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. 2022 May 6;7(2):59.
doi: 10.3390/biomimetics7020059.

Bone Remodeling Process Based on Hydrostatic and Deviatoric Strain Mechano-Sensing

Natalia Branecka  1 , Mustafa Erden Yildizdag  2   3 , Alessandro Ciallella  2   4 , Ivan Giorgio  2   4
Affiliations

Bone Remodeling Process Based on Hydrostatic and Deviatoric Strain Mechano-Sensing

Natalia Branecka et al. Biomimetics (Basel). .

Abstract

A macroscopic continuum model intended to provide predictions for the remodeling process occurring in bone tissue is proposed. Specifically, we consider a formulation in which two characteristic stiffnesses, namely the bulk and shear moduli, evolve independently to adapt the hydrostatic and deviatoric response of the bone tissue to environmental changes. The formulation is deliberately simplified, aiming at constituting a preliminary step toward a more comprehensive modeling approach. The evolutive process for describing the functional adaptation of the two stiffnesses is proposed based on an energetic argument. Numerical experiments reveal that it is possible to model the bone remodeling process with a different evolution for more than one material parameter, as usually done. Moreover, the results motivate further investigations into the subject.

Keywords: bone remodeling; deviatoric strain; hydrostatic strain; mechanical stimuli; mechano-sensing; strain energy density.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Osteocytes in bone matrix (star-shaped) with the formed OLCN connected to osteoblasts on the boundary.
Figure 2
Figure 2
Effect of the load on stimulus. Low mechanical loading results in bone resorption: it is the resorption stimulus zone; subsequently, in the lazy zone (black dotted line), there is no change in bone; with a sufficiently high load, the formation of the stimulus zone occurs in a certain range highlighted with red dotted lines.
Figure 3
Figure 3
Flow chart of processes.
Figure 4
Figure 4
Schematics for the considered pure hydrostatic and pure deviatoric cases.
Figure 5
Figure 5
Deformed shape for the pure hydrostatic case (plots were obtained with a scale factor of 20).
Figure 6
Figure 6
Evolution of moduli and stimuli in time for the purely hydrostatic case.
Figure 7
Figure 7
Deformed shape for the pure deviatoric case (plots were obtained with a scale factor of 20).
Figure 8
Figure 8
Evolution of moduli and stimuli in time for the purely deviatoric case.
Figure 9
Figure 9
Schematic for the tensile test under a uniform load q0.
Figure 10
Figure 10
Deformed shape for the tensile test (plots were obtained with a scale factor of 5).
Figure 11
Figure 11
Evolution of moduli and stimuli in time for the tensile test.
See this image and copyright information in PMC

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