Biomedical Engineering Reference
In-Depth Information
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Fig. 7
Vascular network predicted computationally at day 10 of the distraction process
distribution at day 10 showing the key role it plays during osteogenesis. Finally, by
day 15, endothelial cells have progressed further and considerably amounts of
chondrocytes have started to differentiate (Fig. 6 ). Regarding the ossification
pattern during the first stage of the distraction procedure only intramembranous
ossification occurs.
This model considers the angiogenesis directly in the mathematical formulation
through a random-based approach. Previously, the authors considered this complex
process of vascular ingrowth through a diffusion equation, not modelling the
vascular invasion directly, but only its effect: the advance of the ossification front
[ 49 , 102 ]. Therefore, this work represents an important step-forward in the mod-
elling
of
angiogenesis
in
bone
regeneration
and
specifically
in
distraction
osteogenesis.
4.3 Cell Force-Based Discrete Models: Cell Migration in 3D
Cell migration is essential for tissue development in different physiological and
pathological conditions. Cell movement is guided by input signals from the sur-
roundings. The physical-chemical nature of the extracellular matrix (ECM)
medium and its binding with the transmembrane, allows cells to probe the
mechanical properties of their environment and react to it in an specific way. This
ability of cells to sense ECM flexibility or pre-strain is responsible for cell
behavior and its understanding is crucial. It has become clear in the last few years
that cells extend some lamellipodia and filopodia which attach to the substrate.
They then exert contractile forces in order to explore the properties of their
environment in a process called mechanosensing [ 29 ]. These active forces are
generated by the myosin motors and transmitted to the ECM by means of trans-
membrane proteins (integrins) in so-called focal adhesions.
Here the authors present a 3D migration model of a single cell, which is
regulated by a mechano-sensing mechanism (more details can be found in [ 12 ]).
 
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