Osteocyte lacunar strain determination using multiscale finite element analysis

Abstract

Osteocytes are thought to be the primary mechanosensory cells within bone, regulating both osteoclasts and osteoblasts to control load induced changes in bone resorption and formation. Osteocytes initiate intracellular responses including activating the Wnt/β-catenin signaling pathway after experiencing mechanical forces. In response to changing mechanical loads (strain) the osteocytes signal to cells on the bone surface. However, this process of osteocyte activation appears heterogeneous since it occurs in sub-populations of osteocytes, even within regions predicted to be experiencing similar global strain magnitudes determined based on traditional finite element modeling approaches. Several studies have investigated the strain responses of osteocyte lacunae using finite element (FE) models, but many were limited by the use of idealized geometries (e.g., ellipsoids) and analysis of a single osteocyte. Finite element models by other groups included more details, such as canaliculi, but all were done on models consisting of a single osteocyte. We hypothesized that variation in size and orientation of the osteocyte lacunae within bone would give rise to micro heterogeneity in the strain fields that could better explain the observed patterns of osteocyte activation following load. The osteocytes in our microscale and nanoscale models have an idealized oval shape and some are based on confocal scans. However, all the FE models in this preliminary study consist of multiple osteocytes. The number of osteocytes in the 3D confocal scan models ranged from five to seventeen. In this study, a multi-scale computational approach was used to first create an osteocyte FE model at the microscale level to examine both the theoretical lacunar and perilacunar strain responses based on two parameters: 1) lacunar orientation and 2) lacunar size. A parametric analysis was performed by steadily increasing the perilacunar modulus (5, 10, 15, and 20 GPa). Secondly, a nanoscale FE model was built using known osteocyte dimensions to determine the predicted strains in the perilacunar matrix, fluid space, and cell body regions. Finally, 3-D lacunar models were created using confocal image stacks from mouse femurs to determine the theoretical strain in the lacunae represented by realistic geometries. Overall, lacunar strains decreased by 14% in the cell body, 15% in the fluid space region and 25% in the perilacunar space as the perilacunar modulus increased, indicating a stress shielding effect. Lacunar strains were lower for the osteocytes aligned along the loading axis compared to those aligned perpendicular to axis. Increases in lacuna size also led to increased lacunar strains. These finite element model findings suggest that orientation and lacunar size may contribute to the heterogeneous initial pattern of osteocyte strain response observed in bone following in vivo applied mechanical loads. A better understanding of how mechanical stimuli directly affect the lacunae and perilacunar tissue strains may ultimately lead to a better understanding of the process of osteocyte activation in response to mechanical loading.

Keywords: Finite element model; Lacunae; Osteocyte; Perilacunar matrix; Strain.

Fig. 1

2-D FE Micro model (1 mm × 2 mm × 0.01 mm) showing lacunae of different idealized shapes, sizes and orientations. The loading direction for this model is vertical on the page, corresponding to the longitudinal axis of the bone. The fixed surface is indicated by red X markers. Green represents bone, and purple represents lacunae, with darker pixels representing the perilacunar regions for each shape. Top left - L1, L2, L3 and L4 are four lacunae with sides of equal size. Top right – lacunae with same size but different orientations: 2 V is vertical, 2H is horizontal, 1 CE is diagonal from upper left to lower right, and 1BD is diagonal from upper right to lower left. Bottom – magnified image showing greater detail of the perilacunar regions for each idealized cell.

Fig. 2

2-D FE Nano model with six osteocytes. The loading direction for this model is vertical from top to bottom and the fixed surface is indicated by red X markers . (A) The six osteocytes represent each possible orientation in the matrix. (B) A Representative osteocyte showing the bone matrix region (light green), perilacunar matrix (blue), fluid space (red), and cell body (purple).

Fig. 3

3-D FE nano-model with seventeen lacunae created from a confocal image stack of mouse femoral bone. The load is applied in the longitudinal direction, which is also the longitudinal axis of the bone. (A) Front surface view showing mesh. One incomplete lacuna is lying in the cut plane (purple). (B) With outer surfaces hidden, the realistic lacunar shapes are revealed.

Fig. 4

Comparison of theoretical lacunar strains as a function of perilacunar modulus in osteocyte lacunae with different orientations.

Fig. 5

Comparison of lacunar strains as a function of perilacunar modulus in lacunae of different size.

Fig. 6

Color maps of the third Principal Lagrange Strain values for lacunae in the mid-shaft of the 7 lacunae female murine femur model. The loads were applied to the top surface of the model along the z-axis, in the negative z-direction, which corresponds to the longitudinal axis. The bottom surface of the model was fixed.

Fig. 7

Comparison of normalized strain values in individual osteocytes in Model shown in Fig. 6 shown from coarse to a very fine mesh.