力学环境影响下肿瘤内外血管生成的数值模拟

目的　考察肿瘤内外不同的力学环境对肿瘤血管生成过程中内皮细胞运动的影响，数值生成肿瘤内外血管网络。方法　肿瘤外正常组织和肿瘤组织设为线性粘弹性体。肿瘤外正常组织内皮细胞扩散系数是常数；肿瘤内，肿瘤细胞的活性下降导致组织的黏附力降低，内皮细胞扩散系数设为离中心的幂次函数。建立内皮细胞运动的扩散方程，数值生成肿瘤内外血管网络。结果　当考虑肿瘤内外不同力学环境对内皮细胞运动的影响时，可以获得相对真实的分层毛细血管网络：在肿瘤外层富含毛细血管，越靠近肿瘤中心，血管越稀少在忽略力学环境的影响时，无法得到实验观测到的分层网络。结论　肿瘤内外不同的力学环境对肿瘤血管生成的网络结构有着重要影响。

Numerical Simulation of tumor-induced Angiogenesis in and out of Tumor Incorporating Mechanical Effects

Objective To investigate tumor-induced angiogenesis under the influence posed by the mechanical environments in and out of tumor, and simulate the capillary network numerically. Methods The tissue in and out of tumor is assumed to be linear visco-elastic. The diffusive coefficient of endothelia-cell (EC) keeps constant in normal tissue out of tumor. In tumor, the reduced activity of tumor cells becomes a big obstacle for EC's movement, the coefficient is supposed to be a power function along the distance from the tumor center. An equation for EC movement is established in this model to illustrate the mechanical effect. The capillary network is simulated numerically. Results A relatively realistic capillary network in and out of tumor is gained. The mechanical factor results a layered structure: at the edge of tumor, numerous capillaries are generated, while closer to the tumor center, less the capillary. A Necrotic Region without any vessel exists in the center. However, the model can not generate a layered network without considering the mechanical effect. Conclusion Different mechanical environments in and out of tumor play an important role in the process of tumor-induced angiogenesis.