Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

Everett, Rebecca A.; Packer, Aaron; Kuang, Yang

doi:10.1142/s1793048014300023

Cited by 27 publications

(19 citation statements)

References 25 publications

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“…Furthermore, mathematical models can range wildly in their complexity, which may result in either highly unrealistic or mathematically and computationally untractable models. There have been numerous reviews of the growing literature on mathematical oncology in the past 15 years [15,[23][24][25][26]. However, none of these reviews exclusively and extensively cover mathematical models for prostate cancer.…”

Section: Mathematical Models For Prostate Cancermentioning

confidence: 99%

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

et al. 2020

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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].

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Section: Mathematical Models For Prostate Cancermentioning

confidence: 99%

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

et al. 2020

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“…Droop's equations govern the growth rate of cancer cells [27], where µ represents the maximum cell growth rate and q the minimum concentration of androgen to sustain the tumor. Similar to [28], we assume an androgen-dependent death rate, where R denotes the half saturation level. However, we also assume a time dependent maximum baseline death rate ν , which decreases exponentially at rate d to reflect the cell castration-resistance development due to the decreasing death rate.…”

Section: Model 1: Single Population Modelmentioning

confidence: 99%

“…This implies that when tumor volume is near zero, the steady state of PSA given by: The half-saturation variables K, R, R1, and R2 are estimated from [28]. Table 1 shows definitions, ranges, units, and sources for each of the parameters in our models.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…We implemented the method used by Portz et al [13] for generating future androgen levels by generating a rectangular function based on the average off and on-treatment serum androgen values. Parameter ranges were taken from PKN [13] and Everett et al [28], and the reader is referred to these papers for more details on forecasting serum PSA levels and parameter values of the PKN model. For every patient selected, we fitted 1.5 cycles of treatment and performed parameter estimation.…”

Section: Comparison Of Modelsmentioning

confidence: 99%

“…This model is carefully fitted with clinical prostate-specific antigen (PSA) data, where androgen data was used to model the cell quota and other growth parameters. Everett et al [28] compared the models of Hirata et al [14] and PKN [13] regarding their accuracy of fitting clinical data and predicting future PSA levels. They concluded that while a biologically-based model is important to reveal the underlying processes and my present more robust and better predictions, a simpler model such as that of Hirata et al might also be practical for fitting clinical data and predicting future PSA outcomes of individual patients.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Models of Androgen Resistance in Prostate Cancer Patients under Intermittent Androgen Suppression Therapy

Báez

Kuang

2016

Applied Sciences

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Abstract:Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). We accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). While these models are simplifications of a previously published model, they fit data with similar accuracy and improve forecasting results. Both models describe the progression of androgen resistance. Although Model 1 is simpler than the more realistic Model 2, it can fit clinical data to a greater precision. However, we found that Model 2 can forecast future PSA levels more accurately. These findings suggest that including more realistic mechanisms of androgen dynamics in a two population model may help androgen resistance timing prediction.

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