The incidence of cancers varies with age, if normalized this is called the age-specific incidence. A mathematical model that describes this variation should provide a better understanding of how cancers develop. We suggest that the age-specific incidence should follow an extreme value distribution, based on three widely accepted assumptions: (1) a tumor develops from a single cell, (2) many potential tumor progenitor cells exist in a tissue, and (3) cancer is diagnosed when the first of these many potential tumor cells develops into a tumor. We tested this by comparing the predicted distribution to the age-specific incidence data for colon and prostate carcinomas collected by the Surveillance, Epidemiology and End Results network of 17 cancer registries. We found that colon carcinoma age-specific incidence data is consistent with an extreme value distribution, while prostate carcinomas age-specific incidence data generally follows the distribution. This model indicates that both colon and prostate carcinomas only occur in a subset of the population (22% for prostate and 13.5% for colon.) Because of their very general nature, extreme value distributions might be applicable to understanding other chronic human diseases.

A mathematical model integrating tumor angiogenesis and tumor-targeted cytotoxicity by immune cells was developed to identify the therapeutic window of two distinct modes to treat cancer: (1) an anti-angiogenesis treatment based on the monoclonal antibody bevacizumab that targets tumor vasculature, and (2) immunotherapy involving the injection of unlicensed dendritic cells to boost the anti-tumor adaptive response. The angiogenic cytokine Vascular Endothelial Growth Factor (VEGF) contributes to the immunosuppressive tumor microenvironment, which is responsible for the short-lived therapeutic effect of cancer-targeted immunotherapy. The effect of immunosuppression on the width of the therapeutic window of each treatment was quantified. Experimental evidence has shown that neutralizing immunosuppressive cytokines results in an enhanced immune response against infections and chronic diseases. The model was used to determine treatment protocols involving the combination of anti-VEGF and unlicensed dendritic cell injections that enhance tumor regression. The model simulations predicted that the most effective method to treat tumors involves administering a series of biweekly anti-VEGF injections to disrupt angiogenic processes and limit tumor growth. The simulations also verified the hypothesis that reducing the concentration of the immunosuppressive factor VEGF prior to an injection of unlicensed dendritic cells enhances the cytotoxicity of CD8+ T cells and results in complete tumor elimination. Feasible treatment protocols for tumors that are diagnosed late and have grown to a relatively large size were identified.

Positive feedback loops drive immune cell polarization toward a pro-tumor phenotype that accentuates immunosuppression and tumor angiogenesis. This phenotypic switch leads to the escape of cancer cells from immune destruction. These positive feedback loops are generated by cytokines such as TGF-β, Interleukin-10 and Interleukin-4, which are responsible for the polarization of monocytes and M1 macrophages into pro-tumor M2 macrophages, and the polarization of naive helper T cells intopro-tumor Th2 cells. In this article, we present a deterministic ordinary differential equation (ODE) model that includes key cellular interactions and cytokine signaling pathways that lead to immune cell polarization in the tumor microenvironment. The model was used to simulate various cancer treatments in silico. We identified combination therapies that consist of M1 macrophages or Th1 helper cells, coupled with an anti-angiogenic treatment, that are robust with respect to immune response strength, initial tumor size and treatment resistance. We also identified IL-4 and IL-10 as the targets that should be neutralized in order to make these combination treatments robust with respect to immune cell polarization. The model simulations confirmed a hypothesis based on published experimental evidence that a polarization into the M1 and Th1 phenotypes to increase the M1-to-M2 and Th1-to-Th2 ratios plays a significant role in treatment success. Our results highlight the importance of immune cell reprogramming as a viable strategy to eradicate a highly vascularized tumor when the strength of the immune response is characteristically weak and cell polarization to the pro-tumor phenotype has occurred. [8] [9] [10] [11]. The high proportion of M2 macrophages and Th2 helper cells in the tumor microenvironment makes them an important target of cancer therapies [12] [13] [14] [15] [16]. Positive Feedback Loops Perpetuate Cell PolarizationA tumor is a complex dynamical system, and its survival depends on a diverse set of signaling networks characterized by cytokine-driven positive feedback loops that can reinforce the anti-tumor phenotype or the pro-tumor phenotype of tumor-infiltrating immune cells. For example, M1 macrophages secrete IL-12 which leads to the differentiation of immature helper T cells into Th1 cells. Th1 cells secrete IFN-ϒ which reinforces the M1 macrophage phenotype. This positive feedback loop perpetuates the M1 and Th1 anti-tumor polarization of these cells, which can lead to tumor destruction. On the other hand, M2 macrophages secrete IL-4 and IL-6 [17], [18] which lead to the differentiation of immature helper T cells into Th2 cells. Th2 cells secrete which reinforces the M2 macrophage phenotype. This positive feedback loop perpetuates the M2 and Th2 pro-tumor polarization, leading to tumor escape. More complex immune cell interactions exist. M2 macrophages and Th2 cells secrete TGF-β which converts naïve helper T cells into pro-tumor regulatory T cells (Tregs) [20] and B cells into pro-tumor regulatory B cells (Bregs). Tre...

Colon cancers are thought to be an inevitable result of aging, while testicular cancers are thought to develop in only a small fraction of men, beginning in utero. These models of carcinogenesis are, in part, based upon age-specific incidence data. The specific incidence for colon cancer appears to monotonically increase with age, while that of testicular cancer increases to a maximum value at about 35 years of age, then declines to nearly zero by the age of 80. We hypothesized that the age-specific incidence for these two cancers is similar; the apparent difference is caused by a longer development time for colon cancer and the lack of age-specific incidence data for people over 84 years of age. Here we show that a single distribution can describe the age-specific incidence of both colon carcinoma and testicular cancer. Furthermore, this distribution predicts that the specific incidence of colon cancer should reach a maximum at about age 90 and then decrease. Data on the incidence of colon carcinoma for women aged 85–99, acquired from SEER and the US Census, is consistent with this prediction. We conclude that the age specific data for testicular cancers and colon cancers is similar, suggesting that the underlying process leading to the development of these two forms of cancer may be similar.

In the past, the age-specific incidence of most forms of cancer was widely thought to increase monotonically with age. However, cancer registry data show that the specific incidence for many forms of cancer increases with age, reaches a maximum, and then decreases. At least two hypotheses have been proposed to explain this decrease: the cell senescence hypothesis and the frailty hypothesis. The objective of our work was to formulate a stochastic model of cancer incidence to estimate the lifetime-independent odds ratio (LIOR) measuring the risk of developing a second primary cancer, conditioned on a first cancer diagnosis, relative to the risk of developing a first primary cancer, in two artificial populations: one where cancer susceptibility is universal and one where only a small proportion of individuals are born susceptible, or frail, to developing one or more cancers. The predicted LIOR values were significantly greater than 1, only