Mathematical Modeling and Computer Simulation of Moving Boundary Problems in Biofluids

狄龙9805501 研究者发展了数学模型和计算方法，用于研究生物流体中两个特定的运动边界问题：真核生物纤毛和鞭毛的运动以及脊椎动物胚胎肢芽生长的数学建模和数值模拟。 泡囊和鞭毛轴丝的模型结合了单个动力蛋白臂的离散表示，轴丝弹性结构的力学模型，如微管和连接蛋白，以及周围流体力学的连续描述。 肢芽生长和模式的模型包括一个流体力学描述的肢芽组织，一个反应-扩散-平流组件，管理的时空分布的生长因子和morphogens产生的专门领域，如顶端外胚层嵴和极化活动区，和一个移动的elasticboundary，代表肢芽外胚层的粘弹性。 在三维模型中，肢芽外皮层被建模为由线性弹性元件连接的节点网络。 研究者还发展了一种算法，用于在求解反应扩散对流方程时施加适当的边界条件。 由于每个模型都包括一个流体力学表示，研究人员使用了一个类似的计算方法的基础上浸没边界法和计算机代码共享许多主要的子程序。 本研究计划的目的是发展数学模型和计算方法，以研究复杂生物系统中的移动边界问题。 本论文建立了两类模型：一类是真核生物纤毛和鞭毛的运动模型，另一类是多细胞生物系统的生长动力学模型。 这两种模型都涉及到生物学中粘弹性材料建模的新方法，并具有共同的计算观点。 第一个项目的目标是为单个纤毛或鞭毛建立一个三维模型。 虽然关于真核生物纤毛和鞭毛的生物化学、超微结构和运动已经有了大量的发现，但对控制振荡运动和弯曲的机制还没有很好的了解。 纤毛和鞭毛建模的目标是开发一个三维模型，可以作为研究控制波形的机械化学机制的平台。 生长对于多细胞生物和单细胞生物群落都起着重要的作用。 研究者开发了一个脊椎动物肢体发育模型，该模型包括发育中的肢体芽内细胞和组织的生长和运动，肢体芽内生长因子的运输和生产，以及代表肢体芽外胚层的机械和生物化学特性的移动边界。 该模型的发展和求解相关数学方程的计算方法已应用于研究各种多细胞系统，其中生长是一个基本特征，包括发育生物学中的生长和模式形成，细菌菌落的生长以及肿瘤生长。 该项目的一个重要方面是研究模型的数值方法的发展，这一领域的进展可以用于计算生物流体领域的各种问题。

Dillon9805501 The investigator develops mathematical models andcomputational methods for studying two specific moving boundaryproblems in biofluids: the motion of eukaryotic cilia andflagella and the mathematical modeling and numerical simulationof the growing embryonic vertebrate limb bud. The model for thecilia and flagella axoneme incorporates discrete representationsof the individual dynein arms, a mechanical model of theaxoneme's elastic structures such as the microtubules and nexinlinks, and a continuous description of the surrounding fluidmechanics. The model for limb bud outgrowth and patterningconsists of a fluid-mechanical description of the limb budtissue, a reaction-diffusion-advection component that governs thespatio-temporal distribution of growth factors and morphogensproduced in specialized regions such as the apical ectodermalridge and the zone of polarizing activity, and a moving elasticboundary that represents the limb bud ectoderm's viscoelasticproperties. In the three-dimensional model, the limb bud ectodermis modeled as a network of nodes connected by linear elasticelements. The investigator also develops an algorithm forimposing the appropriate boundary conditions in solving thereaction-diffusion-advection equations. Because each of thesemodels includes a fluid-mechanical representation, theinvestigator uses a similar computational approach based on theimmersed boundary method and the computer codes share many of themajor subroutines. The purpose of this research project is the development ofmathematical models and computational methods for studying movingboundary problems in complex biological systems. The investigatordevelops two types of models: one for the motion of eukaryoticcilia and flagella and the second for the growth dynamics ofmulticellular biological systems. Both of these models involvenew approaches to the modeling of viscoelastic materials inbiology and share a common computational point of view. Theobject in the first project is to develop a three-dimensionalmodel for the individual cilium or flagellum. Although a greatdeal has been discovered regarding the biochemistry,ultrastructure and movement of eukaryotic cilia and flagella, themechanisms governing the control of oscillatory motion andbending are not well understood. The goal of the cilia andflagella modeling is to develop a three-dimensional model thatcan serve as a platform for studying the mechanochemicalmechanisms that control the waveforms. Growth plays an importantprocess for multicellular organisms as well as communities ofsingle cell organisms. The investigator develops a model ofvertebrate limb development that incorporates the growth andmovement of cells and tissue within the developing limb bud, thetransport and production of growth factors within the limb bud,and a moving boundary that represents the mechanical andbiochemical properties of the limb bud ectoderm. The developmentof this model and the computational methods for solving theassociated mathematical equations has application to the study ofa variety of multicellular systems where growth is an essentialfeature, including growth and pattern formation in developmentalbiology, the growth of bacterial colonies, as well as tumorgrowth. An important aspect of this project is the development ofnumerical methods for studying the models; advances in this areacan be used in a variety of problems in the field ofcomputational biofluids.