4D Numerical Analysis of Scaffolds: A New Approach - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 75

Fig. 3 Tensile strength vs.
time for different initial
molecular weight (based
on [ 12 ])

The storage or sterilization processes may pre-degrade the material, leading to re-
duction of degradation time and its initial mechanical strength, but the rate of degra-
dation remains the same. To tune degradation time, specimens with different initial
molecular weight can be created by gamma-irradiation starting from commercial
materials available. Regrettably, this technique also reduces the initial mechanical
properties of the materials.
Equation ( 7 ) is not a very good model for tensile strength, except in the brit-
tle failure regime for amorphous polymers or semi-crystalline polymers below their
glass transition temperature. This is a common problem with highly ductile poly-
mers. In these cases, it is more correct to use true values instead of nominal stress
and strain, by assuming that the deformation occurs at constant volume [ 57 ]. In this
case, the true area, A , is given by A 0 /( 1 + ε) ; where A 0 is the initial area and ε is

the nominal strain. This leads to the true stress being given by ( 1 + ε) ∗ σ a ; where

σ a is the apparent stress based on A 0 .
As it will be shown in the next sections, strength follows the same trend as the
molecular weight:

e − ut (8)
The hydrolytic damage, defined by the ratio between the initial strength of the
virgin material and the current strength, after a certain degradation time, is:

σ t = σ 0 ∗

σ t
σ 0 =

e − ut e − kEwt d h = 1 − 1 − = 1 − (9)

So the hydrolytic damage depends on the hydrolysis kinetic constant, k , the con-
centrations of ester groups, E , the water concentration in the polymer matrix, w ,
and the degradation time t . The hydrolysis kinetic constant, k , is a thermodynamic
quantity associated with the probability of molecular scission, and it depends on
temperature, load applied to the material and pH of the aqueous media. The pH of
the aqueous medium also affects the hydrolysis reaction rates [ 21 ]. Tsuji et al. stud-
ied the hydrolysis of PLLA films at 37 °C in alkaline solution (pH 12) [ 45 ], acid
solution (pH 2.0) [ 47 ] and phosphate-buffered solutions (pH 7.4) [ 46 ]. In the human
body, pH can be considered constant, kept by the organism at a homeostatic value.
Temperature will augment diffusion due to increased molecular flexibility, but
it will also amplify the hydrolysis rate, due to excitement of the molecules that it