iCycle: Integrated, multicriterial beam angle, and profile optimization for generation of coplanar and noncoplanar IMRT plans.

PURPOSE: To introduce iCycle, a novel algorithm for integrated, multicriterial optimization of beam angles, and intensity modulated radiotherapy (IMRT) profiles. METHODS: A multicriterial plan optimization with iCycle is based on a prescription called wish-list, containing hard constraints and objectives with ascribed priorities. Priorities are ordinal parameters used for relative importance ranking of the objectives. The higher an objective priority is, the higher the probability that the corresponding objective will be met. Beam directions are selected from an input set of candidate directions. Input sets can be restricted, e.g., to allow only generation of coplanar plans, or to avoid collisions between patient/couch and the gantry in a noncoplanar setup. Obtaining clinically feasible calculation times was an important design criterium for development of iCycle. This could be realized by sequentially adding beams to the treatment plan in an iterative procedure. Each iteration loop starts with selection of the optimal direction to be added. Then, a Pareto-optimal IMRT plan is generated for the (fixed) beam setup that includes all so far selected directions, using a previously published algorithm for multicriterial optimization of fluence profiles for a fixed beam arrangement Breedveld et al. [Phys. Med. Biol. 54, 7199-7209 (2009)]. To select the next direction, each not yet selected candidate direction is temporarily added to the plan and an optimization problem, derived from the Lagrangian obtained from the just performed optimization for establishing the Pareto-optimal plan, is solved. For each patient, a single one-beam, two-beam, three-beam, etc. Pareto-optimal plan is generated until addition of beams does no longer result in significant plan quality improvement. Plan generation with iCycle is fully automated. RESULTS: Performance and characteristics of iCycle are demonstrated by generating plans for a maxillary sinus case, a cervical cancer patient, and a liver patient treated with SBRT. Plans generated with beam angle optimization did better meet the clinical goals than equiangular or manually selected configurations. For the maxillary sinus and liver cases, significant improvements for noncoplanar setups were seen. The cervix case showed that also in IMRT with coplanar setups, beam angle optimization with iCycle may improve plan quality. Computation times for coplanar plans were around 1-2 h and for noncoplanar plans 4-7 h, depending on the number of beams and the complexity of the site. CONCLUSIONS: Integrated beam angle and profile optimization with iCycle may result in significant improvements in treatment plan quality. Due to automation, the plan generation workload is minimal. Clinical application has started.

Second re-irradiation: efficacy, dose and toxicity in patients who received three courses of radiotherapy with overlapping fields.

PURPOSE: To explore the outcome, cumulative dose and toxicity in 23 patients after a third radiation treatment, with a partial or complete overlap of the previous two irradiated regions. METHODS AND MATERIAL: The dose summation of the three radiation plans was made by the planning system. For patients treated with cyberknife or brachytherapy dose summation was done by dose point calculations. Efficacy and toxicity was scored by looking at the reduction of tumor, pain and bleeding. RESULTS: Symptomatic response was observed in 81% and 73% of the patients after, respectively, the third and second radiation. The median cumulative maximum dose to the tumor and its regions was 133Gy(3) (range: 82-496Gy(3)). The median corrected cumulative dose for the rectum, bowel and bladder resulted in 91Gy(3), 73Gy(3) and 79Gy(3), respectively. Grade 3 acute skin toxicity was only seen in the third radiation course. CONCLUSION: The constraints of 100Gy(3) for rectum, 90Gy(3) for bowel and 110Gy(3) for bladder are safe and can be used as guidelines in the decision for re-irradiation. Symptomatic relieve was seen in 81% of the patients with low grade 3 and no grade 4 acute and late toxicity.

The equivalence of multi-criteria methods for radiotherapy plan optimization.

Several methods can be used to achieve multi-criteria optimization of radiation therapy treatment planning, which strive for Pareto-optimality. The property of the solution being Pareto optimal is desired, because it guarantees that no criteria can be improved without deteriorating another criteria. The most widely used methods are the weighted-sum method, in which the different treatment objectives are weighted, and constrained optimization methods, in which treatment goals are set and the algorithm has to find the best plan fulfilling these goals. The constrained method used in this paper, the 2p element of c (2-phase element-constraint) method is based on the element-constraint method, which generates Pareto-optimal solutions. Both approaches are uniquely related to each other. In this paper, we will show that it is possible to switch from the constrained method to the weighted-sum method by using the Lagrange multipliers from the constrained optimization problem, and vice versa by setting the appropriate constraints. In general, the theory presented in this paper can be useful in cases where a new situation is slightly different from the original situation, e.g. in online treatment planning, with deformations of the volumes of interest, or in automated treatment planning, where changes to the automated plan have to be made. An example of the latter is given where the planner is not satisfied with the result from the constrained method and wishes to decrease the dose in a structure. By using the Lagrange multipliers, a weighted-sum optimization problem is constructed, which generates a Pareto-optimal solution in the neighbourhood of the original plan, but fulfills the new treatment objectives.

Automated non-coplanar beam direction optimization improves IMRT in SBRT of liver metastasis.

PURPOSE: To investigate whether automatically optimized coplanar, or non-coplanar beam setups improve intensity modulated radiotherapy (IMRT) treatment plans for stereotactic body radiotherapy (SBRT) of liver tumors, compared to a reference equi-angular IMRT plan. METHODS: For a group of 13 liver patients, an in-house developed beam selection algorithm (Cycle) was used for generation of 3D-CRT plans with either optimized coplanar-, or non-coplanar beam setups. These 10 field, coplanar and non-coplanar setups, and an 11 field, equi-angular coplanar reference setup were then used as input for generation of IMRT plans. For all plans, the PTV dose was maximized in an iterative procedure by increasing the prescribed PTV dose in small steps until further increase was prevented by constraint violation(s). RESULTS: For optimized non-coplanar setups, D(PTV, max) increased by on average 30% (range 8-64%) compared to the corresponding reference IMRT plan. Similar increases were observed for D(PTV, 99%) and gEUD(a). For optimized coplanar setups, mean PTV dose increases were only approximately 4%. After re-scaling all plans to the clinically applied dose, optimized non-coplanar configurations resulted in the best sparing of organs at risk (healthy liver, spinal cord, bowel). CONCLUSION: Compared to an equi-angular beam setup, computer optimized non-coplanar setups do result in substantial improvements in IMRT plans for SBRT of liver tumors.

A comparison of an algorithm for automated sequential beam orientation selection (Cycle) with simulated annealing.

Some time ago we developed and published a new deterministic algorithm (called Cycle) for automatic selection of beam orientations in radiotherapy. This algorithm is a plan generation process aiming at the prescribed PTV dose within hard dose and dose-volume constraints. The algorithm allows a large number of input orientations to be used and selects only the most efficient orientations, surviving the selection process. Efficiency is determined by a score function and is more or less equal to the extent of uninhibited access to the PTV for a specific beam during the selection process. In this paper we compare the capabilities of fast-simulated annealing (FSA) and Cycle for cases where local optima are supposed to be present. Five pancreas and five oesophagus cases previously treated in our institute were selected for this comparison. Plans were generated for FSA and Cycle, using the same hard dose and dose-volume constraints, and the largest possible achieved PTV doses as obtained from these algorithms were compared. The largest achieved PTV dose values were generally very similar for the two algorithms. In some cases FSA resulted in a slightly higher PTV dose than Cycle, at the cost of switching on substantially more beam orientations than Cycle. In other cases, when Cycle generated the solution with the highest PTV dose using only a limited number of non-zero weight beams, FSA seemed to have some difficulty in switching off the unfavourable directions. Cycle was faster than FSA, especially for large-dimensional feasible spaces. In conclusion, for the cases studied in this paper, we have found that despite the inherent drawback of sequential search as used by Cycle (where Cycle could probably get trapped in a local optimum), Cycle is nevertheless able to find comparable or sometimes slightly better treatment plans in comparison with FSA (which in theory finds the global optimum) especially in large-dimensional beam weight spaces.

A novel approach to multi-criteria inverse planning for IMRT.

Treatment plan optimization is a multi-criteria process. Optimizing solely on one objective or on a sum of a priori weighted objectives may result in inferior treatment plans. Manually adjusting weights or constraints in a trial and error procedure is time consuming. In this paper we introduce a novel multi-criteria optimization approach to automatically optimize treatment constraints (dose-volume and maximum-dose). The algorithm tries to meet these constraints as well as possible, but in the case of conflicts it relaxes lower priority constraints so that higher priority constraints can be met. Afterwards, all constraints are tightened, starting with the highest priority constraints. Applied constraint priority lists can be used as class solutions for patients with similar tumour types. The presented algorithm does iteratively apply an underlying algorithm for beam profile optimization, based on a quadratic objective function with voxel-dependent importance factors. These voxel-dependent importance factors are automatically adjusted to reduce dose-volume and maximum-dose constraint violations.

PTV dose prescription strategies for SBRT of metastatic liver tumours.

PURPOSE: Recently we have demonstrated that our in-house developed algorithm for automated plan generation for fully non-coplanar SBRT of liver patients (designated Cycle) yields plans that are superior to conventionally generated plans of experienced dosimetrists. Here we use Cycle in the comparison of plans with prescription isodoses of 65% or 80% of the isocentre dose. METHODS: Plans were generated using CT-data of 15 previously treated patients. For each patient, both for the 65%- and the 80% strategy, Cycle was used to generate a plan with the maximum isocentre dose, D(isoc), while strictly obeying a set of hard constraints for the organs at risk (OAR). Plans for the two strategies were compared using D(isoc), D(PTV,99%) (the minimum dose delivered to 99% of the PTV), and the generalised equivalent uniform dose, gEUD(PTV)(a), for several values of the parameter a. Moreover, for the OARs, the distance to the constraint values was analysed. RESULTS: The 65% strategy resulted in treatment plans with a higher D(isoc) (average 17.6%, range 7.6-31.1%) than the 80% strategy, at the cost of a somewhat lower D(PTV,99%) (average -2.0%, range -9.6% to 9.3%). On average, voxels with a dose in the 65% strategy, lower than the minimum PTV dose in the 80% strategy, were within 0.2cm from the PTV surface. For a-10, the 65% strategy yielded on average a significantly (P<0.01) higher gEUD(PTV)(a) than the 80% strategy, whereas for highly negative a-values the 80% approach was slightly better, although not significantly. Large variations between patients were observed. Generally, for the OAR the approach to the constraint levels was similar for the two strategies. CONCLUSION: On average, PTV dose delivery is superior with the 65% strategy. However, apart from the isocentre dose, for each applied PTV dose parameter at least one patient would have been better off with the 80% dose prescription strategy.

Computer optimization of noncoplanar beam setups improves stereotactic treatment of liver tumors.

PURPOSE: To investigate whether computer-optimized fully noncoplanar beam setups may improve treatment plans for the stereotactic treatment of liver tumors. METHODS: An algorithm for automated beam orientation and weight selection (Cycle) was extended for noncoplanar stereotactic treatments. For 8 liver patients previously treated in our clinic using a prescription isodose of 65%, Cycle was used to generate noncoplanar and coplanar plans with the highest achievable minimum planning target volume (PTV) dose for the clinically delivered isocenter and mean liver doses, while not violating the clinically applied hard planning constraints. The clinical and the optimized coplanar and noncoplanar plans were compared, with respect to D(PTV,99%), the dose received by 99% of the PTV, the PTV generalized equivalent uniform dose (gEUD), and the compliance with the clinical constraints. RESULTS: For each patient, the ratio between D(PTV,99%) and D(isoc), and the gEUD(-5) and gEUD(-20) values of the optimized noncoplanar plan were higher than for the clinical plan with an average increase of respectively 18.8% (range, 7.8-24.0%), 6.4 Gy (range, 3.4-11.8 Gy), and 10.3 Gy (range, 6.7-12.5). D(PTV,99%)/D(isoc), gEUD(-5), and gEUD(-20) of the optimized noncoplanar plan was always higher than for the optimized coplanar plan with an average increase of, respectively, 4.5% (range, 0.2-9.7%), 2.7 Gy (range, 0.6-9.7 Gy), and 3.4 Gy (range, 0.6-9.9 Gy). All plans were within the imposed hard constraints. On average, the organs at risk were better spared with the optimized noncoplanar plan than with the optimized coplanar plan and the clinical plan. CONCLUSIONS: The use of automatically generated, fully noncoplanar beam setups results in plans that are favorable compared with coplanar techniques. Because of the automation, we found that the planning workload can be decreased from 1 to 2 days to 1 to 2 h.

Fast, multiple optimizations of quadratic dose objective functions in IMRT.

Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved.

Automated selection of beam orientations and segmented intensity-modulated radiotherapy (IMRT) for treatment of oesophagus tumors.

BACKGROUND AND PURPOSE: For some treatment sites, there is evidence in the literature that five to nine equi-angular input beam directions are enough for generating IMRT plans. For oesophagus cancer, there is a report showing that going from four to nine beams may even result in lower quality plans. In this paper, our previously published algorithm for automated beam angle selection (Cycle) has been extended to include segmented IMRT. For oesophagus cancer patients, we have investigated whether automated orientation selection from a large number of equi-angular input beam directions (up to thirty-six) for IMRT optimisation can result in improved lung sparing. MATERIALS AND METHODS: CT-data from five oesophagus patients treated recently in our institute were used for this study. For a prescribed mean PTV dose of 55 Gy, Cycle was used in an iterative procedure to minimise the mean lung dose under the following hard constraints: standard deviation for PTV dose inhomogeneity 2% (1,1 Gy), maximum spinal cord dose 45 Gy. Conformal radiotherapy (CFRT) and IMRT plans for a standard four field oesophagus beam configuration were compared with IMRT plans generated by automated selection from nine or thirty-six equi-angular input beam orientations. Comparisons were also made with dose distributions generated with our commercial treatment planning system (TPS), and with observations in the literature. RESULTS: Using Cycle, automated orientation selection from nine or thirty-six input beam directions resulted in improved lung sparing compared to the four field set-ups. Compared to selection from nine input orientations, selection from thirty-six directions did always result in lower mean lung doses, sometimes with even fewer non-zero weight beams. On average only seven beams with a non-zero weight were enough for obtaining the lowest mean lung dose, yielding clinically feasible plans even in case of thirty-six input directions for the optimisation process. With our commercial TPS we observed the same contra-intuitive, unfavourable results as reported in the literature; nine field equi-angular IMRT plans had substantially higher mean lung doses than plans for the conventional four field set-ups. For all cases, the Cycle plans generated from nine equi-angular input directions were superior compared to similar plans generated with our commercial TPS. CONCLUSIONS: For the studied oesophagus cancer patients the best plans for IMRT were obtained with Cycle, using automated beam orientation selection from thirty-six input beam directions. The lowest mean lung doses could be obtained with, on average, a selection of only seven beams with non-zero weight.