论文标题
基于优化的3D-1D耦合策略，用于肿瘤诱导的血管生成期间组织灌注和化学转运
An optimization based 3D-1D coupling strategy for tissue perfusion and chemical transport during tumor-induced angiogenesis
论文作者
论文摘要
在肿瘤引起的血管生成的背景下，提出了一种新的数学模型和数值方法，以模拟不断增长的毛细血管网络与周围组织之间的流体和化学交换。由于适当的建模假设，毛细血管被减少到其中心线：因此，基于三维方程和一维方程之间的耦合（3D-1D耦合问题）。此外，首次提出了首次提出PDE受限优化公式进行血管生成模拟。在这种方法下，不需要网格符合性，因此该方法特别适合这种应用，因为随着毛细管网络的增长，不需要重新捕捉。为了同时处理感兴趣量的演变和几何形状的变化，采用了离散的杂交策略，将组织和化学物质的连续建模与离散的尖端跟踪模型相结合，以说明血管网络的增长。小费跟踪策略以及一些适当的分支和吻合规则，能够提供毛细管网络的现实表示。
A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. Thanks to proper modeling assumptions the capillaries are reduced to their centerline: a well posed mathematical model is hence worked out, based on the coupling between a three-dimensional and a one-dimensional equation (3D-1D coupled problem). Also the application of a PDE-constrained optimization formulation is here proposed for the first time for angiogenesis simulations. Under this approach no mesh conformity is required, thus making the method particularly suitable for this kind of application, since no remeshing is required as the capillary network grows. In order to handle both the evolution of the quantities of interest and the changes in the geometry, a discrete-hybrid strategy is adopted, combining a continuous modeling of the tissue and of the chemicals with a discrete tip-tracking model to account for the vascular network growth. The tip-tracking strategy, together with some proper rules for branching and anastomosis, is able to provide a realistic representation of the capillary network.
