Computational Mechanobiology in Cartilage and Bone Tissue Engineering: From Cell Phenotype to Tissue Structure - Computational Modeling in Tissue Engineering - page 338

focus on some recent developments, namely (i) a tissue differentiation algorithm
based on substrate stiffness and oxygen tension; (ii) the simultaneous prediction of
tissue structure and phenotype during regenerative events; (iii) performing non-
deterministic simulations to capture variability.
Among the mechanical stimuli proposed as potential mechanoregulators are
• Octahaedral shear stress/strain or maximum principal strain and hydrostatic
stress (Carter and co-workers [ 15 - 17 ]). Quantitative boundaries were only
proposed later by others [ 50 ].
• Principal strain and hydrostatic stress (Claes and Heigele [ 22 , 23 ])
• Octahaedral shear strain and fluid velocity (Prendergast and Huiskes [ 46 , 91 ])
• Others include certain strain invariants [ 34 , 94 ] and strain energy density [ 1 ].
The model by Carter and colleagues [ 15 - 17 ] was used among others in a study
where pseudoarthrosis formation was studied in oblique fractures [ 71 ]. Further-
more, this model has been applied frequently in tendon mechanobiology, such as
fibrocartilaginous metaplasia formation in tendons wrapping around bony promi-
nences [ 39 , 116 ].
The theory by Claes and Heigele [ 22 , 23 ], which is based on Pauwel's ideas
[ 89 ], was mainly applied to problems of fracture healing. A recent model for tissue
differentiation and revascularisation in fracture healing by Simon and co-workers
[ 107 ] implemented a set of rules into a fuzzy-logic controller to simulate regen-
erative events in the fracture callus. The limiting factors for healing were found to
be revascularisation in stable fractures and an inadequate mechanical environment
in unstable fractures. A similar fuzzy logic model was able to predict all stages of
trabecular fracture healing including the final remodelling stages to re-establish a
trabecular structure depending on the loading direction [ 106 ].
The model by Prendergast et al. [ 91 ] accounts for the biphasic nature of most
biological tissues and as such incorporates fluid flow as a stimulus. Its first
implementation into an automated feedback algorithm to simulate the time course
of fracture healing was performed by Lacroix et al. [ 68 ]. The origin of MSCs,
whose migration into the fracture callus was modelled as a diffusive process, was
predicted to have a significant impact on the rate at which healing progressed. The
model was further able to predict the spatio-temporal sequence of phenotypes
occurring during fracture healing. The results provided support for the hypothesis
that fluid flow and shear strain are regulators of MSC differentiation during
fracture healing. Following this initial corroboration, the model was applied to
analyse the influence of fracture gap size and loading on the emerging phenotypes
and the healing outcome [ 67 ]. Further corroboration was achieved by applying the
tissue differentiation model in simulations of other regenerative events. Besides
fracture healing [ 49 , 67 , 68 ], it has been successfully used to predict key events
during distraction osteogenesis [ 8 , 9 , 51 ] osteochondral defect healing [ 55 , 56 ],
implant integration [ 36 , 46 ] and pseudoarthrosis formation [ 43 , 81 ]. Many studies
on scaffold aided tissue repair or scaffold design rely on this algorithm since fluid
perfusion is thought to play a major role in porous scaffolds (see Sect. 4 )