This paper proposes a new geometrical formulation of the coplanar beam orientation problem combined with a hybrid multiobjective genetic algorithm. The approach is demonstrated by optimizing the beam orientation in two dimensions, with the objectives being formulated using planar geometry. The traditional formulation of the objectives associated with the organs at risk has been modified to account for the use of complex dose delivery techniques such as beam intensity modulation. The new algorithm attempts to replicate the approach of a treatment planner whilst reducing the amount of computation required. Hybrid genetic search operators have been developed to improve the performance of the genetic algorithm by exploiting problem-specific features. The multiobjective genetic algorithm is formulated around the concept of Pareto optimality which enables the algorithm to search in parallel for different objectives. When the approach is applied without constraining the number of beams, the solution produces an indication of the minimum number of beams required. It is also possible to obtain non-dominated solutions for various numbers of beams, thereby giving the clinicians a choice in terms of the number of beams as well as in the orientation of these beams.
An investigation has been carried out into the properties of the BANG polymer gel and its use in the dosimetry of low dose rate brachytherapy. It was discovered that the response of the gel was reproducible and linear to 10 Gy. The gel was found to be tissue equivalent with a response independent of energy to within experimental accuracy (standard error of measurement +/- 5%). The slope of the calibration curve was found to increase from 0.28 +/- 0.01 s-1 Gy-1 to 0.50 +/- 0.02 s-1 Gy-1 for an increase in monomer concentration from 6 to 9%. Absorbed dose distributions for a straight applicator containing 36 137Cs sources were measured using the gel and the results compared with measurements made with thermoluminescent dosemeters (TLDs) and calculated values. Good agreement was found for the relative measurements. The root mean square residual percentage errors were 3%, 1% and 4% for the gel and the two groups of TLDs, respectively. There were some significant differences in absolute values of absorbed dose in the gel, possibly owing to the effects of oxygen. Measurements of a complex gynaecological insert were also made and compared with isodose curves from a planning system (Helax TMS), and in areas unaffected by oxygen diffusion the isodose levels from 100 to 50% agreed to within less than 0.5 mm.
Image-guided radiation therapy aims to improve the accuracy of treatment delivery by tracking tumor position and compensating for observed movement. Due to system latency it is sometimes necessary to predict tumor trajectory evolution in order to facilitate changes in beam delivery. Neural networks (NNs) have previously been investigated for predicting future tumor position because of their ability to model non-linear systems. However, no attempt has been made to optimize the NN training algorithms, and no mention has been made of potential errors which can be caused by using NNs for extrapolation purposes. In this work, after giving a brief explanation of NN theory, a comparison is made between 4 different adaptive algorithms for training time-series prediction NNs. New error criteria are introduced which highlight error maxima. Results are obtained by training the NNs using previously published data. A hybrid algorithm combining Bayesian regularization with conjugate-gradient backpropagation is demonstrated to give the best average prediction accuracy, whilst a generalized regression NN is shown to reduce the possibility of isolated large prediction errors.
Respiration induces significant movement of tumours in the vicinity of thoracic and abdominal structures. Real-time image-guided radiotherapy (IGRT) aims to adapt radiation delivery to tumour motion during irradiation. One of the main problems for achieving this objective is the presence of time lag between the acquisition of tumour position and the radiation delivery. Such time lag causes significant beam positioning errors and affects the dose coverage. A method to solve this problem is to employ an algorithm that is able to predict future tumour positions from available tumour position measurements. This paper presents a multiple model approach to respiratory-induced tumour motion prediction using the interacting multiple model (IMM) filter. A combination of two models, constant velocity (CV) and constant acceleration (CA), is used to capture respiratory-induced tumour motion. A Kalman filter is designed for each of the local models and the IMM filter is applied to combine the predictions of these Kalman filters for obtaining the predicted tumour position. The IMM filter, likewise the Kalman filter, is a recursive algorithm that is suitable for real-time applications. In addition, this paper proposes a confidence interval (CI) criterion to evaluate the performance of tumour motion prediction algorithms for IGRT. The proposed CI criterion provides a relevant measure for the prediction performance in terms of clinical applications and can be used to specify the margin to accommodate prediction errors. The prediction performance of the IMM filter has been evaluated using 110 traces of 4-minute free-breathing motion collected from 24 lung-cancer patients. The simulation study was carried out for prediction time 0.1-0.6 s with sampling rates 3, 5 and 10 Hz. It was found that the prediction of the IMM filter was consistently better than the prediction of the Kalman filter with the CV or CA model. There was no significant difference of prediction errors for the sampling rates 5 and 10 Hz. For these sampling rates, the errors of the IMM filter for 0.4 s prediction time were less than 2.1 mm in terms of the 95% CI criterion or 1.1 mm in terms of the standard deviation (SD) or root mean squared errors (RMSE) criterion. For the prediction time of 0.6 s the errors were less than 3.6 mm in terms of the 95% CI criterion or 1.8 mm in terms of the SD/RMSE criterion. The prediction error analysis showed that the average percentage of the target lies outside the 95% CI margin was 5.2% and outside the SD/RMSE margin was 24.3%. This indicates the effectiveness of the 95% CI criterion as a margining strategy to accommodate prediction errors.
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