Simulating Large-Scale Morphogenesis in Planar Tissues

生物技术和医学的前沿发展涉及大规模组织和器官的重建。由于缺乏组织形态发生方面的知识，这项工作可能受到限制。组织形态发生是指活组织发展其大小和形状特征的过程。尽管实时成像技术已经能够观察到形态发生的过程，但在基本认识方面的进展仍然缓慢。该项目旨在改进工具，用于模拟各种相对平面的活组织，并已在实验中进行了广泛的研究。该项目将开发形态发生过程的数值模拟方法，并尝试在平面组织中再现观察到的大规模形态发生结构。该项目通过参与研究为研究生提供培训。该项目涉及组织形态发生的大规模连续体模型的数值模拟，涉及自由边界、体-界面耦合和高度非线性相互作用。本文以反应对流方程和非标准空间偏微分方程为中心，建立了场变量非线性耦合的数学模型。该项目将开发半隐式和全隐式时间步进方法，以避免显式时间步进方法的潜在时间步长限制。由于系统的高度非线性，边界构型必须与速度场和其他场变量一起更新。为此，本文将研究一种基于参考图技术的接口跟踪方法。将进行接近平凡解的线性分析，以帮助设计快速收敛的迭代方法来求解由原始模型的隐式时步离散化导出的非线性系统。模拟了解体外微组织和体内上皮组织形态发生从实时成像数据将进行。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Cutting-edge developments in biotechnology and medicine involve reconstructing large-scale tissues and organs. This work can be limited by lack of knowledge in tissue morphogenesis, the process by which living tissues develop their size-and-shape characteristics. Though live-imaging techniques have enabled the observation of morphogenetic processes, progress in fundamental understanding has been slow. This project aims to improve tools for modeling a wide range of living tissues that are relatively planar and have been extensively studied experimentally. The project will develop methods for numerical simulation of morphogenesis processes and attempt to reproduce the observed large-scale morphogenesis structures in planar tissues. The project provides graduate student training through involvement in the research.This project concerns numerical simulation of large-scale continuum models for tissue morphogenesis that involve free boundaries, bulk-interface coupling, and highly nonlinear interactions. The work centers on a new mathematical model in which the field variables are nonlinearly coupled via reaction-convection equations and non-standard spatial partial differential equations. The project will develop semi-implicit and fully implicit time-stepping methods to avoid a potential time-step restriction for explicit time-stepping methods. Due to the high nonlinearity of the system, the boundary configuration must be updated together with the velocity field as well as other field variables. For this purpose, a novel interface-tracking method based on reference-map techniques will be investigated. Linear analysis close to trivial solutions will be conducted to assist the design of fast-converging iterative methods for solving the nonlinear system derived from the implicit time-stepping discretization of the original model. Simulations to understand in vitro micro-tissue and in vivo epithelial-tissue morphogenesis from live-imaging data will be carried out.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.