论文标题

对前列腺癌生长的细胞毒性和抗血管生成疗法的最佳控制

Optimal control of cytotoxic and antiangiogenic therapies on prostate cancer growth

论文作者

Colli, Pierluigi, Gomez, Hector, Lorenzo, Guillermo, Marinoschi, Gabriela, Reali, Alessandro, Rocca, Elisabetta

论文摘要

前列腺癌在晚期阶段可能是致命的,对于这种癌症,化学疗法可能成为唯一可行的治疗选择。尽管没有适合所有患者的明确临床管理策略,但目前使用多西他赛的细胞毒性化学疗法被视为黄金标准。然而,肿瘤在治疗结论后可能会恢复活性并对多西他赛具有抵抗力。这种情况要求采用新的分娩策略和药物化合物,从而可以改善治疗结果。多西他赛与抗血管生成疗法的结合已被认为是一种有前途的策略。贝伐单抗是最常见的抗血管生成药物,但临床研究并未揭示其与多西他赛的结合有明显的好处。在这里,我们利用了先前的关于经过细胞毒性和抗血管生成疗法的前列腺癌生长的数学建模的工作,并提出了一个最佳控制框架,以鲁棒地计算药物独立的细胞毒性和抗血管生成效应,从而实现肿瘤动力学的最佳治疗疗法。我们描述了最佳控制问题的公式,为此我们证明了至少解决方案的存在,并确定必要的一阶最佳条件。然后,我们基于等几何分析提出数值算法,以在单个联合治疗周期内进行初步模拟研究。我们的结果表明,仅需要细胞毒性化学疗法才能优化治疗性能,我们表明我们的框架可以与多西他赛和贝伐单抗结合疗法,从而产生较高的溶液。我们还说明了这些模拟中计算的最佳药物的细胞毒性如何通过运行涉及多西他赛和新设计药物的方案的非线性最小二乘拟合度来成功地指导药物生产和输送策略。

Prostate cancer can be lethal in advanced stages, for which chemotherapy may become the only viable therapeutic option. While there is no clear clinical management strategy fitting all patients, cytotoxic chemotherapy with docetaxel is currently regarded as the gold standard. However, tumors may regain activity after treatment conclusion and become resistant to docetaxel. This situation calls for new delivery strategies and drug compounds enabling an improved therapeutic outcome. Combination of docetaxel with antiangiogenic therapy has been considered a promising strategy. Bevacizumab is the most common antiangiogenic drug, but clinical studies have not revealed a clear benefit from its combination with docetaxel. Here, we capitalize on our prior work on mathematical modeling of prostate cancer growth subjected to combined cytotoxic and antiangiogenic therapies, and propose an optimal control framework to robustly compute the drug-independent cytotoxic and antiangiogenic effects enabling an optimal therapeutic control of tumor dynamics. We describe the formulation of the optimal control problem, for which we prove the existence of at least a solution and determine the necessary first order optimality conditions. We then present numerical algorithms based on isogeometric analysis to run a preliminary simulation study over a single cycle of combined therapy. Our results suggest that only cytotoxic chemotherapy is required to optimize therapeutic performance and we show that our framework can produce superior solutions to combined therapy with docetaxel and bevacizumab. We also illustrate how the optimal drug-naïve cytotoxic effects computed in these simulations may be successfully leveraged to guide drug production and delivery strategies by running a nonlinear least-square fit of protocols involving docetaxel and a new design drug.

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