A TRIPHASIC THEORY FOR THE SWELLING AND DEFORMATION BEHAVIORS OF ARTICULAR-CARTILAGE

被引:853
作者
LAI, WM
HOU, JS
MOW, VC
机构
[1] COLUMBIA UNIV,DEPT MECH ENGN,ORTHOPAED RES LAB,NEW YORK,NY 10032
[2] COLUMBIA UNIV,DEPT ORTHOPAED SURG,NEW YORK,NY 10032
来源
JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME | 1991年 / 113卷 / 03期
关键词
D O I
10.1115/1.2894880
中图分类号
Q6 [生物物理学];
学科分类号
071011 ;
摘要
Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density c(F). For a uni-uni valent salt such as NaCl, they are given by my(i) = mu(o)i at (RT/M(i))ln[gamma(2) +/- c(c + c(F))] and mu(w) = mu(o)w + [p - RT-phi(2c + c(F)) + B(w)e]/rho(T)w, where R, T, M(i), gamma +/-, phi, rho(T)w and B(w) are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is sigma = - pI - TcI + lambda(s)(trE)I + 2-mu(s)E, where E is the strain tensor and (lamba(s),mu(s)) are the Lame constants of the elastic solid matrix. The chemical-expansion stress (- T(c)) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the "pre-stress" in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.
引用
收藏
页码:245 / 258
页数:14
相关论文
共 36 条