In-Silico Models as a Tool for the Design of Specific Treatments: Applications in Bone Regeneration - Technologies for Medical Sciences - page 6

4 In-Silico Models

In-silico models within the orthopaedic field can be roughly divided in two main
groups: biomechanical and mechanobiological models. The former analyze the
structure and function of biological systems applying laws of mechanics whilst
the latter focus on how the mechanical environment regulates the cell behavior in
different biological processes. Many of these models are based on different tissue
differentiation theories [ 12 , 16 , 28 , 53 , 54 ] which try to provide quantitative or
qualitative rules that relate a mechanical stimulus of an undifferentiated tissue with
the tissue formed (see [ 27 ] for a complete review).

4.1 Tissue Differentiation Theories

Although existing tissue differentiation theories are different in details [ 12 , 16 , 53
28 , 54 ], they share some characteristics. Firstly, they all propose that high mechani-
cal stimulation favors the formation of fibrocartilage tissue, while non stimulated
environments favor bone formation. Secondly, they all develop phenomenologic
rules, with theories derived from empirical observations. Thirdly, they are not
sufficiently validated despite being able to successfully reproduce the main patterns
of fracture healing in specific mechanical environments. And finally, all these
tissue differentiation theories are obviously related to mechanical stimuli, which
is definitely executed by cells whose biological sensing and signaling activities
are implicitly assumed but not directly considered. Two of these algorithms will
be reviewed to analyze their ability to predict bone regeneration in fracture
healing and distraction osteogenesis: the mechanoregulation theory developed by
Prendergast et al. [ 54 ] and that proposed by Gomez-Benito et al. [ 28 ].
Prendergast et al. [ 54 ] developed a simple and different mechanoregulation
concept as compared to the existing theories [ 12 , 16 , 53 ] assuming that tissues are
biphasic with both fluid and solid phases. Existing models to date were static or
linear elastic [ 12 , 16 , 53 ]. They proposed a mechanoregulation pathway regulated
by two biophysical stimuli, the second invariant of the deviatoric strain of the
solid, and the interstitial fluid velocity relative to the solid. Figure 3 shows how
the tissue phenotype (granulation tissue, bone tissue, cartilage and fibrous tissue) is
determined depending on its position in the mechano-regulation diagram. As far as
the authors know, this differentiation law is the only which considers the frequency
of stimulation, by means of the fluid flow. In contrast, Gomez-Benito et al. [ 28 ]and
Garcıa-Aznar et al. [ 23 ] proposed a mathematical model driven exclusively by the
second invariant of the deviatoric strain tensor, assuming that tissues are poroelastic.