Hierarchical micro-adaptation of biological structures by mechanical stimuli

Abstract The objective of this work is to develop a remodeling model for biological matter coupling two different processes in a 3D framework: reorientation of the preferential direction of a given fibered structure and reorientation of the fibrils or filaments that make up such a structure. This work uses the microsphere-based approach to take into account the micro mechanics involved in biological fibered structures regarding both their passive behavior and the reorientation of their micro constituents. Moreover, the macro behavior of the material as a whole is obtained by means of homogenizing the underlying micro response. We associate the orientation space of the integration directions to the physical space of micro-fibrils. To approximate the directional distribution of the fibrils within each fiber bundle, a Bingham probability orientation density function is introduced into the Helmholtz energy function. With all these assumptions, the problem is studied from an energetic point of view, describing the dissipation inherent to remodeling processes, and the evolution equations for both reorientations (change in preferential direction of the network and change in shape of the fibril distribution) re obtained. The model is included in a finite element code which allows computing different geometries and boundary value problems. This results in a complete methodology for characterizing the reorientation evolution of different fibered biological structures, such as cells. Our results show remodeling of fibered structures in two different scales, presenting a qualitatively good agreement with experimental findings in cell mechanics. Hierarchical structures align in the direction of the maximum principal direction of the considered stimulus and narrow in the perpendicular direction. The dissipation rates follows predictable trends although there are no experimental findings to date for comparison. The incorporation of metabolic processes and an insight into cell-oriented mechano-sensing processes can help to overcome the limitations involved.

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