Kuang, Yang

We review and synthesize key findings and limitations of mathematical models for prostate cancer, both from theoretical work and data-validated approaches, especially concerning clinical applications. Our focus is on models of prostate cancer dynamics under treatment, particularly with a view toward optimizing hormone-based treatment schedules and estimating the onset of treatment resistance under various assumptions. Population models suggest that intermittent or adaptive therapy is more beneficial to delay cancer relapse as compared to the standard continuous therapy if treatment resistance comes at a competitive cost for cancer cells. Another consensus among existing work is that the standard biomarker for cancer growth, prostate-specific antigen, may not always correlate well with cancer progression. Instead, its doubling rate appears to be a better indicator of tumor growth. Much of the existing work utilizes simple ordinary differential equations due to difficulty in collecting spatial data and due to the early success of using prostate-specific antigen in mathematical modeling. However, a shift toward more complex and realistic models is taking place, which leaves many of the theoretical and mathematical questions unexplored. Furthermore, as adaptive therapy displays better potential than existing treatment protocols, an increasing number of studies incorporate this treatment into modeling efforts. Although existing modeling work has explored and yielded useful insights on the treatment of prostate cancer, the road to clinical application is still elusive. Among the pertinent issues needed to be addressed to bridge the gap from modeling work to clinical application are (1) real-time data validation and model identification, (2) sensitivity analysis and uncertainty quantification for model prediction, and (3) optimal treatment/schedule while considering drug properties, interactions, and toxicity. To address these issues, we suggest in-depth studies on various aspects of the parameters in dynamical models such as the evolution of parameters over time. We hope this review will assist future attempts at studying prostate cancer.

353 Background: One mechanism leading to castrate-resistant prostate cancer (CRPC) is upregulation of CYP17. Abiraterone acetate (AA) inhibits CYP17 and continuous AA administration (CAAA) is one the most common and effective CRPC treatments. Mathematical models can be potentially powerful clinical tools for optimizing treatment strategies and eliminating guess work. Here, we introduce a new model which builds on our previous work (Morken JD, Packer A, Everett RA, Nagy JD, Kuang Y. Mechanisms of resistance to intermittent androgen deprivation therapy identified in prostate cancer patients by novel computational method. Cancer Res 2014;74:2673-83.) and may be capable of predicting how patients will respond to CAAA and intermittent AA administration (IAAA). We are currently proposing a personalized IAAA protocol on the basis of these results. Methods: In this ongoing retrospective study, we use PSA data from patients whom underwent CAAA to validate the accuracy of our model of tumor growth and evolution. The PSA output is driven by dynamics of three cell populations—castration-sensitive (CS), castration-resistant abiraterone-sensitive (CSAS), and castration-sensitive abiraterone-resistant (CSAR) cells. We fit the model output to PSA data to find parameter values which minimize normalized mean squared error (NMSE). Once parameters are obtained, we ran simulations employing various IAAA protocols. Results: The model’s PSA dynamics are highly accurate. NMSE is very low across patients ranging from 0.0001-0.0085. Conclusions: Our results suggest that there exists an IAAA protocol for each patient that, at worst, yields the same time to tumor progression as CAAA, yet improves quality of life and reduces cost. In nearly 20% of patients, IAAA appears to delay tumor progression over CAAA. The model is accurate at predicting how patients will respond to CAAA and IAAA for patients whose PSA is regularly monitored. Near-future work aims to personalize IAAA protocol based on patient pre CRPC PSA dynamics and to identify a protocol which delays progression for most patients.