In Silico Biology of Bone Regeneration Inside Calcium Phosphate Scaffolds - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 35

the need to optimize scaffolds for site-specific loading requirements [ 8 ]. This model
was improved by including blood vessel growth thereby establishing a framework
to investigate the effect of vascularization on bone formation [ 12 ].
Other studies have modeled the bone regeneration process inside biodegrad-
able polymer-based scaffolds. Stops et al. [ 42 ] further investigated the influence of
mechanical strain and perfusive fluid flow on cell differentiation and proliferation
within a collagen-glycosaminoglycan scaffold. Sanz-Herrera et al. [ 37 ] presented
a multi-scale model of bone regeneration inside a porous scaffold. The biodegrad-
able polymer scaffold degrades hydrolytically, i.e. the water content in the polymer
chemically reacts and breaks down the material, which was modelled accordingly
[ 37 ]. The mechanical properties of the polymer were assumed to relate linearly to its
molecular weight [ 37 ]. The evolution of the bone formation process in a scaffold im-
planted in the femoral condyle of a rabbit was simulated with the model. They found
a good qualitative agreement between the obtained computational and experimen-
tal results [ 37 ]. Although further validation is necessary, the proposed multi-scale
model is a useful tool to investigate the complex phenomena that occur at different
length and time scales, i.e. the bone formation and scaffold resorption at the micro-
scopic scale and the change of mechanical properties at the macroscopic scale [ 37 ].
Lacroix et al. [ 24 ] nicely review the current techniques used for scaffold develop-
ment: from scaffold optimization of scaffolds by mathematical models (e.g. FEM)
to scaffold design using computer aided design (CAD) and scaffold characterization
by computed tomography (CT).
Although the above models can be used to optimize some (mechanical) proper-
ties of scaffolds, e.g. the porosity, the micro-architecture, the Young's modulus and
dissolution rate, they neglect the influence of growth factors and other biochemical
signals on the bone formation process. Moreover, the dissolution process is only
crudely modeled, neglecting the influence of the degradation products (e.g. Ca 2 +
and P i ) on the cellular activities and bone formation process. Carlier et al. [ 11 ] de-
veloped and implemented an experimentally informed bioregulatory model of the
effect of calcium ions released from CaP-based biomaterials on the activity of os-
teogenic cells and mesenchymal stem cell driven ectopic bone formation. The model
describes the effect of CaP biomaterials on the activity of osteogenic cells as a tem-
poral variation of six variables: free extracellular Ca 2 + concentration ( Ca ), MSC
density ( c m ), osteoblast density ( c b ), mineral matrix density ( b ), collagen matrix
density ( m ) and a generic, osteogenic growth factor concentration ( g b ). The sum of
the mineral matrix and the collagen matrix represents the total bone density. The
evolution of each of these continuous variables is described by the following set of
delay differential equations (DDEs) (see Fig. 1 ):

proliferation

differe nt iation

removal
d(t)

A m (t).c m (t). 1 α m .c m (t) .β cm (t)

∂c m (t)
∂t

= − − F 1 (t).c m (t − t 1 ) −

proliferation

differe nti ation rem o val

d b .c b (t) A b (t).c b (t). 1 α b .c b (t) .β cb (t)

∂c b (t)
∂t

= − + F 1 (t).c m (t − t 1 ) −