B Martin

A unified approach for inversion problems in intensity-modulated radiation therapy.

We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraint sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.

Reducing the sensitivity of IMPT treatment plans to setup errors and range uncertainties via probabilistic treatment planning

Treatment plans optimized for intensity modulated proton therapy (IMPT) may be very sensitive to setup errors and range uncertainties. If these errors are not accounted for during treatment planning, the dose distribution realized in the patient may by strongly degraded compared to the planned dose distribution. The authors implemented the probabilistic approach to incorporate uncertainties directly into the optimization of an intensity modulated treatment plan. Following this approach, the dose distribution depends on a set of random variables which parameterize the uncertainty, as does the objective function used to optimize the treatment plan. The authors optimize the expected value of the objective function. They investigate IMPT treatment planning regarding range uncertainties and setup errors. They demonstrate that incorporating these uncertainties into the optimization yields qualitatively different treatment plans compared to conventional plans which do not account for uncertainty. The sensitivity of an IMPT plan depends on the dose contributions of individual beam directions. Roughly speaking, steep dose gradients in beam direction make treatment plans sensitive to range errors. Steep lateral dose gradients make plans sensitive to setup errors. More robust treatment plans are obtained by redistributing dose among different beam directions. This can be achieved by the probabilistic approach. In contrast, the safety margin approach as widely applied in photon therapy fails in IMPT and is neither suitable for handling range variations nor setup errors.

Dosimetry robustness with stochastic optimization

All radiation therapy treatment planning relies on accurate dose calculation. Uncertainties in dosimetric prediction can significantly degrade an otherwise optimal plan. In this work, we introduce a robust optimization method which handles dosimetric errors and warrants for high-quality IMRT plans. Unlike other dose error estimations, we do not rely on the detailed knowledge about the sources of the uncertainty and use a generic error model based on random perturbation. This generality is sought in order to cope with a large variety of error sources. We demonstrate the method on a clinical case of lung cancer and show that our method provides plans that are more robust against dosimetric errors and are clinically acceptable. In fact, the robust plan exhibits a two-fold improved equivalent uniform dose compared to the non-robust but optimized plan. The achieved speedup will allow computationally extensive multi-criteria or beam-angle optimization approaches to warrant for dosimetrically relevant plans.

Accelerating IMRT optimization by voxel sampling

This paper presents a new method for accelerating intensity-modulated radiation therapy (IMRT) optimization using voxel sampling. Rather than calculating the dose to the entire patient at each step in the optimization, the dose is only calculated for some randomly selected voxels. Those voxels are then used to calculate estimates of the objective and gradient which are used in a randomized version of a steepest descent algorithm. By selecting different voxels on each step, we are able to find an optimal solution to the full problem. We also present an algorithm to automatically choose the best sampling rate for each structure within the patient during the optimization. Seeking further improvements, we experimented with several other gradient-based optimization algorithms and found that the delta-bar-delta algorithm performs well despite the randomness. Overall, we were able to achieve approximately an order of magnitude speedup on our test case as compared to steepest descent.

WE‐B‐350‐02: Patient Motion & 4D Inverse Planning

Motion of the patient and inner organs does not substantially change the spatial dose distribution in photon therapy in the room coordinate system, aside from the build‐up region. In other words, organs move within a static “dose cloud”. Using this approximation it is easy to understand the consequences of motion: systematic errors (lack of accuracy) lead to an offset of the dose distribution in the frame of the organs, and random errors (lack of precision) lead to dose blurring. Dose blurring can be described in a statistical way by use of a motion probability (density) function (PDF). The motion‐blurred dose distribution is obtained by a convolution of the “sharp” (static case) dose distribution with the motion PDF. This holds true for both inter‐ and intra‐fraction motions. If intra‐fraction motion is present during an IMRT treatment, the dose distribution will also be affected by an “interplay” effect, in addition to the blurring. It has been shown that the interplay effect averages out during the course of a fractionated treatment, and that it is usually negligible after a typical number of fractions. The convolution model relies on the linear superimposition principle, which holds true for dose values but not for the biological effect. This issue has recently been addressed and will be discussed. Several investigations have now looked at the feasibility of un‐doing the motion blur through the use if intensity‐modulation. In principle it should indeed be possible to de‐convolve the motion PDF from the intensity maps, to compensate for motion effects. This approach has been called 4D optimization or 4D inverse planning. Motion de‐convolution cannot, however, compensate motion effects exactly and it cannot be applied in a naive straight‐forward way, because that would lead to undeliverable intensity maps with sharp spikes and negative values. The method of choice is rather to include the motion PDF in the IMRToptimization process. It has been shown that this can indeed yield a surprisingly high degree of motion compensation and it can even compete with other motion compensation methods such as gated delivery. However, this is only true if the motion characteristics (the PDF) are known with great precision. If the actually realized motion PDF deviates substantially from the planned PDF, the method becomes less useful and can, in principle, make things worse. More recently, uncertainties in the knowledge of the motion characteristics have been taken into account by use of robust optimization techniques. With these one can now compensate for motion effects in an approximate way for a large class of motion characteristics. In terms of the sparing of normal structures, the results are in between the use of conventional margins and the idealistic case of perfect motion compensation. The resulting intensity maps exhibit “horns”, which can shave off a few mm from the margins. Educational Objectives: 1. Understand the concepts of motion blur and PDF. 2. Understand the idea of de‐blurring a dose distribution through “4D” motion optimization. 3. Be able to discuss the relative potential and limitations of 4D motion optimization in comparison with margins and gating.

SU-FF-T-116: Multicriteria IMRT Planning with Equivalent Uniform Dose (EUD) Objectives: Tumor Dose Homogeneity vs. Critical Structure Sparing

Purpose: To quantify the tradeoff between target dose homogeneity and critical structure sparing in two typical IMRT situations (prostate, para‐spinal). Furthermore, to determine the sensitivity to the response model used for critical structures (maximum vs. mean dose). Method and Materials: An EUD‐based multicriteria linear programming environment has been developed. In this work, we enforce a tumor minimum dose and compute solutions which efficiently tradeoff the tumor maximum dose and organ‐at‐risk (OAR) EUD (α⋅max dose+(1 − α) ⋅mean dose). Pareto surfaces resulting from different OAR α values are compared. The technique is applied to the RTOG horseshoe target and circular OAR geometry (varying the OARs size and location), and to two clinical cases. Results: Mathematically, if the maximum and mean doses of a structure are correlated then the choice of α does not affect the shape of the Pareto frontier. We demonstrate that this correlation is stronger for smaller OARs (a single voxel has a large impact on the mean), and also for symmetrically located OARs, which have a large set of outer ring voxels near the maximum level, as opposed to asymmetrically located OARs where the maximum dose is more localized. As the dose requirements in the tumor get more strict, we see less variance with α, since the feasible solution space is smaller. We consistently see little to no difference between Pareto surfaces for α from 0.5 to 1. Conclusion: By characterizing the conditions under which the Pareto frontier is insensitive to α, we highlight situations where it may not be necessary to know the best value of α, i.e., the exact tissue organization between purely serial and purely parallel. In general we see smooth Pareto surfaces but in some cases there were kinks pointing to outstanding treatment plans.

SU‐GG‐T‐120: Design of a Next Generation Treatment Planning System That Incorporates Motion and Uncertainty in Inverse Planning

Purpose: The safety margin approach to handle uncertainty and motion in radiotherapytreatment planning has limitations. For example, in the context of respiratory motion, the safety margin concept is over‐conservative and leads to increased doses to lung or liver tissue. Furthermore, in intensity‐modulated proton therapy (IMPT), the safety margin approach fails and cannot be applied successfully. Therefore, future treatment planning systems should have the option to directly incorporate uncertainty and organ motion into treatment plan optimization for IMRT and IMPT. We suggest a mathematical basis and practical implementation guidelines for a next generation treatment planning system that can handle various types of uncertainty within a coherent framework. Method and Materials: Mathematically, our program follows the probabilistic approach: The delivered dose, and hence the objective function, depend on a set of random variables that parameterize the uncertainty. Treatment planning is performed by optimizing the expected value of the objective function. Practically, this approach was implemented in C++ in an object‐oriented setting. A key component of the program is an abstract base class called DoseDeliveryModel. A particular type of uncertainty is implemented in a derived class. Aspects that are specific to the type of uncertainty considered can be hidden in derived classes, whereas the remaining program communicates with the DoseDeliveryModel via standardized public member functions. Results and Conclusion: Different applications have been implemented: Those include setup errors, respiratory motion with variations in the breathing pattern, or range uncertainties in IMPT. As a result, we obtain treatment plans that are qualitatively different from conventional plans. For IMPT we obtain plans that are robust against range and setup errors that simply cannot be obtained by margin approaches. For moving lung tumors a reduction of integral lungdose in the order of 10 – 20% was observed. Research partially supported by Siemens Medical Solutions.

SU-GG-T-125: Incorporating Uncertainty in Radiation Therapy Optimization with Scenario and Voxel Sampling

Purpose: The inclusion of motion and uncertainty in treatment plan optimization requires the use of a potentially large number of geometric instances (scenarios), which may be computationally intractable. We seek to provide a fast, flexible approach that is practical to implement. Method and Materials: When using a gradient‐based optimization method, we have found that not every voxel and scenario needs to be computed at every step to converge to a near‐optimal solution. We first create a model of the dose actually delivered to the patient for a given set of beamlet intensities and geometric scenario. Based on this dose, we calculate the value of an objective function, a measure of how far a dose is from satisfying our clinical goals. We typically minimize the expected value of this objective function. On each step of the optimization, we use several scenario samples to estimate the expected objective. To further speed up the estimate, we only calculate the dose to a fraction of the voxels within the patient per scenario. We use this sampling to estimate the gradient, which we use in a gradient‐based optimization algorithm. At each step of the algorithm we use sample new scenarios and voxels. We automatically tune the sampling rate for various structures by choosing the number of scenarios and voxels samples per step that minimizes the variance in the estimated objective. Results: So far we have tested the algorithm on 5 cases with a variety of treatment sites and several different motion models for IMRT and IMPT. Based on these cases, we find that voxel sampling combined with scenario sampling is over an order of magnitude faster than scenario sampling alone. This acceleration is achieved without sacrificing plan quality. Conclusion: The new approach is a fast, flexible way of incorporating uncertainty into the optimization.

SU‐GG‐T‐126: Robust Optimization for Lung Treatment in the Presence of Dosimetric Errors

Purpose: Intensity modulated radio therapy (IMRT) has the ability to deliver highly conformal dose distributions to tumors of complex shape. Uncertainties, such as breathing motion, can substantially degrade the quality of an otherwise optimized treatment plan. Furthermore, the quality of robustly optimized plans significantly depend on how well the underlying dose calculation matches the actual delivered dose to the treated organ.Method and Materials: We present two planing concepts for IMRT using robust optimization techniques. The first concept relies on pencil beam based calculation of the delivered dose. The second method employs Monte Carlo dose calculation. The robust optimization techniques seeks to minimize the expectation value of the deviation of the delivered and prescribed dose with an uncertainty model relying on several random variables. Results: When comparing the deposited dose of one pencil beam using Monte Carlo calculations of up to 10∧7 particles to dose calculations using pencil beam based algorithms, we observe a significant laterally scattered dose that is not capture with simple pencil beam algorithms, amounting to up to 30%. Furthermore, a comparison of the dose before and after sequencing reveals errors of up to 5%. We developed a novel robust optimization algorithm that provides optimized IMRT plans which are inherently robust against dosimetric errors. Conclusion: If the treated structure does not reveal significant inhomogeneities, using a computationally less expensive pencil beam calculation can allow for other ways treatment optimizations, such as beam‐angle optimization, that are otherwise not accessible without extensive approximations.

SU‐FF‐T‐57: Accelerating IMRT Optimization by Voxel Sampling

Purpose: To develop a new algorithm to accelerate IMRT optimization by voxel sampling. Methods and Materials: We note that standard gradient descent is fairly slow due to the time spent calculating the dose to the patient. We realized that a reasonable estimate of the objective function and gradient could be obtained by calculating the dose to only a fraction of the voxels in the patient. To avoid adding a systematic error, we randomly sample the voxels at each step to create an unbiased estimate of the gradient. Supposing sufficient samples are chosen, the errors in the gradient will tend to cancel each other out as the algorithm progresses. Uniform sampling is inefficient, however, since small, important organs tend to need a higher sampling rate while large, less critical organs could use a lower rate. We developed an algorithm to tune the sampling rates for each objective by minimizing the variance of the estimate of the objective for a fixed overall sampling rate. With the errors in the estimated gradient, we could not use techniques like conjugate gradient to further accelerate performance. However, we found that the delta‐bar‐delta algorithm provided an additional speed boost. Results: For our example case of a lung patient with 384,979 voxels and 1460 beamlets we were able to achieve a speed improvement of approximately three times using uniform sampling, 14 times using automatically tuned sampling, and 20 times using delta‐bar‐delta with automatically tuned sampling. While the algorithms are randomized, the results were very reliable and stable in our experience. Conclusions: Voxel sampling proves to be a viable way to dramatically improve the speed of IMRT optimization. It could be particularly helpful for applications such as temporo‐spatial optimization and multi‐criteria optimization, where a great many variants of a problem are optimized.