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Mathematical models for analysis of tissue regeneration in articular cartilage

机译：用于分析关节软骨组织再生的数学模型

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摘要

A supervised learning artificial neural network (ANN) method was developed for predicting structure-function relationships of elastin-like polypeptide (ELP) hydrogels in the context of articular cartilage repair applications. The ANN method was used to analyze two experimental data sets consisting of 22 and 16 unique ELP polymer formulations. The first data set used structural ELP characteristics of the 22 formulations to predict resulting hydrogel mechanical properties above and below the gel-transition temperature. The second data set explored the use of structural characteristics of the ELP hydrogels to predict mechanical properties, biochemical properties, and biological metabolites in cell-seeded tissue constructs. These functional outcomes are of interest to the experimentalist in the determination of an optimal hydrogel formulation for application to tissue regeneration in articular cartilage. The ANN was implemented in a custom compiled code based on the Scaled Conjugate Gradient minimization algorithm. For the first data set, the trained ANN demonstrated excellent accuracy in prediction of hydrogel dynamic shear modulus at physiological temperature, based on polymer design characteristics (molecular weight, concentration and crosslink density). A methodology for incorporation of supervised learning ANNs into rapid screening of intermediate data sets for experimental ELP preparations was proposed, and demonstrated high potential for accelerated realization of optimal design outcomes. For the second data set, the trained ANN was able to make many accurate predictions for key mechanical and biological outcomes.;A mathematical model and numerical solutions are presented for an interface problem that models an in vitro experiment for regeneration of articular cartilage in a localized defect region. In this experiment, a cylindrical cartilage explant has a core region removed and replaced with a nutrient-rich hydrogel. The gel-tissue aggregate is then immersed in media for a period of several weeks. An axisymmetric reaction-diffusion model of this experiment was developed to capture coupling between cell-mediated nutrient absorption and matrix biosynthesis, and diffusive transport of nutrients and matrix constituents. The reaction governing turnover of the hydrogel to newly synthesized tissue was modeled via a level set method that captures the moving gel-tissue interface as a function of a reaction rate controlling degradation of the hydrogel and the accumulation of newly synthesized matrix.;An extension of this model is presented, including the local effects of curvature on the speed of the moving interface. A 1-dimensional model was also developed as a simplification of the axisymmetric model. After nondimensionalization, finite difference numerical solutions were employed to simulate cartilage regeneration as a function of cell mediated reaction rates in the model. Both the cases of external media maintained at a homeostatic nutrient concentration, and at a higher concentration associated with the nutrient-rich hydrogel were considered. Via a detailed parametric analysis using the model, regeneration times required to completely degrade the hydrogel were determined. Potential effects of local curvature along the gel-tissue interface are discussed, and a comparison of regeneration times for the 1-dimensional and axisymmetric model is made.
机译：开发了一种监督学习的人工神经网络（ANN）方法，以预测在关节软骨修复应用中弹性蛋白样多肽（ELP）水凝胶的结构-功能关系。 ANN方法用于分析由22种和16种独特的ELP聚合物配方组成的两个实验数据集。第一个数据集使用22种配方的结构ELP特性预测了高于和低于凝胶转变温度的水凝胶机械性能。第二组数据探索了ELP水凝胶的结构特征在细胞接种的组织构建物中预测力学性能，生化特性和生物代谢产物的用途。这些功能性结果对于确定适用于关节软骨组织再生的最佳水凝胶制剂的实验者很感兴趣。 ANN是基于比例共轭梯度最小化算法的定制编译代码中实现的。对于第一个数据集，训练有素的人工神经网络基于聚合物的设计特征（分子量，浓度和交联密度）在预测生理温度下的水凝胶动态剪切模量方面表现出出色的准确性。提出了一种将有监督的学习型人工神经网络纳入快速筛选实验ELP制备的中间数据集的方法，并证明了加速实现最佳设计结果的巨大潜力。对于第二个数据集，训练有素的人工神经网络能够对关键的机械和生物学结果做出许多准确的预测。提出了针对界面问题的数学模型和数值解，该模型为体外实验中的局部关节软骨再生建模缺陷区域。在该实验中，圆柱形软骨外植体的核心区域被去除，并被营养丰富的水凝胶代替。然后将凝胶组织聚集体浸入培养基中数周。建立了本实验的轴对称反应扩散模型，以捕获细胞介导的养分吸收与基质生物合成之间的耦合，以及养分和基质成分的扩散运输。通过水平集方法对控制水凝胶向新合成组织的周转的反应进行建模，该方法捕获了移动的凝胶-组织界面，作为控制水凝胶降解和新合成基质积累的反应速率的函数。提出了该模型，包括曲率对移动界面速度的局部影响。一维模型也被开发为轴对称模型的简化。在无量纲化之后，采用有限差分数值解来模拟软骨再生与模型中细胞介导的反应速率的关系。都考虑了外部培养基保持稳态营养浓度和与富含营养的水凝胶相关的较高浓度的情况。通过使用该模型的详细参数分析，可以确定完全降解水凝胶所需的再生时间。讨论了沿凝胶-组织界面的局部曲率的潜在影响，并对一维模型和轴对称模型的再生时间进行了比较。

著录项

  • 作者

    Olson, Sarah D.;

  • 作者单位

    North Carolina State University.;

  • 授予单位 North Carolina State University.;
  • 学科 Mathematics.;Biomedical engineering.
  • 学位 Ph.D.
  • 年度 2008
  • 页码 144 p.
  • 总页数 144
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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