化疗通常用于治疗前列腺癌晚期，即癌细胞已经扩散到前列腺腺体外。该治疗使用细胞毒药物来针对快速生长和分裂的细胞。另一方面，这种癌症肿瘤的生长取决于血管生成。本文在与前列腺癌治疗相关的二维空间中对弥散界面模型进行了数字研究。提出的模型描述了由普通营养物抑制的肿瘤生长和产生前列腺特异性抗原。更确切地说，该模型中细胞毒化疗的效应是通过考虑肿瘤动力学中的时间相关函数来评估的。同时，考虑到另一个与抗血管生成治疗相关的函数，以展示营养物动力学中肿瘤内部营养供应的减少。在这里，我们提出了一种无网格逼近方法，即直接径向基函数的分段加权（D-RBF-PU）方法的广义形式，用于在医学肿瘤学中运用该模型的数值模拟。该方法利用每个补丁中较少的试点数来逼近每个测试点的试验函数。因此，该方法的时间复杂度小于D-RBF-PU技术。此外，采用了一阶半隐式时间离散化来处理时间变量。因此，通过使用零填充不完整三角分解预处理的双共轭梯度稳定方法，可迭代地解决每个时间步长的线性代数方程组。最终，在不使用任何自适应算法的情况下获得的结果展示了前列腺肿瘤对化疗、抗血管生成治疗和联合治疗的反应。版权所有©2023 Elsevier Ltd。保留所有权利。

Chemotherapy is usually applied to treat advanced prostate cancer that cancer cells spread outside the prostate gland. The treatment uses cytotoxic drugs to target cells that grow and divide quickly. On the other hand, the growth of such cancerous tumors depends on angiogenesis. In this paper, we numerically study a diffuse-interface model in a two-dimensional space related to the therapies of prostate cancer. The proposed model describes the tumor growth driven by a generic nutrient and producing the prostate-specific antigen. More precisely, the effect of cytotoxic chemotherapy in the model is evaluated by considering a time-dependent function in the tumor dynamics. Also, another function related to the antiangiogenic therapy is considered to show the reducing intratumoral nutrient supply in the nutrient dynamics. Here, a meshless approximation, i.e., a generalized form of the direct radial basis function partition of unity (D-RBF-PU) method is presented for finding the numerical simulations of this model utilizing in medical oncology. The method uses the lower number of trial points in each patch than the original D-RBF-PU scheme for approximating the trial function per test point. Hence, the time complexity of the method is less than the D-RBF-PU technique. Besides, a semi-implicit time discretization of order 1 has been used to deal with the time variable. Consequently, a linear system of algebraic equations could be solved iteratively per time step by the use of the biconjugate gradient stabilized method with zero-fill incomplete lower-upper preconditioner. Finally, the obtained results without using any adaptive algorithm demonstrate the response of the prostate tumor growth to the chemotherapy, antiangiogenic therapy and a combined therapy.Copyright © 2023 Elsevier Ltd. All rights reserved.