A three-dimensional mathematical model of a viscoelastic osteocyte and its interaction with the surrounding flow*

Osteocytes, the most prevalent bone cells, regulate bone remodeling through mechanotransduction whereby they sense mechanical stimuli and respond by releasing biochemical signals that, in this context, cause other cells to grow or degrade bone. The cells are encased in bone with arms or processes that connect to each other through the surrounding bone material. The bone's hardness can make experimental studies difficult. Models have risen as a promising alternative. At the same time, the complex geometry of the system can prove challenging for modelers and many have made simplifying assumptions in their studies. While this is understandable and useful, we wish to fully understand the implications of these assumptions and to also better understand the forces that can arise during mechanotransduction. To consider such questions, we have developed a three-dimensional model of an osteocyte that can be used to consider the forces that the surrounding fluid exerts on the osteocyte. We model the cell membrane and cytoskeleton as an interconnected network of viscoelastic elements or damped springs. In addition to the viscoelastic forces along each spring, we include other forces to model the properties of the cell that include a non-negligible bending rigidity, total and local area conservation of the membrane, and total volume conservation. They are prescribed using corresponding energies and the resulting forces are computed using the principle of virtual work. The fluid is modeled using the lattice-Boltzmann (D3Q19) method and the fluid-structure interactions are handled using the immersed boundary method. We share our results for this model including estimated motion and forces on an idealized ellipsoidal osteocyte immersed in the flow.