This work considers the propagation of a tumor from the stage of a small avascular sphere in a host tissue and the progressive onset of a tumor neovasculature stimulated by a pro-angiogenic factor secreted by hypoxic cells.

The way new vessels are formed involves cell sprouting from pre-existing vessels and following a trail via a chemotactic mechanism (CM).

Namely, it is first proposed a detailed general family of models of the CM, based on a statistical mechanics approach. The key hypothesis is that the CM is composed by two components: i) the well–known bias induced by the angiogenic factor gradient; ii) the presence of stochastic changes of the velocity direction, thus giving rise to a diffusive component. Then, some further assumptions and simplifications are applied in order to derive a specific model to be used in the simulations.

The tumor progression is favored by its acidic aggression towards the healthy cells. The model includes the evolution of many biological and chemical species.

Numerical simulations show the onset of a traveling wave eventually replacing the host tissue with a fully vascularized tumor. The results of simulations agree with experimental measures of the vasculature density in tumors, even in the case of particularly hypoxic tumors.

这项工作考虑了肿瘤在宿主组织中从小无血管球的阶段开始的扩散以及由低氧细胞分泌的促血管生成因子刺激的肿瘤新脉管系统的逐步发作。

形成新血管的方式包括从已有血管中萌发细胞，并通过趋化机制（CM）追踪细胞。

即，首先基于统计力学方法提出了详细的通用模型系列。关键假设是CM由两个部分组成：i）血管生成因子梯度引起的众所周知的偏差；ii）速度方向出现随机变化，从而产生了扩散分量。然后，应用一些进一步的假设和简化，以便得出要在仿真中使用的特定模型。

对健康细胞的酸性侵袭有利于肿瘤的进展。该模型包括许多生物和化学物种的进化。

数值模拟显示行波的发生，最终用完全血管化的肿瘤替代了宿主组织。模拟结果与肿瘤中脉管系统密度的实验测量结果吻合，即使是在低氧肿瘤中也是如此。