Optimization of HDR brachytherapy dose distributions using linear programming with penalty costs

A linear optimization model for high dose rate brachytherapy using a novel distance metric

Purpose.We propose a linear network-based optimization model (LNBM) for high dose rate brachytherapy (HDR-BT) that uses a novel distance metric to measure the discrepancy between the dose delivered and the prescription. Unlike models in the literature, LNBM takes advantage of the adjacency structure of the patients' voxels by formalizing them into a network.Methods.We apply LNBM to a set of 7 cervical cancer cases treated with HDR-BT. State-of-the-art commercial optimization software solves LNBM to global optimality. The results of LNBM are compared with those of inverse planning by simulated annealing (IPSA) based on tumor coverage, dosimetric indices for the critical organs at risk (OARs), isodose contour plots, and two metrics of homogeneity new to this work (hot-spots volumes and diameters).Results.LNBM produces plans with improved tumor coverage and with improved isodose contour plots and dosimetric indices for OARs that receive highest dose (bladder and rectum in this study) when compared with IPSA. Using new metrics of homogeneity, we also demonstrate that LNBM produces more homogeneous plans on these cases. An analysis of the solutions of LNBM shows that they use a significant part of the voxel network structure, providing evidence that the plans produced are different from those created using traditional penalty approaches and are more directly guided by the geometry of the patients' anatomy.Conclusions.The proposed linear network-based optimization model efficiently generates more homogeneous high quality treatment plans for HDR-BT.

Applying the column generation method to the intensity modulated high dose rate brachytherapy inverse planning problem

Objective.Intensity modulated high dose rate brachytherapy (IMBT) is a rapidly developing application of brachytherapy where anisotropic dose distributions can be produced at each source dwell position. This technique is made possible by placing rotating metallic shields inside brachytherapy needles or catheters. By dynamically directing the radiation towards the tumours and away from the healthy tissues, a more conformal dose distribution can be obtained. The resulting treatment planning involves optimizing dwell position and shield angle (DPSA). The aim of this study was to investigate the column generation method for IMBT treatment plan optimization.Approach.A column generation optimization algorithm was developed to optimize the dwell times and shield angles. A retrospective study was performed on 10 prostate cases using RapidBrachyMCTPS. At every iteration, the plan was optimized with the chosen DPSA which would best improve the cost function that was added to the plan. The optimization process was stopped when the remaining DPSAs would not add value to the plan to limit the plan complexity.Main results.The average number of DPSAs and voxels were 2270 and 7997, respectively. The column generation approach yielded near-optimal treatment plans by using only 11% of available DPSAs on average in ten prostate cases. The coverage and organs at risk constraints passed in all ten cases.Significance.The column generation method produced high-quality deliverable prostate IMBT plans. The treatment plan quality reached a plateau, where adding more DPSAs had a minimal effect on dose volume histogram parameters. The iterative nature of the column generation method allows early termination of the treatment plan creation process as soon as the dosimetric indices from dose volume histogram satisfy the clinical requirements or if their values stabilize.

Dosimetric impact of a robust optimization approach to mitigate effects from rotational uncertainty in prostate intensity-modulated brachytherapy

BACKGROUND

Intensity-modulated brachytherapy (IMBT) is an emerging technology for cancer treatment, in which radiation sources are shielded to shape the dose distribution. The rotatable shields provide an additional degree of freedom, but also introduce an additional, directional, type of uncertainty, compared to conventional high-dose-rate brachytherapy (HDR BT).

PURPOSE

We propose and evaluate a robust optimization approach to mitigate the effects of rotational uncertainty in the shields with respect to planning criteria.

METHODS

A previously suggested prototype for platinum-shielded prostate ¹⁶⁹ Yb-based dynamic IMBT is considered. We study a retrospective patient data set (anatomical contours and catheter placement) from two clinics, consisting of six patients that had previously undergone conventional ¹⁹² Ir HDR BT treatment. The Monte Carlo-based treatment planning software RapidBrachyMCTPS is used for dose calculations. In our computational experiments, we investigate systematic rotational shield errors of ±10° and ±20°, and the same systematic error is applied to all dwell positions in each scenario. This gives us three scenarios, one nominal and two with errors. The robust optimization approach finds a compromise between the average and worst-case scenario outcomes.

RESULTS

We compare dose plans obtained from standard models and their robust counterparts. With dwell times obtained from a linear penalty model (LPM), for 10° errors, the dose to urethra ( D 0.1 c c $D_{0.1cc}$ ) and rectum ( D 0.1 c c $D_{0.1cc}$ and D 1 c c $D_{1cc}$ ) increase with up to 5% and 7%, respectively, in the worst-case scenario, while with the robust counterpart, the corresponding increases were 3% and 3%. For all patients and all evaluated criteria, the worst-case scenario outcome with the robust approach had lower deviation compared to the standard model, without compromising target coverage. We also evaluated shield errors up to 20° and while the deviations increased to a large extent with the standard models, the robust models were capable of handling even such large errors.

CONCLUSIONS

We conclude that robust optimization can be used to mitigate the effects from rotational uncertainty and to ensure the treatment plan quality of IMBT.

Incorporating Treatment Time into Butterfly Optimization to Reduce Total Treatment Time for Vaginal Cylinder Brachytherapy

Purpose

For patient comfort and safety, irradiation times should be kept at a minimum while maintaining high treatment quality. In this study of high dose rate (HDR) therapy with a vaginal cylinder, we used the butterfly optimization algorithm (BOA) to simultaneously optimize individual dwell times for precise dose conformity and for the reduction of total dwell time.

Material and methods

BOA is a population-based, meta-heuristic algorithm that averts local minima by conducting intensive local and global searching based on switching probability. We constructed an objective function (a stimulus intensity function) that consisted of two components. The first one was the root-mean-squared dose error (RMSE) defined as the square root of the sum of squared differences between the prescribed and delivered dose at the constraint points. The second component was weighted total treatment time. Eight previously treated cases were retrospectively reviewed by re-optimizing the clinical treatment plans with BOA. 

Results

Compared to the eight original plans generated with the commercial adaptive volume optimization algorithm (AVOA), the BOA-optimized plans reduced treatment times by 5.4% to 8.9%, corresponding to a time-saving of 13.1 to 47.7 seconds with the activities on the treatment day and saving from 29.3 to 64.6 seconds if treated with an activity of 5 CI. Dose deviations from the prescription were smaller than in the original plans.

Conclusion 

Dose optimizations based on the BOA algorithm yield closer dose conformity in vaginal HDR treatment than AVOA. Incorporating total treatment time into the optimization algorithm reduces the delivery time while having only a small effect on dose conformity.

Evaluation of dose differences between intracavitary applicators for cervical brachytherapy using knowledge-based models

PURPOSE

Currently, there is a lack of patient-specific tools to guide brachytherapy planning and applicator choice for cervical cancer. The purpose of this study is to evaluate the accuracy of organ-at-risk (OAR) dose predictions using knowledge-based intracavitary models, and the use of these models and clinical data to determine the dosimetric differences of tandem-and-ring (T&R) and tandem-and-ovoids (T&O) applicators.

MATERIALS AND METHODS

Knowledge-based models, which predict organ D_2cc, were trained on 77/75 cases and validated on 32/38 for T&R/T&O applicators. Model performance was quantified using ΔD_2cc=D_2cc,actual-D_{2cc,predicted}, with standard deviation (σ(ΔD_2cc)) representing precision. Model-predicted applicator dose differences were determined by applying T&O models to T&R cases, and vice versa, and compared to clinically-achieved D_2cc differences. Applicator differences were assessed using a Student's t-test (p < 0.05 significant).

RESULTS

Validation T&O/T&R model precision was 0.65/0.55 Gy, 0.55/0.38 Gy, and 0.43/0.60 Gy for bladder, rectum and sigmoid, respectively, and similar to training. When applying T&O/T&R models to T&R/T&O cases, bladder, rectum and sigmoid D_2cc values in EQD2 were on average 5.69/2.62 Gy, 7.31/6.15 Gy and 3.65/0.69 Gy lower for T&R, with similar HRCTV volume and coverage. Clinical data also showed lower T&R OAR doses, with mean EQD2 D_2cc deviations of 0.61 Gy, 7.96 Gy (p < 0.01) and 5.86 Gy (p < 0.01) for bladder, rectum and sigmoid.

CONCLUSIONS

Accurate knowledge-based dose prediction models were developed for two common intracavitary applicators. These models could be beneficial for standardizing and improving the quality of brachytherapy plans. Both models and clinical data suggest that significant OAR sparing can be achieved with T&R over T&O applicators, particularly for the rectum.

An inverse planning simulated annealing algorithm with adaptive weight adjustment for LDR pancreatic brachytherapy

PURPOSE

The inverse planning simulated annealing (IPSA) algorithm has shown good results in cancer surgical treatment planning. However, an adaptive approach has not well been proposed for different shapes and sizes of tumors. The purpose of this study was to propose an adaptive, efficient and safe algorithm to get high-quality treatment dose planning, which is presented for pancreatic cancer.

METHODS

An algorithm employs an optimized IPSA and an adaptive process for adjusting the weight of organs at risk (OAR) and tumor. The algorithm, which was combined with ant colony optimization, was further optimized to reduce the number of needles. It could meet the clinical dose objectives within the tumors, reduce the dose distribution within the OAR and minimize the number of needles. Ten clinical cases were chosen randomly from patients, previously successfully treated in clinic to test our method. The algorithm was validated against clinical cases, using clinically relevant dose parameters.

RESULTS

The results were compared with clinical results in ten cases, indicating that the dose distribution within the tumor meets the clinical dose objectives. The dose received by OAR had been greatly reduced, and the number of needles could be reduced by about 50%. It was a significant improvement over the clinical treatment planning.

CONCLUSIONS

In this paper, we have devised an algorithm to optimize the treatment planning in brachytherapy. The method in this paper could meet the clinical dose objectives and reduce the difficulty of operation. The results were clinically acceptable. This algorithm is also applicable to other cancers such as lung cancer.

Optimization in treatment planning of high dose-rate brachytherapy - Review and analysis of mathematical models

Treatment planning in high dose-rate brachytherapy has traditionally been conducted with manual forward planning, but inverse planning is today increasingly used in clinical practice. There is a large variety of proposed optimization models and algorithms to model and solve the treatment planning problem. Two major parts of inverse treatment planning for which mathematical optimization can be used are the decisions about catheter placement and dwell time distributions. Both these problems as well as integrated approaches are included in this review. The proposed models include linear penalty models, dose-volume models, mean-tail dose models, quadratic penalty models, radiobiological models, and multiobjective models. The aim of this survey is twofold: (i) to give a broad overview over mathematical optimization models used for treatment planning of brachytherapy and (ii) to provide mathematical analyses and comparisons between models. New technologies for brachytherapy treatments and methods for treatment planning are also discussed. Of particular interest for future research is a thorough comparison between optimization models and algorithms on the same dataset, and clinical validation of proposed optimization approaches with respect to patient outcome.

An automated optimization tool for high-dose-rate (HDR) prostate brachytherapy with divergent needle pattern

Focal high-dose-rate (HDR) for prostate cancer has gained increasing interest as an alternative to whole gland therapy as it may contribute to the reduction of treatment related toxicity. For focal treatment, optimal needle guidance and placement is warranted. This can be achieved under MR guidance. However, MR-guided needle placement is currently not possible due to space restrictions in the closed MR bore. To overcome this problem, a MR-compatible, single-divergent needle-implant robotic device is under development at the University Medical Centre, Utrecht: placed between the legs of the patient inside the MR bore, this robot will tap the needle in a divergent pattern from a single rotation point into the tissue. This rotation point is just beneath the perineal skin to have access to the focal prostate tumor lesion. Currently, there is no treatment planning system commercially available which allows optimization of the dose distribution with such needle arrangement. The aim of this work is to develop an automatic inverse dose planning optimization tool for focal HDR prostate brachytherapy with needle insertions in a divergent configuration. A complete optimizer workflow is proposed which includes the determination of (1) the position of the center of rotation, (2) the needle angulations and (3) the dwell times. Unlike most currently used optimizers, no prior selection or adjustment of input parameters such as minimum or maximum dose or weight coefficients for treatment region and organs at risk is required. To test this optimizer, a planning study was performed on ten patients (treatment volumes ranged from 8.5 cm(3)to 23.3 cm(3)) by using 2-14 needle insertions. The total computation time of the optimizer workflow was below 20 min and a clinically acceptable plan was reached on average using only four needle insertions.

Volume and landmark analysis: comparison of MRI measurements obtained with an endorectal coil and with a phased-array coil

AIM

To compare prostate volumes and distances between anatomical landmarks on MRI images obtained with a phased-array coil (PAC) only and with a PAC and an endorectal coil (ERC).

MATERIALS AND METHODS

Informed consent was waived for this Health Insurance Portability and Accountability Act-compliant study. Fifty-nine men underwent PAC-MRI and ERC-MRI at 1.5 (n = 3) or 3 T (n = 56). On MRI images, two radiologists independently measured prostate volume and distances between the anterior rectal wall (ARW) and symphysis pubis at the level of the verumontanum; ARW and symphysis pubis at the level of the mid-symphysis pubis; and bladder neck and mid-symphysis pubis. Differences between measurements from PAC-MRI and ERC-MRI were assessed with the Wilcoxon RANK SUM test. Inter-reader agreement was assessed using the concordance correlation coefficient (CCC).

RESULTS

Differences in prostate volume between PAC-MRI and ERC-MRI [median: -0.75 mm(3) (p = 0.10) and median: -0.84 mm(3) (p = 0.06) for readers 1 and 2, respectively] were not significant. For readers 1 and 2, median differences between distances were as follows: -10.20 and -12.75 mm, respectively, ARW to symphysis pubis at the level of the verumontanum; -6.60 and -6.08 mm, respectively, ARW to symphysis pubis at the level of the mid-symphysis pubis; -3 and -3 mm respectively, bladder neck to mid-symphysis pubis. All differences in distance were significant for both readers (p ≤ 0.0005). Distances were larger on PAC-MRI (p ≤ 0.0005). Inter-reader agreement regarding prostate volume was almost perfect on PAC-MRI (CCC: 0.99; 95% CI: 0.98-1.00) and ERC-MRI (CCC: 0.99; 95% CI: 0.99-1.00); inter-reader agreement for distance measurements varied (CCCs: 0.54-0.86).

CONCLUSION

Measurements of distances between anatomical landmarks differed significantly between ERC-MRI and PAC-MRI, although prostate volume measurements did not.

Role of step size and max dwell time in anatomy based inverse optimization for prostate implants

In high dose rate (HDR) brachytherapy, the source dwell times and dwell positions are vital parameters in achieving a desirable implant dose distribution. Inverse treatment planning requires an optimal choice of these parameters to achieve the desired target coverage with the lowest achievable dose to the organs at risk (OAR). This study was designed to evaluate the optimum source step size and maximum source dwell time for prostate brachytherapy implants using an Ir-192 source. In total, one hundred inverse treatment plans were generated for the four patients included in this study. Twenty-five treatment plans were created for each patient by varying the step size and maximum source dwell time during anatomy-based, inverse-planned optimization. Other relevant treatment planning parameters were kept constant, including the dose constraints and source dwell positions. Each plan was evaluated for target coverage, urethral and rectal dose sparing, treatment time, relative target dose homogeneity, and nonuniformity ratio. The plans with 0.5 cm step size were seen to have clinically acceptable tumor coverage, minimal normal structure doses, and minimum treatment time as compared with the other step sizes. The target coverage for this step size is 87% of the prescription dose, while the urethral and maximum rectal doses were 107.3 and 68.7%, respectively. No appreciable difference in plan quality was observed with variation in maximum source dwell time. The step size plays a significant role in plan optimization for prostate implants. Our study supports use of a 0.5 cm step size for prostate implants.

IPIP: A new approach to inverse planning for HDR brachytherapy by directly optimizing dosimetric indices

PURPOSE

Many planning methods for high dose rate (HDR) brachytherapy require an iterative approach. A set of computational parameters are hypothesized that will give a dose plan that meets dosimetric criteria. A dose plan is computed using these parameters, and if any dosimetric criteria are not met, the process is iterated until a suitable dose plan is found. In this way, the dose distribution is controlled by abstract parameters. The purpose of this study is to develop a new approach for HDR brachytherapy by directly optimizing the dose distribution based on dosimetric criteria.

METHODS

The authors developed inverse planning by integer program (IPIP), an optimization model for computing HDR brachytherapy dose plans and a fast heuristic for it. They used their heuristic to compute dose plans for 20 anonymized prostate cancer image data sets from patients previously treated at their clinic database. Dosimetry was evaluated and compared to dosimetric criteria.

RESULTS

Dose plans computed from IPIP satisfied all given dosimetric criteria for the target and healthy tissue after a single iteration. The average target coverage was 95%. The average computation time for IPIP was 30.1 s on an Intel(R) Core 2 Duo CPU 1.67 GHz processor with 3 Gib RAM.

CONCLUSIONS

IPIP is an HDR brachytherapy planning system that directly incorporates dosimetric criteria. The authors have demonstrated that IPIP has clinically acceptable performance for the prostate cases and dosimetric criteria used in this study, in both dosimetry and runtime. Further study is required to determine if IPIP performs well for a more general group of patients and dosimetric criteria, including other cancer sites such as GYN.

Dosimetric analysis and comparison of IMRT and HDR brachytherapy in treatment of localized prostate cancer

Radical radiotherapy is one of the options for the management of prostate cancer. In external beam therapy, 3D conformal radiotherapy (3DCRT) and intensity modulated radiotherapy (IMRT) are the options for delivery of increased radiation dose, as vital organs are very close to the prostate and a higher dose to these structures leads to an increased toxicity. In brachytherapy, low dose rate brachytherapy with permanent implant of radioactive seeds and high dose rate brachytherapy (HDR) with remote after loaders are available. A dosimetric analysis has been made on IMRT and HDR brachytherapy plans. Ten cases from each IMRT and HDR brachytherapy have been taken for the study. The analysis includes comparison of conformity and homogeneity indices, D100, D95, D90, D80, D50, D10 and D5 of the target. For the organs at risk (OAR), namely rectum and bladder, V100, V90 and V50 are compared. In HDR brachytherapy, the doses to 1 cc and 0.1 cc of urethra have also been studied. Since a very high dose surrounds the source, the 300% dose volumes in the target and within the catheters are also studied in two plans, to estimate the actual volume of target receiving dose over 300%. This study shows that the prescribed dose covers 93 and 92% of the target volume in IMRT and HDR brachytherapy respectively. HDR brachytherapy delivers a much lesser dose to OAR, compared to the IMRT. For rectum, the V50 in IMRT is 34.0cc whilst it is 7.5cc in HDR brachytherapy. With the graphic optimization tool in HDR brachytherapy planning, the dose to urethra could be kept within 120% of the target dose. Hence it is concluded that HDR brachytherapy may be the choice of treatment for cancer of prostate in the early stage.

Radiobiological evaluation of the influence of dwell time modulation restriction in HIPO optimized HDR prostate brachytherapy implants

Purpose

One of the issues that a planner is often facing in HDR brachytherapy is the selective existence of high dose volumes around some few dominating dwell positions. If there is no information available about its necessity (e.g. location of a GTV), then it is reasonable to investigate whether this can be avoided. This effect can be eliminated by limiting the free modulation of the dwell times. HIPO, an inverse treatment plan optimization algorithm, offers this option. In treatment plan optimization there are various methods that try to regularize the variation of dose non-uniformity using purely dosimetric measures. However, although these methods can help in finding a good dose distribution they do not provide any information regarding the expected treatment outcome as described by radiobiology based indices.

Material and methods

The quality of 12 clinical HDR brachytherapy implants for prostate utilizing HIPO and modulation restriction (MR) has been compared to alternative plans with HIPO and free modulation (without MR). All common dose-volume indices for the prostate and the organs at risk have been considered together with radiobiological measures. The clinical effectiveness of the different dose distributions was investigated by calculating the response probabilities of the tumors and organs-at-risk (OARs) involved in these prostate cancer cases. The radiobiological models used are the Poisson and the relative seriality models. Furthermore, the complication-free tumor control probability, P₊ and the biologically effective uniform dose (D¯¯) were used for treatment plan evaluation and comparison.

Results

Our results demonstrate that HIPO with a modulation restriction value of 0.1-0.2 delivers high quality plans which are practically equivalent to those achieved with free modulation regarding the clinically used dosimetric indices. In the comparison, many of the dosimetric and radiobiological indices showed significantly different results. The modulation restricted clinical plans demonstrated a lower total dwell time by a mean of 1.4% that was proved to be statistically significant (p = 0.002). The HIPO with MR treatment plans produced a higher P₊ by 0.5%, which stemmed from a better sparing of the OARs by 1.0%.

Conclusions

Both the dosimetric and radiobiological comparison shows that the modulation restricted optimization gives on average similar results with the optimization without modulation restriction in the examined clinical cases. Concluding, based on our results, it appears that the applied dwell time regularization technique is expected to introduce a minor improvement in the effectiveness of the optimized HDR dose distributions.