Multiscale Approach to Understand the Multiphysics Phenomena in Bone Adaptation - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 54

the Poisson-Boltzmann problem, has also to be found since it appears in some of
these effective parameters.
Now that a multiphysics representation of bone tissue has been built, we are
able to simulate its poro-elastic behaviour, and thus to improve our understanding
of the mechano-transduction of the bone remodelling signals.
4 Some Illustrative Results Through 5 Questions Dealing
with Bone Remodelling Signals
The great difficulty of carrying out experimental investigations of in situ bone
poro-mechanical behaviour renders theoretical investigations crucial. Modelling
and computational approaches become thus increasingly common tools for testing
hypothesis for the regulation of bone remodelling [ 1 , 150 ].
In this section, we propose to illustrate the great interest of adopting a coupled
viewpoint to treat the in silico issues of bone remodelling. The classical continuum
or micro-mechanically based models of bone behaviour use the sole poro-
mechanical description [ 24 , 132 ]. The mechanical stimuli acting at the cell scale
(pressure, shear stress, drag forces, etc.) are downscaled from this poro-mechanical
description and somehow converted into biochemical signals regulating the
remodelling activity [ 1 ]. In this manner, the nature of the incoming signals is
thought to be purely mechanical.
Hereafter, we propose to illustrate the necessity to strongly modify the para-
digm of in silico bone adaptation by answering to 5 questions related to the
mechano-sensation and mechano-transduction of bone remodelling signals.
4.1 First Question: Is the Classical Poro-Elasticity Sufficient
to Describe Bone Behaviour?
To elucidate the cellular and molecular mechanisms of bone adaptation or bone
pathologies, the in vivo fluid environment of bone cells has to be thoroughly
described. Indeed, it is commonly accepted that the stimuli initiating the bone
remodelling process are correlated to the hydro-mechanical state of bone tissue
(see Sect. 2 ).
However, due to the heterogeneity of bone material and the multiscale structure
of the bone porosity, from the vascularity (on the order of magnitude of 10 lm) to
the lacuno-canalicular network (canalicular space of 0 : 01 0 : 1 lm and lacunar
space of 1 10 lm) [ 25 ], a precise determination of the fluid velocity and pressure
fields surrounding the osteocytes remains a tremendous feat.
Since the interstitial bone fluid flow is induced by the skeleton strains, the Biot
poro-elasticity theory [ 15 ] has been used to mimic bone behaviour. It is thus