More than eighty percent of pancreatic cancer involves ductal adenocarcinoma with an abundant desmoplastic extracellular matrix surrounding the solid tumor entity. This aberrant tumor microenvironment facilitates a strong resistance of pancreatic cancer to medication. Although various therapeutic strategies have been reported to be effective in mice with pancreatic cancer, they still need to be tested quantitatively in wider animal-based experiments before being applied as therapies. To aid the design of experiments, we develop a cell-based mathematical model to describe cancer progression under therapy with a specific application to pancreatic cancer. The displacement of cells is simulated by solving a large system of stochastic differential equations with the Euler–Maruyama method. We consider treatment with the PEGylated drug PEGPH20 that breaks down hyaluronan in desmoplastic stroma followed by administration of the chemotherapy drug gemcitabine to inhibit the proliferation of cancer cells. Modeling the effects of PEGPH20 + gemcitabine concentrations is based on Green’s fundamental solutions of the reaction–diffusion equation. Moreover, Monte Carlo simulations are performed to quantitatively investigate uncertainties in the input parameters as well as predictions for the likelihood of success of cancer therapy. Our simplified model is able to simulate cancer progression and evaluate treatments to inhibit the progression of cancer.

中文翻译：

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胰腺癌早期治疗的计算模型。

超过80％的胰腺癌涉及导管腺癌，其周围实体瘤实体周围有大量的成骨细胞外基质。这种异常的肿瘤微环境促进了胰腺癌对药物的强烈耐药性。尽管已经报道了各种治疗策略对胰腺癌小鼠有效，但是在用作治疗方法之前，仍需要在更广泛的基于动物的实验中对其进行定量测试。为帮助设计实验，我们开发了一种基于细胞的数学模型来描述在胰腺癌治疗中的癌症进展。通过用Euler-Maruyama方法求解大型随机微分方程组，可以模拟细胞的位移。我们考虑用聚乙二醇化药物PEGPH20进行治疗，该药物可分解增生基质中的透明质酸，然后给予化疗药物吉西他滨抑制癌细胞的增殖。对PEGPH20 +吉西他滨浓度的影响进行建模是基于格林的反应扩散方程的基本解。此外，进行蒙特卡洛模拟以定量研究输入参数中的不确定性以及癌症治疗成功可能性的预测。我们的简化模型能够模拟癌症进展并评估抑制癌症进展的治疗方法。对PEGPH20 +吉西他滨浓度的影响进行建模是基于格林的反应扩散方程的基本解。此外，执行蒙特卡洛模拟以定量研究输入参数的不确定性以及癌症治疗成功可能性的预测。我们的简化模型能够模拟癌症进展并评估抑制癌症进展的治疗方法。对PEGPH20 +吉西他滨浓度的影响进行建模是基于格林的反应扩散方程的基本解。此外，执行蒙特卡洛模拟以定量研究输入参数的不确定性以及癌症治疗成功可能性的预测。我们的简化模型能够模拟癌症进展并评估抑制癌症进展的治疗方法。