Multiscale Approach to Understand the Multiphysics Phenomena in Bone Adaptation - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 58

behaviour of the collagen-apatite matrix that constitutes the solid part of bone, or by
the stress-induced streaming potentials. The use of our model to interpret available
experimental data could provide a definitive answer to this question. Here we refer
to the in vivo recording of stress-generated potentials during walking measured by
Cochran et al. [ 23 ] thanks to electrodes implanted on a canine radius. In this study, a
simultaneous recording of bone strain is provided. Despite the parasite effects
generated by locomotion (interactions with other legs action), the loading can be
approximatively represented by vertical cyclic loading conditions.
According to the results of our homogenization procedure, piezo-electricity and
double layer potential vanish at the macroscale. Consequently, the macroscopic
electric potential should be identified as streaming potentials.
To check the validity of this statement, we propose to recover the electric
potentials measured on a walking dog by Cochran et al. [ 23 ]. Following the idea of
Salzstein and Pollack [ 138 ], an estimation of the streaming potentials induced by
the stress-generated fluid flow can be made. Indeed, invoking the Onsager reci-
procity, the streaming potential field are shown to be proportional to the macro-
scopic pressure field [ 74 ]. Thus, mimicking the walking induced strain of Cochran
et al. [ 23 ] by harmonic axial loading, the macroscopic pressure field can be com-
puted [ 109 ]. In this calculation, the electrical parameters of the cortical micro-
structure are those used by Lemaire et al. [ 84 ], whereas the poro-elastic parameters
are those of Rémond et al. [ 131 ]. In addition, the electric conductivity is taken as
the one of a 0 : 01 M chloride potassium solution at 37 C(0 : 1735 S.m 1).
The comparison in Fig. 8 between experimental and numerical results suggests
that the solution of the poro-elastic model can satisfactory represent electric
phenomena induced by walking activity. This is an indirect validation of the poro-
elastic models of cortical bone and it suggests that the streaming potentials
developing in response to the strain-induced bone fluid movements are likely to be
the physiologically observed electric potentials.
4.4 Fourth Question: What are the Consequences
of the Electro-Chemical Couplings on the Shear
Sensitivity of the Osteocytes?
If osteocytes have been proposed to play a major role in sensing mechanical
signals and regulating bone remodelling [ 63 , 142 , 148 ], they were also shown to
directly participate in the calcium homeostasis by regulating the dissolution and
deposition of calcium in the lacuno-canalicular space [ 125 , 126 ]. The presence of
such chemical gradients (such as directional calcium fluxes between the bone
matrix and the interstitial fluid [ 91 ]) can result in an osmotic fluid flow. This
directional movement of calcium from or into the bone can affect the fluid flow
within the canaliculus and, consequently, the shear stress felt by the osteocytes, as
illustrated by Fig. 9 .
Shear stresses are linked to the velocity gradient. Thus it is necessary to
investigate how the velocity gradients are affected near the cell process membrane,