In-Silico Models as a Tool for the Design of Specific Treatments: Applications in Bone Regeneration - Technologies for Medical Sciences - page 9

phenomena. For instance, Prendergast et al. [ 54 ] demonstrated the consistency of
the model at implant to bone interfaces [ 54 ] and afterwards in a bone chamber
[ 24 - 26 ] and osteochondral defects [ 41 ]. They also succeed in simulating the
outcome of bone healing within the fracture callus for different gap sizes and loading
magnitudes [ 46 ]. This model has then been taken up by Andreykiv et al. [ 2 ],
Isaksson et al. [ 39 ], Byrne [ 10 ] and Boccaccio et al. [ 8 ]. In distraction osteogenesis,
Isaksson et al. [ 38 ] have been able to predict the main tissue distributions for
different frequencies of distraction and for moderate and low distraction rates in
long bone distraction osteogenesis. Nevertheless, they were not able to reproduce
the evolution of the reaction force during the distraction period. In mandibular
distraction osteogenesis, Boccaccio et al. [ 6 , 7 ] examined the influence of the rate
of distraction and the latency period duration within the fracture callus of a human
mandible submitted to symphyseal distraction osteogenesis.
G omez-Benito et al. [ 28 ]andGarcıa-Aznar et al. [ 23 ] proposed a continuum
evolutive model which considers as state variables the concentration of five cell
phenotypes (mesenchymal stem cells, fibroblasts, cartilage cells, bone cells and
dead cells). The evolution of the concentration of each skeletal cell type is con-
sidered to be function of the proliferation, migration and differentiation processes.
In addition, they incorporated for the first time in their mechanoregulation model the
mathematical formulation of callus growth. They succeeded in simulating the main
processes that occur during fracture healing [ 23 , 28 ]. In particular, this mechano-
biological regulatory model predicted a geometry of the callus, tissue differentiation
patterns and fracture stiffness similar to those reported in the literature with different
gap sizes [ 28 ] and the influence of the interfragmentary movement on the callus
growth, shape and tissue types [ 23 ]. Since fracture healing and distraction repair
share similar biological processes and strain-related bone tissue reactions, this
model could be applied to simulate distraction osteogenesis. In the model explained
the differentiation process was function of the mechanical stimulus and time (the
time that stem cells need to differentiate into specialized cells). However, with this
differentiation concept, as there is a similar mechanical environment within the
gap after the first days of distraction, a similar distraction osteogenesis outcome
would be predicted with any mechanical factor analyzed (e.g. distraction rate). In
fact, this model and others based on different mechanoregulatory differentiation
rules [ 16 , 28 , 54 ] were used to simulate the influence of different distraction rates.
They were able to successfully predict the distraction osteogenesis process for
moderate and low distraction rates but not for high distraction rates (e.g. 2 mm/day).
Therefore, the model needed to be extended further by introducing the effect of the
load history on the process of cell differentiation. Cell differentiation was assumed
to depend on the load history in such way that cells will differentiate only if they
have been subjected to a specific mechanical environment during a period of time
[ 62 ]. Thus, the maturation state of the cell type is included in the model as a state
variable (see Reina-Romo et al. [ 56 ] for further details). The model incorporating
the maturation state of the cells was just an extension of the previously proposed
model. This extended model was also able to predict the regenerative process in
different examples of fracture healing [ 23 , 28 , 29 ].