4D Numerical Analysis of Scaffolds: A New Approach - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 77

end groups at the n th discrete time point, the degradation equation can be solved
and it can proceed to the next time step (or increment).
When a process is composed of a sequence of reactions, the overall rate is de-
termined by the slowest reaction, named the rate-limiting step [ 19 ]. Klyosov and
Rabinowitch [ 22 ] reported that the rate limiting step may change between the be-
ginning of the reaction and after a certain degree of substrate conversion.
The degree of crystallinity may also be a crucial factor, since hydrolysis occurs
mainly in the amorphous domains. Water and enzymes degrade the more accessible
amorphous region, but are unable to attack the less accessible crystalline portions.
The water permeability along the crystalline region is much smaller than amorphous
region. The observed increase in percentage of the crystalline phase is explained by
the faster degradation that occurs in the amorphous region. Polymers with low crys-
tallinity showed increased hydrolysis rates [ 36 , 37 ]. As the crystallinity increases
steadily throughout the reaction, substrate becomes increasingly resistant to further
hydrolysis [ 10 , 11 ], therefore affecting the kinetics of the process [ 20 , 55 ]. To model
this phenomenon, knowing the initial crystalline degree, two different rates can be
considered for both phases, and two different hydrolytic damage values should be
calculated and added according to the volume fractions. The crystallinity of copoly-
mers ( X %) can be determined by dividing the observed heat of fusion in a DSC
(Differential Scanning Calorimetry) test, by the theoretical value for perfectly crys-
talline polymer according to:

h m
h 0 m

X % = (11)

Crystallinity also affects the mechanical properties of materials. Their glass tran-
sition temperature is lowered due to water uptake, which can lead to recrystalliza-
tion of the polymer. Hence, material processing and storage conditions have a great
influence on mechanical and degradation properties [ 35 ].

6 Surface vs. Bulk Erosion

All degradable polymers share the property of eroding upon degradation. The wa-
ter ingress triggers the chemical polymer degradation leading to the creation of
oligomers and monomers. Progressive degradation changes the microstructure of
the bulk through the formation of pore via which oligomers are released. Concomi-
tantly, the pH inside pores begins to be controlled by degradation products, which
typically have some acid-base functionality. Finally, oligomers and monomers are
released, leading to the weight loss of polymer devices. The distinction made be-
tween surface (or heterogeneous) and bulk (or homogeneous) eroding materials is
used to classify degradable polymers.
Different types of erosion are illustrated in Fig. 4 .InFig. 4 c, there is a typical
case of homogeneous or bulk erosion without autocatalysis, in which diffusion oc-
curs instantaneously. Hence, the decrease in molecular weight, the reduction in me-
chanical properties, and the loss of mass occur simultaneously throughout the entire