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.

Construction is a notoriously hazardous industry and heavy alcohol use is common. This project created an agent-based modeling (ABM) simulation to explore the impact of alcohol on safety outcomes. Simulation modeling is useful in occupational safety research because it generates immediate results and bypasses ethical concerns. In this project, workers and foremen interacted on a virtual jobsite with hazards present, where positive blood alcohol concentration (BAC) decreased hazard awareness, reaction time, and foreman competency. Three scenarios of baseline, increased, and decreased alcohol consumption were analyzed for changes in near misses, injuries, and fatalities. Additional scenarios of improved training and engineering controls were explored also for comparison. Simulation results show that a decrease in alcohol consumption leads to a significant reduction in injuries by up to 12%, and an increase has the opposite effect. Neither of the scenarios significantly impact fatalities due to fatalities' low base rate. Safety training has a comparable impact but improving engineering controls outweighed both.

It has been recently shown that an additional therapeutic gain may be achieved if a radiotherapy plan is altered over the treatment course using a new treatment paradigm referred to in the literature as spatiotemporal fractionation. Because of the nonconvex and large-scale nature of the corresponding treatment plan optimization problem, the extent of the potential therapeutic gain that may be achieved from spatiotemporal fractionation has been investigated using stylized cancer cases to circumvent the arising computational challenges. This research aims at developing scalable optimization methods to obtain high-quality spatiotemporally fractionated plans with optimality bounds for clinical cancer cases. In particular, the treatment-planning problem is formulated as a quadratically constrained quadratic program and is solved to local optimality using a constraint-generation approach, in which each subproblem is solved using sequential linear/quadratic programming methods. To obtain optimality bounds, cutting-plane and column-generation methods are combined to solve the Lagrangian relaxation of the formulation. The performance of the developed methods are tested on deidentified clinical liver and prostate cancer cases. Results show that the proposed method is capable of achieving local-optimal spatiotemporally fractionated plans with an optimality gap of around 10%–12% for cancer cases tested in this study. Summary of Contribution: The design of spatiotemporally fractionated radiotherapy plans for clinical cancer cases gives rise to a class of nonconvex and large-scale quadratically constrained quadratic programming (QCQP) problems, the solution of which requires the development of efficient models and solution methods. To address the computational challenges posed by the large-scale and nonconvex nature of the problem, we employ large-scale optimization techniques to develop scalable solution methods that find local-optimal solutions along with optimality bounds. We test the performance of the proposed methods on deidentified clinical cancer cases. The proposed methods in this study can, in principle, be applied to solve other QCQP formulations, which commonly arise in several application domains, including graph theory, power systems, and signal processing.

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 D98 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.

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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.

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.

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 radiobiological 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.

PURPOSETraditionally, 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.METHODSThis 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.RESULTSThe 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.CONCLUSIONSUnconstrained 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.

The majority of cancer-related fatalities are due to metastatic disease. Chemotherapeutic agents are administered along with radiation in chemoradiotherapy (CRT) to control the primary tumor and systemic disease such as metastasis. This work introduces a mathematical model of CRT treatment scheduling to obtain optimal drug and radiation protocols with the objective of minimizing metastatic cancer cell populations at multiple potential sites while maintaining a desired level of control on the primary tumor. Dynamic programming framework is used to determine the optimal radiotherapy fractionation regimen and the drug administration schedule. We design efficient DP data structures and use structural properties of the optimal solution to reduce the complexity of the resulting DP algorithm. We derive closed-form expressions for optimal chemotherapy schedules in special cases. The results suggest that if there is only an additive and spatial cooperation between the chemotherapeutic drug and radiation with no interaction between them, then radiation and drug administration schedules can be decoupled. In that case, regardless of the chemo- and radio sensitivity parameters, the optimal radiotherapy schedule follows a hypofractionated scheme. However, the structure of the optimal chemotherapy schedule depends on model parameters such as chemotherapy-induced cell kill at primary and metastatic sites, as well as the ability of primary tumor cells to initiate successful metastasis at different body sites. In contrast, an interactive cooperation between the drug and radiation leads to optimal split-course concurrent CRT regimens. Additionally, under dynamic radio sensitivity parameters due to the reoxygenation effect during therapy, we observe that it is optimal to immediately start the chemotherapy and administer a few large radiation fractions at the beginning of the therapy, while scheduling smaller fractions in later sessions. We quantify the trade-off between the new and traditional objectives of minimizing the metastatic population size and maximizing the primary tumor control probability, respectively, for a cervical cancer case. The trade-off information indicates the potential for significant reduction in the metastatic population with minimal loss in the primary tumor control.

The majority of cancer-related fatalities are due to metastatic disease. In chemoradiotherapy, chemotherapeutic agents are administered along with radiation to increase damage to the primary tumor and control systemic disease such as metastasis. This work introduces a mathematical model to obtain optimal drug and radiation protocols in a chemoradiotherapy scheduling problem with the objective of minimizing metastatic cancer cell populations at multiple potential sites while maintaining a minimum level of damage to the primary tumor site. We derive closed-form expressions for an optimal chemotherapy fractionation regimen. A dynamic programming framework is used to determine the optimal radiotherapy fractionation regimen. Results show that chemotherapeutic agents do not change the optimal radiation fractionation regimens, and vice-versa. Interestingly, we observe that regardless of radio-sensitivity parameters, hypo-fractionated schedules are optimal solutions for the radiotherapy fractionation problem. Furthermore, it is optimal to immediately start radiotherapy. However, for chemotherapy, we find that the structure of the optimal schedule depends on model parameters such as chemotherapy-induced cell-kill at primary and metastatic sites, as well as the ability of primary tumor cells to initiate successful metastasis at different body sites. We quantify the trade-off between the new and traditional objectives of minimizing the metastatic population size and maximizing the tumor control probability, respectively, for a cervical cancer case. The trade-off information indicates the potential for significant reduction in the metastatic population with minimal loss in primary tumor control.

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.

In concurrent chemoradiotherapy, chemotherapeutic agents are administered during the course of radiotherapy to enhance the primary tumor control. However, that 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 radiation fractionation schemes.

Purpose:In split‐course radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated by radiobiological considerations. However, using modern image‐guidance, it also provides an approach to reduce normal tissue dose by exploiting tumor shrinkage. In this work, we consider the optimal design of split‐course 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.Methods:We introduce a dynamic tumor model that incorporates three factors: radiation induced cell kill, tumor shrinkage, and tumor cell repopulation. The design of splitcourse radiotherapy is formulated as a mathematical optimization problem in which the total dose to the liver 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.Results: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 split‐course treatments in terms of liver sparing depends on model assumptions. However, the model predicts large liver dose reductions by more than a factor of two for plausible model parameters.Conclusion: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 split‐course radiotherapy for selected disease sites where substantial tumor regression translates into reduced target volumes.

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.