Optimization Approaches for the Design of Additively Manufactured Scaffolds - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 114

non-porous block of material, searching for a topologically optimized scaffold unit
according to porosity and stiffness requirements.
Following the success of topology optimization methods, both the number of
parameters implemented during FEA analysis as well as the conditions studied in
a real representation of physical environment, have increased tremendously. As an
example, mechano-regulation models have been recently developed to study the
biophysical stimulus exerted by different scaffold microstructures on the cells and
hence their effect on the regenerative process [ 37 - 39 ]. Results derived from these
studies pointed out the considerable impact of scaffold micro-architecture on tis-
sue regeneration outcome and contributed to the development of hugely optimized
designs.

2.1 Topological Optimization by Load-Adaptive Scaffold
Architecturing (LASA) Algorithm

The present method envisages an innovative strategy for the fabrication of highly
optimized structures, based on an apriori FEA of the physiological load set at the
implant site. The resulting scaffold micro-architecture does not follow a regular ge-
ometrical pattern; on the contrary, it is based on the results of a numerical study.
The algorithm was applied to a solid free-form fabrication process, using poly( ε -
caprolactone) (PCL) as the starting material for the processing of additive manu-
factured structures. The proposed methodology is initially presented for a simple
proof-of-principle geometry and then extended to an illustrative case study, consid-
ering a 3D model of the proximal femur, subject to physiological loading conditions.
Femur bone was chosen as a target, since it represents an anatomic part with well
described biomechanical behavior.

2.1.1 Theory and Calculation

Given an elastic continuum C , to which a load system is applied, the stress at every
point P of the domain is described by a stress tensor σ (

3 ). Being σ sym-
metrical for reasons of statics, for every P there exists an orthonormal reference
frame R , which makes σ diagonal. The three components of the diagonalized stress
tensor, σ 1 , σ 2 , and σ 3 are the so-called principal stresses, which correspond to pure
compression/tension occurring along the three axes ( x 1 ,x 2 ,x 3 )of R . A technique
for ideally carving within C , while minimizing the reduction of stiffness, consists
in placing the residual material along the principal directions, thus minimizing the
distortion of the structure due to shear stresses.
With this consideration, the best solution for the definition of the scaffold design
could be to drive the position and direction of the solid material according to the
vector field of the principal stresses. Being the trabeculae oriented along principal
stress directions, they work in almost pure tension/compression mode, which results

3 ×

∈ R