To estimate the delivered dose to the patient during intra-fraction or throughout the whole treatment, it is important to determine the contribution of dose accumulated at different patient geometries to the overall dose. Dose mapping utilizes deformable image registration to map doses deposited on patient geometries at different times. Inputs to the dose mapping process are the irradiated and reference images, the displacement vector field, and a dose mapping algorithm. Thus accuracy of the mapped dose depends on the DVF and dose mapping algorithm. Dose mapping had been the subject of many research studies however, up to now there is no gold standard DIR or dose mapping algorithm. This thesis compares current dose mapping algorithms under different conditions such as choosing the planning target and dose grid size, and introduces new tool to estimate the required spatial accuracy of a DVF. 11 lung patients were used for this thesis work. IMRT plans were generated on the end of inhale breathing phases with 66 Gy as the prescription dose. Demons DVF’s were generated using the Pinnacle treatment planning system DIR interface. Dtransform, Tri-linear with sub-voxel division, and Pinnacle dose mapping algorithms were compared to energy transfer with mass sub-voxel mapping. For breathing phase 50% on 11 patients, tissue density gradients were highest around the edge of the tumor compared to the CTV and the PTV edge voxels. Thus treatment plans generated with margin equal to zero on the tumor might yield the highest dose mapping error (DME). For plans generated on the tumor, there was no clinical effect of DME on the MLD, lung V20, and Esophagus volume indices. Statistically, MLD and lung V20 DME were significant. Two patients had D98 Pinnacle-DME of 4.4 and 1.2 Gy. In high dose gradient regions DVF spatial accuracy of ~ 1 mm is needed while 8 to 10 mm DVF accuracy can be tolerated before introducing any considerable dose mapping errors inside the CTV. By using ETM with mass sub-voxel mapping and adapting the reported DVF accuracy, the findings of this thesis have the potential to increase the accuracy of 4D lung planning.

Modern big data often emerge as tensors. Standard statistical methods are inadequate to deal with datasets of large volume, high dimensionality, and complex structure. Therefore, it is important to develop algorithms such as low-rank tensor decomposition for data compression, dimensionality reduction, and approximation. With the advancement in technology, high-dimensional images are becoming ubiquitous in the medical field. In lung radiation therapy, the respiratory motion of the lung introduces variabilities during treatment as the tumor inside the lung is moving, which brings challenges to the precise delivery of radiation to the tumor. Several approaches to quantifying this uncertainty propose using a model to formulate the motion through a mathematical function over time. [Li et al., 2011] uses principal component analysis (PCA) to propose one such model using each image as a long vector. However, the images come in a multidimensional arrays, and vectorization breaks the spatial structure. Driven by the needs to develop low-rank tensor decomposition and provided the 4DCT and Displacement Vector Field (DVF), we introduce two tensor decompositions, Population Value Decomposition (PVD) and Population Tucker Decomposition (PTD), to estimate the respiratory lung motion with high levels of accuracy and data compression. The first algorithm is a generalization of PVD [Crainiceanu et al., 2011] to higher order tensor. The second algorithm generalizes the concept of PVD using Tucker decomposition. Both algorithms are tested on clinical and phantom DVFs. New metrics for measuring the model performance are developed in our research. Results of the two new algorithms are compared to the result of the PCA algorithm.