Optimizing the movement of a single absorber for 1D non-uniform dose delivery by (fast) simulated annealing

Inverse and forward optimization of one- and two-dimensional intensity-modulated radiation therapy-based treatment of concave-shaped planning target volumes: the case of prostate cancer

BACKGROUND

Intensity-modulated radiation therapy (IMRT) was suggested as a suitable technique to protect the rectal wall, while maintaining a satisfactory planning target volume (PTV) irradiation in the case of high-dose radiotherapy of prostate cancer. However, up to now, few investigations tried to estimate the expected benefit with respect to conventional three-dimensional (3D) conformal radiotherapy (CRT).

PURPOSE

Estimating the expected clinical gain coming from both 1D and 2D IMRT against 3DCRT, in the case of prostate cancer by mean of radiobiological models. In order to enhance the impact of IMRT, the case of concave-shaped PTV including prostate and seminal vesicles (P+SV) was considered.

MATERIALS AND METHODS

Five patients with concave-shaped PTV including P+SV were selected. Two different sets of constraints were applied during planning: in the first one a quite large inhomogeneity of the dose distribution within the PTV was accepted (set (a)); in the other set (set (b)) a greater homogeneity was required. Tumor control probability (TCP) and normal tissue control probability (NTCP) indices were calculated through the Webb-Nahum and the Lyman-Kutcher models, respectively. Considering a dose interval from 64.8 to 100.8 Gy, the value giving a 5% NTCP for the rectum was found (D(NTCP(rectum)=5%)) using two different methods, and the corresponding TCP(NTCP(rectum)=5%) and NTCP(NTCP(rectum)=5%) for the other critical structures were derived. With the first method, the inverse optimization of the plans was performed just at a fixed 75.6 Gy ICRU dose; with the second method (applied to 2/5 patients) inverse treatment plannings were re-optimized at many dose levels (from 64.8 to 108 Gy with 3.6 Gy intervals). In this case, three different values of alpha/beta (10, 3, 1.5)were used for TCP calculation. The 3DCRT plan consisted of a 3-fields technique; in the IMRT plans, five equi-spaced beams were applied. The Helios Inverse Planning software from Varian was used for both the 2D IMRT and the 1D IMRT inverse optimization, the last one being performed fixing only one available pair of leaves for modulation. A previously proposed forward 1D IMRT 'class solution' technique was also considered, keeping the same irradiation geometry of the inversely optimized IMRT techniques.

RESULTS

With the first method, the average gains in TCP(NTCP(rectum)=5%) of the 2D IMRT technique, with respect 3DCRT, were 10.3 and 7.8%, depending on the choice of the DVHs constraints during the inverse optimization procedure (set (a) and set (b), respectively). The average gain (DeltaTCP(NTCP(rectum)=5%)) coming from the inverse 1D IMRT optimization was 5.0%, when fixing the set (b) DVHs constraints. Concerning the forward 1D IMRT optimization, the average gain in TCP(NTCP(rectum)=5%) was 4.5%. The gain was found to be correlated with the degree of overlapping between rectum and PTV. When comparing 2D IMRT and 1D IMRT, in the case of the more realistic set (b) constraints, DeltaTCP(NTCP(rectum)=5%) was always less than 3%, excepting one patient with a very large overlap region. Basing our choice on this result, the second method was applied to this patient and one of the remaining. Through the inverse re-optimization of the treatment plans at each dose level, the gain in TCP(NTCP(rectum)=5%) of the inverse 2D technique was significantly higher than the ones obtained by applying the first method (concerning the two patients: +6.1% and +2.4%), while no significant benefit was found for inverse 1D. The impact of changing the alpha/beta ratio was less evident in the patient with the lower gain in TCP(NTCP(rectum)=5%).

CONCLUSIONS

The expected benefit due to IMRT with respect to 3DCRT seems to be relevant when the overlap between PTV and rectum is high. Moreover, the difference between the inverse 2D and the simpler inverse or forward 1D IMRT techniques resulted in being relatively modest, with the exception of one patient, having a very large overlap between rectum and PTV. Optimizing the inverse planning at each dose level to find TCP(NTCP(rectum)=5%)e level to find TCP(NTCP(rectum)=5%) can improve the performances of inverse 2D IMRT, against a significant increase of the time for planning. These results suggest the importance of selecting the patients that could have significant benefit from the application of IMRT.

Conformal irradiation of concave-shaped PTVs in the treatment of prostate cancer by simple 1D intensity-modulated beams

BACKGROUND

In the case of concave-shaped PTVs including prostate (P) and seminal vesicles (SV), intensity-modulated radiation therapy (IMRT) should improve the therapeutic ratio of the treatment of prostate cancer.

PURPOSE

Comparing IMRT by simple 1D modulations with conventional 3D conformal therapy (i.e. non-IMRT) in the treatment of concave-shaped PTVs including P+SV.

MATERIALS AND METHODS

For five patients having a concave-shaped PTV (P+SV) previously treated at our Institute with conformal radiotherapy, conventional 3- and 4-fields conformal plans were compared with IMRT plans in terms of biological indices. IMRT plans were generated by using five equi-spaced beams with a partial shielding of the rectum obtainable with our single-absorber modulation technique (Fiorino C, Lev A, Fusca M, Cattaneo GM, Rudello F, Calandrino R. Dynamic beam modulation by using a single dynamic absorber. Phys. Med. Biol. 1995;40:221-240). The modulation was one-dimensional and the shape of the beams was at single minimum in correspondence with the 'core' of the rectum; the beam intensity in the minimum was set equal to 20 or 40% of the open beam intensity. All plans were simulated on the CADPLAN TPS using a pencil-beam based algorithm (with 18 MV X-rays). Tumour control probability (TCP) and normal tissue complication probabilities (NTCPs) (for rectum, bladder and femoral head) were calculated for all situations when varying the isocentre dose from 60 to 90 Gy. Dose distributions were corrected taking dose fractionation into account through the linear-quadratic model; for the TCP/NTCP estimations the Webb-Nahum and the Lyman-Kutcher models were respectively applied. Three different scores were considered: (a) increase of TCP while keeping rectum NTCP equal to 5% (TCP(5%)); (b) increase of the uncomplicated tumour control probability (P+); (c) increase of the biological-based scoring function (S+), developed by Mohan et al. (Mohan R, Mageras GS, Baldwin B, Clinically relevant optimization of 3D conformal treatments. Med. Phys. 1992;19:933-944). The impact of the uncertainty in the knowledge of the parameters of the biological models was investigated for TCP(5%).

RESULTS

(a) The average gain in TCP(5%) when considering IMRT against non-IMRT conformal plans was 7.3% (range 5.0-13.5%); (b) the average increase of P+ was 3.4% (range: 1. 0-8.5%); and (c) the average increase of S+ was 5.4% (range 2.9-12. 4%). The largest gain was found for one patient (patient 5) showing a significantly larger overlapping between PTV and rectum.

CONCLUSIONS

Simple 1D-IMRT may clearly improve the therapeutic ratio in the treatment of concave-shaped PTVs including P and SV. In the range of clinically suitable values, the impact of the uncertainty of the parameters n and sigma(alpha) does not significantly alter the main results concerning the gain in TCP(5%). The reported gain in terms of P+ and S+ should be considered with great caution because of the intrinsic uncertainties of the model's parameters and, for bladder, because the 'true' DVH (considering variations of the shape and dimension due to variable filling) may be very different from the DVH calculated on a single CT scan. Further investigations should consider inversely-optimised 1D and 2D-IMRT plan in order to compare them in terms of cost-benefit.

1D dynamic beam modulation: methods to counteract inertia effects

Dynamic modulation can be affected by inaccuracies when the required acceleration is larger than the highest allowed by the mechanical characteristics of the whole apparatus. In this study, inertia effects have been investigated with regard to the single absorber 1D modulation, analysing primarily how the acceleration performed by the modulating system affects the realization of 'single absorber' fluence profiles and the type of correction which could be devised. The observed percentage deviations from desired modulation at the lowest fluence coordinate of single minimum fluence profiles, when no correction is applied, were almost negligible for 'easy' modulations of the incident fluence (i.e. slow gradients); deviations became increasingly relevant as the moving absorber executed steeper gradients (a 17.6% higher dose being delivered in the minimum position when a 0.2 modulation is required). By applying the proposed corrections, the single absorber performances were improved to a satisfactory level, with a maximum deviation from desired modulation in the minima within 1.6%.

Dose calculation and dosimetry tests for clinical implementation of 1D tissue-deficit compensation by a single dynamic absorber

BACKGROUND AND PURPOSE

In this study the possibilities for implementing 1D tissue-deficit compensation techniques by a dynamic single absorber were investigated. This research firstly involved a preliminary examination on the accuracy of a pencil beam-based algorithm, implemented for irregularly shaped photon beams in our 3D treatment planning system (TPS) (Cadplan 2.7, Varian-Dosetek Oy), in calculating dose distributions delivered in ID non-uniform fields. Once the reliability of the pencil beam (PB) algorithm for dose calculations in non-uniform beams was verified, we proceeded to test the feasibility of tissue-deficit compensation using our single absorber modulator. As an example, we considered a mantle field technique.

MATERIALS AND METHODS

To evaluate the accuracy of the method employed in calculating dose distributions delivered in 1D non-uniform fields, three different fluence profiles, which could be considered as a small sample representative of clinically relevant applications, were selected. The incident non-uniform fluences were simulated by the sum of simple blocked fields (i.e. with rectangular 'strip' blocks, one per beam) properly weighed by the 'modulation factors' Fi, defined in each interval of the subdivided profile as the ratio between the desired fluence and the open field fluence. Depth dose distributions in a cubic phantom were then calculated by the TPS and compared with the corresponding doses (at 5 and 10 cm acrylic depths) delivered by the single absorber modulation system. In the present application, the absorber speed profile able to compensate for the tissue deficit along the cranio-caudal direction and then homogenizing the dose distribution on a 'midline' isocentric plane with sufficient accuracy can be directly derived from anatomic data, such as the SSDs (source-skin distances) along the patient contour. The compensation can be verified through portal dosimetry techniques (using a traditional port film system).

RESULTS

The technique was tested in isocentric conditions on the humanoid RANDO phantom in a clinically suitable situation. The agreement between expected/calculated and measured incident/exit dose profiles was found to be within 4%, with deviations generally around 1-2%. As for the PB accuracy investigation for dose calculations in non-uniform fields, calculated versus measured dose profiles were found to be in good agreement, indicating a satisfactory accuracy of the method employed for dose calculation in 1D non-uniform photon beams. A better performance should be expected if the incident fluences could be directly inserted in the TPS.

CONCLUSIONS

The results show that the proposed technique should be sufficiently reliable for clinical application. The main advantages are its simplicity and the possibility of application on Linacs which have no complex options for dynamic control of collimators.