Tissue strain amplification at the osteocyte lacuna: a microstructural finite element analysis

Abstract

A parametric finite element model of an osteocyte lacuna was developed to predict the microstructural response of the lacuna to imposed macroscopic strains. The model is composed of an osteocyte lacuna, a region of perilacunar tissue, canaliculi, and the surrounding bone tissue. A total of 45 different simulations were modeled with varying canalicular diameters, perilacunar tissue material moduli, and perilacunar tissue thicknesses. Maximum strain increased with a decrease in perilacunar tissue modulus and decreased with an increase in perilacunar tissue modulus, regardless of the thickness of the perilacunar region. An increase in the predicted maximum strain was observed with an increase in canalicular diameter from 0.362 to 0.421 microm. In response to the macroscopic application of strain, canalicular diameters increased 0.8% to over 1.0% depending on the perilacunar tissue modulus. Strain magnification factors of over 3 were predicted. However, varying the size of the perilacunar tissue region had no effect on the predicted perilacunar tissue strain. These results indicate that the application of average macroscopic strains similar to strain levels measured in vivo can result in significantly greater perilacunar tissue strains and canaliculi deformations. A decrease in the perilacunar tissue modulus amplifies the perilacunar tissue strain and canaliculi deformation while an increase in the local perilacunar tissue modulus attenuates this effect.

Fig. 1

(a) Atomic force microscopy image of an osteocyte lacunae on a polished section of cortical bone. (b) Transmission electron image of an osteocyte and its lacunae (courtesy of Jian Feng, University of Missouri at Kansas City, Department of Oral Biology). (c) Finite element mesh shown for a perilacunar thickness of 5 μm and canaliculi diameter of 0.425 μm. The canaliculi, lacuna, and perilacunar tissue are labeled.

Fig. 2

Mesh convergence results for maximum lacunar effective strain. Differences in model predicted strains converged to less than 2% at a mesh density of 605,400 nodes for both thicknesses (3 and 10 μm) and moduli (15 and 35 GPa) considered.

Fig. 3

Perilacuna strain increased 97% when the canaliculi (of either diameter) were included in the model. An increase in the diameter of the canaliculi from 0.362 to 0.421 μm resulted in an increase of 2.31% in the measured maximum perilacunar.

Fig. 4

Both the measured maximum strain increased with a decrease in perilacunar modulus and decreased with an increase in perilacunar modulus, regardless of the thickness of the perilacunar region.

Fig. 5

Fringe plots of the strain experienced by the perilacunar region and its surrounding material showing that a low perilacunar modulus led to higher strains than a high modulus: (left) a perilacunar region with a material modulus of 15 GPa (right) a perilacunar region with a material modulus of 35 GPa.

Fig. 6

Strain magnification factor. There is an average strain magnification factor of 1.36, 2.68, and 2.73 for the model with no canaliculi, a canaliculi diameter of 0.362 μm, and a canaliculi diameter of 0.425 μm, respectively.

Fig. 7

The measured percent change in canaliculi diameter ranges from 0.811% to 1.015% across the perilacunar tissue properties.