Background: Androgens bind to the androgen receptor (AR) in prostate cells and are essential survival factors for healthy prostate epithelium. Most untreated prostate cancers retain some dependence upon the AR and respond, at least transiently, to androgen ablation therapy. However, the relationship between endogenous androgen levels and cancer etiology is unclear. High levels of androgens have traditionally been viewed as driving abnormal proliferation leading to cancer, but it has also been suggested that low levels of androgen could induce selective pressure for abnormal cells. We formulate a mathematical model of androgen regulated prostate growth to study the effects of abnormal androgen levels on selection for pre-malignant phenotypes in early prostate cancer development.

Results: We find that cell turnover rate increases with decreasing androgen levels, which may increase the rate of mutation and malignant evolution. We model the evolution of a heterogeneous prostate cell population using a continuous state-transition model. Using this model we study selection for AR expression under different androgen levels and find that low androgen environments, caused either by low serum testosterone or by reduced 5α-reductase activity, select more strongly for elevated AR expression than do normal environments. High androgen actually slightly reduces selective pressure for AR upregulation. Moreover, our results suggest that an aberrant androgen environment may delay progression to a malignant phenotype, but result in a more dangerous cancer should one arise.

Conclusions: The model represents a useful initial framework for understanding the role of androgens in prostate cancer etiology, and it suggests that low androgen levels can increase selection for phenotypes resistant to hormonal therapy that may also be more aggressive. Moreover, clinical treatment with 5α-reductase inhibitors such as finasteride may increase the incidence of therapy resistant cancers.

Background: Doxorubicin is a common anticancer agent used in the treatment of a number of neoplasms, with the lifetime dose limited due to the potential for cardiotoxocity. This has motivated efforts to develop optimal dosage regimes that maximize anti-tumor activity while minimizing cardiac toxicity, which is correlated with peak plasma concentration. Doxorubicin is characterized by poor penetration from tumoral vessels into the tumor mass, due to the highly irregular tumor vasculature. I model the delivery of a soluble drug from the vasculature to a solid tumor using a tumor cord model and examine the penetration of doxorubicin under different dosage regimes and tumor microenvironments.

Methods: A coupled ODE-PDE model is employed where drug is transported from the vasculature into a tumor cord domain according to the principle of solute transport. Within the tumor cord, extracellular drug diffuses and saturable pharmacokinetics govern uptake and efflux by cancer cells. Cancer cell death is also determined as a function of peak intracellular drug concentration.

Results: The model predicts that transport to the tumor cord from the vasculature is dominated by diffusive transport of free drug during the initial plasma drug distribution phase. I characterize the effect of all parameters describing the tumor microenvironment on drug delivery, and large intercapillary distance is predicted to be a major barrier to drug delivery. Comparing continuous drug infusion with bolus injection shows that the optimum infusion time depends upon the drug dose, with bolus injection best for low-dose therapy but short infusions better for high doses. Simulations of multiple treatments suggest that additional treatments have similar efficacy in terms of cell mortality, but drug penetration is limited. Moreover, fractionating a single large dose into several smaller doses slightly improves anti-tumor efficacy.

Conclusion: Drug infusion time has a significant effect on the spatial profile of cell mortality within tumor cord systems. Therefore, extending infusion times (up to 2 hours) and fractionating large doses are two strategies that may preserve or increase anti-tumor activity and reduce cardiotoxicity by decreasing peak plasma concentration. However, even under optimal conditions, doxorubicin may have limited delivery into advanced solid tumors.