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Multi-level modelling of elastic filament networks

弹性丝网络的多层次建模

基本信息

批准号：
1812069
负责人：
金额：
--
依托单位：
University of Leeds
依托单位国家：
英国
项目类别：
Studentship
财政年份：
2016
资助国家：
英国
起止时间：
2016 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=studentship-1812069
关键词：
Multi level modelling elastic filament

项目摘要

Many materials are made up of interconnected networks of narrow fibres. This includes everyday items such as paper, felt and nappies, but also sophisticated materials fabricated for specific purposes, such as scaffolds used in tissue engineering, and self-assembled networks of small proteins that have applications including restoring lost tooth enamel. It is often important to control the mechanical properties of these networks for their given application. To help design and fabricate better materials it is advantageous to have a structure-function relation between controllable microscopic properties (e.g. fibre thickness) and the corresponding macroscopic properties. However, no trusted relation exists, necessitating costly and time-consuming experiments to be performed.Not all fibre networks are synthetic. Mammalian cells contain a network of protein filaments known as the cellular cytoskeleton which plays a load-bearing role in a number of important cellular functions, and for this reason has long been the subject of scrutiny from biophysicists. A key development was the introduction of computer modelling just over a decade ago, which lead to a rapid increase in our understanding of such networks. For example, it became possible to measure to what extent the network deforms uniformly (or 'affinely'), and delineate combinations of network density and fibre thickness for which affinity is, or is not, expected. Since affinity was also shown to be strongly coupled to material stiffness, this issue is of central importance.Current computer modelling of elastic fibre networks is limited due to the sub-optimal algorithms being employed. Although two-dimensional networks are straightforward, in three-dimensions only small networks, not representative of the real material, can be simulated. Placing the fibres on a lattice increases the system size, but again no longer represents real materials. The simulation methodology follows the original template set down over 10 years ago, where the network response is formulated as a matrix equation that is solved using an iterative algorithm. System sizes can be increased by preconditioning the matrix (roughly, guessing a partial solution in advance), but only basic preconditioners have been employed. This is despite the fact that the computer science community have already devised far more advanced methods, including one known as algebraic multi-grid which has been proven to give enormous increases in speed for standard problems.The purpose of this project is to design, implement and optimise a computer model for determining the mechanical properties of elastic fibre networks that employs algebraic multigrid preconditioning, making it the most efficient software solution for this class of material. This will be used to construct the first structure-function relation for large systems quantitatively representative of real materials. The linear solver will be implemented first, and this will be used to answer outstanding questions with regards cytoskeleton research. We shall then implement a non-linear solver for when the load applied to the system (or the deformation imposed upon it) is no longer small, and employ this to quantitatively understand recent puzzling experimental measurements on tissue scaffolds and protein networks. Beneficiaries will be companies and other academic groups who will be able to freely use our algorithms, which will be optimal (up to scaling) ad therefore future proof. We will also exploit the range of contacts within Leeds to further develop and apply the model to non-woven fibres, peptide gels and tissue engineering scaffolds.

许多材料都是由相互连接的窄纤维网络组成的。这包括日常用品，如纸张，毛毡和尿布，但也包括为特定目的制造的复杂材料，如组织工程中使用的支架，以及小蛋白质的自组装网络，其应用包括恢复丢失的牙釉质。对于它们的特定应用，控制这些网络的机械性能通常是重要的。为了帮助设计和制造更好的材料，有利的是在可控的微观性质（例如纤维厚度）和相应的宏观性质之间具有结构-功能关系。然而，由于不存在可信关系，因此需要进行昂贵且耗时的实验。并非所有光纤网络都是合成的。哺乳动物细胞含有蛋白质丝网络，称为细胞骨架，其在许多重要的细胞功能中起着承重作用，因此长期以来一直是生物药理学家的研究对象。一个关键的发展是十多年前引入计算机建模，这导致我们对这种网络的理解迅速增加。例如，可以测量网络均匀变形（或“亲和”）的程度，并描绘网络密度和纤维厚度的组合，预期亲和性或不亲和性。由于亲和力也被证明是强烈耦合到材料的刚度，这个问题是至关重要的。目前的计算机建模的弹性纤维网络是有限的，由于次优算法正在使用。虽然二维网络是直接的，但在三维中，只能模拟不代表真实的材料的小网络。将纤维放置在晶格上增加了系统的尺寸，但不再代表真实的材料。模拟方法遵循10年前制定的原始模板，其中网络响应被公式化为使用迭代算法求解的矩阵方程。系统的大小可以通过预处理矩阵（粗略地说，预先猜测部分解）来增加，但只使用了基本的预处理器。尽管计算机科学界已经设计出了更先进的方法，包括一种被称为代数多重网格的方法，该方法已被证明可以大大提高标准问题的速度。本项目的目的是设计、实现和优化一个计算机模型，用于确定采用代数多重网格预处理的弹性纤维网络的力学性能，使其成为这类材料最有效的软件解决方案。这将用于构建定量代表真实的材料的大型系统的第一个结构-功能关系。线性求解器将首先实现，这将用于回答有关细胞骨架研究的突出问题。然后，我们将实现一个非线性求解器，当施加到系统上的负载（或施加在其上的变形）不再小时，并利用它来定量地理解最近令人困惑的组织支架和蛋白质网络的实验测量。受益者将是公司和其他学术团体，他们将能够自由使用我们的算法，这将是最佳的（可扩展的）广告，因此是未来的证明。我们还将利用利兹的联系范围，进一步开发和应用模型，以非织造纤维，肽凝胶和组织工程支架。