Computational Mechanobiology in Cartilage and Bone Tissue Engineering: From Cell Phenotype to Tissue Structure - Computational Modeling in Tissue Engineering - page 353

elastic modulus and stimulus). These inputs and outputs from 100 factorial designs
were used to train a neural network, i.e. determine the weights of its connections.
Once trained, the network, which does not contain any a priori rules, is then able to
very quickly predict outputs when given a set of input values. This neural network
thus eliminates the need for the RVE FE simulations and can be incorporated as a
material formulation at the integration point level which speeds up simulations
tremendously. The model was applied to the remodelling of a femoral head loaded
with 7000 cycles per day for 100 days. Simulations were about 1000 times faster
than with the classical approach.
Theoretical models of cells that account for their interaction with the pericellular
(PCM) and extracellular matrix (ECM) and are coupled to tissue level models
''can provide information on biophysical parameters that cannot be measured
experimentally in situ at the cellular level, e.g., the stress-strain, fluid flow, physi-
cochemical, and electrical states in the immediate vicinity of the cell'' [ 40 ]. By
investigating cell-matrix interactions using a biphasic multiscale model, the transient
heterogeneity of the microscopic mechanical environment due to the differences in
mechanical properties between cells and their ECM could be shown. Adding a PCM
to the model had a significant effect on the stress and strain fields within the
chondrocytes suggesting a biomechanically functional role for the PCM [ 40 ].
A method to couple macroscopic FE and microscopic Voxel-FE simulations to
investigate bone regeneration was presented in Sanz-Herrera et al. [ 101 ]. Bone
remodelling and cell migration were solved at the macroscopic level. The infor-
mation was passed to the microscopic level and used to simulate bone growth and
scaffold resorption in the representative volume elements. Using homogenisation
techniques, the mechanical properties derived from the representative volume
elements were then passed up again to the macroscopic model. The model was
applied to the formation of immature and mature bone in a non-resorbing ceramic
scaffold in a rabbit femoral defect. The principal model behaviour and the effect of
different macroscopic locations on the evolution of local RVEs was investigated.
Later, Sanz-Herrera et al. [ 102 ] studied scaffold-aided bone tissue regeneration in
a rabbit femur in more detail. Variations of scaffold stiffness, porosity, pore size,
degradation mode and seeding were simulated. The femur was modelled macro-
scopically only and its mechanical properties were dependent on the apparent
density of the bone that was allowed to remodel depending on the local strain
energy density. Macroscopic properties in the repair zone were derived from
microscale analyses of both the solid and the fluid domains of the scaffold. In turn,
stimuli and cell densities derived at the macroscopic level were used to determine
the rate of microscopic bone formation in the scaffold. The mechanical stimulus
used was based on local strain energy density and biomaterial stiffness. Degra-
dation via scaffold hydrolysis was also included. The highest rate of bone
formation was predicted in the stiffest scaffold and no bone formation in the
softest. Compared to a non-seeded scaffold, pre-seeding led to higher rates of
earlier bone formation. Higher rates were also observed for increased mean pore
sizes while fast resorption kinetics were predicted to lead to scaffold collapse.