spectrum

A very simple and general procedure that extracts constant-evolution-frequency data from a truncated multidimensional (2D, 3D, 4D, etc.) FID is described, generalized, analyzed, and illustrated. The method replaces Fourier transformation of the evolution dimension with a linear model created from a separate, high-quality 1D FID. The equivalent of high resolution in the evolution dimension can be achieved without obtaining an extensive multidimensional FID. The analysis of the 1D FID can also be used to predict the signal to noise ratio of the extracted slices that will result from various evolution dimension sampling protocols, making it possible to developa priorian optimal sampling strategy for the multidimensional FID. The evolution dimension need not be sampled periodically. The procedure has a potential signal-to-noise ratio advantage because it extracts usable information from a multidimensional FID at short evolution times before the magnetization has decayed significantly.     

Optimal nonlinear approximation

We introduce a definition of nonlinear n-widths and then determine the n-widths of the unit ball of the Sobolev spaceW _p ^r inL _q. We prove that in the sense of these widths the manifold of splines of fixed degree with n free knots is optimal for approximating functions in these Sobolev spaces.This author was supported by NSF Grant DMS 8620108This author was supported by NSF Grant DMS 8803585     

Assignment of the NMR spectra of a potent ribonucleotide reductase inactivator - utilization of HMQC-TOCSY to establish connectivities in exchange broadened spectra

Inverted and Suppressed Direct Response (IDR and SDR, respectively) HMQC-TOCSY experiments are evaluated relative to the conventional HMQC-TOCSY experiment in the assignment of the congested proton and carbon spectra of a 2-acetylpyridine thiocarbonohydrazone used to potentiate the antiviral drug acyclovir. Spectra with moderate overlap can be most expeditiously interpreted using the inverted direct response HMQC-TOCSY variant; spectra with severe overlap can be more readily interpreted if direct responses are suppressed.