Department of Translational Hematology and Oncology Research, Cleveland Clinic, Cleveland, OH, USA.
Department of Mathematics and Computer Science, Adelphi University, Garden City, NY, USA.
J Math Biol. 2021 Oct 11;83(5):47. doi: 10.1007/s00285-021-01671-6.
In previous work, we focused on the optimal therapeutic strategy with a pair of drugs which are collaterally sensitive to each other, that is, a situation in which evolution of resistance to one drug induces sensitivity to the other, and vice versa. Yoona (Bull Math Biol 8:1-34,Yoon et al. 2018) Here, we have extended this exploration to the optimal strategy with a collaterally sensitive drug sequence of an arbitrary length, N. To explore this, we have developed a dynamical model of sequential drug therapies with N drugs. In this model, tumor cells are classified as one of N subpopulations represented as [Formula: see text]. Each subpopulation, [Formula: see text], is resistant to '[Formula: see text]' and each subpopulation, [Formula: see text] (or [Formula: see text], if [Formula: see text]), is sensitive to it, so that [Formula: see text] increases under '[Formula: see text]' as it is resistant to it, and after drug-switching, decreases under '[Formula: see text]' as it is sensitive to that drug(s). Similar to our previous work examining optimal therapy with two drugs, we found that there is an initial period of time in which the tumor is 'shaped' into a specific makeup of each subpopulation, at which time all the drugs are equally effective ([Formula: see text]). After this shaping period, all the drugs are quickly switched with duration relative to their efficacy in order to maintain each subpopulation, consistent with the ideas underlying adaptive therapy. West(Canver Res 80(7):578-589Gatenby et al. 2009) and Gatenby (Cancer Res 67(11):4894-4903West et al. 2020). Additionally, we have developed methodologies to administer the optimal regimen under clinical or experimental situations in which no drug parameters and limited information of trackable populations data (all the subpopulations or only total population) are known. The therapy simulation based on these methodologies showed consistency with the theoretical effect of optimal therapy .
在之前的工作中，我们专注于一对相互协同敏感的药物的最佳治疗策略，即一种对一种药物的耐药性进化会诱导对另一种药物的敏感性，反之亦然(Yoon 等人，2018 年，《 Bull Math Biol》，第 8 卷，第 1-34 页)。在这里，我们将这一探索扩展到了具有任意长度协同敏感药物序列的最佳策略，N。为了探索这一点，我们开发了一种具有 N 种药物的序贯药物治疗的动力学模型。在这个模型中，肿瘤细胞被分为 N 个亚群之一，用[Formula: see text]表示。每个亚群[Formula: see text]对'[Formula: see text]'有耐药性，而每个亚群[Formula: see text](或[Formula: see text]，如果[Formula: see text])对其敏感，因此[Formula: see text]在对其耐药时会在'[Formula: see text]'下增加，而在药物切换后，由于对药物敏感，会在'[Formula: see text]'下减少。与我们之前研究两种药物最佳治疗的工作类似，我们发现存在一个初始时间段，在此期间，肿瘤被“塑造成”特定的每个亚群组成，此时所有药物的效果都相等([Formula: see text])。在这个塑造期之后，所有药物都会根据其疗效快速切换，以维持每个亚群，这与适应性治疗的理念一致。West 和 Gatenby（Canver Res，第 80 卷，第 578-589 页；Gatenby 等人，2009 年；Cancer Res，第 67 卷，第 4894-4903 页；West 等人，2020 年）。此外，我们还开发了在临床或实验情况下实施最佳方案的方法，在这些情况下，不知道药物参数和有限的可跟踪群体数据（所有亚群或仅总群体）的信息。基于这些方法的治疗模拟与最佳治疗的理论效果一致。
