Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, United States of America.
PLoS One. 2020 May 14;15(5):e0233031. doi: 10.1371/journal.pone.0233031. eCollection 2020.
In order to determine correct dosage of chemotherapy drugs, the effect of the drug must be properly quantified. There are two important values that characterize the effect of the drug: εmax is the maximum possible effect of a drug, and IC50 is the drug concentration where the effect diminishes by half. There is currently a problem with the way these values are measured because they are time-dependent measurements. We use mathematical models to determine how the εmax and IC50 values depend on measurement time and model choice. Seven ordinary differential equation models (ODE) are used for the mathematical analysis; the exponential, Mendelsohn, logistic, linear, surface, Bertalanffy, and Gompertz models. We use the models to simulate tumor growth in the presence and absence of treatment with a known IC50 and εmax. Using traditional methods, we then calculate the IC50 and εmax values over fifty days to show the time-dependence of these values for all seven mathematical models. The general trend found is that the measured IC50 value decreases and the measured εmax increases with increasing measurement day for most mathematical models. Unfortunately, the measured values of IC50 and εmax rarely matched the values used to generate the data. Our results show that there is no optimal measurement time since models predict that IC50 estimates become more accurate at later measurement times while εmax is more accurate at early measurement times.
为了确定化疗药物的正确剂量，必须对药物的效果进行适当的量化。有两个重要的值可以描述药物的效果：εmax 是药物的最大可能效果，IC50 是药物效果减半的浓度。目前，这些值的测量方法存在问题，因为它们是时间相关的测量。我们使用数学模型来确定 εmax 和 IC50 值如何随测量时间和模型选择而变化。我们使用了七种常微分方程模型（ODE）进行数学分析；指数模型、门德尔松模型、逻辑斯谛模型、线性模型、曲面模型、贝塔朗菲模型和戈梅茨模型。我们使用这些模型模拟了存在和不存在已知 IC50 和 εmax 的情况下肿瘤的生长。然后，我们使用传统方法在五十天内计算了这些值的 IC50 和 εmax 值，以展示所有七种数学模型中这些值的时间依赖性。一般趋势是，对于大多数数学模型，测量的 IC50 值随着测量天数的增加而降低，而测量的 εmax 值随着测量天数的增加而增加。不幸的是，IC50 和 εmax 的测量值很少与生成数据时使用的值匹配。我们的结果表明，由于模型预测 IC50 估计在后期测量时间会变得更准确，而 εmax 在早期测量时间会更准确，因此没有最佳的测量时间。
