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Implementation and Validation of Finite Element Framework for Passive and Active Membrane Transport in Deformable Multiphasic Models of Biological Tissues and Cells

机译：在生物组织和细胞的可变形多相模型中被动和主动膜运输的有限元框架的实现和验证

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摘要

The chondrocyte is the only cell type in articular cartilage, and its role is to maintain cartilage integrity by synthesizing and releasing macromolecules into the extracellular matrix (ECM) or breaking down its damaged constituents (Stockwell, 1991). The two major constituents of the ECM are type II collagen and aggrecans (aggregating proteoglycans). Proteoglycans have a high negative charge which attracts cations and increases the osmolarity, while also lowering the pH of the interstitial fluid. The fibrillar collagen matrix constrains ECM swelling that results from the Donnan osmotic pressure produced by proteoglycans (Wilkins et al., 2000). Activities of daily living produce fluctuating mechanical loads on the tissue which also alter the mechano-electro-chemical environment of chondrocytes embedded in the ECM. These conditions affect the physiology and function of chondrocytes directly (Wilkins et al., 2000; Guilak et al., 1995; Guilak et al., 1999). Relatively few studies of in situ chondrocyte mechanics have been reported in the biomechanics literature, in contrast to the more numerous experimental studies of the mechanobiological response of live cartilage explants to various culture and loading conditions. Analyses of chondrocyte mechanics can shed significant insights in the interpretation of experimental mechanobiological responses. Predictions from carefully formulated biomechanics models may also generate hypotheses about the mechanisms that transduce signals to chondrocytes via mechanical, electrical and chemical pathways. Therefore, computational tools that can model the response of cells, embedded within a charged hydrated ECM, to various loading conditions may serve a valuable role in mechanobiological studies.;Computational modeling has become a necessary tool to study biomechanics with complex geometries and mechanisms (De et al., 2010). Usually, theoretical and computational models of cell physiology and biophysics are formulated in 1D, deriving solutions by solving ordinary differential equations, such as cell volume regulation (Tosteson and Hoffman, 1960), pH regulation (Boron and De Weer, 1976), and Ca2+ regulation (Schuster et al., 2002). Cell modeling software, such as The Virtual Cell (vcell.org Moraru et al. (2008)), analyze stationary cell shapes and isolated cells. To model the cell-ECM system while accounting for ECM deformation, the fibrillar nature of the ECM, interstitial fluid flow, solute transport, and electrical potential arising from Donnan or streaming effects, we adopt the multiphasic theory framework (Ateshian, 2007). This framework serves as the foundation of multiphasic analyses in the open source finite element software FEBio (Maas et al., 2012; Ateshian et al., 2013), which was developed specifically for biomechanics and biophysics, and offers a suitable environment to solve complex models of cell-ECM interactions in 3D.;In the studies proposed here, we will extend the functionality of FEBio to further investigate the cell-ECM system. These extensions and studies are summarized in the following chapters:;Chapter 1: This introductory chapter provides the general background and specific aims of this dissertation.;Chapter 2: Cell-ECM interactions depend significantly on the ECM response to external loading conditions. For fibrillar soft tissues such as articular cartilage, it has been shown that modeling the ECM using a continuous fiber distribution produces much better agreement with experimental measurements of its response to loading. However, evaluating the stress and elasticity tensors for such distributions is computationally very expensive in a finite element analysis. In this aim we develop a new numerical integration scheme to calculate these tensors more efficiently than standard techniques, only accounting for fibers that are in tension.;Chapter 3: Cell-ECM interactions also depend significantly on accurate modeling of selective transport across the cell membrane. However, the thickness of this membrane is typically three orders of magnitude smaller than the cell size, which poses significant numerical challenges when modeling the membrane using the finite element method, such as element locking. To date, no existing finite element software offers a multiphasic membrane element. In this aim, we formulate and implement a new membrane element in FEBio, which can accommodate fluid and solute transport within the biphasic and multiphasic framework, to model passive and selective transport across the cell membrane.;Chapter 4: This aim extends Aim 2 to incorporate reactions across multiphasic membrane elements in FEBio, to model the conformational reactions of cell membrane transporters, such as carrier-mediated transporters and membrane pumps. This implementation is verified against standard models for the regulation of cell volume, pH, and Ca2+.;Chapter 5: This final chapter provides a summary of the advances contributed in this dissertation, along with suggestions for future aims related to the topics covered here.;With the completion of these aims, we have extended the modeling capabilities for cell physiology and mechanobiology to more complex multicellular systems embedded within their ECM, while subjected to a range of varying mechanical, electrical or chemical loading conditions.
机译：软骨细胞是关节软骨中唯一的细胞类型，其作用是通过合成大分子并将其释放到细胞外基质（ECM）或分解其受损成分来维持软骨完整性（Stockwell，1991）。 ECM的两个主要成分是II型胶原蛋白和聚集蛋白聚糖（聚集蛋白聚糖）。蛋白聚糖具有高的负电荷，该负电荷吸引阳离子并增加渗透压，同时也降低组织液的pH。纤维状胶原基质抑制了由蛋白聚糖产生的Donnan渗透压导致的ECM肿胀（Wilkins等，2000）。日常生活活动在组织上产生波动的机械负荷，这也改变了嵌入ECM中的软骨细胞的机械电化学环境。这些条件直接影响软骨细胞的生理和功能（Wilkins等，2000； Guilak等，1995； Guilak等，1999）。在生物力学文献中，相对较少的原位软骨细胞力学研究报道，与之相比，关于软骨活体外植体对各种培养和负荷条件的力学生物学响应的实验研究则更多。软骨细胞力学分析可以解释实验力学生物学反应中的重要见解。精心制定的生物力学模型的预测也可能会产生关于通过机械，电气和化学途径将信号转导至软骨细胞的机制的假设。因此，可以模拟嵌入带电水合ECM中的细胞对各种负荷条件的响应的计算工具可能在力学生物学研究中发挥重要作用。;计算建模已成为研究具有复杂几何形状和机制的生物力学的必要工具（De等（2010）。通常，细胞生理学和生物物理学的理论模型和计算模型是用一维公式化的，它是通过求解常微分方程（例如细胞体积调节（Tosteson和Hoffman，1960年），pH调节（Boron和De Weer，1976年）和Ca2 + （Schuster et al。，2002）。细胞建模软件，例如The Virtual Cell（vcell.org Moraru et al。（2008）），可以分析固定细胞的形状和分离的细胞。为了在考虑ECM变形，ECM的纤维状性质，间隙流体流动，溶质输运以及Donnan或流效应产生的电势的同时对细胞ECM系统进行建模，我们采用了多相理论框架（Ateshian，2007年）。该框架是开源有限元软件FEBio（Maas等人，2012; Ateshian等人，2013）中多相分析的基础，该软件专为生物力学和生物物理学开发，为解决复杂问题提供了合适的环境。 3D中的细胞-ECM相互作用模型。;在本文提出的研究中，我们将扩展FEBio的功能以进一步研究细胞-ECM系统。这些扩展和研究在以下各章中进行了概括：第1章：本介绍性章节提供了本论文的总体背景和具体目标。第2章：细胞-ECM相互作用在很大程度上取决于ECM对外部负载条件的响应。对于纤维状软组织，例如关节软骨，已经表明，使用连续纤维分布对ECM建模可以更好地与实验测量其对负荷响应的一致性。但是，在有限元分析中，评估这种分布的应力和弹性张量在计算上非常昂贵。在这个目标中，我们开发了一种新的数值积分方案，以比标准技术更有效地计算这些张量，仅考虑了处于拉伸状态的纤维。;第3章：细胞-ECM相互作用也显着依赖于跨细胞膜选择性转运的准确模型。然而，该膜的厚度通常比孔的尺寸小三个数量级，这在使用有限元方法（例如，元素锁定）对膜进行建模时提出了重大的数值挑战。迄今为止，尚无现有的有限元软件提供多相膜元件。为此，我们在FEBio中制定并实施了一种新的膜元件，该膜元件可以在双相和多相框架内容纳流体和溶质的运输，以模拟跨细胞膜的被动和选择性运输。;第4章：该目标将目标2扩展至在FEBio中将跨多相膜元件的反应纳入其中，以模拟细胞膜转运蛋白的构象反应，例如载体介导的转运蛋白和膜泵。对照标准模型对细胞体积，pH和Ca2 +的调节，验证了该实现。第五章：最后一章总结了本论文的进展。以及与本文涵盖的主题相关的未来目标的建议。随着这些目标的完成，我们将细胞生理学和力学生物学的建模功能扩展到了嵌入在其ECM中的更复杂的多细胞系统，同时受到了各种变化的影响。机械，电气或化学负载条件。

著录项

  • 作者

    Hou, Chieh.;

  • 作者单位

    Columbia University.;

  • 授予单位 Columbia University.;
  • 学科 Mechanical engineering.;Biomedical engineering.
  • 学位 Ph.D.
  • 年度 2018
  • 页码 165 p.
  • 总页数 165
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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