Optimization Approaches for the Design of Additively Manufactured Scaffolds - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 121

Fig. 6 Stiffness values for
structures with the same total
porosity obtained according
to different scaffold
architectures achieved by
increasing fiber spacing and
thickness
The femur head was chosen, subject to physiological loading conditions. In prin-
ciple, using clinical CT scans and extracting the region of interest (ROI) with a
commercial software (e.g., Mimics, Materialise NV, Leuven, Belgium), subject-
specific geometries can be processed. For the purposes of the present study, how-
ever, a widely accepted 3D model of an adult human femur was used (3rd genera-
tion composite femur, Dept. Mechanical and Industrial Engineering, Ryerson Uni-
versity, Ontario, Canada) [ 44 ]. The model was further simplified by considering the
whole femur as constituted by an isotropic linear elastic material with homogeneous
Young's modulus and constant Poisson's ratio. Although bone is actually heteroge-
neous, non-linear and anisotropic, these simplifications are often made when mod-
eling bone using FEA [ 45 , 46 ]. The femur bone domain was discretized by 19,079
tetrahedral 4-nodes elements. Previous studies have confirmed that tetrahedron is the
best choice for meshing human femur and that it is well suited to model irregular
geometries, due to its quadratic displacement behavior [ 47 ].
For the purposes of the present study, a force of 250 N parallel to the femur
shaft axis was applied on the top surface of the femur head, distributed on a circular
area of 1.5 cm radius. In the pioneering work by Koch [ 48 ], describing the laws
of bone architecture—following the early studies by Wolff and Cullman—load on
the femur was assumed approximately 30 % of the body weight in the bilateral
standing position. The line of action of the force was defined as the line joining
the center of the head of the femur to the center of gravity of the lower end of
this bone. Further studies have demonstrated the importance of taking into account
forces exerted by muscles on the femur head, especially for describing single-limb
stand [ 49 ]. However, simplified loading conditions have often been used, such as
concentrated loads directed along the femur shaft direction [ 50 ] or, alternatively, at
an angle of 20° to the shaft axis in the coronal plane [ 51 ].
The FE problem was solved in COMSOL Multiphysics under the hypothesis of
static linear analysis. Pointwise stress tensor and principal stress directions were
calculated for the entire femur volume. A text file containing the directions of prin-
cipal stresses as a function of the position was generated and exported into MAT-