A cancer model with nonlocal free boundary dynamics
A cancer model with nonlocal free boundary dynamics
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DOI：
10.1007/s00285-022-01813-4
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发表时间：
2022-10
影响因子：
1.9
通讯作者：
A. Friedman;Wenrui Hao;King-Yeung Lam
中科院分区：
文献类型：
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作者：
A. Friedman;Wenrui Hao;King-Yeung Lam
肿瘤边界处的癌细胞沿着氧梯度的方向移动，而肿瘤内远处的癌细胞处于坏死状态。本文介绍了一个简单的数学模型，占这些事实。该模型由癌细胞、细胞毒性T细胞和氧气组成，满足一个偏微分方程组。一些模型参数代表抗癌药物的效果。肿瘤边界是一个自由边界，其动力学由癌细胞在边界处的运动决定。该模型模拟了径向对称和轴向对称的肿瘤，它表明，肿瘤的大小可能会增加或减少，这取决于药物的“强度”。存在性定理证明，在径向对称的情况下，在时间的全球和当地的任何形状的肿瘤。在径向对称情形下，证明了在不同条件下，肿瘤可以单调收缩，也可以单调膨胀。
Cancer cells at the tumor boundary move in the direction of the oxygen gradient, while cancer cells far within the tumor are in a necrotic state. This paper introduces a simple mathematical model that accounts for these facts. The model consists of cancer cells, cytotoxic T cells, and oxygen satisfying a system of partial differential equations. Some of the model parameters represent the effect of anti-cancer drugs. The tumor boundary is a free boundary whose dynamics is determined by the movement of cancer cells at the boundary. The model is simulated for radially symmetric and axially symmetric tumors, and it is shown that the tumor may increase or decrease in size, depending on the “strength" of the drugs. Existence theorems are proved, global in-time in the radially symmetric case, and local in-time for any shape of tumor. In the radially symmetric case, it is proved, under different conditions, that the tumor may shrink monotonically, or expand monotonically.