Multiscale Approach to Understand the Multiphysics Phenomena in Bone Adaptation - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 43

when loads are normally transferred into a fluid flow, which is subsequently
adequately sensed by the osteocyte, it is still possible that the transduction of the
mechanical signal to a chemical signal that takes place within the osteocyte is
affected. As a consequence, the production of signalling molecules by
mechanically stimulated osteocytes will be altered. In vivo, this biochemical
cell-to-cell communication becomes more and more understood [ 28 ]. Diffusive
mechanism alone gives a prohibitively long transit time generating very dif-
ferent chemical environments of osteocytes according to their position [ 68 , 124 ].
Based on in vivo tracer perfusion studies showing the link between mechanical
loading and mass transport within bone tissue [ 67 , 89 , 155 ], other transport
mechanisms have been proposed: load-induced fluid flow and concomitant
convective mixing [ 68 , 121 , 152 ] or Taylor-Aris dispersion [ 141 ]. However,
based on a theoretical study, it was predicted that neither diffusion nor stress
induced fluid flow is capable of sustaining osteocyte viability, and thus that
cyclic stress could stimulate an active mass transport in bone [ 119 ].
• The electro-chemical avenue of research When studying fluid transfer in
nanoporous materials such as the lacuno-canalicular system, other concurrent
phenomena to pressure-driven flow, such as electro-osmosis or osmosis, may
exist. These coupled effects could generate an opposite flow, resulting in a
decrease in the apparent permeability [ 3 , 78 ], ionic permselectivity effects
[ 59 , 76 ], and a modification of the Biot model and the Darcy law [ 74 , 86 , 102 ].
This phenomenon is due to an important property inherent to most of the bio-
logical porous media: they present a surface charge on their pore surface.
Indeed, within cortical bone, the lacuno-canalicular pores tend to present a
negative surface charge, due to the presence of fatty acids on the bone matrix
[ 94 ] and of phospholipids on the cell membrane [ 98 ]. This negative charge is
compensated by the adsorption of cations on the surface forming the inner
compact layer commonly referred to as the immobile Stern layer. However, the
majority of the excess of positively charged counter-ions are located in the
electrolyte aqueous solution in the vicinity of the solid phase, forming an outer
diffuse layer composed of mobile charges. Together with the fixed charged
groups of the solid matrix, these ions form the so-called electrical double layer,
as shown in Fig. 4 [ 52 , 75 ]. When advected by the interstitial fluid, the mobile
charge population of the double-layer generates the macroscopically observed
streaming currents and the concomitant streaming potential [ 74 ]. The gradient of
this potential engenders the electrophoretic movement of the mobile charges
opposing to the streaming current. Due to the viscous drag interaction, the ions
pull the liquid with them resulting in an electro-osmotic seepage flow opposing
the pressure-gradient driven flow, and thus limiting the apparent permeability.
Moreover, due to the possible overlap of similarly charged ionic layers, the
Donnan pressure may cause swelling effects changing the macroscopic hydro-
mechanical behaviour of the porous materials, as, for instance, visible in clayey
media [ 79 , 88 ].