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TECHNICAL PAPERS

A Molecular Model of Proteoglycan-Associated Electrostatic Forces in Cartilage Mechanics

[+] Author and Article Information
M. D. Buschmann, A. J. Grodzinsky

Continuum Electromechanics Group, Laboratory for Electromagnetic and Electronic Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139

J Biomech Eng 117(2), 179-192 (May 01, 1995) (14 pages) doi:10.1115/1.2796000 History: Received April 04, 1993; Revised July 26, 1994; Online October 30, 2007

Abstract

Measured values of the swelling pressure of charged proteoglycans (PG) in solution (Williams RPW, and Comper WD; Biophysical Chemistry 36:223, 1990) and the ionic strength dependence of the equilibrium modulus of PG-rich articular cartilage (Eisenberg SR, and Grodzinsky AJ; J Orthop Res 3: 148, 1985) are compared to the predictions of two models. Each model is a representation of electrostatic forces arising from charge present on spatially fixed macromolecules and spatially mobile micro-ions. The first is a macroscopic continuum model based on Donnan equilibrium that includes no molecular-level structure and assumes that the electrical potential is spatially invariant within the polyelectrolyte medium (i.e. zero electric field). The second model is based on a microstructural, molecular-level solution of the Poisson-Boltzmann (PB) equation within a unit cell containing a charged glycosaminoglycan (GAG) molecule and its surrounding atmosphere of mobile ions. This latter approach accounts for the space-varying electrical potential and electrical field between the GAG constituents of the PG. In computations involving no adjustable parameters, the PB-cell model agrees with the measured pressure of PG solutions to within experimental error (10%), whereas the ideal Donnan model overestimates the pressure by up to 3-fold. In computations involving one adjustable parameter for each model, the PB-cell model predicts the ionic strength dependence of the equilibrium modulus of articular cartilage. Near physiological ionic strength, the Donnan model overpredicts the modulus data by 2-fold, but the two models coincide for low ionic strengths (C0 < 0.025M) where the spatially invariant Donnan potential is a closer approximation to the PB potential distribution. The PB-cell model result indicates that electrostatic forces between adjacent GAGs predominate in determining the swelling pressure of PG in the concentration range found in articular cartilage (20–80 mg/ml). The PB-cell model is also consistent with data (Eisenberg and Grodzinsky, 1985, Lai WM, Hou JS, and Mow VC; J Biomech Eng 113: 245, 1991) showing that these electrostatic forces account for ̃ 1/2 (290kPa) the equilibrium modulus of cartilage at physiological ionic strength while absolute swelling pressures may be as low as ̃ 25 – 100kPa. This important property of electrostatic repulsion between GAGs that are highly charged but spaced a few Debye lengths apart allows cartilage to resist compression (high modulus) without generating excessive intratissue swelling pressures.

Copyright © 1995 by The American Society of Mechanical Engineers
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