Treatment simulation approaches for the estimation of the distributions of treatment quality parameters generated by geometrical uncertainties

Analytical probabilistic modeling of RBE-weighted dose for ion therapy

Particle therapy is especially prone to uncertainties. This issue is usually addressed with uncertainty quantification and minimization techniques based on scenario sampling. For proton therapy, however, it was recently shown that it is also possible to use closed-form computations based on analytical probabilistic modeling (APM) for this purpose. APM yields unique features compared to sampling-based approaches, motivating further research in this context. This paper demonstrates the application of APM for intensity-modulated carbon ion therapy to quantify the influence of setup and range uncertainties on the RBE-weighted dose. In particular, we derive analytical forms for the nonlinear computations of the expectation value and variance of the RBE-weighted dose by propagating linearly correlated Gaussian input uncertainties through a pencil beam dose calculation algorithm. Both exact and approximation formulas are presented for the expectation value and variance of the RBE-weighted dose and are subsequently studied in-depth for a one-dimensional carbon ion spread-out Bragg peak. With V and B being the number of voxels and pencil beams, respectively, the proposed approximations induce only a marginal loss of accuracy while lowering the computational complexity from order [Formula: see text] to [Formula: see text] for the expectation value and from [Formula: see text] to [Formula: see text] for the variance of the RBE-weighted dose. Moreover, we evaluated the approximated calculation of the expectation value and standard deviation of the RBE-weighted dose in combination with a probabilistic effect-based optimization on three patient cases considering carbon ions as radiation modality against sampled references. The resulting global γ-pass rates (2 mm,2%) are [Formula: see text]99.15% for the expectation value and [Formula: see text]94.95% for the standard deviation of the RBE-weighted dose, respectively. We applied the derived analytical model to carbon ion treatment planning, although the concept is in general applicable to other ion species considering a variable RBE.

Proton Treatment Room Concepts for Precision and Efficiency

Proton radiation therapy involves accurate delivery of proton beams to targets inside the body without direct visual control of the internal anatomy. Targeting of the tumor and avoidance of critical structures within the patient have to be both accurate and precise to achieve the desired therapeutic results. Good understanding of proton radiation delivery and patient alignment concepts in the treatment room is essential to achieve this goal. This overview article presents treatment room concepts that will ensure precise proton beam delivery and, at the same time, guarantee an efficient patient throughput. Concepts discussed include effective patient immobilization, image-guided alignment verification, appropriate training of radiotherapists, and the physician's integrative role in understanding the complex spatial relationships between tumor, organs at risk, treatment beam configuration, and application of proton radiation dose. It will be demonstrated that in addition to the technical armamentarium, now commonplace in modern radiation oncology departments, the interaction between radiation oncologist, medical physicist and radiotherapist is important for efficient operation of a proton treatment facility.

Surface-constrained nonrigid registration for dose monitoring in prostate cancer radiotherapy

This paper addresses the issue of cumulative dose estimation from cone beam computed tomography (CBCT) images in prostate cancer radiotherapy. It focuses on the dose received by the surfaces of the main organs at risk, namely the bladder and rectum. We have proposed both a surface-constrained dose accumulation approach and its extensive evaluation. Our approach relied on the nonrigid registration (NRR) of daily acquired CBCT images on the planning CT image. This proposed NRR method was based on a Demons-like algorithm, implemented in combination with mutual information metric. It allowed for different levels of geometrical constraints to be considered, ensuring a better point to point correspondence, especially when large deformations occurred, or in high dose gradient areas. The three following implementations: 1) full iconic NRR; 2) iconic NRR constrained with landmarks (LCNRR); 3) NRR constrained with full delineation of organs (DBNRR). To obtain reference data, we designed a numerical phantom based on finite-element modeling and image simulation. The methods were assessed on both the numerical phantom and real patient data in order to quantify uncertainties in terms of dose accumulation. The LCNRR method appeared to constitute a good compromise for dose monitoring in clinical practice.

Consideration of the likely benefit from implementation of prostate image-guided radiotherapy using current margin sizes: a radiobiological analysis

OBJECTIVE

To estimate the benefit of introduction of image-guided radiotherapy (IGRT) to prostate radiotherapy practice with current clinical target volume-planning target volume (PTV) margins of 5-10 mm.

METHODS

Systematic error data collected from 50 patients were used together with a random error of σ=3.0 mm to model non-IGRT treatment. IGRT was modelled with residual errors of Σ=σ=1.5 mm. Population tumour control probability (TCP(pop)) was calculated for two three-dimensional conformal radiotherapy techniques: two-phase and concomitant boost. Treatment volumes and dose prescriptions were ostensibly the same. The relative field sizes of the treatment techniques, distribution of systematic errors and correlations between movement axes were examined.

RESULTS

The differences in TCP(pop) between the IGRT and non-IGRT regimes were 0.3% for the two-phase and 1.5% for the concomitant boost techniques. A 2-phase plan, in each phase of which the 95% isodose conformed to its respective PTV, required fields that were 3.5 mm larger than those required for the concomitant boost plan. Despite the larger field sizes, the TCP (without IGRT) in the two-phase plan was only 1.7% higher than the TCP in the concomitant boost plan. The deviation of craniocaudal systematic errors (p=0.02) from a normal distribution, and the correlation of translations in the craniocaudal and anteroposterior directions (p<0.0001) were statistically significant.

CONCLUSIONS

The expected population benefit of IGRT for the modelled situation was too small to be detected by a clinical trial of reasonable size, although there was a significant benefit to individual patients. For IGRT to have an observable population benefit, the trial would need to use smaller margins than those used in this study. Concomitant treatment techniques permit smaller fields and tighter conformality than two phases planned separately.

[Image-guided and adaptive radiotherapy]

Image-guided radiotherapy (IGRT) aims to take into account anatomical variations occurring during irradiation by visualization of anatomical structures. It may consist of a rigid registration of the tumour by moving the patient, in case of prostatic irradiation for example. IGRT associated with intensity-modulated radiotherapy (IMRT) is strongly recommended when high-dose is delivered in the prostate, where it seems to reduce rectal and bladder toxicity. In case of significant anatomical deformations, as in head and neck tumours (tumour shrinking and decrease in volume of the salivary glands), replanning appears to be necessary, corresponding to the adaptive radiotherapy. This should ideally be "monitored" and possibly triggered based on a calculation of cumulative dose, session after session, compared to the initial planning dose, corresponding to the concept of dose-guided adaptive radiotherapy. The creation of "planning libraries" based on predictable organ positions (as in cervical cancer) is another way of adaptive radiotherapy. All of these strategies still appear very complex and expensive and therefore require stringent validation before being routinely applied.

Comparisons of treatment optimization directly incorporating systematic patient setup uncertainty with a margin-based approach

PURPOSE

To develop a probabilistic treatment planning (PTP) method which is robust to systematic patient setup errors and to compare PTP plans with plans generated using a planning target volume (PTV) margin optimized to give the same target coverage probability as the PTP plan.

METHODS

Plans adhering to the RTOG-0126 protocol are developed for 28 prostate patients using PTP and margin-based planning. For PTP, an objective function that simultaneously considers multiple possible patient positions is developed. PTP plans are optimized using clinical target volume (CTV) structures and organ at risk (OAR) structures. The desired CTV coverage probability is 95%. Plans that cannot achieve a 95% CTV coverage probability are re-optimized with a desired CTV coverage probability reduced by 5% until the desired CTV coverage probability is achieved. Margin-based plans are created which achieve the same CTV coverage probability as the PTP plans by iterative adjustment of the CTV-to-PTV margin. Postoptimization, probabilistic dose-volume coverage metrics are used to compare the plans.

RESULTS

For equivalent target coverage probability, PTP plans significantly reduce coverage probability for rectum objectives (-17% for D(35) < 65 Gy, p = 0.0010; -23% for D(25) < 70 Gy, p < 0.0001; and -27% for D(15) < 75 Gy, p < 0.0001). Physician assessment indicates PTP plans are entirely preferred 71% of the time while margin-based plans are entirely preferred 7% of the time.

CONCLUSIONS

For plans having the same target coverage probability, PTP has potential to reduce rectal doses while maintaining CTV coverage probability. In blind comparisons, physicians prefer PTP plans over optimized margin plans.

Intensity modulation under geometrical uncertainty: a deconvolution approach to robust fluence

A deconvolution algorithm has been developed to obtain robust fluence for external beam radiation treatment under geometrical uncertainties. Usually, the geometrical uncertainty is incorporated in the dose optimization process for inverse treatment planning to determine the additional intensity modulation of the beam to counter the geometrical uncertainty. Most of these approaches rely on dose convolution which is subject to the error caused by patient surface curvature and internal inhomogeneity. In this work, based on an 1D deconvolution algorithm developed by Ulmer and Kaissl, a fluence-deconvolution approach was developed to obtain robust fluence through the deconvolution of the nominal static one given by any treatment planning system. It incorporates the geometrical uncertainty outside the dose optimization procedure and therefore avoids the error of dose convolution. Robust fluences were calculated for a 4 x 4 cm flat field, a prostate IMRT and a head and neck IMRT plan in a commercial treatment planning system. The corresponding doses were simulated for 30 fractions with the random Gaussian distribution of the iso-centers showing good agreement with the nominal static doses. The feasibility of this deconvolution approach for clinical IMRT planning has been demonstrated. Because it is separated from the optimization procedure, this method is more flexible and easier to integrate into different existing treatment planning systems to obtain robust fluence.

Comparisons of treatment optimization directly incorporating random patient setup uncertainty with a margin-based approach

The purpose of this study is to incorporate the dosimetric effect of random patient positioning uncertainties directly into a commercial treatment planning system's IMRT plan optimization algorithm through probabilistic treatment planning (PTP) and compare coverage of this method with margin-based planning. In this work, PTP eliminates explicit margins and optimizes directly on the estimated integral treatment dose to determine optimal patient dose in the presence of setup uncertainties. Twenty-eight prostate patient plans adhering to the RTOG-0126 criteria are optimized using both margin-based and PTP methods. Only random errors are considered. For margin-based plans, the planning target volume is created by expanding the clinical target volume (CTV) by 2.1 mm to accommodate the simulated 3 mm random setup uncertainty. Random setup uncertainties are incorporated into IMRT dose evaluation by convolving each beam's incident fluence with a sigma = 3 mm Gaussian prior to dose calculation. PTP optimization uses the convolved fluence to estimate dose to ensure CTV coverage during plan optimization. PTP-based plans are compared to margin-based plans with equal CTV coverage in the presence of setup errors based on dose-volume metrics. The sensitivity of the optimized plans to patient-specific setup uncertainty variations is assessed by evaluating dose metrics for dose distributions corresponding to halving and doubling of the random setup uncertainty used in the optimization. Margin-based and PTP-based plans show similar target coverage. A physician review shows that PTP is preferred for 21 patients, margin-based plans are preferred in 2 patients, no preference is expressed for 1 patient, and both autogenerated plans are rejected for 4 patients. For the PTP-based plans, the average CTV receiving the prescription dose decreases by 0.5%, while the mean dose to the CTV increases by 0.7%. The CTV tumor control probability (TCP) is the same for both methods with the exception of one case in which PTP gave a slightly higher TCP. For critical structures that do not meet the optimization criteria, PTP shows a decrease in the volume receiving the maximum specified dose. PTP reduces local normal tissue volumes receiving the maximum dose on average by 48%. PTP results in lower mean dose to all critical structures for all plans. PTP results in a 2.5% increase in the probability of uncomplicated control (P+), along with a 1.9% reduction in rectum normal tissue complication probability (NTCP), and a 0.7% reduction in bladder NTCP. PTP-based plans show improved conformality as compared with margin-based plans with an average PTP-based dosimetric margin at 7100 cGy of 0.65 cm compared with the margin-based 0.90 cm and a PTP-based dosimetric margin at 3960 cGy of 1.60 cm compared with the margin-based 1.90 cm. PTP-based plans show similar sensitivity to variations of the uncertainty during treatment from the uncertainty used in planning as compared to margin-based plans. For equal target coverage, when compared to margin-based plans, PTP results in equal or lower doses to normal structures. PTP results in more conformal plans than margin-based plans and shows similar sensitivity to variations in uncertainty.

Evaluation of clinical margins via simulation of patient setup errors in prostate IMRT treatment plans

This work evaluates: (i) the size of random and systematic setup errors that can be absorbed by 5 mm clinical target volume (CTV) to planning target volume (PTV) margins in prostate intensity modulated radiation therapy (IMRT); (ii) agreement between simulation results and published margin recipes; and (iii) whether shifting contours with respect to a static dose distribution accurately predicts dose coverage due to setup errors. In 27 IMRT treatment plans created with 5 mm CTV-to-PTV margins, random setup errors with standard deviations (SDs) of 1.5, 3, 5 and 10 mm were simulated by fluence convolution. Systematic errors with identical SDs were simulated using two methods: (a) shifting the isocenter and recomputing dose (isocenter shift), and (b) shifting patient contours with respect to the static dose distribution (contour shift). Maximum tolerated setup errors were evaluated such that 90% of plans had target coverage equal to the planned PTV coverage. For coverage criteria consistent with published margin formulas, plans with 5 mm margins were found to absorb combined random and systematic SDs = 3 mm. Published recipes require margins of 8-10 mm for 3 mm SDs. For the prostate IMRT cases presented here a 5 mm margin would suffice, indicating that published recipes may be pessimistic. We found significant errors in individual plan doses given by the contour shift method. However, dose population plots (DPPs) given by the contour shift method agreed with the isocenter shift method for all structures except the nodal CTV and small bowel. For the nodal CTV, contour shift DPP differences were due to the structure moving outside the patient. Small bowel DPP errors were an artifact of large relative differences at low doses. Estimating individual plan doses by shifting contours with respect to a static dose distribution is not recommended. However, approximating DPPs is acceptable, provided care is taken with structures such as the nodal CTV which lie close to the surface.

A comparison of techniques for simulating set-up error and uncertainty in head and neck IMRT

We have compared four computational methods for quantifying the effect of set-up error and uncertainty on delivered doses to targets and organs at risk in the intensity modulated radiation therapy treatment of head and neck cancer. These four methods were direct simulation, simple convolution, plus two modified convolution approaches. Discrepancies of up to 20% in the equivalent uniform dose (EUD) between direct simulation and simple convolution were estimated for the relatively superficial parotid gland at a systematic set-up error of 6 mm standard deviation and a random uncertainty of 2 mm standard deviation. Truncated convolution agreed with direct simulation to within 6% for all situations studied. However, of the four methods, only direct simulation can quantify the range of outcomes (EUD) associated with a finite number of courses and fractions. Our results are particularly relevant to the design of dose escalation studies in head and neck cancer.

Efficient on-line setup correction strategies using plan-intent functions

With the introduction of image-guided radiation therapy (IGRT) delivery systems on-line set-up correction strategies have gained in popularity. Usually, the correction workload of these strategies is high compared to off-line strategies as daily setup corrections have to be performed based on a predefined action level. In this work, it is proposed that on-line strategies must not only be judged in terms of workload but also in terms of efficacy. While workload can be easily predicted for such strategies, the efficacy must ultimately reflect the efficiency with which the original treatment plan intent is met. The purpose of this work is to investigate the tradeoff between workload and efficacy of three different on-line set-up correction strategies: The common fixed action level strategy and two novel on-line setup correction strategies, i.e., a dose-volume histogram (DVH) constraint and an equivalent uniform dose (EUD) score strategy that aim directly for better compliance with original treatment plan intent. All strategies were reformulated in terms of a score function that reflected treatment plan intent. A retrospective study was conducted on 5 prostate patients (7-field conformal, 79.8 Gy, 42 fractions). PTV margins were 10 mm except in the posterior direction (7 mm). The original treatment plan intent for these patients was defined using a set of DVH constraints. The results show that the on-line setup correction strategy based on a fixed action level of 3 mm resulted in a considerable correction workload. For larger action levels, a dose benefit (in terms of EUD) in the rectum and bladder was observed for all patients which is clinically "fortuitous" but difficult to take advantage of. In contrast, the application of the two novel strategies generally resulted in a controlled decrease of the dose to the rectum and the bladder with a smaller workload. It is concluded that using information about target anatomy and the planned dose distribution allows the design of specific correction strategies that are better tailored to the individual patient and that comply effectively with initial treatment plan intent.

Robust treatment planning for intensity modulated radiotherapy of prostate cancer based on coverage probabilities

BACKGROUND AND PURPOSE

To evaluate an optimization approach where coverage probabilities are incorporated into the optimization of intensity modulated radiotherapy (IMRT) to overcome the problem of margin definition in the case of overlapping planning target volume and organs at risk.

PATIENTS AND METHODS

IMRT plans were generated for three optimization approaches: based on a planning CT plus margin (A), on prostate and rectum contours from five pre-treatment CT plus margin (B), and on coverage probabilities (C). For approach (C), the probability of organ occupation was computed for each voxel from five pre-treatment CTs and the population distribution of systematic setup error and it was used as local weight in the costfunctions. Monte Carlo simulations of treatment courses were used to compute the probability distribution of prostate and rectal wall equivalent uniform dose (EUD).

RESULTS

Treatment simulations showed best and most robust results for prostate and rectal wall EUD within the population for (C). For (A) the rectal wall EUD was on average about 1.5 Gy greater than in (C), while the prostate EUD was lower than those from (C) for most of the patients for (B) (especially for those with great organ motion).

CONCLUSIONS

The incorporation of coverage probabilities as local weights allows for dose escalation as well as improved rectal sparing and results in a safer and more robust IMRT treatment.