A Dynamic Programming Approach to Adaptive Fractionation

We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive fractionation, because it allows us to assess how close to optimal different methods are, and (ii) heuristic methods proposed in this paper are near-optimal, and therefore, can be used to evaluate the best possible benefit of using an adaptive fraction size. The essence of adaptive fractionation is to increase the fraction size when the tumor and organ-at-risk (OAR) are far apart (a "favorable" anatomy) and to decrease the fraction size when they are close together. Given that a fixed prescribed dose must be delivered to the tumor over the course of the treatment, such an approach results in a lower cumulative dose to the OAR when compared to that resulting from standard fractionation. We first establish a benchmark by using the DP algorithm to solve the problem exactly. In this case, we characterize the structure of an optimal policy, which provides guidance for our choice of heuristics. We develop two intuitive, numerically near-optimal heuristic policies, which could be used for more complex, high-dimensional problems. Furthermore, one of the heuristics requires only a statistic of the motion probability distribution, making it a reasonable method for use in a realistic setting. Numerically, we find that the amount of decrease in dose to the OAR can vary significantly (5 - 85%) depending on the amount of motion in the anatomy, the number of fractions, and the range of fraction sizes allowed. In general, the decrease in dose to the OAR is more pronounced when: (i) we have a high probability of large tumor-OAR distances, (ii) we use many fractions (as in a hyper-fractionated setting), and (iii) we allow large daily fraction size deviations.Comment: 17 pages, 4 figures, 1 tabl

The Perils of Adapting to Dose Errors in Radiation Therapy

We consider adaptive robust methods for lung cancer that are also dose-reactive, wherein the treatment is modified after each treatment session to account for the dose delivered in prior treatment sessions. Such methods are of interest because they potentially allow for errors in the delivered dose to be corrected as the treatment progresses, thereby ensuring that the tumor receives a sufficient dose at the end of the treatment. We show through a computational study with real lung cancer patient data that while dose reaction is beneficial with respect to the final dose distribution, it may lead to exaggerated daily underdose and overdose relative to non-reactive methods that grows as the treatment progresses. However, by combining dose reaction with a mechanism for updating an estimate of the uncertainty, the magnitude of this growth can be mitigated substantially. The key finding of this paper is that reacting to dose errors – an adaptation strategy that is both simple and intuitively appealing – may backfire and lead to treatments that are clinically unacceptable.Natural Sciences and Engineering Research Council of Canada (Canadian Institutes of Health Research Collaborative Health Research Project Grant 398106-2011

Evaluating setup accuracy of a positioning device for supine pelvic radiotherapy

MSc., Faculty of Science, University of the Witwatersrand, 2011Aim: This study aimed at evaluating the accuracy of the treatment setup margin in external beam radiotherapy in cervical cancer patients treated supine with or without the CIVCO “kneefix and feetfix”TM immobilizing devices. Methods and materials: 2 groups of 30 cervical cancer patients each, who were treated supine with two parallel opposed fields or a four-field “box” technique were selected randomly. The treatment fields were planned with a 2 cm setup margin defined radiographically. The first group was treated without any immobilization and the second group was treated with the “kneefix and feetfix”TM immobilization device. Both groups of patients were selected from the patients treated on one of two linear accelerators (linac), which had weekly mechanical quality control (QC). All patients had pre-treatment verifications on the treatment machine in which a megavoltage Xray film was taken to compare with the planning simulation film. Both films were approved by the radiation oncologist managing the patient. In this study the position of the treatment couch as at the approved machine film was taken as the intended or planned position for the immobilized patients. The digital readouts of the daily treatment position of the couch were recorded for each patient as the absolute X (lateral), Y (longitudinal), and Z (vertical) position of the couch from the record and verify system interfaced to the treatment machine. A total of 1241 (582 for the immobilized and 659 for the non-immobilized patient group) daily treatment setup positions were recorded in terms of the X, Y and Z coordinates of the couch corresponding to the Medio-lateral (ML), Supero-inferior (SI) and Antero-posterior (AP) directions of the patient, respectively. The daily translational setup deviation of the patient was calculated by taking the difference between the planned (approved) and daily treatment setup positions in each direction. Each patient’s systematic setup error (mi) and the population mean setup deviation (M), was calculated. Random ( ) and systematic ( ) setup errors were then calculated for each group in each direction. The translational setup variations found in the AP, iii ML, SI directions were compared with the 2 cm x 2 cm x 2 cm Planning Target Volume (PTV). Couch tolerance limits with the immobilization device were suggested based on the ± 2SD (standard deviation) obtained for each translational movement of the treatment couch. Result: The random and systematic errors for the immobilized patient group were less than those for the non-immobilized patient group. For the immobilized patient group, the systematic setup error was greater than the random error in the ML and SI direction as shown in Table I. Table I: The random and systematic errors in the setup in the Antero-posterior (AP), Medio-lateral (ML) and Supero-inferior (SI) directions and the suggested couch tolerance limits for both patient groups. Almost all treatment setup positions had less than 2 cm variation in the AP setup for both patient groups however; one third of the immobilized positions had more than 2 cm variation in the setup in the ML and SI directions. Conclusion: The “kneefix and feetfix”TM immobilizing device resulted in a minor improvement in both the random and systematic setup errors. The systematic setup errors need to be investigated further. There are measurable patient rotations of more than 2 cm in the setup margin with the immobilizing device and this should be confirmed with an imaging study. The 2 cm margin in the ML and SI directions Immobilized patient group Non-immobilized patient group AP (cm) ML (cm) SI (cm) AP (cm) ML (cm) SI (cm) Random error (!) 0.30 1.35 1.26 0.37 2.74 7.83 Systematic error (") 0.19 1.55 1.64 0.33 1.70 8.11 Suggested couch tolerance limits (±2SD) 0.70 4.04 4.08 0.88 4.76 N/A iv established at simulation should not be changed for these patients. A 1 cm tolerance in the AP setup margin could be introduced at this institution

Application of constrained optimization methods in health services research: Report 2 of the ISPOR Optimization Methods Emerging Good Practices Task Force

Background Constrained optimization methods are already widely used in health care to solve problems that represent traditional applications of operations research methods, such as choosing the optimal location for new facilities or making the most efficient use of operating room capacity. Objectives In this paper we illustrate the potential utility of these methods for finding optimal solutions to problems in health care delivery and policy. To do so, we selected three award-winning papers in health care delivery or policy development, reflecting a range of optimization algorithms. Two of the three papers are reviewed using the ISPOR Constrained Optimization Good Practice Checklist, adapted from the framework presented in the initial Optimization Task Force Report. The first case study illustrates application of linear programming to determine the optimal mix of screening and vaccination strategies for the prevention of cervical cancer. The second case illustrates application of the Markov Decision Process to find the optimal strategy for treating type 2 diabetes patients for hypercholesterolemia using statins. The third paper (described in Appendix 1) is used as an educational tool. The goal is to describe the characteristics of a radiation therapy optimization problem and then invite the reader to formulate the mathematical model for solving it. This example is particularly interesting because it lends itself to a range of possible models, including linear, nonlinear, and mixed-integer programming formulations. From the case studies presented, we hope the reader will develop an appreciation for the wide range of problem types that can be addressed with constrained optimization methods, as well as the variety of methods available. Conclusions Constrained optimization methods are informative in providing insights to decision makers about optimal target solutions and the magnitude of the loss of benefit or increased costs associated with the ultimate clinical decision or policy choice. Failing to identify a mathematically superior or optimal solution represents a missed opportunity to improve economic efficiency in the delivery of care and clinical outcomes for patients. The ISPOR Optimization Methods Emerging Good Practices Task Force’s first report provided an introduction to constrained optimization methods to solve important clinical and health policy problems. This report also outlined the relationship of constrained optimization methods relative to traditional health economic modeling, graphically illustrated a simple formulation, and identified some of the major variants of constrained optimization models, such as linear programming, dynamic programming, integer programming, and stochastic programming. The second report illustrates the application of constrained optimization methods in health care decision making using three case studies. The studies focus on determining optimal screening and vaccination strategies for cervical cancer, optimal statin start times for diabetes, and an educational case to invite the reader to formulate radiation therapy optimization problems. These illustrate a wide range of problem types that can be addressed with constrained optimization methods

Three Essays on Radiotherapy Treatment Planning Optimization

Radiation therapy is one of the most common and effective methods of treating cancer. There are two main types: external and internal. External to the patient, a linear accelerator aims beams of radiation toward the patient; internal to the patient, radioactive sources are placed temporarily or permanently at the treatment site to deposit dose locally. Both methods of treatment can deliver complex dose distributions to a patient. The radiation damages both tumorous tissue and nearby healthy organs; treatment planning optimization determines how to deliver a dose distribution that maximizes tumor kill while sparing nearby healthy organs as much as possible. This thesis studies three treatment planning problems: the first two are in the context of external radiation therapy and the third is in the context of internal radiation therapy. Conventional planning is based on only the physical geometry of the patient anatomy. In chapter II, we propose two models that incorporate (additional) liver function information for planning liver cancer treatment to preserve as much post-treatment liver function as possible and compare this to a conventional approach that ignores liver function information. Conventional plans assume the patient geometry does not change between the time of patient imaging and later treatments. Although the patient geometry can be updated at treatment for plan adaptation, current practice may lead to plans that result in significantly worse quality than originally intended due to its myopic nature. In chapter III, we propose a model that produces a plan that caters to each potential patient geometry while considering both day-of and cumulative impact. In high-dose rate brachytherapy, the patient undergoes anesthesia due to the need to implant catheters for radiation source placement before planning. Consideration of multiple conflicting criteria in treatment planning results in challenging optimization problems. Current commercial systems require iterative guess-and-checking of optimization input parameters to make trade-offs among criteria, but a plan must be finalized quickly to minimize anesthesia administration. In chapter IV, we develop a practical optimization engine that generates a trade-off surface and feeds into a graphical user interface that provides the clinician more control to make trade-offs without trial-and-error optimizations.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140827/1/vwwu_1.pd

Optimization Methods for Volumetric Modulated Arc Therapy and Radiation Therapy under Uncertainty.

Treatment plan optimization is crucial in the success of radiation therapy treatments. In order to deliver the prescribed radiation dose to the tumor without damaging the healthy organs, plans must be carefully designed so that collectively the dose delivered from different angles achieves the desired treatment outcome. The development of Volumetric Modulated Arc Therapy (VMAT) enables planners to explore additional benefits compared to traditional Intensity Modulated Radiation Therapy (IMRT). By rotating the gantry and attached source continuously, VMAT treatments can be delivered in a short period of time. While clinics can benefit from improved equipment utilization and less patient discomfort, treatment planning for VMAT is challenging because of the restrictions associated with the continuous gantry motion. We propose a new column generation based algorithm that explicitly considers the physical constraints, and constructs the treatment plan in an iterative process that searches for the maximum marginal improvement in each iteration. Implemented with GPU-based parallel computing, our algorithm is very efficient in generating high quality plans compared to idealized 177-angle IMRT plans. While treatments can benefit from VMAT in many ways, the capital expenditure in upgrading to a dedicated VMAT system is an important factor for clinics. Conventional IMRT machines can deliver VMAT treatments with constant rate of radiation output and gantry speed (VMATC). The absence of the ability to dynamically change the dose rate and gantry speed makes VMATC different in nature from VMAT. We propose two optimization frameworks for optimizing the machine parameters in the treatment, and recommend one configuration that consistently produces high quality plans compared to VMAT treatments. Finally, we consider uncertainties in radiation therapy treatments associated with errors in the daily setup process. We propose a stochastic programming based model that explicitly incorporates the range of uncertain outcomes in both the daily and cumulative dose distributions. While the problem is difficult to solve directly, we use a dynamic sampling procedure that can guarantee close to optimal solutions by establishing bounds on the optimal objective. Experiments with clinical cases show that the stochastic plans outperform the conventional approach, and reveal important information for planning adaptive treatments.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99813/1/feipeng_1.pd

A novel combination of Cased-Based Reasoning and Multi Criteria Decision Making approach to radiotherapy dose planning

In this thesis, a set of novel approaches has been developed by integration of Cased-Based Reasoning (CBR) and Multi-Criteria Decision Making (MCDM) techniques. Its purpose is to design a support system to assist oncologists with decision making about the dose planning for radiotherapy treatment with a focus on radiotherapy for prostate cancer. CBR, an artificial intelligence approach, is a general paradigm to reasoning from past experiences. It retrieves previous cases similar to a new case and exploits the successful past solutions to provide a suggested solution for the new case. The case pool used in this research is a dataset consisting of features and details related to successfully treated patients in Nottingham University Hospital. In a typical run of prostate cancer radiotherapy simple CBR, a new case is selected and thereafter based on the features available at our data set the most similar case to the new case is obtained and its solution is prescribed to the new case. However, there are a number of deficiencies associated with this approach. Firstly, in a real-life scenario, the medical team considers multiple factors rather than just the similarity between two cases and not always the most similar case provides with the most appropriate solution. Thus, in this thesis, the cases with high similarity to a new case have been evaluated with the application of the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). This approach takes into account multiple criteria besides similarity to prescribe a final solution. Moreover, the obtained dose plans were optimised through a Goal Programming mathematical model to improve the results. By incorporating oncologists’ experiences about violating the conventionally available dose limits a system was devised to manage the trade-off between treatment risk for sensitive organs and necessary actions to effectively eradicate cancer cells. Additionally, the success rate of the treatment, the 2-years cancer free possibility, has a vital role in the efficiency of the prescribed solutions. To consider the success rate, as well as uncertainty involved in human judgment about the values of different features of radiotherapy Data Envelopment Analysis (DEA) based on grey numbers, was used to assess the efficiency of different treatment plans on an input and output based approach. In order to deal with limitations involved in DEA regarding the number of inputs and outputs, we presented an approach for Factor Analysis based on Principal Components to utilize the grey numbers. Finally, to improve the CBR base of the system, we applied Grey Relational Analysis and Gaussian distant based CBR along with features weight selection through Genetic Algorithm to better handle the non-linearity exists within the problem features and the high number of features. Finally, the efficiency of each system has been validated through leave-one-out strategy and the real dataset. The results demonstrated the efficiency of the proposed approaches and capability of the system to assist the medical planning team. Furthermore, the integrated approaches developed within this thesis can be also applied to solve other real-life problems in various domains other than healthcare such as supply chain management, manufacturing, business success prediction and performance evaluation