Linear programming is a versatile mathematical tool for optimizing radiation therapy treatment plans. For planning purposes, dose constraint points, possible treatment beams, and an objective function are defined. Dose constraint points are specified in and about the target volume and normal structures with minimum and maximum dose values assigned to each point. A linear objective function is designed that defines the goal of optimization. A list of potential treatment beams is defined by energy, angle, and wedge selection. Then, linear programming calculates the relative weights of all the potential beams such that the objective function is optimized and doses to all constraint points are within the prescribed limits. Historically, linear programming has been used to improve conventional treatment techniques. It can also be used to create sophisticated, complex treatment plans suitable for delivery by computer-controlled therapy techniques.

Intensity modulated radiotherapy (IMRT) requires extensive knowledge of multileaf collimator (MLC) leaf positioning accuracy, precision, and long-term reproducibility. We have developed a technique to efficiently measure the absolute position of each MLC leaf, over the range of leaf positions utilized in IMRT, based on dosimetric information. A single radiographic film was exposed to 6 MV x-rays for twelve exposures: one open field with a radio-opaque marker tray present, and eleven fields (1 x 28 cm strips via 1 cm gaps between opposed leaf pairs) separated by 2 cm center to center. The process was repeated while varying direction of leaf travel; each film was digitized using a commercial film dosimetry system. The digital images were manipulated to remove translation and rotation of the film data with respect to the collimator coordinate system by extraction of radiation dose profiles perpendicular to the MLC leaf motion and measuring the center of the x-ray leakage between leaves. Radiation dose profiles in the direction of leaf motion were acquired through the center of each leaf pair (leaves 2-28), which provided leaf position information every 2 cm with 0.2 mm precision. Nine separate leaf reproducibility studies over a 90 day period which evaluated 600 measurement points on each film show 0.3 mm precision for 95% confidence, while hysteresis studies show 0.5 mm precision. Absolute leaf position error measurements demonstrated a radial dependence, with a maximum of 1.5 mm at 16.4 cm from central axis, due to rotational error at calibration. Recalibration of the MLC leaves based utilizing this tool yields absolute leaf position measurements where 91.5% of all leaves/positions were within 0.5 mm, with a mean error of 0.1 mm and a maximum error less than 1.0 mm.

Robust optimization generates scenario‐based plans by a minimax optimization method to find optimal scenario for the trade‐off between target coverage robustness and organ‐at‐risk (OAR) sparing. In this study, 20 lung cancer patients with tumors located at various anatomical regions within the lungs were selected and robust optimization photon treatment plans including intensity modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT) plans were generated. The plan robustness was analyzed using perturbed doses with setup error boundary of ±3 mm in anterior/posterior (AP), ±3 mm in left/right (LR), and ±5 mm in inferior/superior (IS) directions from isocenter. Perturbed doses for D99, D98, and D95 were computed from six shifted isocenter plans to evaluate plan robustness. Dosimetric study was performed to compare the internal target volume‐based robust optimization plans (ITV‐IMRT and ITV‐VMAT) and conventional PTV margin‐based plans (PTV‐IMRT and PTV‐VMAT). The dosimetric comparison parameters were: ITV target mean dose (Dmean), R95(D95/Dprescription), Paddick's conformity index (CI), homogeneity index (HI), monitor unit (MU), and OAR doses including lung (Dmean, V20 Gy and V15 Gy), chest wall, heart, esophagus, and maximum cord doses. A comparison of optimization results showed the robust optimization plan had better ITV dose coverage, better CI, worse HI, and lower OAR doses than conventional PTV margin‐based plans. Plan robustness evaluation showed that the perturbed doses of D99, D98, and D95 were all satisfied at least 99% of the ITV to received 95% of prescription doses. It was also observed that PTV margin‐based plans had higher MU than robust optimization plans. The results also showed robust optimization can generate plans that offer increased OAR sparing, especially for normal lungs and OARs near or abutting the target. Weak correlation was found between normal lung dose and target size, and no other correlation was observed in this study.

Spatially fractionated radiotherapy (GRID) was designed to treat large tumors while sparing skin, and it is usually delivered with a linear accelerator using a commercially available block or multileaf collimator (LINAC‐GRID). For deep‐seated (skin to tumor distance false(>8 cmfalse)) tumors, it is always a challenge to achieve adequate tumor dose coverage. A novel method to perform GRID treatment using helical tomotherapy (HT‐GRID) was developed at our institution. Our approach allows treating patients by generating a patient‐specific virtual GRID block (software‐generated) and using IMRT technique to optimize the treatment plan. Here, we report our initial clinical experience using HT‐GRID, and dosimetric comparison results between HT‐GRID and LINAC‐GRID. This study evaluates 10 previously treated patients who had deep‐seated bulky tumors with complex geometries. Five of these patients were treated with HT‐GRID and replanned with LINAC‐GRID for comparison. Similarly, five other patients were treated with LINAC‐GRID and replanned with HT‐GRID for comparison. The prescription was set such that the maximum dose to the GTV is 20 Gy in a single fraction. Dosimetric parameters compared included: mean GTV dose (DGTVmean), GTV dose inhomogeneity (valley‐to‐peak dose ratio (VPR)), normal tissue doses (DNmean), and other organs‐at‐risk (OARs) doses. In addition, equivalent uniform doses (EUD) for both GTV and normal tissue were evaluated. In summary, HT‐GRID technique is patient‐specific, and allows adjustment of the GRID pattern to match different tumor sizes and shapes when they are deep‐seated and cannot be adequately treated with LINAC‐GRID. HT‐GRID delivers a higher DGTVmean, EUD, and VPR compared to LINAC‐GRID. HT‐GRID delivers a higher DNmean and lower EUD for normal tissue compared to LINAC‐GRID. HT‐GRID plans also have more options for tumors with complex anatomical relationships between the GTV and the avoidance OARs (abutment or close proximity).PACS numbers: 87.55.D, 87.55.de, 87.55.ne, 87.55.tg

A variation of simulated annealing optimization called 'constrained simulated annealing' is used with a simple annealing schedule to optimize beam weights and angles in radiation therapy treatment planning. Constrained simulated annealing is demonstrated using two contrasting objective functions which incorporate both biological response and dose-volume considerations. The first objective function maximizes the probability of a complication-free treatment (PCFT) by minimizing the normal tissue complications subject to the constraint that the entire target volume receives a prescribed minimum turmourcidal dose with a specified dose homogeneity. Probabilities of normal tissue complication are based on published normal tissue complication probability functions and computed from dose-volume histograms. The second objective function maximizes the isocentre dose subject to a set of customized normal tissue dose-volume and target volume dose homogeneity constraints (MVDL). Although the PCFT objective function gives consistently lower estimates of normal tissue complication probabilities, the ability to specify individualized dose-volume limits, and therefore the individualized probability of complication, for an individual organ makes the MDVL objective function more useful for treatment planning.