A molecular theory of cartilage viscoelasticity
A molecular theory of cartilage viscoelasticity
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DOI：
10.1016/0301-4622(95)00115-8
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发表时间：
1996-03-07
影响因子：
3.8
通讯作者：
Kovach, IS
中科院分区：
文献类型：
--
作者：
Kovach, IS
关于软骨力学主题的最近工作已经开始关注软骨的微观结构与其宏观力学性质之间的关系（Bader等人，生物化学生物物理学Acta，1116（1992）147-154; Buschmann，PhD Thesis，马萨诸塞州理工学院，1992; Kovach，Biophys.化学成分：53（1995）181-187; Lai等人，生物化学工程杂志，113（1991）245-248; Armstrong和Mow，J Bone Jt.外科医生、64 A（1982）88;杰克逊和詹姆斯，生物流变学，19（1982）317-330）。本文综述了最近的理论发展，并提出了一个全面的解释的粘弹性软骨的分子结构。在这样做时，开发了非线性圆柱Poisson-Boltzmann方程的封闭形式混合解，以描述由多糖电荷引起的平衡弹性的电荷依赖分量（Benham，J. Chem. Phys.，79（4）（1983）1969- 1973; Einevoll和Hemmer，J. Phys. Chem.，89（1）（1988）474-484; Fixman，J. Chem. Phys.，70（11）（1979）4995-5001; Ramanathan和Woodburg，J. Chem. Phys.，82（3）（1985）1482-1491; Wennerstrom等人，J. Chem. Phys.，76（9）（1982）4665-4670）。该解与文献（Buschmann，PhD Thesis，马萨诸塞州理工学院，1992）中的数值解一致。对平衡弹性的不依赖于电荷的熵贡献以类似于最近针对浓缩蛋白聚糖溶液提出的方式来解释（Kovach，Biophys.化学成分：53（1995）181-187）。该方法利用溶液的晶格模型，经受Bragg-Williams型近似以导出多糖构型熵的体积依赖性（Flory，Principles of Polymer Chemistry，Cornell University Press，Ithaca，NY，1953; Huggins，Some properties of Solutions of Long-chain Compounds，1941，pp. 151-157; Stanley，Introduction to Phase Transitions and Critical Phenomena，Oxford University Press，Oxford，1971）。这两个贡献一起精确地再现了先前由Maroudas（Maroudas和Bannon，Biorheology，18（1981）619-632）确定的实验确定的软骨渗透压。根据Kirkwood-Riseman型模型（柯克伍德和Riseman，J. Chem. Phys.，16（6）（1948）573-579）。该方法显示出准确地预测软骨的水力渗透性，如先前由Maroudas（Madouras，Ann. Rheum. Dis.，34（suppl.3）（1975）77）。通过使用一个准静态近似（忽略惯性效应）的时间依赖性响应的均匀压缩力的确定，也被发现是在良好的协议与文献中的实验值。
Recent work on the subject of cartilage mechanics has begun to focus on the relationship between the microscopic structure of cartilage and its macroscopic mechanical properties (Bader et al., Biochem. Biophys. Acta, 1116 (1992) 147-154; Buschmann, PhD Thesis, Massachusetts Institute of Technology, 1992; Kovach, Biophys. Chem., 53 (1995) 181-187; Lai et al., J. Biochem. Eng., 113 (1991) 245-248; Armstrong and Mow, J Bone Jt. Surg., 64A (1982) 88; Jackson and James, Biorheology, 19 (1982) 317-330). This paper reviews recent theoretical developments and presents a comprehensive explanation of the viscoelastic properties of cartilage in terms of molecular structure. In doing this, a closed form hybrid solution to the non-linear, cylindrical Poisson-Boltzmann equation is developed to describe the charge-dependent component of the equilibrium elasticity arising from polysaccharide charge (Benham, J. Chem. Phys., 79 (4) (1983) 1969-.1973; Einevoll and Hemmer, J. Phys. Chem., 89 (1) (1988) 474-484; Fixman, J. Chem. Phys., 70 (11) (1979) 4995-5001; Ramanathan and Woodburg, J. Chem. Phys., 82 (3) (1985) 1482-1491; Wennerstrom et al., J. Chem. Phys., 76 (9) (1982) 4665-4670). This solution agrees with numerical solutions found in the literature (Buschmann, PhD Thesis, Massachusetts Institute of Technology, 1992). The charge-independent, entropic contribution to the equilibrium elasticity is explained in a manner similar to that recently presented for concentrated proteoglycan solution (Kovach, Biophys. Chem., 53 (1995) 181-187). This approach exploits a lattice model of the solution, subject to a Bragg-Williams type approximation to derive the volume dependence of polysaccharide configuration entropy (Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953; Huggins, Some properties of Solutions of Long-chain Compounds, 1941, pp. 151-157; Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, Oxford, 1971). Together, these two contributions accurately reproduce the experimentally determined osmotic pressure of cartilage as previously determined by Maroudas (Maroudas and Bannon, Biorheology, 18 (1981) 619-632). The time-dependent, or creep, phenomena which cartilage exhibits when subject to mechanical load is explained in terms of frictional drag on the polysaccharide chain monomers in terms of a Kirkwood-Riseman type model (Kirkwood and Riseman, J. Chem. Phys., 16 (6) (1948) 573-579). This approach is shown to accurately predict the hydraulic permeability of cartilage as previously determined by Maroudas (Madouras, Ann. Rheum. Dis., 34 (suppl. 3) (1975) 77). By use of a quasi-static approximation (neglecting inertial effects) the time-dependent response to a uniform compressive force is determined and also found to be in good agreement with experimental values from the literature.