scholarly journals 23Na MRI accurately measures fixed charge density in articular cartilage

2002 ◽  
Vol 47 (2) ◽  
pp. 284-291 ◽  
Author(s):  
Erik M. Shapiro ◽  
Arijitt Borthakur ◽  
Alexander Gougoutas ◽  
Ravinder Reddy
Keyword(s):  
Articular Cartilage ◽  
Charge Density ◽  
Fixed Charge ◽  
Fixed Charge Density ◽  
23Na Mri

Dependence of Electrical Conductivity on Fixed Charge Density in Articular Cartilage

1983 ◽  
Vol &NA; (177) ◽  
pp. 283???288 ◽  
Author(s):  
ISAO HASEGAWA ◽  
SHINYA KURIKI ◽  
SHIGEO MATSUNO ◽  
GORO MATSUMOTO
Keyword(s):  
Electrical Conductivity ◽  
Articular Cartilage ◽  
Charge Density ◽  
Fixed Charge ◽  
Fixed Charge Density

A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage

1991 ◽  
Vol 113 (3) ◽  
pp. 245-258 ◽  
Author(s):  
W. M. Lai ◽  
J. S. Hou ◽  
V. C. Mow
Keyword(s):  
Articular Cartilage ◽  
Charge Density ◽  
Fixed Charge ◽  
Solid Matrix ◽  
Confined Compression ◽  
Fixed Charge Density ◽  
Chemical Expansion ◽  
Chemical Potentials ◽  
Free Swelling ◽  
Triphasic Theory

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 cF. For a uni-uni valent salt such as NaCl, they are given by μi = μoi + (RT/Mi)ln[γ±2c (c + c F)] and μW = μow + [p − RTφ(2c + cF) + Bwe]/ρTw, where R, T, Mi, γ±, φ, ρTw and Bw 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 σ = − pI − TcI + λs(trE)I + 2μsE, where E is the strain tensor and (λs,μs) are the Lame´ constants of the elastic solid matrix. The chemical-expansion stress (− Tc) 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.

Indentation Determined Mechanoelectrochemical Properties and Fixed Charge Density of Articular Cartilage

2004 ◽  
Vol 32 (3) ◽  
pp. 370-379 ◽  
Author(s):  
X. Lux Lu ◽  
Daniel D. N. Sun ◽  
X. Edward Guo ◽  
Faye H. Chen ◽  
W. Michael Lai ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Charge Density ◽  
Fixed Charge ◽  
Fixed Charge Density

Effects of Inhomogeneous Fixed Charge Density on the Electrical Signals for Chondrocytes in Cartilage

2000 ◽  
Author(s):  
W. M. Lai ◽  
D. D. Sun ◽  
G. A. Ateshian ◽  
X. E. Guo ◽  
V. C. Mow
Keyword(s):  
Signal Transduction ◽  
Articular Cartilage ◽  
Charge Density ◽  
Streaming Potential ◽  
Potential Difference ◽  
Fixed Charge ◽  
Diffusion Potential ◽  
Solid Matrix ◽  
Fixed Charge Density ◽  
Transduction Mechanisms

Abstract An important step toward understanding the signal transduction mechanisms that modulate cellular activities is the accurate prediction of the mechanical and electro-chemical environment of the cells in well-defined experimental configurations. One such configuration is the steady permeation experiment (e.g., bioreactors) in the open circuit condition. Using our triphasic theory, we have calculated the strain, velocity and the electric potential fields inside a layer of charged articular cartilage, through which a uni-univalent salt (e.g., NaCl) solution permeates under a constant pressure difference across the layer. The fluid flow through the tissue gives rise to an electrical potential difference across the tissue. This potential difference is the well-known “streaming potential” that is measured by Ag/AgCl electrodes placed across the tissue on the outside. Our results show that inside the tissue, in addition to the streaming potential caused by fluid convection, there is also a “diffusion potential” caused by cation and anion concentration gradients that are induced by the gradient of fixed charge density (FCD) inside the tissue. The gradient of FCD may be intrinsic, i.e., the tissue has an inhomogeneous FCD distribution, or it may also be caused by a non-uniform compaction of the solid matrix as is the case in steady permeation where the drag force exerted by the permeating fluid onto the solid matrix causes a compressive strain field inside the tissue. In this experimental configuration, the diffusion potential would compete against the streaming potential. The magnitude and the polarity of the electric field depend, amongst other material parameters, on the compressive stiffness of the tissue. For softer tissue (e.g., aggregate modulus <0.54 MPa for a set of realistic material and testing parameters), the diffusion potential dominates over the streaming potential and vice versa for stiffer tissue. For articular cartilage what the cells see in situ is the combined electrical effect of intrinsic and deformation induced inhomogeneity of FCD. The present results provide not only quantitative information, but also new insight into an important problem in biotechnology. These results also demonstrate that for proper interpretation of the mechano-electrochemical signal transduction mechanisms that is needed for modulating cellular biosynthetic activities, one must not ignore the important effects of diffusion potential.

Sign in / Sign up

Export Citation Format

Share Document