标题： 用于曲率控制生长过程中细胞和组织演化的水平集方法 显示英文标题

标题： A level-set method for the evolution of cells and tissue during curvature-controlled growth

摘要： 大多数生物组织通过在组织界面附近合成新物质而生长，其中空间相互作用可能对局部生长速率产生强烈的几何影响。 这些几何影响可能是机械性的，或者是细胞行为性质的。 几何对组织生长的控制已在许多体内和体外实验中得到证实，包括骨重塑、伤口愈合和组织工程支架。 在本文中，我们提出了一种数学模型的推广，该模型捕捉了曲率对细胞密度和组织形状联合演化的机械影响。 这种推广使我们能够通过基于水平集的方法模拟突然的拓扑变化，如组织碎片化和组织融合，以及三维情况。 开发的水平集方法引入了另一个欧拉场，除了水平集函数之外。 这个额外的场表示在界面未来位置预期的组织合成细胞的表面密度。 使用这种基于水平集的方法进行的数值测试表明，细胞的数值守恒是模拟精度的良好指标，特别是在组织界面出现尖点时。 我们将这个新模型应用于几种曲率控制的组织演化情况，包括碎片化和融合。 显示英文摘要

摘要： Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or cell behavioural in nature. The control of geometry on tissue growth has been evidenced in many in-vivo and in-vitro experiments, including bone remodelling, wound healing, and tissue engineering scaffolds. In this paper, we propose a generalisation of a mathematical model that captures the mechanistic influence of curvature on the joint evolution of cell density and tissue shape during tissue growth. This generalisation allows us to simulate abrupt topological changes such as tissue fragmentation and tissue fusion, as well as three dimensional cases, through a level-set-based method. The level-set method developed introduces another Eulerian field than the level-set function. This additional field represents the surface density of tissue synthesising cells, anticipated at future locations of the interface. Numerical tests performed with this level-set-based method show that numerical conservation of cells is a good indicator of simulation accuracy, particularly when cusps develop in the tissue's interface. We apply this new model to several situations of curvature-controlled tissue evolutions that include fragmentation and fusion.