用病毒治疗肿瘤的抛物—双曲自由边界问题模型

发布时间：2018-04-19 20:54

本文选题：肿瘤 + 病毒　；参考：《东华大学》2007年硕士论文

【摘要】： 本文我们考虑一种向肿瘤注射可复制病毒的癌症治疗方法。病毒感染肿瘤细胞，然后在其中复制，最终引起肿瘤细胞死亡(溶解)。一旦肿瘤细胞死亡，，其中的病毒释放并感染邻近的肿瘤细胞。然而，一个影响病毒治疗效果的主要因素是免疫响应，它会限制可复制病毒的复制和扩散。肿瘤细胞，可复制病毒和免疫响应之间的竞争被描述为一个偏微分方程的非线性系统的自由边界问题，其中自由边界是肿瘤的表面。模型中，免疫响应方程是一个半线性椭圆方程，包含一个趋化性项。这一项用以描述由受感染细胞密度的梯度引起的免疫响应的运动。我们假设，趋化性项敏感度系数与免疫响应的扩散系数相比很小。在这一假设下，我们证明这一自由边界的解的全局性和唯一性。而对于大的趋化性敏感系数，全局存在性尚未得证。
[Abstract]:In this paper, we consider a cancer treatment method that injects replicable viruses into tumors. The virus infects tumor cells and then replicates in them, leading to the death of tumor cells. Once the tumor cells die, the virus releases and infects adjacent tumor cells. However, an important factor affecting the efficacy of viral therapy is the immune response, which limits replication and spread of replicable viruses. The competition between tumor cells replicable viruses and immune responses is described as a free boundary problem for a nonlinear system with partial differential equations where the free boundary is the surface of the tumor. In the model, the immune response equation is a semi-linear elliptic equation with a chemotactic term. This term is used to describe the movement of the immune response caused by the gradient of the density of infected cells. We assume that the chemotaxis sensitivity coefficient is small compared with the diffusion coefficient of immune response. Under this assumption, we prove that the solution of this free boundary is global and unique. But for the large chemotaxis sensitivity coefficient, the global existence has not been proved.
【学位授予单位】：东华大学
【学位级别】：硕士
【学位授予年份】：2007
【分类号】：R730.5;O175.2;R311

【共引文献】