Multiscale modeling provides differentiated insights to fluid flow-driven stimulation of bone cellular activities

Abstract

Both the shape of bone organs and the micro-architecture of bone tissue are significantly influenced by the prevailing mechanical loading. In this context, several of the most striking and hence also most debated issues relate to the question how bone is actually able to sense and process its mechanical environment. Among other stimuli, it has been hypothesized that the macroscopic mechanical loading induces pressure gradients in the pore spaces of bone tissue, and that these pressure gradients lead to fluid flow exciting the cells that are located in the pore spaces. Since in vitro tests confirmed that cells subjected to the flow of the surrounding fluid indeed respond in form of altered expression activities, the scientific community has in large part embraced the fluid flow-hypothesis. However, direct experimental evidence as to the actual occurrence of sufficiently fast fluid flow (in order to reach the cell responses observed in vitro) has not been attained so far. In this paper, a multiscale modeling strategy is presented (inspired by the well-established concept of continuum micromechanics), allowing for upscaling (or homogenization) of the fluid flow contributions in the canalicular, lacunar, and vascular pores in terms of a corresponding macroscopic permeability of bone tissue. The same model also allows for proceeding the opposite way, namely for downscaling macroscopically acting pressure gradients to the pore levels. Thus, physiologically relevant mechanical loading conditions can be related straightforwardly to the correspondingly arising pore-scale pressure gradients, and, through considering the resulting pressure gradients in suitable transport laws, also to related fluid velocities. When comparing the such computed fluid velocities with the fluid velocities that were shown to efficiently excite bone cells in vitro, it turns out that pressure-driven fluid flow in the canalicular pores is probably not a potent mechanical stimulus for osteocytes, whereas fluid flow in the vascular pores may indeed reach the required fluid velocities and hence excite the therein residing osteoblasts, osteoclasts, and bone lining cells. In conclusion, this paper provides important, unprecedented insights as to the observation scale-specific cellular mechanosensation in bone.