Prostate cancer is one of the most prevalent cancers in men, with increasing incidence worldwide. This public health concern has inspired considerable effort to study various aspects of prostate cancer treatment using dynamical models, especially in clinical settings. The standard of care for metastatic prostate cancer is hormonal therapy, which reduces the production of androgen that fuels the growth of prostate tumor cells prior to treatment resistance. Existing population models often use patients’ prostate-specific antigen levels as a biomarker for model validation and for finding optimal treatment schedules; however, the synergistic effects of drugs used in hormonal therapy have not been well-examined. This paper describes the first mathematical model that explicitly incorporates the synergistic effects of two drugs used to inhibit androgen production in hormonal therapy. The drugs are cyproterone acetate, representing the drug family of anti-androgens that affect luteinizing hormones, and leuprolide acetate, representing the drug family of gonadotropin-releasing hormone analogs. By fitting the model to clinical data, we show that the proposed model can capture the dynamics of serum androgen levels during intermittent hormonal therapy better than previously published models. Our results highlight the importance of considering the synergistic effects of drugs in cancer treatment, thus suggesting that the dynamics of the drugs should be taken into account in optimal treatment studies, particularly for adaptive therapy. Otherwise, an unrealistic treatment schedule may be prescribed and render the treatment less effective. Furthermore, the drug dynamics allow our model to explain the delay in the relapse of androgen the moment a patient is taken off treatment, which supports that this delay is due to the residual effects of the drugs.

前列腺癌是男性最常见的癌症之一，在世界范围内的发病率呈上升趋势。这种公共卫生问题激发了人们对使用动态模型研究前列腺癌治疗各个方面的巨大努力，尤其是在临床环境中。转移性前列腺癌的护理标准是激素疗法，它可以减少雄激素的产生，而雄激素会在治疗抵抗之前促进前列腺肿瘤细胞的生长。现有的人群模型通常使用患者的前列腺特异性抗原水平作为模型验证和寻找最佳治疗方案的生物标志物；然而，激素治疗中使用的药物的协同作用尚未得到充分检验。本文描述了第一个数学模型，该模型明确地结合了两种用于抑制激素治疗中雄激素产生的药物的协同作用。这些药物是醋酸环丙孕酮（代表影响促黄体生成激素的抗雄激素药物家族）和醋酸亮丙瑞林（代表促性腺激素释放激素类似物的药物家族）。通过将模型拟合到临床数据，我们表明所提出的模型可以比以前发表的模型更好地捕捉间歇性激素治疗期间血清雄激素水平的动态。我们的结果强调了考虑药物在癌症治疗中的协同作用的重要性，因此表明在最佳治疗研究中应考虑药物的动力学，特别是对于适应性治疗。除此以外，可能会开出不切实际的治疗计划并降低治疗效果。此外，药物动力学使我们的模型能够解释患者停止治疗时雄激素复发的延迟，这支持这种延迟是由于药物的残留作用。