Department of Mathematics, Ariel University, Ariel 4070000, Israel.
Department of Chemical Engineering, Ariel University, Ariel 4070000, Israel.
Cells. 2022 Jul 28;11(15):2325. doi: 10.3390/cells11152325.
In recent years, mathematical models have developed into an important tool for cancer research, combining quantitative analysis and natural processes. We have focused on Chronic Lymphocytic Leukemia (CLL), since it is one of the most common adult leukemias, which remains incurable. As the first step toward the mathematical prediction of in vivo drug efficacy, we first found that logistic growth best described the proliferation of fluorescently labeled murine A20 leukemic cells injected in immunocompetent Balb/c mice. Then, we tested the cytotoxic efficacy of Ibrutinib (Ibr) and Cytarabine (Cyt) in A20-bearing mice. The results afforded calculation of the killing rate of the A20 cells as a function of therapy. The experimental data were compared with the simulation model to validate the latter's applicability. On the basis of these results, we developed a new ordinary differential equations (ODEs) model and provided its sensitivity and stability analysis. There was excellent accordance between numerical simulations of the model and results from in vivo experiments. We found that simulations of our model could predict that the combination of Cyt and Ibr would lead to approximately 95% killing of A20 cells. In its current format, the model can be used as a tool for mathematical prediction of in vivo drug efficacy, and could form the basis of software for prediction of personalized chemotherapy.
近年来，数学模型已经发展成为癌症研究的重要工具，将定量分析和自然过程结合在一起。我们专注于慢性淋巴细胞白血病（CLL），因为它是最常见的成人白血病之一，仍然无法治愈。作为对体内药物疗效进行数学预测的第一步，我们首先发现逻辑增长最能描述荧光标记的鼠 A20 白血病细胞在免疫功能正常的 Balb/c 小鼠中的增殖。然后，我们测试了伊布替尼（Ibr）和阿糖胞苷（Cyt）在 A20 荷瘤小鼠中的细胞毒性作用。结果计算了治疗过程中 A20 细胞的杀伤率。将实验数据与模拟模型进行比较，以验证后者的适用性。基于这些结果，我们开发了一个新的常微分方程（ODEs）模型，并对其进行了敏感性和稳定性分析。模型的数值模拟与体内实验结果非常吻合。我们发现，我们模型的模拟可以预测 Cyt 和 Ibr 的联合使用将导致 A20 细胞的大约 95%的杀伤。在目前的形式下，该模型可用于体内药物疗效的数学预测，并可以作为预测个体化化疗的软件的基础。
