Computational Methods in the Modeling of Scaffolds for Tissue Engineering - Computational Modeling in Tissue Engineering - page 106

reasons the reconstruction step is vital to obtain the correct characterization and
numerical analysis. The second example (Fig. 2 b) selected shows a volume of one
cylindrical sample of a PLA (poly-lactide acid) polymer with glass composite
biomaterial [ 13 ]. PLA and glass particles were identified using the gray values for
each material allowing separation of the material properties for the computational
analysis.
Until now it has been possible to obtain a complete structural characterization
of irregular structure scaffolds. However, the heterogeneity of the geometry in
non-regular scaffold minimizes the use of scaffold models since each sample is
unique. Therefore it is difficult to know whether the modeled scaffold is repre-
sentative of the real scaffolds used. For RP scaffolds the steps to follow are easier
(Fig 2 c). Initially the desired design (CAD) of pores is drawn, through a repre-
sentative volume element (for example of a gyroid shape in Fig. 2 c) and the
complete scaffold (cylindrical volume) are designed [ 14 ]. After the scaffold fab-
rication using RP techniques (stereolithography in this example) is characterized
by means of micro-CT method allowing comparison of the initial design with the
final product.

3 Computational Evaluation of Mechanical Properties
of Scaffold

3.1 Mechanical Properties Depending on the Scaffold
Microstructure

The desired mechanical properties of porous scaffolds vary depending on the
clinical applications. It is therefore desirable to be able to control and tune such
properties on a specific case basis. The digital scaffold reconstruction methodology
showed above offers the possibility to develop the scaffold structure maintaining
the specific micro pores. The Finite Element Method (FEM) can be used to predict
the mechanical properties of a scaffold. FEM is a numerical technique that gives
approximate solutions through partial differential equations. Defining the problem
from the geometry, the domain is divided in finite sub-domains called elements.
Through an adequate mesh of elements, the bulk material properties and the
loading conditions that correspond to the scaffold are applied. In tissue engi-
neering, the FEM is used principally to determine the effective mechanical
properties of the porous scaffold. For example, the method allows to calculate the
effective Young's modulus E f under compression (Eq. 1 ) dependent on the reac-
tion force R computed at the nodes, the total cross section area of the scaffold A,
and the axial strain applied e ¼ Dl
l

[ 6 , 9 ].

E f ¼ R
Ae

ð 1 Þ