IMAGE-BASED FINITE ELEMENT MODELS FOR THE INVESTIGATION OF OSTEOCYTE MECHANOTRANSDUCTION

Philipp Schneider (1), Davide Ruffoni (1), David Larsson (1), Ilaria Chiapparini (1), Ralph Müller (1)

1. Institute for Biomechanics, ETH Zurich, Zurich, Switzerland

Introduction

It is widely accepted that osteocytes transduce

mechanical signals in bone. To better understand

the micromechanical response of the osteocyte

lacunae to imposed macroscopic strains, finite

element (FE) models were introduced to predict

how mechanical loads act on the lacuno-canalicular

network (LCN) [Bonivtch et al, 2007]. Yet, these

FE analyses were based on idealized LCN models.

Recent progress in imaging allows quantitative

assessment of bone microstructure in 3D down to

the level of individual osteocyte lacunae and its

canaliculi [Dierolf et al, 2010; Schneider et al,

2011]. Our goal was to study the influence of the

microstructure on the mechanical response to

imposed macroscopic strains by combining true 3D

LCN data with image-based FE modeling.

Methods

First, an idealized LCN geometry was created,

which was composed of an ellipsoid (minor and

major semiaxis equal to 4 and 9 μm, respectively)

and 18 canaliculi with a diameter of 200 nm (Figure

1 left) similar to [Bonivtch et al, 2007], resulting in

a model size of 27×27×27 μm3 at 67 nm voxel size.

The image-based model represented one osteocyte

lacuna and the radiating canaliculi within the mid-

diaphysis of a C57BL/6 (B6) mouse at 12 weeks,

assessed using ptychographic X-ray computed

tomography [Dierolf et al, 2010] at the cSAXS

beamline of the Swiss Light Source at 65 nm voxel

size. FE models were created by direct conversion

of image voxels into 8-noded cubic brick elements.

A uniaxial displacement was applied corresponding

to an apparent compressive strain of 1% along the

z-direction (Figure 1 top). The FE models (E = 25

GPa, � = 0.3) were solved at the Swiss National

Supercomputing Centre using parFE [Arbenz et al,

2008]. The micromechanical perilacunar

environment was characterized in terms of principal

compressive strains and strain magnification, which

was calculated for both models by dividing the

principal strain by the apparent compressive strain.

Results and Discussion

In Figure 1 (bottom), the magnification of the

compressive strain is illustrated for one z-slice. In

the top row, red voxels specify regions where the

strain magnification was larger than 1.5. Figure 2

shows the compressive strain magnification as a

function of the distance from the LCN surface.

Figure 1: LCN FE models (left: ideal, right: image-

based) and compressive strain magnification.

Figure 2: Compressive strain increase and strain

magnification against distance from LCN surface.

For both models, high magnification (> 1.5: red

regions in Figure 1) was limited to pericanalicunar

regions (distance from LCN surface < 0.5 μm).

When excluding the layer next to the LCN surface

(gray bar in Figure 2) to avoid discretization errors,

the maximal compressive strain increase was 63%

and 157%, equivalent to a 1.6x rise in strain

magnification for the image-based vs. idealized

model. Briefly, FE based on image-based models

leads to higher strain magnification, which plays a

pivotal role in bone mechanotransduction.

References

Bonivtch et al, J Biomech, 40:2199-2206, 2007

Dierolf et al, Nature, 467:436-439, 2010

Schneider et al, Bone, 49:304-311, 2011.

Arbenz et al, Int J Num Meth Eng, 73:927-47, 2008.

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S436 Presentation 1484 − Topic 31. Mechanobiology and cell biomechanics

Journal of Biomechanics 45(S1) ESB2012: 18th Congress of the European Society of Biomechanics