Review: Mathematical Modeling of Prostate Cancer and Clinical Application

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.Prostate cancer (PCa) is the leading cause of cancer in US men (behind non-melanoma skin cancers), as well as the second leading cause of cancer-related mortality in men. The American Cancer Society estimates that in 2020, 191,930 Americans will be diagnosed with prostate cancer, with approximately 21.5% of all new cancer cases in men. The average five-year survival rate for all cases of prostate cancer is about 99%, which is a 31% point higher than in the 1970s [1]. However, once cancer metastasizes, the five-year survival rate drops to 30%, an increase of 10 percentage-point compared to the 1970s [2]. While the incidence of prostate cancer in the US is decreasing (see Figure 1), one possible cause is doctors' discouragement of early PCa diagnosis due to the fear of overtreating cancer. Globally, the incidence of prostate cancer is increasing, especially among developing nations [3].

A QSP model of prostate cancer immunotherapy to identify effective combination therapies

“…In this study, we developed a new mathematical model of PCa to predict effective combination immunotherapies. Compared with the existing PCa models 46,59,[76][77][78][79][80][81] , we included more mechanistic details about the tumor microenvironment. These extensions allowed us to test different types of immunotherapy and obtain a comprehensive view of the treatment effects.…”

Combination therapy for mCRPC with immune checkpoint inhibitors, ADT and vaccine: A mathematical model

“…Monotherapy with anti-CTLA-4 or anti-PD-1 in clinical trials did not improve tumor growth in most cases. Mathematical models of prostate cancer that consider treatment with androgen deprivation are reviewed in a number of papers (e.g., [ 50 – 52 ]); models with intermittent androgen ablation strategies aimed to reduce androgen resistance were developed in [ 50 , 53 ], where additional references are given.…”

Personalized Immunotherapy Treatment Strategies for a Dynamical System of Chronic Myelogenous Leukemia

“…Mathematical modelling through first-order Ordinary Differential Equations (ODEs) has been a powerful tool in understanding cancer evolution for nearly fifty years [ 7 , 8 , 9 , 10 ]. As computer performance continues to grow at more affordable costs [ 11 ], the so-called in silico experimentation begins to play a larger role in understanding cancer biology.…”

“…Further, one may include in these models the constantly evolving survival mechanisms of cancer cells, the immune system response, and the application of cancer therapies such as chemotherapy, immunotherapy, and cancer vaccines, among others. Cell–cell interaction models suggest that intermittent therapy is more beneficial to delay cancer relapse as compared to the standard continuous therapy [ 10 ].…”