As the immune system has a significant role in tumor progression, in this paper, we develop a data-driven mathematical model to study the interactions between immune cells and the osteosarcoma microenvironment. Osteosarcoma tumors are divided into three clusters based on their relative abundance of immune cells as estimated from their gene expression profiles. We then analyze the tumor progression and effects of the immune system on cancer growth in each cluster. Cluster 3, which had approximately the same number of naive and M2 macrophages, had the slowest tumor growth, and cluster 2, with the highest population of naive macrophages, had the highest cancer population at the steady states. We also found that the fastest growth of cancer occurred when the anti-tumor immune cells and cytokines, including dendritic cells, helper T cells, cytotoxic cells, and IFN-$\gamma$, switched from increasing to decreasing, while the dynamics of regulatory T cells switched from decreasing to increasing. Importantly, the most impactful immune parameters on the number of cancer and total cells were the activation and decay rates of the macrophages and regulatory T cells for all clusters. This work presents the first osteosarcoma progression model, which can be later extended to investigate the effectiveness of various osteosarcoma treatments.

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-$\gamma$ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells.

Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we develop a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients, and observe differences in the patterns of tumor growth between the groups. For instance, in tumors with a smaller density of naive macrophages than activated macrophages, a higher activation rate of macrophages leads to an increase in cancer cell density, demonstrating a negative effect of macrophages. Other tumors however, exhibit an opposite trend, showing a positive effect of macrophages in controlling tumor size. Although the results indicate that for all patients the size of the tumor is sensitive to the parameters related to macrophages, such as their activation and death rate, this research demonstrates that no single biomarker could predict the dynamics of tumors.

Since the outcome of treatments, particularly immunotherapeutic interventions, depends on the tumor immune micro-environment (TIM), several experimental and computational tools such as flow cytometry, immunohistochemistry, and digital cytometry have been developed and utilized to classify TIM variations. In this project, we identify immune pattern of clear cell renal cell carcinomas (ccRCC) by estimating the percentage of each immune cell type in 526 renal tumors using the new powerful technique of digital cytometry. The results, which are in agreement with the results of a large-scale mass cytometry analysis, show that the most frequent immune cell types in ccRCC tumors are CD8+ T-cells, macrophages, and CD4+ T-cells. Saliently, unsupervised clustering of ccRCC primary tumors based on their relative number of immune cells indicates the existence of four distinct groups of ccRCC tumors. Tumors in the first group consist of approximately the same numbers of macrophages and CD8+ T-cells and and a slightly smaller number of CD4+ T cells than CD8+ T cells, while tumors in the second group have a significantly high number of macrophages compared to any other immune cell type (P-value $$<0.01$$< 0.01 ). The third group of ccRCC tumors have a significantly higher number of CD8+ T-cells than any other immune cell type (P-value $$<0.01$$< 0.01 ), while tumors in the group 4 have approximately the same numbers of macrophages and CD4+ T-cells and a significantly smaller number of CD8+ T-cells than CD4+ T-cells (P-value $$<0.01$$< 0.01 ). Moreover, there is a high positive correlation between the expression levels of IFNG and PDCD1 and the percentage of CD8+ T-cells, and higher stage and grade of tumors have a substantially higher percentage of CD8+ T-cells. Furthermore, the primary tumors of patients, who are tumor free at the last time of follow up, have a significantly higher percentage of mast cells (P-value $$<0.01$$< 0.01 ) compared to the patients with tumors for all groups of tumors except group 3.

Many colon cancer patients show resistance to their treatments. Therefore, it is important to consider unique characteristic of each tumor to find the best treatment options for each patient. In this study, we develop a data driven mathematical model for interaction between the tumor microenvironment and FOLFIRI drug agents in colon cancer. Patients are divided into five distinct clusters based on their estimated immune cell fractions obtained from their primary tumors’ gene expression data. We then analyze the effects of drugs on cancer cells and immune cells in each group, and we observe different responses to the FOLFIRI drugs between patients in different immune groups. For instance, patients in cluster 3 with the highest T-reg/T-helper ratio respond better to the FOLFIRI treatment, while patients in cluster 2 with the lowest T-reg/T-helper ratio resist the treatment. Moreover, we use ROC curve to validate the model using the tumor status of the patients at their follow up, and the model predicts well for the earlier follow up days.

Since all tumors are unique, they may respond differently to the same treatments. Therefore, it is necessary to study their characteristics individually to find their best treatment options. We built a mathematical model for the interactions between the most common chemotherapy drugs and the osteosarcoma microenvironments of three clusters of tumors with unique immune profiles. We then investigated the effects of chemotherapy with different treatment regimens and various treatment start times on the behaviors of immune and cancer cells in each cluster. Saliently, we suggest the optimal drug dosages for the tumors in each cluster. The results show that abundances of dendritic cells and HMGB1 increase when drugs are given and decrease when drugs are absent. Populations of helper T cells, cytotoxic cells, and IFN-$\gamma$ grow, and populations of cancer cells and other immune cells shrink during treatment. According to the model, the MAP regimen does a good job at killing cancer, and is more effective than doxorubicin and cisplatin combined or methotrexate alone. The results also indicate that it is important to consider the tumor’s unique growth rate when deciding the treatment details, as fast growing tumors need early treatment start times and high dosages.