Strain Amplification in the Bone Mechanosensory System

Abstract In this work we suggest a mechanism whereby the bone deformation driven flow of bone fluid through the glycocalyx surrounding an osteocytic cell process in its canaliculus will lead to strains in the cell process membrane which are many times those in the whole bone. We shall describe a mechanism whereby the low magnitude of the strain applied to the whole bone (0.1% to 0.3%) is amplified by nearly two orders of magnitude at the membrane of the cell process. The possibility of this strain amplification depends upon the values of the certain physical and biological parameters. These parameters include the elastic constants of the cell membrane, the elastic constants of the fibers that constitute the glycocalyx. the pre-tension in the fibers and cell membrane, the permeability of bone fluid through the glycocalyx, the physical dimensions of the cell process, the canaliculus, the fibers and fiber spacing of the glycocalyx. The model employed is an interactive micro-macro mechanical model. It was analyzed numerically. The micro model is a detailed model of the structure and contents of a canaliculus and the macro model is poroelasticity. A mechanical loading range from 1 MPa to 20 MPa at different frequencies, 1Hz to 20Hz, were considered. We calculated the ratio of the drag force on the fibers to the shear force on the osteocyte membrane in a canaliculus and found that the drag force is at least 50 times larger than the shear on the cell membrane. We also calculated the strain al the membrane, as well as the strain amplification ratio, and found that the strain amplification ratio reached a maximum value of 65 for this loading range. Thus the proposed mechanism amplifies the strain applied to the whole bone when it is experienced at the osteocyte process membrane.