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.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Malgorzata Peszynska
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Worcester Polytechnic Institute
United States
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