Computational Methods in the Modeling of Scaffolds for Tissue Engineering - Computational Modeling in Tissue Engineering - page 108

compressive strain than tensile strains. Hexagonal structures lead to lesser vari-
ability of major strain distributions (compressive strain from 0.25 to 0.75%) on the
walls than the gyroid structures (from tensile value of 0.25% until compressive
values of 1%) [ 5 ]. Thus, the stimuli not only is dependent on the uniform distri-
bution of pores, but also depend on pore shape [ 6 , 14 ].

3.2 Scaffold Degradation and Tissue Regeneration

Optimum scaffold degradation is related directly with the temporal mechanical
properties needed to substitute the tissue damage. Few computational studies try to
explore the scaffold implantation and in vivo response. One example is to correlate
the relationship between the scaffold geometry with the resorption of the scaffold,
but independently of its composition [ 15 ]. Another study based on multiscale
simulation [ 16 ] shows that the degradation kinetic of polymer (PLGA, poly (lactic-
co-glycolic acid) is fast and has a negative effect in the balance of tissue regen-
eration within scaffolds.
Another example selected here to explain the scaffold degradation was devel-
oped by Adachi et al. [ 17 ]. They proposed a framework to simulate bone regen-
eration, which includes the degradation rate. They evaluated the mechanical
function in the bone regeneration process by changing the strain energy at the
bone-scaffold system. Scaffolds with lattice-like and spherical pore structures
were assessed (Fig. 4 ). The scaffold degradation was assumed to be due to
hydrolysis, decreasingthe polymer molecular weight W, and therefore inducing a
decrease in the scaffold Young's modulus E S (Eq. 2 ). E S0 is the initial scaffold
Young's modulus and W 0 is the initial molecular weight. The rate of degradation is
affected by the morphology of the scaffold microstructure, and large surface areas
accelerate the diffusion of water molecules into the bulk of the polymers.

E s ¼ E s0 w ð t Þ
w 0

ð 2 Þ

Bone formation and bone resorption are accomplished by osteoblastic and
osteoclastic cellular activities respectively. New bone formation was modeled
using the rate equation for trabecular surface remodeling (Eq. 3 ) based on the
uniform stress hypothesis [ 18 , 19 ]. Here, r c is the representative stress at point x c
on the bone or scaffold surface on which the osteoblasts form new bone matrix,
and r d is the representative stress in the neighboring area around point x c. S
denotes the surface; r r is the stress at neighboring point x r within the sensing
distance l L l ¼ x r x c ð j j Þ and w ð l Þ½ w ð l Þ 0 ð 0 l l L Þ is the decaying

weighting function.

r d ¼ R S w ð t Þ r r dS

R S w ð t Þ dS

ð 3 Þ