A parabolic-hyperbolic free boundary problem modelling tumor treatment with virus
A parabolic-hyperbolic free boundary problem modelling tumor treatment with virus
复制标题
模拟病毒肿瘤治疗的抛物线-双曲自由边界问题
DOI：
10.1142/s0218202507001838
复制
发表时间：
2007-01-01
影响因子：
3.5
通讯作者：
Zhang, Hui
中科院分区：
文献类型：
--
作者：
Tao, Youshan;Zhang, Hui
我们考虑了一种癌症治疗方法，它包括将具有复制能力的病毒注射到肿瘤中。病毒感染肿瘤细胞，在肿瘤细胞内复制，最终导致肿瘤细胞死亡。当受感染的细胞死亡时，它们内部的病毒被释放出来，然后继续感染邻近的肿瘤细胞。然而，影响病毒剂效力的主要因素是免疫应答，其可能限制有复制能力的病毒的复制和传播。将肿瘤细胞、具有复制能力的病毒和免疫反应之间的竞争建模为非线性偏微分方程组的自由边界问题，其中自由边界是肿瘤的表面。在该模型中，免疫应答方程是半线性抛物方程，包括用于描述由感染细胞密度梯度诱导的免疫应答的运动的趋化性项。在假设趋化敏感系数小于免疫反应扩散系数的条件下，证明了该自由边界问题解的整体存在唯一性.对于大的趋化系数，全局存在仍然是开放的。
We consider a procedure for cancer therapy which consists of injecting replication-competent viruses into the tumor. The viruses infect tumor cells, replicate inside them, and eventually cause their death. As infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. However, a major factor influencing the efficacy of virus agents is the immune response that may limit the replication and spread of the replication-competent virus. The competition between tumor cells, a replication-competent virus and an immune response is modelled as a free boundary problem for a nonlinear system of partial differential equations, where the free boundary is the surface of the tumor. In this model, the immune response equation is a semilinear parabolic equation, including a chemotaxis term which is used to describe the movement of the immune response induced by gradients of the infected cell density. Under the assumption that the chemotactic sensitivity coefficient is small compared with the diffusion coefficient of the immune response, we prove the global existence and uniqueness of the solution of this free boundary problem. For large chemotactic coefficient, the global existence is still open.