Modeling the Dynamics of Heterogeneity of Solid Tumors in Response to Chemotherapy
Modeling the Dynamics of Heterogeneity of Solid Tumors in Response to Chemotherapy
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DOI：
10.1007/s11538-017-0359-1
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发表时间：
2017-12-01
影响因子：
3.5
通讯作者：
Levy, Doron
中科院分区：
文献类型：
--
作者：
Cho, Heyrim;Levy, Doron
在本文中，我们推广了Lorz等人提出的实体肿瘤耐药动力学模型。(公牛数学生物77：1-22,2015)。与原始的径向对称模型类似，我们遵循的量取决于与耐药水平相对应的表型变量。对原模型进行了三方面的修正：(1)考虑了更一般的增长周期，考虑了耐药水平对大剂量药物的敏感性。(Ii)我们增加了癌细胞的空间扩散项，并调整了所有扩散项(对于营养素和药物)，从而使资源和药物的渗透性受到细胞浓度的限制。(Iii)我们添加了一个突变术语，其突变核对应于定期发生或很少发生的突变。我们研究了在持续输注和开关输注细胞毒和细胞抑制药物的情况下癌细胞出现耐药的动力学。虽然原始的Lorz模型有一个渐近轮廓，其中癌细胞要么完全耐药，要么完全敏感，而我们的模型允许出现部分耐药水平。我们表明，药物浓度的增加与延迟复发相关。然而，当癌症复发时，就会选择更多的抗性特征。我们进一步表明，与总药物浓度相同的连续药物输注相比，开关药物输注也选择了更多的耐药特征。在一定条件下，我们的模型预测了一种异质肿瘤的出现，其中不同抗性水平的癌细胞共存于空间的不同区域。
In this paper, we extend the model of the dynamics of drug resistance in a solid tumor that was introduced by Lorz et al. (Bull Math Biol 77:1-22, 2015). Similarly to the original, radially symmetric model, the quantities we follow depend on a phenotype variable that corresponds to the level of drug resistance. The original model is modified in three ways: (i) We consider a more general growth term that takes into account the sensitivity of resistance level to high drug dosage. (ii) We add a diffusion term in space for the cancer cells and adjust all diffusion terms (for the nutrients and for the drugs) so that the permeability of the resource and drug is limited by the cell concentration. (iii) We add a mutation term with a mutation kernel that corresponds to mutations that occur regularly or rarely. We study the dynamics of the emerging resistance of the cancer cells under continuous infusion and on-off infusion of cytotoxic and cytostatic drugs. While the original Lorz model has an asymptotic profile in which the cancer cells are either fully resistant or fully sensitive, our model allows the emergence of partial resistance levels. We show that increased drug concentrations are correlated with delayed relapse. However, when the cancer relapses, more resistant traits are selected. We further show that an on-off drug infusion also selects for more resistant traits when compared with a continuous drug infusion of identical total drug concentrations. Under certain conditions, our model predicts the emergence of a heterogeneous tumor in which cancer cells of different resistance levels coexist in different areas in space.