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.

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells’ location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells’ diffusion and immune cells’ influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes’ diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

The intricate network of interactions between cells and molecules in the tumor microenvironment creates a heterogeneous ecosystem. The proximity of the cells and molecules to their activators and inhibitors is essential in the progression of tumors. Here, we develop a system of partial differential equations coupled with linear elasticity to investigate the effects of spatial interactions on the tumor microenvironment. We observe interesting cell and cytokine distribution patterns, which are heavily affected by macrophages. We also see that cytotoxic T cells get recruited and suppressed at the site of macrophages. Moreover, we observe that anti-tumor macrophages reorganize the patterns in favor of a more spatially restricted cancer and necrotic core. Furthermore, the adjoint-based sensitivity analysis indicates that the most sensitive model’s parameters are directly related to macrophages. The results emphasize the widely acknowledged effect of macrophages in controlling cancer cells population and spatially arranging cells in the tumor microenvironment.

The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model’s parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies.

Recent studies have reported increases in early-onset cancer cases (diagnosed less than 50 years of age) and raised questions about whether the increase is related to earlier diagnosis from nonspecific medical tests as reflected by decreasing tumor-size-at-diagnosis (apparent effects) or actual increases in underlying cancer risk (true effects), or both. The classic Multistage Clonal Expansion (MSCE) model assumes cancer detection at the first malignant cell’s emergence, although later modifications have included lag-times or stochasticity in detection to represent the delay in tumor detection. In this study, we introduced an approach to explicitly incorporate tumor-size-at-diagnosis in the MSCE framework accounting for improvements in cancer detection over time to distinguish between apparent and true increases in early-onset cancer incidence. The model was structurally identifiable and provided better parameter estimation than the classic model. The model was applied to colorectal, breast, and thyroid cancers to examine changes in cancer risk while accounting for detection improvements over time in three representative birth cohorts (1950–1954, 1965–1969, and 1980–1984). The analyses suggested accelerated carcinogenic events and shorter mean sojourn times (the average time from the first malignant cell emergence to cancer detection) in more recent cohorts. Furthermore, using this model to examine the screening impact on the incidence of breast and colorectal cancers, for which both have established screening protocols, provided results that align with well-documented differences in screening effects between these cancers. These findings underscore the importance of incorporating tumor-size-at-diagnosis in cancer modeling and support true increases in early-onset cancer risk in recent years for breast, colorectal, and thyroid cancers. Significance: A model of early-onset cancer trends that distinguishes true risk from detection effects accurately captures cancer kinetics, trends in cancer progression, and the impact of screening, which could inform cancer prevention strategies. This article is part of a special series: Driving Cancer Discoveries with Computational Research, Data Science, and Machine Learning/AI .

Osteosarcoma is the most common malignant bone tumor in children and adolescents with a poor prognosis. To describe the progression of osteosarcoma, we expanded a system of data-driven ODE from a previous study into a system of Reaction-Diffusion-Advection (RDA) equations and coupled it with Biot equations of poroelasticity to form a bio-mechanical model. The RDA system includes the spatio-temporal information of the key components of the tumor microenvironment. The Biot equations are comprised of an equation for the solid phase, which governs the movement of the solid tumor, and an equation for the fluid phase, which relates to the motion of cells. The model predicts the total number of cells and cytokines of the tumor microenvironment and simulates the tumor’s size growth. We simulated different scenarios using this model to investigate the impact of several biomedical settings on tumors’ growth. The results indicate the importance of macrophages in tumors’ growth. Particularly, we have observed a high co-localization of macrophages and cancer cells, and the concentration of tumor cells increases as the number of macrophages increases.