Coupling systems biology with multiscale mechanics, for computer simulations of bone remodeling

Bone remodeling is a process involving removal of mature bone tissue and subsequent formation of new bone tissue. This process is driven by complex actions of biological cells and biochemical factors, and it is sensitive to the loads applied onto the skeleton. Herein, we develop a mathematical framework describing this process at the (macroscopic) level of cortical bone, by combining, for the first time, bone cell population kinetics with multiscale bone mechanics. Key variables are concentrations of biological cells (osteoclasts, osteoblasts and their progenitors) and biochemical factors (RANK, RANKL, OPG, PTH, and TGF- β ), as well as mechanical strains, both at the (“macroscopic”) level of cortical bone and at the (“microscopic”) level of the extravascular bone matrix. Multiscale bone mechanics delivers, as a function of the vascular porosity, the relation between the macroscopic strains resulting from the loads, and the microscopic strains, which are known to modulate, either directly, or via poromechanical couplings such as hydrostatic pressure or fluid flow, the expression or proliferation behavior of the biological cells residing in, or attached to the extravascular bone matrix. Hence, these microscopic strains enter the biochemical kinetics laws governing cell expression, proliferation, differentiation, and apoptosis. Without any additional phenomenologically motivated paradigm, this novel approach is able to explain the experimentally observed evolutions of bone mass in postmenopausal osteoporosis and under microgravity conditions: namely, a decrease of bone loss over time.