Biomedical Engineering Reference
In-Depth Information
4. Predicting Degradation of PEG Hydrogels
Predictions of the swelling and degradation of hybrid gels may be important in
the design of scaffolds for tissue engineering. The scaffold will presumably be
replaced by tissue due to degradation by host cells or proliferation of
transplanted cells. During the dissolution process, the scaffold will become
weaker as bonds are broken, either by hydrolysis or by cell-derived enzymatic
activity. In either case, the timing of degradation is crucial as the scaffold may
dissolve before the strength of the new tissue has developed. Mechanical
conditioning strengthens a variety of engineered tissues [74, 75], while stem cell
differentiation is influenced by mechanical properties [76, 77]. Changes in the
scaffold stiffness during degradation may thus complicate production of new
tissues.
In a hydrolytically degradable gel, the kinetics of bond breakage may be
assumed to be pseudo-first order due to buffering of the aqueous solution. In
highly swollen gels, the hydrolysis rate constants may be further assumed to be
similar to the solution values or at least constant throughout the degradation
process [24, 78]. For enzymatic degradation, Michaelis-Menten kinetics apply
[35]. With these assumptions, predicting when a PEG chain is released from the
gel is a simple matter of combinatorics. In Figure 4A, four-arm PEG-acrylate is
assumed to react with an enzymatically degradable peptide to form a network
[70]. The probability that exactly three of the arms are still attached to the
network as illustrated on the figure is
( )
4
3
p
(1
−
p
)
where
p
is the fraction of
3
peptides that are intact and
( )
4
3
is a binomial coefficient. Similarly, the amount
of PEG released by the hydrogel is given as (1-
p
)
4
. Degradation of more complex
hydrogels, such as those formed from the free-radical polymerization of acrylate-
oligolactide-PEG-oligolactide-acrylate, may also be predicted in a similar
manner (Figure 4B) [78-80]. Calculation of mass loss from the hydrogel as bonds
are hydrolyzed relies primarily on accurate values for the bond hydrolysis rate
constant, the length of the formed polyacrylate chain and the number of lactide
units connecting the PEG to the polyacrylate chain. If bonds are broken on both
sides of a PEG, the PEG is released from the gel. An entire polyacrylate chain
may similarly be released at high conversions [79]. The fraction of intact bonds
decays exponentially over time due to the pseudo-first order nature of the
process. Predicted release of PEG or polyacrylate over time may be compared to
the experimentally measured mass loss, with excellent agreement [79]. Final
dissolution of the hydrogel may be predicted by considering the degradation to
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