SIAM Journal on Applied Mathematics, Volume 81, Issue 2, Page 434-453, January 2021.
We present a mathematical study of the emergence of phenotypic heterogeneity in vascularized tumors. Our study is based on formal asymptotic analysis and numerical simulations of a system of nonlocal parabolic equations that describes the phenotypic evolution of tumor cells and their nonlinear dynamic interactions with the oxygen, which is released from the intratumoral vascular network. Numerical simulations are carried out both in the case of arbitrary distributions of intratumor blood vessels and in the case where the intratumoral vascular network is reconstructed from clinical images obtained using dynamic optical coherence tomography. The results obtained support a more in-depth theoretical understanding of the eco-evolutionary process which underpins the emergence of phenotypic heterogeneity in vascularized tumors. In particular, our results offer a theoretical basis for empirical evidence indicating that the phenotypic properties of cancer cells in vascularized tumors vary with the distance from the blood vessels, and establish a relation between the degree of tumor tissue vascularization and the level of intratumor phenotypic heterogeneity.

中文翻译：

---

模拟血管化肿瘤中表型异质性的出现

SIAM应用数学杂志，第81卷，第2期，第434-453页，2021年1月。
我们目前对血管化肿瘤中表型异质性的出现进行数学研究。我们的研究基于非局部抛物线方程组的形式渐近分析和数值模拟，该系统描述了肿瘤细胞的表型演变及其与氧气的非线性动态相互作用，氧气从肿瘤内血管网络释放出来。在肿瘤内血管任意分布的情况下和从利用动态光学相干断层扫描获得的临床图像重建瘤内血管网络的情况下，都进行了数值模拟。获得的结果支持对生态进化过程的更深入的理论理解，生态进化过程为血管化肿瘤中表型异质性的出现奠定了基础。尤其是，