Geometrical pre-planning for conformal radiotherapy.

The optimum selection of beams and arcs in conformal techniques is of the outmost importance in modern radiotherapy. In this work we give a description of an analytic method to aid optimum selection, which is based on minimizing the intersection between beams and organs at risk (OAR) and on minimizing the intersection between the beam and the planning target volume (PTV). An arc-selection function that permits selection of irradiation arcs based on individual beam feasibility is introduce. The method simulates the treatment process by defining a computed beam feasibility, for every possible set of gantry-table angles, by taking into account accurately computer intersection volumes between the OAR and beams. The beams are shaped to conform the target using realistic parameters for the treatment process. The results are displayed on a virtual sphere centred at the isocenter with color-coded regions indicating beam feasibility. Arcs selections are performed by searching the map for successive gantry positions at a certain table angle, with feasibility values greater than a user-specified threshold. The accuracy of the method was confirmed by using geometrical regular shapes, as well as real clinical cases.

Methodology for lognormal modelling of malignant pleural mesothelioma survival time distributions: a study of 5580 case histories from Europe and USA.

A truncated left-censored and right-censored lognormal model has been validated for representing pleural mesothelioma survival times in the range 5-200 weeks for data subsets grouped by age for males, 40-49, 50-59, 60-69, 70-79 and 80+ years and for all ages combined for females. The cases available for study were from Europe and USA and totalled 5580. This is larger than any other pleural mesothelioma cohort accrued for study. The methodology describes the computation of reference baseline probabilities, 5-200 weeks, which can be used in clinical trials to assess results of future promising treatment methods. This study is an extension of previous lognormal modelling by Mould et al (2002 Phys. Med. Biol. 47 3893-924) to predict long-term cancer survival from short-term data where the proportion cured is denoted by C and the uncured proportion, which can be represented by a lognormal, by (1 - C). Pleural mesothelioma is a special case when C = 0.

Multiobjective evolutionary optimization of the number of beams, their orientations and weights for intensity-modulated radiation therapy.

We propose a hybrid multiobjective (MO) evolutionary optimization algorithm (MOEA) for intensity-modulated radiotherapy inverse planning and apply it to optimize the number of incident beams, their orientations and intensity profiles. The algorithm produces a set of efficient solutions, which represent different clinical trade-offs and contains information such as variety of dose distributions and dose-volume histograms. No importance factors are required and solutions can be obtained in regions not accessible by conventional weighted sum approaches. The application of the algorithm using a test case, a prostate and a head and neck tumour case is shown. The results are compared with MO inverse planning using a gradient-based optimization algorithm.

Multiobjective inverse planning for intensity modulated radiotherapy with constraint-free gradient-based optimization algorithms.

We consider the behaviour of the limited memory L-BFGS algorithm as a representative constraint-free gradient-based algorithm which is used for multiobjective (MO) dose optimization for intensity modulated radiotherapy (IMRT). Using a parameter transformation, the positivity constraint problem of negative beam fluences is entirely eliminated: a feature which to date has not been fully understood by all investigators. We analyse the global convergence properties of L-BFGS by searching for the existence and the influence of possible local minima. With a fast simulated annealing (FSA) algorithm we examine whether the L-BFGS solutions are globally Pareto optimal. The three examples used in our analysis are a brain tumour, a prostate tumour and a test case with a C-shaped PTV. In 1% of the optimizations global convergence is violated. A simple mechanism practically eliminates the influence of this failure and the obtained solutions are globally optimal. A single-objective dose optimization requires less than 4 s for 5400 parameters and 40000 sampling points. The elimination of the problem of negative beam fluences and the high computational speed permit constraint-free gradient-based optimization algorithms to be used for MO dose optimization. In this situation, a representative spectrum of possible solutions is obtained which contains information such as the trade-off between the objectives and range of dose values. Using simple decision making tools the best of all the possible solutions can be chosen. We perform an MO dose optimization for the three examples and compare the spectra of solutions, firstly using recommended critical dose values for the organs at risk and secondly, setting these dose values to zero.

A geometry based optimization algorithm for conformal external beam radiotherapy.

A geometric solution of the problem of optimal orientation of beams in conformal external radiotherapy is presented. The method uses geometric derived quantities which consider the intersection volume between organs at risk (OAR) and the beam shape. In comparison to previous geometric methods a true 3D volume computation is used which takes into account beam divergence, concave shapes, as well as treatment settings such as individual beam shaping by blocks or multi-leaf collimators. For standard dosimetric cost functions used by dose optimization algorithms a corresponding set of geometric objective functions is proposed. We compare the correlations between geometric and dosimetric cost functions for two clinical cases, a prostate and a head tumour case. A correlation is observed for the prostate case, whereas for the head case it is less pronounced due to the larger part of overlapping volumes between the beams which cannot be considered by the used objectives. In comparison to not-optimized beam directions the dose distribution is significantly better for the beam directions found by the optimization of a geometric multi-objective cost function. An optimal dose distribution can easily be achieved using the geometric model. This is shown by comparing for the two cases the dose-volume histograms (DVH) of manually optimized plans by experienced planners and the DVHs of the geometrically found optimal solutions. In comparison to the manually optimized plans the solutions found by the geometric method significantly reduce the average dose in the OARs and NT, while maintaining the same PTV coverage. The optimization requires only a few seconds and could be used to improve the performance of inverse planning algorithms in radiotherapy for the determination of the optimal direction of beams.