4D Numerical Analysis of Scaffolds: A New Approach - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 72

To fully model the erosion process, a complex mathematical model is needed
to account for all the reaction steps and for the structural and morphologic details.
The parameters in such a model require extensive experimentation. Numerical tech-
niques have been used [ 5 , 15 , 17 , 29 , 56 , 58 ] to solve the corresponding equations
for devices of both simple and complicated geometries, in the context of drug re-
lease systems. However, these models did not account for the mechanical properties
degradation of these devices.
Polymer degradation is the first step of the erosion phenomenon. The complete
erosion of the polymer is known to take substantially longer than the complete loss
of tensile strength. During this first phase, aqueous solution penetrates the polymer,
followed by hydrolytic degradation, converting these very long polymer chains into
shorter water-soluble fragments, which can be regarded as a reverse polyconden-
sation process. For example, PLA becomes soluble in water for molecular weight,
M n , below

≈ 20 . 000 (g / mol) [ 59 ].

4 Hydrolytic Damage

Hydrolytic damage can be defined as the time-dependent cumulative irreversible
damage due to the hydrolytic cleavage of polymeric molecules. After immersion of
a biodegradable polymeric device in an aqueous medium, water uptake is the very
first event that occurs, up to a saturation of water concentration that depends on
the hydrophilicity of the polymer, its crystalline degree, the temperature, pH and
flow of the media. This step is accompanied by volume expansion due to the fluid
ingress, usually designated by swelling. The intrusion of water then triggers the
chemical polymer degradation, leading to the scission of molecules and the creation
of oligomers. The penetrating water rapidly creates a negative gradient of water con-
centrations from the surface to the centre as expected from a pure diffusion view-
point. However, this gradient vanishes in a couple of hours or days, when the spec-
imen saturates. Diffusion of small molecules like water is rather fast as compared
with degradation that can take several months. Therefore, one can consider that hy-
drolysis of ester bonds starts homogeneously along the volume from the beginning,
promoting bulk erosion [ 25 ]. This assumption is very precise for small thickness de-
vices, such as fibers or films. Water uptake can also lead to further recrystallization
of the polymer. Water acts as a plasticizer, lowering the glass transition temperature
and softening the material.
The water concentration ( w ) along the thickness, and during incubation, is deter-
mined using Fick's equation:

dt = D 1 ∂ 2 w

+ D 2 ∂ 2 w
∂y 2

+ D 3 ∂ 2 w
∂z 2

dw

(1)

∂x 2

In the case of isotropic polymers, diffusion has no preferential direction, and
D 1 = D 2 = D 3 = D . The diffusion coefficient D of the material can be determined