Funded Projects
2020 - 2025 UT Health San Antonio; Optimal Scheduling of Physicians and Certified Registered Nurses ; Role: PI
2020 - 2021 UTSA; INTRA: Towards Spatiotemporally Robust Radiation Therapy ; Role: PI
2017 - 2018 BGSU; Summer Research Grant: Robustness in Cancer Treatments Guided by Cell Oxygenation; Role: PI
Peer-reviewed Papers
Nima Ebadi, Ruiqi Li, Arun Das, Arkajyoti Roy, Papanikolaou Nikos, Peyman Najafirad
Abstract. Adaptive radiotherapy (ART) is an advanced technology in modern cancer treatment that incorporates progressive changes in patient anatomy into active plan/dose adaption during the fractionated treatment. However, the clinical application relies on the accurate segmentation of cancer tumors on low-quality on-board images, which has posed challenges for both manual delineation and deep learning-based models. In this paper, we propose a novel sequence transduction deep neural network with an attention mechanism to learn the shrinkage of the cancer tumor based on patients’ weekly cone-beam computed tomography (CBCT). We design a self-supervised domain adaption (SDA) method to learn and adapt the rich textural and spatial features from pre-treatment high-quality computed tomography (CT) to CBCT modality in order to address the poor image quality and lack of labels. We also provide uncertainty estimation for sequential segmentation, which aids not only in the risk management of treatment planning but also in the calibration and reliability of the model. Our experimental results based on a clinical non-small cell lung cancer (NSCLC) dataset with sixteen patients and ninety-six longitudinal CBCTs show that our model correctly learns weekly deformation of the tumor over time with an average dice score of 0.92 on the immediate next step, and is able to predict multiple steps (up to 5 weeks) for future patient treatments with an average dice score reduction of 0.05. By incorporating the tumor shrinkage predictions into a weekly re-planning strategy, our proposed method demonstrates a significant decrease in the risk of radiation-induced pneumonitis up to 35% while maintaining the high tumor control probability.
Value of Intermediate Imaging in Adaptive Robust Radiotherapy Planning to Manage Radioresistance
Arkajyoti Roy, Shaunak Dabadghao, and Ahmadreza Marandi
Abstract. In radiotherapy, uncertainties in tumor radioresistance and its progression can degrade the efficacy of deterministic treatments. While a robust methodology can overcome this, it often produces overly conservative or suboptimal decisions, especially when there are changes in time. We aim to develop an adaptive radiotherapy planning framework that can reduce over-conservatism yet remain robust to the uncertainties in radioresistance. Specifically, intermediate imaging is used to update the uncertainty at each stage and curb over-conservatism. While additional imaging reduces uncertainty, it accrues costs such as extra radiation to organs, which deters continuous imaging. We probe this trade-off in uncertainty and cost of observation by computing and comparing results from two-stage, three-stage, and four-stage robust models. The three robust models are also compared to two currently practiced deterministic methods, one that does not account for radioresistance and one that assumes a constant radioresistance. All five models are evaluated on a clinical prostate case. The three robust models improve control of the tumor compared to the deterministic model ignoring radioresistance, at comparable radiation dose to critical organs. The robust models also reduce tumor overdose and organ dose compared to the deterministic model assuming a constant radioresistance. Increasing the number of intermediate imaging leads to further improvements, especially on tumor dose criteria under best-case and nominal scenarios. Under the worst-case, intermediate images provide no additional benefit as robust optimization inherently protects against the worst-case. The proposed method is generic and can include additional sources of uncertainties that reduce the effect of radiation.
Amal Bakchan, Arkajyoti Roy, and Kasey Faust
Abstract. Social distancing policies (SDPs) implemented worldwide in response to COVID-19 pandemic have led to spatiotemporal variations in water demand and wastewater flow, creating potential operational and service-related quality issues in water-sector infrastructure. Understanding water-demand variations is especially challenging in contexts with limited availability of smart meter infrastructure, hindering utilities’ ability to respond in real time to identified system vulnerabilities. Leveraging water and wastewater infrastructures’ interdependencies, this study proposes the use of high-granular wastewater-flow data as a proxy to understand both water and wastewater systems’ behaviors during active SDPs. Enabled by a random-effects model of wastewater flow in an urban metropolitan city in Texas, we explore the impacts of various SDPs (e.g., stay home-work safe, reopening phases) using daily flow data gathered between March 19, 2019, and December 31, 2020. Results indicate an increase in residential flow that offset a decrease in nonresidential flow, demonstrating a spatial redistribution of wastewater flow during the stay home-work safe period. Our results show that the three reopening phases had statistically significant relationships to wastewater flow. While this yielded only marginal net effects on overall wastewater flow, it serves as an indicator of behavioral changes in water demand at sub-system spatial scales given demand-flow interdependencies. Our assessment should enable utilities without smart meters in their water system to proactively target their operational response during pandemics, such as (1) monitoring wastewater-flow velocity to alleviate potential blockages in sewer pipes in case of decreased flows, and (2) closely investigating any consequential water-quality problems due to decreased demands.
Impacts of COVID-19 Social Distancing Policies on Water Demand: A Population Dynamics Perspective
Amal Bakchan, Arkajyoti Roy, and Kasey Faust
Abstract. Social distancing policies (SDPs) implemented in response to the COVID-19 pandemic have led to temporal and spatial shifts in water demand across cities. Water utilities need to understand these demand shifts to respond to potential operational and water-quality issues. Aided by a fixed-effects model of citywide water demand in Austin, Texas, we explore the impacts of various SDPs (e.g., time after the stay home-work safe order, reopening phases) using daily demand data gathered between 2013 and 2020. Our approach uses socio-technical determinants (e.g., climate, water conservation policy) with SDPs to model water demand, while accounting for spatial and temporal effects (e.g., geographic variations, weekday patterns). Results indicate shifts in behavior of residential and non-residential demands that offset the change at the system scale, demonstrating a spatial redistribution of water demand after the stay home-work safe order. Our results show that some phases of Texas’s reopening phases had statistically significant relationships to water demand. While this yielded only marginal net effects on overall demand, it underscores behavioral changes in demand at sub-system spatial scales. Our discussions shed light on SDPs’ impacts on water demand. Equipped with our empirical findings, utilities can respond to potential vulnerabilities in their systems, such as water-quality problems that may be related to changes in water pressure in response to demand variations.
Sruthi Sivabhaskar, Ruiqi Li, Arkajyoti Roy, Neil Kirby, Mohamad Fakhreddine, and Nikos Papanikoloaou
Abstract.Purpose: Accurate positioning of multileaf collimator (MLC) leaves during volumetric modulated arc therapy (VMAT) is essential for accurate treatment delivery. We developed a linear regression, support vector machine, random forest, extreme gradient boosting (XGBoost), and an artificial neural network (ANN) for predicting the delivered leaf positions for VMAT plans.Methods: For this study, 160 MLC log files from 80 VMAT plans were obtained from a single institution treated on three Elekta Versa HD linear accelerators. The gravity vector, X1 and X2 jaw positions, leaf gap, leaf position, leaf velocity, and leaf acceleration were extracted and used as model inputs. The models were trained using 70% of the log files and tested on the remaining 30% of the log files. Mean absolute error (MAE), root mean square error (RMSE), the coefficient of determination R2, and fitted line plots showing the relationship between delivered and predicted leaf positions were used to evaluate model performance. Results: The models achieved the following errors: linear regression (MAE = 0.158 mm, RMSE = 0.225 mm), support vector machine (MAE = 0.141 mm, RMSE = 0.199 mm), random forest (MAE = 0.161 mm, RMSE = 0.229 mm), XGBoost (MAE = 0.185 mm, RMSE = 0.273 mm), and ANN (MAE = 0.361 mm, RMSE = 0.521 mm). A significant correlation between a plan’s gamma passing rate (GPR) and the prediction errors of linear regression, support vector machine, and random forest is seen (P < 0.045).Conclusions: We examined various models to predict the delivered MLC positions for VMAT plans treated with Elekta linacs. Linear regression, support vector machine, random forest, and XGBoost achieved lower errors than ANN. Models that can accurately predict the individual leaf positions during treatment can help identify leaves that are deviating from the planned position, which can improve a plan’s GPR.
Drivers of Declining Water Access in Alaska
Meredith Brown, Lauryn Spearing, Arkajyoti Roy, Jessica Kaminsky, Kasey Faust
Abstract. A majority of homes in the United States (U.S.) receive household water services via complete in-home plumbing. Observers tend to assume that in the U.S. there is an upward trend in plumbing access; yet in some Alaska communities, the rate is in fact a downward trend. This study seeks to identify, while considering the spatiotemporal variations in the region, the sociodemographic parameters that are correlated with the rates of in-home plumbing in Alaska communities. Equipped with American Community Survey data from 2011 to 2015, we employed a fixed-effects regression analysis. Our findings show that, concerning complete in-home plumbing, there was a statistically significant decrease (p < 0.05) in close to a quarter (23% percent) of census-designated places in Alaska. Access to complete plumbing is correlated to multiple sociodemographic characteristics, including the percentage of households that 1) receive social security, 2) are valued under $150,000, and 3) are renter-occupied units paying for one or more utilities. Our results help decision-makers efficiently allocate government funds by showing where service is deteriorating as well as the potential predictors of such decline. Our study reveals the pressing need to invest in not only new water systems, but also maintenance, operations, and capital improvements.
Measuring Ethical Development of Engineering Students Across Universities and Class Years
Michaela LaPatin, Arkajyoti Roy, Cristina Poleacovschi, Kate Padgett-Walsh, Scott Feinstein, Cassandra Rutherford, Luan Nguyen, Kasey Faust
Abstract. While the technical aspects of engineering are emphasized in education and industry, the ethical aspects are, in some ways, just as vital. Engineering instructors should teach undergraduates about their ethical responsibilities in the realm of engineering. Students would then be more likely to grasp their responsibilities as professionals. For many students, undergraduate study is a time of growth and change, with their ethical development just beginning to take shape. In this study, we aim to understand the progression of ethical development for engineering undergraduate students and identify key factors that may contribute to their development. To help us assess ethical development, we deployed in Fall 2020 a survey to undergraduate engineering students at two universities; the survey entailed the Defining Issues Test-2 (DIT-2). The DIT-2 evaluates ethical development based on Kohlberg’s theory of moral development; the test recognizes three levels of morality—preconventional, conventional, and postconventional. This study evaluates the associations between students’ university and class year and their Personal Interest, Maintaining Norms, and N2 scores. We utilized the results of a multivariate analysis of variance (MANOVA) to address the following research question: Is a student’s ethical development associated with their university and class year? The results of the analysis reveal that students’ ethical development appear to differ between universities and to lie along a continuum, changing from first-year students to seniors of engineering undergraduate study.
Managing Tumor Changes during Radiotherapy using a Deep Learning Model
Ruiqi Li, Arkajyoti Roy, Noah Bice, Neil Kirby, Mohamad Fakhreddin, and Niko Papanikolaou
Abstract.Purpose: We propose a treatment planning framework that accounts for weekly lung tumor shrinkage using cone beam computed tomography (CBCT) images with a deep learning-based model. Methods: Sixteen patients with non-small cell lung cancer (NSCLC) were employed with one planning CT and six weekly CBCTs each. A deep learning-based model was applied to predict the weekly deformation of the primary tumor based on the spatial and temporal features extracted from previous weekly CBCTs. Starting from Week 3, the tumor contour at Week N was predicted by the model based on the input from all the previous weeks (1,2…N-1), and was evaluated against the manually contoured tumor using Dice coefficient, precision, average surface distance and Hausdorff distance. Information about the predicted tumor was then entered into the treatment planning system and the plan was re-optimized every week. The objectives were to maximize the dose coverage in the target region while minimizing the toxicity to the surrounding healthy tissue. Dosimetric evaluation of the target and organs at risk (heart, lung, esophagus, spinal cord) was performed on four cases, comparing between a conventional plan (ignoring tumor shrinkage) and the shrinkage-based plan.Results: The primary tumor volumes decreased on average by 38% ± 26% during six weeks of treatment. Dice coefficients (DSC) and average surface distance (ASD) between the predicted tumor and the actual tumor for Week 3, 4, 5, 6 were (0.81, 0.82, 0.79, 0.78) and (1.49, 1.59, 1.92, 2.12) mm, respectively, which were significantly superior to the score of (0.70, 0.68, 0.66, and 0.63) and (2.81, 3.22, 3.69, and 3.63) mm between the rigidly transferred tumors ignoring shrinkage and the actual tumor. While target coverage metrics were maintained for the re-optimized plans, lung mean dose dropped by 2.32, 0.36, 2.38, and 1.65 Gy for four sample cases when compared to the original plan. Doses in other organs such as esophagus were also reduced for some cases. Conclusion: We developed a deep learning-based model for tumor shrinkage prediction. This model used CBCTs and contours from previous weeks as input and produced reasonable tumor contours with a high prediction accuracy (DSC, precision, HD, ASD). The proposed framework maintained target coverage while reducing dose in the lungs and esophagus.
Treatment Plan Quality Control using Multivariate Control Charts
Arkajyoti Roy, Reisa Widjaja, Min Wang, Dan Cutright, Mahesh Gopalakrishnan, and Bharat B. Mittal
Abstract.Purpose: Statistical process control tools such as control charts were recommended by the American Association of Physicists in Medicine (AAPM) Task Group 218 for radiotherapy quality assurance. However, the tools needed to analyze multivariate, correlated data that is often encountered in treatment plan quality measures, are lacking. In this study, we develop quality control tools that can model multivariate plan quality measures with correlations and account for patient-specific risk-factors, without adding a significant burden to clinical workflow.Methods and Materials: A multivariate, quality control chart is developed that includes a risk-adjustment model, Hotelling’s T2 statistic, and principal component analysis (PCA). PCA accounts for correlations among a set of organ-at-risk (OAR) dose-volume histogram (DVH) points that serves as proxies for plan quality. Risk-adjustment models estimate the principal components from PCA using a set of patient- and treatment-specific risk factors. The resulting residuals from the risk-adjustment models are used to compute the Hotelling’s T2 statistic; the corresponding multivariate control chart is then plotted based on the beta distribution followed by the statistic. Further, the box-cox transformation is used to account for non-normality in DVH points. We investigate the application of the proposed methodology via three multivariate control charts—a conventional chart that ignores risk-adjustment and PCA, a risk-adjusted chart ignoring PCA, and a PCA-based, risk-adjusted chart. These control charts are evaluated on 69 head-and-neck cases. Results: The conventional multivariate control chart fails to account for important patient-specific risk factors, including volumes and cross-sectional areas of the tumor and OARs and distances in-between. This failure leads to a larger number of false alarms. While the multivariate risk-adjusted control chart is able to reduce false alarms, it fails to account for correlations in DVH points. The multivariate PCA-based, risk-adjusted control chart can detect unusual plans after accounting for the correlations. By replanning, improvements are shown on an unusual plan identified by both risk-adjusted methods. Conclusions: The multivariate risk-adjusted control chart developed here enables quality control of plans prior to delivery. This methodology is generic and can be readily applied for other radiotherapy quality assurance protocols, such as gamma analysis pass-rates.
Kasey Faust, Arkajyoti Roy, Scott Feinstein, Cristina Poleacovschi, and Jessica Kaminsky
Abstract. In 2019, the number of displaced persons worldwide reached a historic peak. When those displaced arrive in hosting cities, local utilities, often with no additional money, are tasked with meeting unexpected demands. One way to recoup these costs is to raise rates. Publics are not, though, always willing to share their own financial resources and utilities. In this empirical study, we use statistical models to assess residents’ perceived individual responsibility—or willingness to pay—for these expanded services. Here we seek to not only identify if an individual is willing to financially support the provision of services for those displaced via increase in their own rates, but also, how long they are willing to support these services. Further, we explore factors that influence this perceived individual responsibility. Enabling this study is survey data from the German public in 2016, a time when asylum seekers displaced by instability in the Middle East encountered increased public opposition. We find respondents who are male, wealthier, more highly educated, and more urban are more willing to pay for services for displaced populations. These results can inform awareness campaigns or changes in rates and rate structures.
Gender and Engineering Identity among Upper-Division Undergraduate Students
Leigh Hamlet, Arkajyoti Roy, Giovanna Scalone, Regina Lee, Cristina Poleacovschi, and Jessica Kaminsky
Abstract. The construction industry’s long-term health depends upon continued efforts to understand historically excluded students’ attrition from engineering programs. For women, lack of identification with engineering may motivate their departure. As professional persistence relates to engineering identity, it benefits attrition interventions to understand this identity development. Focusing upon students demonstrating some persistence in engineering, this research examines if and how engineering identity differs across gender among upper-division undergraduates. Surveying eleven American public university civil and construction engineering programs, the authors capture how central engineering is to self-concept, how positively students view engineers and perceive others to view engineers, and how students feel they belong. Using structural equation modeling, the authors find that among upper-division students and compared to cis men, cis women more strongly define themselves as engineers, are more confident of their place among fellow engineers, and feel more positively about engineers. A stronger engineering identity may help cis women cope with marginalization and may be limited to the upper-division undergraduate years. This study offers guidance for sustaining upper-division cis women’s strong engineering identity.
Estimating Customer Churn under Competing Risks
Pallav Routh, Arkajyoti Roy, and Jeff Meyers
Abstract. Customer churn management focuses on identifying potential churners and implementing incentives that can cure churn. The success of a churn management program depends on accurately identifying potential churners and understanding what conditions contribute to churn. However, in the presence of uncertainties in the process of churn, such as competing risks and unpredictable customer behaviour, the accuracy of the prediction models can be limited. To overcome this, we employ a competing risk methodology within a random survival forest framework that accurately computes the risks of churn and identifies relationships between the risks and customer behaviour. In contrast to existing methods, the proposed model does not rely on a specific functional form to model the relationships between risk and behaviour, and does not have underlying distributional assumptions, both of which are limitations faced in practice. The performance of the method is evaluated using data from a membership-based firm in the hospitality industry, where customers face two competing churning events. The proposed model improves prediction accuracy by up to 20%, compared to conventional models. The findings from this work can allow marketers to identify and understand churners, and develop strategies on how to design and implement incentives.
Identity of Engineering Expertise: Implicitly Biased and Sustaining the Gender Gap
Featured as Editor’s Choice Paper.Cristina Poleacovschi, Kasey Faust, Arkajyoti Roy, and Scott Feinstein
Abstract. Experts bring the necessary comprehensive and authoritative knowledge to address issues as they arise throughout a project. This expertise is critical for construction and engineering organizations due to each project’s dynamic and unique characteristics. Practitioners often perceive expertise as objective across demographics; however, this study demonstrates that it is in fact subjective with gender implicit biases concerning expertise ratings. Enabling this study is survey data spanning 279 employees from a single construction and engineering company. The results revealed that men were likely to receive higher expertise ratings as compared to women. Further, this study found that men were likely to rate women’s expertise lower as compared to men’s expertise, while women’s expertise ratings show marginal difference based on gender. This research identified gender implicit biases within one large construction and engineering company, which may be typical within the industry more widely. Finally, the research contributes to the role congruity theory by showing the alignment and misalignment between expertise roles and gender roles.
Robust Optimization with Time-Dependent Uncertainty in Radiation Therapy
Best Paper Award.On Correlations in IMRT Planning Aims
Best Poster Award.Peer-reviewed Proceedings
Li, R., Ebadi, N., Boutilier, J., Rad, P., Buatti, J., De Oliveira, M., Kirby, N, Papanikolaou, N., Bonnen, M., Roy, A. (2022), "A Data-Driven Fluence Map Optimization Approach to Mitigate the Risk of Deep Learning Tumor Segmentation Misclassification", Medical Physics; 49(6).
Sivabhaskar, S., Li, R., Buatti, J., De Oliveira, M., Bonnen, M., Roy, A., Kirby, N, Stathakis, S., Papanikolaou, N. (2022), "Predicting 3D Gamma Passing Rates of Head-And-Neck Volumetric Modulated Arc Therapy Using Machine and Deep Learning Models", Medical Physics; 49(6).
Li, R., Ebadi, N., Das, A., Roy, A., Kirby, N, Papanikolaou, N., Bonnen, M., Rad, P. (2022), "Longitudinal Lung Tumor Segmentation On CBCTs Using Sequential Transduction Neural Network and Self-Supervised Domain Adaptation", Medical Physics; 49(6).
Sivabhaskar, S., Li, R., Kirby, N., Roy, A., Papanikolaou, N. (2022), "Comparison of machine and deep learning models predicting Elekta MLC leaf positions for VMAT", Radiotherapy and Oncology; 170(S1), S1439-S1440.
Bakchan, A., Roy, A., Faust, K. (2022) "Using Wastewater Flow to Understand Water System’s Demand Behavior during COVID-19 Pandemic in an Urban Metropolitan City in Texas". Construction Research Congress: CRC 2022, forthcoming. [Full-length paper].
Widjaja, R., Roy, A., Gopalakrishnan, M., Mittal, B (2021), "Power Transformations On Multivariate Non-Normal Radiotherapy Plan Quality Measures", Medical Physics; 48(6).
Li, R., Roy, A., Kirby, N., Bice, N., Sivabhaskar, S., Fakhreddine, M., Papanikolaou, N. (2021), "Managing Tumor Changes During Fractionated Radiotherapy: Evaluation On a Deep-Learning-Based Predictive Model and a Re-Planning Strategy", Medical Physics; 48(6).
Sivabhaskar, S., Papanikolaou, N., Kirby, N., Li, R., Roy, A. (2021), "Machine Learning Models to Predict the Delivered Positions of Elekta Multileaf Collimator Leaves for Volumetric Modulated Arc Therapy", Medical Physics; 48(6).
Cutright, D., Gopalakrishnan, M., & Roy, A. (2020), “Update On DVH Analytics: An Open-Source DICOM-RT Database Application”, Medical Physics; 47(6), E442-443.
Li, R., Das, A., Nice, N., Rad, P., Roy, A., Kirby, N., & Papanikolaou, N. (2020), “A Depthwise Separable Convolution Neural Network for Survival Prediction of Head & Neck Cancer”, Medical Physics ; 47(6), E405-406.
Cutright, D., Wu, T., Roy, A., Gopalakrishnan, M., & Mittal, B. (2020), “Automated Identification of DICOM-RT Structures Using Map Projections and Machine Learning”, Medical Physics; 47(6), E583.
Roy, A., Cutright, D., Gopalakrishnan, M., & Mittal, B. (2019), “Machine Learning in IMRT Plan Evaluation”, Medical Physics; 46(6):E107-E107.
Roy, A., Cutright, D., Gopalakrishnan, M., Yeh, A., & Mittal, B. (2018), “Anatomy-Adjusted Treatment Plan Quality Control”, Medical Physics; 45(6):E377-E377.
Cutright, D., Gopalakrishnan, M., Roy, A., Panchal, A., & Mittal, B. (2018), “DVH Analytics: An Open-Source DICOM-RT Database”, Medical Physics; 45(6):E652-E652.
Roy, A. & Nohadani, O. (2017), “Robustness in Hypoxia-Guided IMRT Planning”, Medical Physics; 44(6):2751.
Roy, A. & Nohadani, O. (2016), “Incorporating Time-Dependent Hypoxia in IMRT Planning”, Medical Physics; 43(6):3322.
Nohadani, O., Roy, A., & Das, I. (2015), “Unexpected Correlations Amongst Recommended Planning Aims in IMRT”, International Journal of Radiation Oncology·Biology·Physics; 93(3):E609.
Roy, A., Refaat, T., Baccus, I., Cutright, D., Sathiaseelan, V., Mittal, B. & Nohadani, O. (2015), “A Retrospective Correlation Analysis On Dose-Volume Control Points and Treatment Outcomes”, Medical Physics; 42(6):3347.
Nohadani, O., Roy, A. & Das, I. (2015), “Large-Scale DVH Quality Study: Correlated Aims Lead Relaxations”, Medical Physics; 42(6):3457.
Roy, A. & Nohadani, O. (2013), “Time-Resolved Stochastic IMRT Planning”, Medical Physics; 40(6):354.
Roy, A., Das, I., Srivastava, S., & Nohadani, O. (2013), “Analysis of Planner Dependence in IMRT”, Medical Physics; 40(6):260.
Loveless, A., Roy, A., Das, I., & Nohadani, O. (2013) “On Augmented DVH Analysis”, Medical Physics; 40(6):261.
Nohadani, O., Medawar, C., Roy, A., Srivastava, S., & Das, I. (2012) “Metrics for Comparing Dose Volume Histograms”, Medical Physics; 39(6):3851.
Editor-reviewed Magazine Articles
Roy, A., Nguyen, L., LaPatin, M., Poleacovschi, C., & Faust, K. (Dec 2020). Ethics in Engineering Education during COVID-19 Pandemic. ORMS Today Magazine, 47(6).
Nohadani, O., & Roy, A. (Jun 2016). Better cancer treatment leverages uncertainties. ISE Magazine, 49(6), 54.
Doctoral Dissertation
Roy, A. (2015). Decision-Making in Radiation Therapy in the Presence of Uncertainties (Doctoral dissertation, Purdue University).