Cross-scale mechanobiological regulation of cylindrical compressible liquid inclusion via coating

The double-bag theory in modern anatomy suggests that structures with coatings are commonly found in human body at various length scales, such as osteocyte processes covered by pericellular matrix and bones covered by muscle tissue. To understand the mechanical behaviors and physiological responses of such biological structures, we develop an analytical model to quantify surface effects on the deformation of a coated cylindrical compressible liquid inclusion in an elastic matrix subjected to remote loading. Our analytical solution reveals that coating can either amplify or attenuate the volumetric strain of the inclusion, depending on the relative elastic moduli of inclusion, coating, and matrix. For illustration, we utilize this solution to explore amplification/attenuation of volumetric strain in musculoskeletal systems, nerve cells, and vascular tissues. We demonstrate that coating often plays a crucial role in mechanical regulation of the development and repair of human tissues and cells. Our model provides qualitative analysis of cross-scale mechanical response of coated liquid inclusions, helpful for constructing mechanical microenvironment of cells.