Biomedical Engineering Reference
In-Depth Information
rela
tive
f
luid
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G
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Fig. 3
Mechanoregulation diagram for bone formation and resorption based on mechanical strain
andfluidflow [
54
]
4.1.1
Computational Simulations to Evaluate the Effect of External
LMHF Cyclical Displacements
In this section it is shown that a differentiation theory alone is able to provide
insight into the bone healing process. The differentiation theory proposed by
Prendergast et al. [
54
] has been used to computationally determine the influence
of an external mechanical stimulus based on a LMHF displacement of the fractured
fragments on the bone healing process (see [
30
] for further details). In particular,
it has been implemented to predict the most appropriate frequency of stimulation
that optimizes the bone healing time [
31
]. An axisymmetric simplified model of the
fracture callus in the metatarsus of a sheep was simulated [
16
] at two different time
points, 1 and 4 weeks after fracture (see Fig.
4
). A cyclical displacement of 0.02 mm
was applied at the top of cortical bone with different frequencies of stimulation
(1, 50 and 100 Hz) in order to evaluate their impact on tissue differentiation. Figure
4
shows the evolution of the magnitudes of some mechanical variables: octahedral
strain, second invariant of the deviatoric strain tensor and fluid flow. It can be
observed that the only mechanical stimulus affected by the frequency of stimulation
is the fluid flow whilst the other mechanical variables (octahedral strain and second
invariant of the deviatoric strain tensor) are just slightly modified. The major
variations of the fluid flow occur for frequencies of stimulation higher than 50 Hz.
According to the differentiation rule proposed by Prendergast et al. [
54
] an increase
in the frequency of stimulation may promote chondrogenesis and endochondral
ossification (Fig.
3
).
This simulation provides the cues to perform experiments with the aim to
improve the bone healing process. According to computational results, it was
decided to stimulate the fracture site with a frequency higher than 50 Hz aiming
