Chemotherapy is a common treatment for advanced prostate cancer. The standard approach relies on cytotoxic drugs, which aim at inhibiting proliferation and promoting cell death. Advanced prostatic tumors are known to rely on angiogenesis, i.e. the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical studies have been investigating antiangiogenic therapy for advanced prostate cancer, either as monotherapy or in combination with standard cytotoxic protocols. However, the complex genetic alterations that originate and sustain prostate cancer growth complicate the selection of the best chemotherapeutic approach for each patient’s tumor. Here, we present a mathematical model of prostate cancer growth and chemotherapy that may enable physicians to test and design personalized chemotherapeutic protocols in silico. We use the phase-field method to describe tumor growth, which we assume to be driven by a generic nutrient following reaction–diffusion dynamics. Tumor proliferation and apoptosis (i.e. programmed cell death) can be parameterized with experimentally-determined values. Cytotoxic chemotherapy is included as a term downregulating tumor net proliferation, while antiangiogenic therapy is modeled as a reduction in intratumoral nutrient supply. An additional equation couples the tumor phase field with the production of prostate-specific antigen, which is a prostate cancer biomarker that is extensively used in the clinical management of the disease. We prove the well posedness of our model and we run a series of representative simulations leveraging an isogeometric method to explore untreated tumor growth as well as the effects of cytotoxic chemotherapy and antiangiogenic therapy, both alone and combined. Our simulations show that our model captures the growth morphologies of prostate cancer as well as common outcomes of cytotoxic and antiangiogenic mono therapy and combined therapy. Additionally, our model also reproduces the usual temporal trends in tumor volume and prostate-specific antigen evolution observed in experimental and clinical studies.

中文翻译：

---

具有化疗和抗血管生成作用的前列腺癌生长相场模型的数学分析和模拟研究

化疗是晚期前列腺癌的常见治疗方法。标准方法依赖于旨在抑制增殖和促进细胞死亡的细胞毒性药物。已知晚期前列腺肿瘤依赖于血管生成，即通过肿瘤产生的化学信号传导局部微脉管系统的生长。因此，一些临床研究一直在研究晚期前列腺癌的抗血管生成疗法，无论是作为单一疗法还是与标准细胞毒性方案相结合。然而，起源和维持前列腺癌生长的复杂基因改变使为每个患者的肿瘤选择最佳化疗方法变得复杂。这里，我们提出了一个前列腺癌生长和化疗的数学模型，可以让医生在计算机上测试和设计个性化的化疗方案。我们使用相场方法来描述肿瘤生长，我们假设它是由反应扩散动力学后的通用营养素驱动的。肿瘤增殖和凋亡（即程序性细胞死亡）可以用实验确定的值参数化。细胞毒性化学疗法被包括作为下调肿瘤净增殖的术语，而抗血管生成疗法被建模为减少肿瘤内营养供应。另一个方程将肿瘤相位场与前列腺特异性抗原的产生相结合，这是一种广泛用于疾病临床管理的前列腺癌生物标志物。我们证明了我们模型的良好定性，并利用等几何方法进行了一系列具有代表性的模拟，以探索未经治疗的肿瘤生长以及细胞毒性化疗和抗血管生成治疗的效果，无论是单独的还是联合的。我们的模拟表明，我们的模型捕获了前列腺癌的生长形态以及细胞毒性和抗血管生成单一疗法和联合疗法的常见结果。此外，我们的模型还重现了在实验和临床研究中观察到的肿瘤体积和前列腺特异性抗原进化的通常时间趋势。我们的模拟表明，我们的模型捕获了前列腺癌的生长形态以及细胞毒性和抗血管生成单一疗法和联合疗法的常见结果。此外，我们的模型还重现了在实验和临床研究中观察到的肿瘤体积和前列腺特异性抗原进化的通常时间趋势。我们的模拟表明，我们的模型捕获了前列腺癌的生长形态以及细胞毒性和抗血管生成单一疗法和联合疗法的常见结果。此外，我们的模型还重现了在实验和临床研究中观察到的肿瘤体积和前列腺特异性抗原进化的通常时间趋势。