Theory and applications of motions of anisotropic interfacial networks

各向异性界面网络运动理论与应用

• 批准号: 18F18016
• 负责人: SVADLENKA KAREL
• 金额: $ 1.47万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2018
• 资助国家: 日本
• 起止时间: 2018-07-25 至 2020-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18F18016/
• 关键词: interface dynamics; interfacial network; MBO scheme; level set method; volume preservation; cellular patterns; interface network; anisotropic energy

Considering the gradient flow of anisotropic surface energy constrained by volume preservation, we developed a level set-based method for realizing anisotropic motion of an interface network. First, we considered a variational approach to a vector-type Merriman-Bence-Osher (MBO) thresholding scheme with penalization technique, which realized volume-preserving crystalline motion with a smoothing technique but required an ad hoc scheme to satisfy the correct junction angles. Motivated by cellular pattern formations in sensory epithelium, we considered anisotropic motions driven by cell-cell adhesion. Due to the complexity of tricellular junctions, we then developed an MBO-type convolution scheme with localized auction dynamics which realizes correct cell contact angles and features good compatibility with level set representation and a solid mathematical background including stability and convergence. Here, cell-cell junctions are implicitly represented using level sets and succeeding dynamics are numerically determined by thresholding. We addressed several aspects pertinent to cell biology, e.g., our localization step prevents cells from unnatural splitting during rearrangement. Our method successfully reproduced development of cellular patterns in sensory systems, including cell sorting, total engulfment, and cell internalization. These simulations were implemented using C programming language and Matlab software. Results have been submitted for publication, as well as, presented and well received in local and overseas conferences.

考虑到各向异性表面能在体积守恒约束下的梯度流，提出了一种基于水平集的实现界面网络各向异性运动的方法。首先，我们考虑了一个变分方法的矢量型Merriman-Bence-Osher（MBO）阈值计划与惩罚技术，实现了保体积的晶体运动与平滑技术，但需要一个特设的计划，以满足正确的结角。受感觉上皮细胞模式形成的启发，我们考虑了细胞-细胞粘附驱动的各向异性运动。由于三细胞连接的复杂性，我们然后开发了一个MBO型卷积方案与本地拍卖动力学，实现正确的细胞接触角和功能良好的兼容性与水平集表示和坚实的数学背景，包括稳定性和收敛性。在这里，细胞-细胞连接隐含地表示使用水平集和后续的动态数值确定的阈值。我们讨论了与细胞生物学相关的几个方面，例如，我们的定位步骤防止了细胞在重排过程中不自然的分裂。我们的方法成功地再现了感觉系统中细胞模式的发展，包括细胞分选、总吞噬和细胞内化。这些模拟使用C编程语言和Matlab软件实现。研究结果已提交出版，并在本地和海外会议上发表，受到好评。

项目成果

Mathematics of Cellular Pattern Formation in Sensory Epithelia

感觉上皮细胞模式形成的数学

• 发表时间: 2019
• 作者: Lia Ooi;Takakazu Matsuura and Izumi C. Mori;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina Mohammad;Rhudaina Mohammad;Rhudaina Mohammad;Karel Svadlenka
• 通讯作者: Karel Svadlenka

Modeling cell-to-cell adhesion dynamics in multicellular organisms

模拟多细胞生物中的细胞间粘附动力学

• 发表时间: 2019
• 作者: Lia Ooi;Takakazu Matsuura and Izumi C. Mori;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD
• 通讯作者: Rhudaina MOHAMMAD

Mosaic Cellular Patterns of Sensory Epithelial Tissues: An Interface Evolution Problem

感觉上皮组织的马赛克细胞模式：界面进化问题

• 发表时间: 2019
• 作者: Lia Ooi;Takakazu Matsuura and Izumi C. Mori;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina MOHAMMAD;Rhudaina Mohammad;Rhudaina Mohammad
• 通讯作者: Rhudaina Mohammad

On some extensions of thresholding schemes

关于阈值方案的一些扩展

• 发表时间: 2018
• 作者: Kametaka Yoshinori;Watanabe Kohtaro;Nagai Atsushi;Takemura Kazuo;Yamagishi Hiroyuki;Sekido Hiroto;和田健志;佐々木 建昭，讃岐 勝，稲葉 大樹;上田好寛;Svadlenka Karel
• 通讯作者: Svadlenka Karel

Modeling Cellular Dynamics in TissueMorphogenesis: A Level Set-based Approach

组织形态发生中的细胞动力学建模：基于水平集的方法

• 发表时间: 2020
• 作者: Lia Ooi;Takakazu Matsuura and Izumi C. Mori;Rhudaina MOHAMMAD
• 通讯作者: Rhudaina MOHAMMAD