Computational Mechanobiology in Cartilage and Bone Tissue Engineering: From Cell Phenotype to Tissue Structure - Computational Modeling in Tissue Engineering - page 355

then able to predict both the macroscopic response to equibiaxial stretch tests as
well as the non-affine and heterogeneous fibre network rearrangement as measured
during deformation using polarimetric fibre alignment imaging. The model thus
allowed for the simultaneous prediction of experimental data acquired at multiple
length scales and provides insight into how macroscopically applied loads translate
into highly heterogeneous fibre deformations, both tensile and compressive, which
have relevance to cellular mechanotransduction.
Relatively few studies have combined architectural considerations with models
of tissue differentiation and regeneration of osseous and chondral tissues. The
multiscale bone growth model by Sanz-Herrera et al. [ 101 , 102 ] was extended to
study the effect of pore structure on directional bone growth [ 103 ]. Scaffolds with
idealised isotropic (spherical) and anisotropic (ellipsoid) pore structures as well as
realistic pore structures were simulated and anisotropic elasticity and permeability
tensors derived from the homogenisation process and passed to the macroscopic
scaffold domain. While the net rate of bone formation was found to be similar for
the various architectures once they were sufficiently interconnected, the initial
anisotropy determined the directions of bone growth. This was caused by the
influence of the pore architecture both on the microscopic deformation and on cell
migration/fluid perfusion.
Trabecular healing in a vertebral body was investigated using a multiscale
approach in Boccaccio et al. [ 11 ]. The spinal segment L3-L4-L5 with a mild
wedge fracture in the L4 vertebra was used to derive the poroelastic boundary
conditions for representative volume elements in the repair zone. An idealised
trabecular structure with a 0.5 mm diastasis served as the microdomain and was
used to predict the patterns of tissue differentiation based on fluid flow and shear
strain [ 91 ] during the first 100 days after fracture. Equivalent material properties
of the RVEs were then derived an passed up to their locations in the fracture gap.
The predicted tissue differentiation patterns were consistent with those observed in
vivo. The primary bone formation mode was endochondral ossication with new
woven bone occupying most of the space within the fracture site about 7-8 weeks
post fracture. The final stage predicted by the model was bone remodelling leading
to the formation of a new trabecular architecture.
6 Conclusion
Computational engineering methods penetrate biology at many levels. Experimental
and computational data is continuously being acquired at all levels from the
molecular to the organism (or even population) level. Ultimately a coupling of the
relevant time and length scales is envisioned but significant challenges remain at
each individual level. Experimentation and simulation have to inform one another in
an iterative and closely coupled fashion. Once confidence in a model for a certain
phenomenon is established, the number of experiments needed can be reduced
drastically to the level necessary for parameter identification. Furthermore, neural