A stochastic control approach to intrafraction motion management in intensity-modulated radiotherapy.

Objective.The goal of this research is to demonstrate proof-of-principle for managing intrafraction motion via feedback control of delivered dose to achieve dosimetry comparable to respiratory gating without compromising delivery efficiency.Approach. We develop a stochastic control approach for step-and-shoot intensity-modulated radiotherapy (IMRT) in which the cumulative delivered dose and future trajectory of intrafraction motion are dynamically estimated by combining pre-treatment four-dimensional computed tomography imaging and intrafraction respiratory-motion surrogates. The IMRT plan is then re-optimized in real time to ensure delivery of the planned dose in the presence of free-breathing motion. We compare the performance of the proposed approach against traditional motion-management techniques, namely, respiratory gating and internal target volume (ITV) planning, using the four-dimensional extended cardiac-torso computational phantom.Main results.We simulate the delivery of treatment plans for a lung tumor in the presence of variable breathing amplitude, tumor size, and location. Results show that the proposed method reduces irradiated tissue volume compared to ITV treatment. Additionally, it significantly reduces treatment time compared to traditional respiratory-gated treatment, without compromising the dosimetric quality.Significance.Respiratory gating is a common technique to manage intrafraction motion. While gating supports reduced treatment volumes, it also prolongs the treatment delivery time. The proposed stochastic control approach can help improve the delivery efficiency of respiratory gating without compromising the dose quality.

Technical Note: Cumulative dose modeling for organ motion management in MRI-guided radiation therapy.

PURPOSE: To develop a method for continuous online dose accumulation during irradiation in MRI-guided radiation therapy (MRgRT) and to demonstrate its application in evaluating the impact of internal organ motion on cumulative dose. METHODS: An intensity-modulated radiation therapy (IMRT) treatment plan is partitioned into its unique apertures. Dose for each planned aperture is calculated using Monte Carlo dose simulation on each phase of a four-dimensional computed tomography (4D-CT) dataset. Deformable image registration is then performed both (a) between each frame of a cine-MRI acquisition obtained during treatment and a reference frame, and (b) between each volume of the 4D-CT phases and a reference phase. These registrations are used to associate each cine image with a 4D-CT phase. Additionally, for each 4D-CT phase, the deformation vector field (DVF) is used to warp the pre-calculated dose volumes per aperture onto the reference CT dataset. To estimate the dose volume delivered during each frame of the cine-MRI acquisition, we retrieve the pre-calculated warped dose volume for the delivered aperture on the associated 4D-CT phase and adjust it by a rigid translation to account for baseline drift and instances where motion on the cine image exceeds the amplitude observed between 4D-CT phases. RESULTS: The proposed dose accumulation method is retrospectively applied to a liver cancer case previously treated on an MRgRT platform. Cumulative dose estimated for free-breathing and respiration-gated delivery is compared against dose calculated on static anatomy. In this sample case, the target minimum dose and D 98 varied by as much as 5% and 7%, respectively. CONCLUSION: We demonstrate a technique suitable for continuous online dose accumulation during MRgRT. In contrast to other approaches, dose is pre-calculated per aperture and phase and then retrieved based on a mapping scheme between cine MRI and 4D-CT datasets, aiming at reducing the computational burden for potential real-time applications.

Intra-fraction motion prediction in MRI-guided radiation therapy using Markov processes.

Internal organ motion during radiation delivery may lead to underdosing of cancer cells or overdosing of normal tissue, potentially causing treatment failure or normal-tissue toxicity. Organ motion is of particular concern in the treatment of lung and abdominal cancers, where breathing induces large tumor displacement and organ deformation. A new generation of radiotherapy devices is equipped with on-board MRI scanners to acquire a real-time movie of the patient's anatomy during radiation delivery. The goal of this research is to develop, calibrate, and test motion predictive models that employ real-time MRI images to provide the short-term trajectory of respiration-induced anatomical motion during radiation delivery. A semi-Markov model predicts transitions between the phases of a respiratory cycle, and a Markov model predicts transitions to future respiratory cycles, leading to accurate motion forecasting over longer-term horizons. The intended application for this work is real-time tracking and re-optimization of intensity-modulated radiation delivery.

Relaxing leaf-motion restrictions in dynamic multileaf collimator leaf sequencing.

PURPOSE: Traditionally, unidirectional leaf-sweeping schemes have been employed to deliver IMRT plans using the dynamic multileaf collimator (DMLC) technique. The goal of this research is to investigate the potential impact of relaxing the leaf-motion restrictions in DMLC IMRT on the beam-modulation quality and the delivery efficiency. METHODS: This research relaxes the initial and final leaf-position constraints as well as the unidirectional leaf-motion restriction that have been traditionally imposed on DMLC leaf sequencing and develops exact and heuristic solution approaches to allow for an unconstrained and bidirectional leaf motion. The exact approach employs mixed-integer programming (MIP) techniques and the proposed heuristic method uses stochastic search algorithms while utilizing the special structure of the problem. The trade-off between beam-modulation quality and delivery efficiency is quantified and compared to that of unidirectional leaf-sweeping schemes. RESULTS: The performance of the developed approaches is tested on liver and head-and-neck cancer cases. Results validate that unconstrained leaf trajectories can significantly improve the beam-modulation quality at small beam-on time values. However, this gain reduces as the available beam-on time increases. Additionally, the proposed heuristic approach can achieve near-optimal solutions with significantly smaller computational effort compared to the MIP solution approach. CONCLUSIONS: Unconstrained leaf trajectories have the potential to enhance the fluence-modulation quality for cases in which the available beam-on time is limited. This gain is primarily attributed to the relaxation of the initial and final leaf positions. The unidirectionality restriction alone does not appear to be a limiting factor.

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.

Accounting for patient heterogeneity in nurse staffing using a queueing-theory approach.

Evidence from observational studies suggests that inadequate nurse staffing in hospitals and heavy nurse workload may compromise patient safety and quality of care. There are recommended minimum nurse-to-patient ratios for different types of inpatient care settings. However, nursing-care intensity may vary across different patients within an inpatient unit depending on the severity of their medical condition, potentially rendering fixed nurse-to-patient ratios ineffective. This study aims at developing nurse-staffing strategies that explicitly account for patient heterogeneity. Using queueing theory, we develop a stochastic framework to model direct nursing care provided in inpatient-care units. The stochastic model is then used to measure different performance metrics that evaluate the efficiency and timeliness of inpatient-care delivery. The trade-off between those performance metrics and the nursing staff level is quantified, which can assist clinicians with determining minimum nursing staff levels that ensure timely delivery of nursing care to a given patient mix.

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.

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.

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.

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/ß-ratio of the tumor is larger than the α/ß-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/ß-ratio of the OAR is larger than α/ß-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.

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.

Exploring trade-offs between VMAT dose quality and delivery efficiency using a network optimization approach.

To formulate and solve the fluence-map merging procedure of the recently-published VMAT treatment-plan optimization method, called VMERGE, as a bi-criteria optimization problem. Using an exact merging method rather than the previously-used heuristic, we are able to better characterize the trade-off between the delivery efficiency and dose quality. VMERGE begins with a solution of the fluence-map optimization problem with 180 equi-spaced beams that yields the 'ideal' dose distribution. Neighboring fluence maps are then successively merged, meaning that they are added together and delivered as a single map. The merging process improves the delivery efficiency at the expense of deviating from the initial high-quality dose distribution. We replace the original merging heuristic by considering the merging problem as a discrete bi-criteria optimization problem with the objectives of maximizing the treatment efficiency and minimizing the deviation from the ideal dose. We formulate this using a network-flow model that represents the merging problem. Since the problem is discrete and thus non-convex, we employ a customized box algorithm to characterize the Pareto frontier. The Pareto frontier is then used as a benchmark to evaluate the performance of the standard VMERGE algorithm as well as two other similar heuristics. We test the exact and heuristic merging approaches on a pancreas and a prostate cancer case. For both cases, the shape of the Pareto frontier suggests that starting from a high-quality plan, we can obtain efficient VMAT plans through merging neighboring fluence maps without substantially deviating from the initial dose distribution. The trade-off curves obtained by the various heuristics are contrasted and shown to all be equally capable of initial plan simplifications, but to deviate in quality for more drastic efficiency improvements. This work presents a network optimization approach to the merging problem. Contrasting the trade-off curves of the merging heuristics against the Pareto approximation validates that heuristic approaches are capable of achieving high-quality merged plans that lie close to the Pareto frontier.

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.

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.