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Mathematical models and numerical methods for analysis of mechanical and chemical loading in articular cartilage.

机译：用于分析关节软骨机械和化学负荷的数学模型和数值方法。

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摘要

Articular cartilage is the primary load-bearing soft tissue in diarthroidal joints. Multiphasic continuum mixture models have been used to describe the relative contribution of effects due to solid, fluid, and ionic phases in cartilage. This research is motivated by the need to quantify differences between normal and osteoarthritic mechanical and physico-chemical states in cartilage. In this dissertation, three studies were conducted involving the development of numerical methods and mathematical models pertaining to the cell and extracellular matrix (ECM) of articular cartilage.; In the first investigation, an accelerated numerical method for the continuous spectrum biphasic poroviscoelastic model of cartilage was developed. The method was based on an alternate formulation of the quasi-linear viscoelastic law, a model for intrinsic dissipation in cartilage ECM in which the solid matrix stress depends on the strain rate via a hereditary integral with a continuous relaxation spectrum. It was implemented using quadrature integration in combination with interpolation of the strain history. The accuracy and cost of the method were compared to a theoretical solution of the 1-D confined compression stress-relaxation problem.; The second study consisted of the formulation and application of a triphasic mechano-chemical model to analyze osmotic loading experiments for an isolated cartilage cell. The model was formulated under the hypothesis that the cell membrane was permeable to both water and ions. A non-zero chemical-expansion stress was required to balance the elastic stress. Since the existence of an intracellular chemical-expansion stress is not well established, it was hypothesized that the cell model should be modified to include a selectively permeable membrane.; The third investigation consisted of the formulation and application of a mechano-chemical model to analyze osmotic loading experiments for an isolated chondron. The chondron is comprised of a cartilage cell and its encapsulating pericellular matrix (PCM). In the chondron, the cell membrane was assumed to be permeable to water, but impermeable to ions. Parametric and asymptotic analyses were conducted to compare cell, PCM, and chondron deformation under osmotic loading.
机译：关节软骨是脉络膜关节的主要承重软组织。多相连续介质混合物模型已用于描述由于软骨中的固相，流体和离子相而产生的相对影响。这项研究的动机是需要量化软骨中正常和骨关节炎的机械和理化状态之间的差异。本文进行了三项研究，涉及与关节软骨细胞和细胞外基质（ECM）有关的数值方法和数学模型的发展。在首次研究中，开发了一种用于连续谱双相软骨弹性模型的加速数值方法。该方法基于准线性粘弹性定律的替代公式，准线性粘弹性定律是软骨ECM内在耗散的模型，其中固体基质应力取决于具有连续弛豫谱的遗传积分的应变率。它是使用正交积分结合应变历史插值来实现的。该方法的准确性和成本与一维约束压缩应力松弛问题的理论解进行了比较。第二项研究包括三相机械化学模型的建立和应用，以分析分离的软骨细胞的渗透负荷实验。该模型是在细胞膜对水和离子都可渗透的假设下制定的。需要非零的化学膨胀应力来平衡弹性应力。由于不能很好地确定细胞内化学膨胀应力的存在，因此假设应该修改细胞模型以包括选择性渗透膜。第三次调查包括机械化学模型的制定和应用，以分析孤立的罐子的渗透负荷实验。软骨由软骨细胞及其包裹的细胞周围基质（PCM）组成。在软骨球中，细胞膜被认为是水可渗透的，但是离子是不可渗透的。进行了参数和渐近分析，以比较渗透负荷下的细胞，PCM和软骨变形。

著录项

  • 作者

    Schugart, Richard Charles.;

  • 作者单位

    North Carolina State University.;

  • 授予单位 North Carolina State University.;
  • 学科 Mathematics.; Biophysics Medical.
  • 学位 Ph.D.
  • 年度 2005
  • 页码 146 p.
  • 总页数 146
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;生物物理学;
  • 关键词

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