Fractionated Treatment Planning of Radiation Therapy Considering Biological Response



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The goal of radiation therapy for cancer patients is to kill tumor cells by damaging their DNA. For the majority of patients, the prescribed dose is divided into several treatment sessions (fractionated treatment plan) to avoid lethal damage to the surrounding healthy organs called organs at risk (OARs). In conventional practice, the treatment policy is to deliver an equal amount of radiation dose to the patient over multiple treatment sessions. Such an approach neglects different uncertainties associated with tumor dynamics, biological response to radiation, and organ motion that occur during radiation treatment. In this dissertation we are proposing methods to tackle the current challenges and shortcomings in radiotherapy treatment planning.

In the first part of this dissertation, a constrained Partially Observable Markov Decision Process (POMDP) approach is proposed based on an extended biological model of cell survival to incorporate the biological response from the patient in the fractionated radiotherapy plan. A Gompertzian growth function is used to explain dependence of tumor growth rate on its density and shape. The aim of our model is to maximize the expected biological equivalent dose (EBED) of tumor, while keeping the OAR survival under control. Because the condition of a tumor can change and it is not fully observable through CT images during the treatment horizon, POMDP enables us to consider the tumor symptoms through probabilistic belief and partial observation probabilities. We provide a control limit policy to investigate whether there is an advantage of using POMDP over the conventional plan in terms of tumor damage and OAR sparing. Numerical results showed potential impact of the POMDP policies to enhance tumor coverage compared to the conventional plan. The resulting policies suggested the use of a low dose at earlier sessions, and a higher dose at later sessions. This result reflects the impact of tumor density and shape on its growth and biological response. The POMDP policy was not recommended if the tumor was a late responding tissue and its corresponding OAR was an early responding tissue.

Unlike photon, the proton’s linear energy transfer (LET) increases as it penetrates the body. Therefore, proton therapy can be modulated to provide a better biological effectiveness. In the second part of this dissertation, we develop an LET-based IMPT optimization model that guarantees homogeneous biological effectiveness on the tumor structure and minimum damage to the OARs. The outcomes of this model serve as the action set in a constrained MDP framework developed to provide an optimal decision-making policy for dynamic and personalized fractionated proton therapy treatment plans. The tumor state is predicted using a random forest classification model built on radiomics data from CT images. The proposed model is implemented on the two cases of prostate cancer and pediatric ependymoma and compared to a regular IMPT model as the threshold. The results demonstrate that the LET-based IMPT model improves biological effectiveness and tumor control probability (TCP). Randomized MDP policies suggest a smaller dose target for a high tumor cell count where the tumor growth rate is at its lowest value. But as the tumor cell count decreases, a larger amount of dose is suggested to destroy faster growing tumor.

Proton’s unique physical characteristics make proton therapy sensitive to organ motion such that a voxel can receive a nonuniform dose deposition between different fractions. Therefore, biological effectiveness of the treatment might deviate from the planned effectiveness. In the last part of this dissertation we develop a model to optimize the fractionation and IMPT problems at the same time. We use 4DCT data set for planning a 3D delivery technique to handle complex respiratory motion patterns while avoiding sophisticated 4D delivery systems. Two models are used to solve this problem; a statistical mean-variance model, and a robust worst-case model. The worst-case robust model provides a more robust dose distribution over all structures compared to statistical mean-variance model. Both models suggest larger amount of radiation dose in the first week of treatment and gradually decreasing the dose towards the last week. The resulting weekly mean BED is shown to be almost equal in all treatment weeks, compensating for the increased repair effect resulting from nonuniform voxel dose between fractions. Because of conservatism of worst-case robust model, a larger total dose has to be delivered in every treatment week to achieve the same biological effectiveness as statistical mean-variance model.



Radiation therapy, Biological Response, Biological Effectiveness, Personalized Treatment Plan, POMDP, MDP, Radiomics, Motion Uncertainty, 4DCT, Proton LET