Biomedical Engineering Reference
In-Depth Information
Chapter 2
Modeling Collagen-Proteoglycan Structural
Interactions in the Human Cornea
Xi Cheng, Hamed Hatami-Marbini, and Peter M. Pinsky
Abstract
The cornea is a supremely organized connective tissue making it ideal
for modeling and probing possible roles of collagen-PG interactions in the extra-
cellular matrix. The cornea can be viewed as a reinforced electrolyte gel involving
molecular-scale interactions between collagen fibrils, proteoglycans (PGs) and the
mobile ions in the interfibrillar space. The swelling property of the tissue cannot
be adequately predicted by Donnan theory for osmotic pressure. We propose an
alternative unit cell approach based on a thermodynamic framework that employs
a mean-field approximation for the electrostatic free energy and which accounts
for a non-uniform electrostatic potential. The model is used to show that the equi-
librium swelling pressure can be explained when the geometrical effect of elec-
trolyte exclusion due to collagen fibril volume is considered. The model is further
refined by dividing the PGs into collagen fibril coating and volumetric partitions.
The model suggests that the PG coatings overlap at low hydration and set up re-
pulsive forces that may act to maintain the collagen lattice order. Finally, we intro-
duce a molecular-level unit cell in which volumetric domains within the unit cell
are associated with the macromolecular GAGs and results from the continuum and
molecular-level models are compared.
X. Cheng
)
Department of Mechanical Engineering, Stanford University, 496 Lomita Mall,
Stanford, CA, USA
e-mail:
pinsky@stanford.edu
X. Cheng
e-mail:
cx1012@stanford.edu
·
H. Hatami-Marbini
·
P.M. Pinsky (
Present address:
H. Hatami-Marbini
School of Mechanical and Aerospace Engineering, Oklahoma State University,
218 Engineering North, Stillwater, OK, USA
e-mail:
hhatami@okstate.edu
