Ehsan Salari

Multicriteria VMAT optimization

PURPOSE To make the planning of volumetric modulated arc therapy (VMAT) faster and to explore the tradeoffs between planning objectives and delivery efficiency. METHODS A convex multicriteria dose optimization problem is solved for an angular grid of 180 equi-spaced beams. This allows the planner to navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus organ at risk sparing. The selected plan is then made VMAT deliverable by a fluence map merging and sequencing algorithm, which combines neighboring fluence maps based on a similarity score and then delivers the merged maps together, simplifying delivery. Successive merges are made as long as the dose distribution quality is maintained. The complete algorithm is called VMERGE. RESULTS VMERGE is applied to three cases: a prostate, a pancreas, and a brain. In each case, the selected Pareto-optimal plan is matched almost exactly with the VMAT merging routine, resulting in a high quality plan delivered with a single arc in less than 5 min on average. CONCLUSIONS VMERGE offers significant improvements over existing VMAT algorithms. The first is the multicriteria planning aspect, which greatly speeds up planning time and allows the user to select the plan, which represents the most desirable compromise between target coverage and organ at risk sparing. The second is the user-chosen epsilon-optimality guarantee of the final VMAT plan. Finally, the user can explore the tradeoff between delivery time and plan quality, which is a fundamental aspect of VMAT that cannot be easily investigated with current commercial planning systems.

The dependence of optimal fractionation schemes on the spatial dose distribution

We consider the fractionation problem in radiation therapy. Tumor sites in which the dose-limiting organ at risk (OAR) receives a substantially lower dose than the tumor, bear potential for hypofractionation even if the α/β-ratio of the tumor is larger than the α/β-ratio of the OAR. In this work, we analyze the interdependence of the optimal fractionation scheme and the spatial dose distribution in the OAR. In particular, we derive a criterion under which a hypofractionation regimen is indicated for both a parallel and a serial OAR. The approach is based on the concept of the biologically effective dose (BED). For a hypothetical homogeneously irradiated OAR, it has been shown that hypofractionation is suggested by the BED model if the α/β-ratio of the OAR is larger than α/β-ratio of the tumor times the sparing factor, i.e. the ratio of the dose received by the tumor and the OAR. In this work, we generalize this result to inhomogeneous dose distributions in the OAR. For a parallel OAR, we determine the optimal fractionation scheme by minimizing the integral BED in the OAR for a fixed BED in the tumor. For a serial structure, we minimize the maximum BED in the OAR. This leads to analytical expressions for an effective sparing factor for the OAR, which provides a criterion for hypofractionation. The implications of the model are discussed for lung tumor treatments. It is shown that the model supports hypofractionation for small tumors treated with rotation therapy, i.e. highly conformal techniques where a large volume of lung tissue is exposed to low but nonzero dose. For larger tumors, the model suggests hyperfractionation. We further discuss several non-intuitive interdependencies between optimal fractionation and the spatial dose distribution. For instance, lowering the dose in the lung via proton therapy does not necessarily provide a biological rationale for hypofractionation.

A Column-generation-based Method for Multi-criteria Direct Aperture Optimization

Navigation-based multi-criteria optimization has been introduced to radiotherapy planning in order to allow the interactive exploration of trade-offs between conflicting clinical goals. However, this has been mainly applied to fluence map optimization. The subsequent leaf sequencing step may cause dose discrepancy, leading to human iteration loops in the treatment planning process that multi-criteria methods were meant to avoid. To circumvent this issue, this paper investigates the application of direct aperture optimization methods in the context of multi-criteria optimization. We develop a solution method to directly obtain a collection of apertures that can adequately span the entire Pareto surface. To that end, we extend the column generation method for direct aperture optimization to a multi-criteria setting in which apertures that can improve the entire Pareto surface are sequentially identified and added to the treatment plan. Our proposed solution method can be embedded in a navigation-based multi-criteria optimization framework, in which the treatment planner explores the trade-off between treatment objectives directly in the space of deliverable apertures. Our solution method is demonstrated for a paraspinal case where the trade-off between target coverage and spinal-cord sparing is studied. The computational results validate that our proposed method obtains a balanced approximation of the Pareto surface over a wide range of clinically relevant plans.

Optimization approaches to volumetric modulated arc therapy planning

Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for improvements are discussed.

Optimal partial-arcs in VMAT treatment planning

We present a method for improving the delivery efficiency of VMAT by extending the recently published VMAT treatment planning algorithm vmerge to automatically generate optimal partial-arc plans. A high-quality initial plan is created by solving a convex multicriteria optimization problem using 180 equi-spaced beams. This initial plan is used to form a set of dose constraints, and a set of partial-arc plans is created by searching the space of all possible partial-arc plans that satisfy these constraints. For each partial-arc, an iterative fluence map merging and sequencing algorithm (vmerge) is used to improve the delivery efficiency. Merging continues as long as the dose quality is maintained above a user-defined threshold. The final plan is selected as the partial-arc with the lowest treatment time. The complete algorithm is called pmerge. Partial-arc plans are created using pmerge for a lung, liver and prostate case, with final treatment times of 127, 245 and 147 . Treatment times using full arcs with vmerge are 211, 357 and 178 s. The mean doses to the critical structures for the vmerge and pmerge plans are kept within 5% of those in the initial plan, and the target volume covered by the prescription isodose is maintained above 98% for the pmerge and vmerge plans. Additionally, we find that the angular distribution of fluence in the initial plans is predictive of the start and end angles of the optimal partial-arc. We conclude that VMAT delivery efficiency can be improved by employing partial-arcs without compromising dose quality, and that partial-arcs are most applicable to cases with non-centralized targets.

Accounting for the tongue-and-groove effect using a robust direct aperture optimization approach

PURPOSE Traditionally, the tongue-and-groove effect due to the multileaf collimator architecture in intensity-modulated radiation therapy (IMRT) has typically been deferred to the leaf sequencing stage. The authors propose a new direct aperture optimization method for IMRT treatment planning that explicitly incorporates dose calculation inaccuracies due to the tongue-and-groove effect into the treatment plan optimization stage. METHODS The authors avoid having to accurately estimate the dosimetric effects of the tongue-and-groove architecture by using lower and upper bounds on the dose distribution delivered to the patient. They then develop a model that yields a treatment plan that is robust with respect to the corresponding dose calculation inaccuracies. RESULTS Tests on a set of ten clinical head-and-neck cancer cases demonstrate the effectiveness of the new method in developing robust treatment plans with tight dose distributions in targets and critical structures. This is contrasted with the very loose bounds on the dose distribution that are obtained by solving a traditional treatment plan optimization model that ignores tongue-and-groove effects in the treatment planning stage. CONCLUSIONS A robust direct aperture optimization approach is proposed to account for the dosimetric inaccuracies caused by the tongue-and-groove effect. The experiments validate the ability of the proposed approach in designing robust treatment plans regardless of the exact consequences of the tongue-and-groove architecture.

A mathematical programming approach to the fractionation problem in chemoradiotherapy

In concurrent chemoradiotherapy, chemotherapeutic agents are administered during the course of radiotherapy to enhance the primary tumor control. However, this treatment often comes at the expense of increased risk of normal-tissue complications. The additional biological damage is mainly attributed to two mechanisms of action, which are the independent cytotoxic activity of chemotherapeutic agents and their interactive cooperation with radiation. The goal of this study is to develop a mathematical framework to obtain drug and radiation administration schedules that maximize the therapeutic gain for concurrent chemoradiotherapy. In particular, we analyze the impact of incorporating these two mechanisms into the radiation fractionation problem. Considering each mechanism individually, we first derive closed-form expressions for the optimal radiation fractionation regimen and the corresponding drug administration schedule. We next study the case in which both mechanisms are simultaneously present and develop a dynamic programming framework to determine optimal treatment regimens. Results show that those chemotherapeutic agents that interact with radiation may change optimal radiation fractionation regimens. Moreover, administration of chemotherapeutic agents possessing both mechanisms may give rise to optimal non-stationary fractionation schemes.

Quantifying the Trade-off Between IMRT Treatment Plan Quality and Delivery Efficiency Using Direct Aperture Optimization

Beam-on time is an important measure of the delivery efficiency in intensity-modulated radiation therapy (IMRT). Traditionally, minimizing beam-on time has been postponed until the leaf sequencing stage, where the treatment plan quality is already determined and fixed. However, there is a trade-off between the beam-on time and the treatment plan quality. The aim of this study is to incorporate the beam-on time into the treatment plan optimization stage using a direct aperture optimization approach that allows for explicitly quantifying the trade-off. The proposed approach can provide clinicians with valuable information for each patient case so that they can design clinically attractive yet efficient treatment plans. Using the special structure of the problem, we propose an exact solution approach that sequentially characterizes segments of the Pareto-efficient frontier. In addition, an approximate solution technique that is applicable to more classes of evaluation criteria is developed. Our approximate technique is tested on clinical cancer cases, and its performance is compared with the general approximation techniques that are available for convex bicriteria optimization problems. The results of our experiments validate that our approach can achieve a more accurate representation of the Pareto-efficient frontier with less computational effort.

Exploiting tumor shrinkage through temporal optimization of radiotherapy

In multi-stage radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated mostly by radiobiological considerations, but also provides an approach to reduce normal tissue dose by exploiting tumor shrinkage. The paper considers the optimal design of multi-stage treatments, motivated by the clinical management of large liver tumors for which normal liver dose constraints prohibit the administration of an ablative radiation dose in a single treatment. We introduce a dynamic tumor model that incorporates three factors: radiation induced cell kill, tumor shrinkage, and tumor cell repopulation. The design of multi-stage radiotherapy is formulated as a mathematical optimization problem in which the total dose to the normal tissue is minimized, subject to delivering the prescribed dose to the tumor. Based on the model, we gain insight into the optimal administration of radiation over time, i.e. the optimal treatment gaps and dose levels. We analyze treatments consisting of two stages in detail. The analysis confirms the intuition that the second stage should be delivered just before the tumor size reaches a minimum and repopulation overcompensates shrinking. Furthermore, it was found that, for a large range of model parameters, approximately one-third of the dose should be delivered in the first stage. The projected benefit of multi-stage treatments in terms of normal tissue sparing depends on model assumptions. However, the model predicts large dose reductions by more than a factor of 2 for plausible model parameters. The analysis of the tumor model suggests that substantial reduction in normal tissue dose can be achieved by exploiting tumor shrinkage via an optimal design of multi-stage treatments. This suggests taking a fresh look at multi-stage radiotherapy for selected disease sites where substantial tumor regression translates into reduced target volumes.

Spatiotemporal radiotherapy planning using a global optimization approach

This paper aims at quantifying the extent of potential therapeutic gain, measured using biologically effective dose (BED), that can be achieved by altering the radiation dose distribution over treatment sessions in fractionated radiotherapy. To that end, a spatiotemporally integrated planning approach is developed, where the spatial and temporal dose modulations are optimized simultaneously. The concept of equivalent uniform BED (EUBED) is used to quantify and compare the clinical quality of spatiotemporally heterogeneous dose distributions in target and critical structures. This gives rise to a large-scale non-convex treatment-plan optimization problem, which is solved using global optimization techniques. The proposed spatiotemporal planning approach is tested on two stylized cancer cases resembling two different tumor sites and sensitivity analysis is performed for radio-biological and EUBED parameters. Numerical results validate that spatiotemporal plans are capable of delivering a larger BED to the target volume without increasing the BED in critical structures compared to conventional time-invariant plans. In particular, this additional gain is attributed to the irradiation of different regions of the target volume at different treatment sessions. Additionally, the trade-off between the potential therapeutic gain and the number of distinct dose distributions is quantified, which suggests a diminishing marginal gain as the number of dose distributions increases.