Nonlinear dynamics of membrane skeleton in osteocyte

Osteocytes play an important role in mechanosensation and conduction in bone tissue, and the change of mechanical environment can affect the sensitivity of osteocytes to external stimulation. The structure of osteocytes will be changed when they are subjected to vibrations, which influence the mechanosensitivity of osteocytes and alter the regulation of bone remodeling process. As an important mechanotransduction structure in osteocytes, the membrane skeleton greatly affects the mechanosensation and conduction of osteocytes. However, the dynamic responses of membrane skeleton to the vibration and the structural changes of membrane skeleton are unclear. Therefore, we applied a nonlinear dynamics method to explain the time-dependent changes of membrane skeleton. The semi-ellipsoidal reticulate shell structure of membrane skeleton is built based on the experimental observation in our previous work. Then, the nonlinear dynamic equations of membrane skeleton are established according to the theory of plate and shell dynamics, and the displacement-time curves, phase portraits, and Poincaré maps of membrane skeleton structure were obtained. The numeration results show that under the vibration stimulation of 15 Hz, 30 Hz, 60 Hz, and 90 Hz, the membrane skeleton is destroyed after a transient equilibrium position vibration. The vibration of 15 Hz has the most destructive effect on the membrane skeleton, the natural frequency of membrane skeleton may be less than 15 Hz. In addition, the chaos phenomenon occurs to the membrane skeleton during vibration. As a damping factor, the existence of viscosity alleviates the damage of structure. This study can help us to understand the oscillation characteristic of membrane skeleton in osteocyte.