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Author ORCID Identifier


Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Leili Shahriyari

Subject Categories

Applied Mathematics | Dynamic Systems | Physical Sciences and Mathematics


Cancer is a complex disease where every tumor has its own characteristics, and thus different tumors may respond differently to the same treatments. Osteosarcoma, which is a rare type of cancer with poor prognosis, is especially characterized by its high heteogeneity. Therefore, it is important to study the progression of osteosarcoma tumors in different groups of patients with distinct characteristics. The immune system has been reported to play an important role in the development of various cancers with some immune cells having anti-tumor effects and others having pro-tumor effects. With recent advances in digital cytometry methods, which are techniques to estimate the fractions of various cell types from gene expression data of a bulk of cells, it became possible to obtain relative abundance of immune cells in tumors. In this project, we review common digital cytometry methods, compare their performances and report the best method. We apply this best performing digital cytometry method to estimate abundance of immune cells in osteosarcoma tumors, and perform clustering using the estimated immune fractions to find groups of tumors with distinct immune compositions. We then model the growth of osteosarcoma tumors in each group while taking into account the interactions between immune cells and cancer cells. Lastly, we investigate the effects of adding chemotherapy on the progression of osteosarcoma, find the optimal chemotherapy dosages for tumors in each cluster, and compare the behaviors of immune and cancer cells under several conditions such as different treatment regimens and various treatment start times.