Abstract
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.
Highlights
The past 20 years have seen an accelerating development of mathematical models for prostate cancer
Mathematical models play a vital role in the study of prostate cancer dynamics
Is superior to continuous androgen suppression therapy (CAS) at delaying the relapse of metastasized cancer, if androgen dependent (AD) cells have some competitive advantages over androgen independent (AI) cells in an androgen-rich environment
Summary
The past 20 years have seen an accelerating development of mathematical models for prostate cancer. One reason is the success of earlier work to explain and replicate experimental and clinical data. Another reason is the availability of experimental and clinical data due to collaborations with physicians and advancements in technology. Far, modeling efforts have utilized a broad range of model types and methods to uncover some fundamentals about prostate cancer progression and the efficacy of its treatments. Sci. 2020, 10, 2721 of these results, perhaps due to each modeling effort being somewhat independent of the others. We systematically synthesize existing results and summarize general limitations from mathematical modeling work relating to prostate cancer
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