CONFOCAL MICROSCOPY BASED DIGITAL FINITE ELEMENT ANALYSIS OF LOCAL STRAINS IN AND AROUND IN SITU OSTEOCYTES

Participants: B.R. McCreadie, S.J. Hollister

Keywords: finite element analysis, confocal microscopy, osteocyte

Introduction

The location and interconnectedness of osteocytes in bone suggest that they may act as strain sensors, controlling the modeling and/or remodeling processes in bone based on the strains they experience. This abstract describes a method by which the osteocyte lacunae were directly imaged by confocal microscopy and a finite element model constructed from these images. By applying strains previously determined at the trabecular level, the strain distribution in and around the cell was determined for two lacunae of different shapes and sizes.

Materials and Methods

Several thick slices were obtained from the proximal portion of a canine humerus and immediately fixed and stored in 70% ethanol for 96 hours. The slices were stained with basic fuchsin, then ground and polished to approximately 100 µm thick. Slides of the humerus sections were prepared and observed using a Bio-Rad MRC 600 confocal microscope equipped with a 60x 1.40 NA oil-immersion lens. Resulting pixel dimensions were 0.273 µm in the x-y plane. Serial sections were obtained at increments of 1.0 µm as measured by the microscope stage movement. This increment was later corrected as explained below.

A separate slide was made by applying nominal 4 µm diameter fluorescent microspheres (Molecular Probes, Eugene, OR) to a microscope slide and cover slide. A slice of rat humerus was placed between the cover slip and slide using immersion oil as a mounting medium. A single series of images was obtained through both sets of beads. The images were compiled into a 3-D data set using PV-Wave (Visual Numerics, Boulder, Colorado). The distances between half-maximum pixel values were obtained in each direction for 3 beads each from both sides of the bone specimen. Based on the known size of the voxels in the xy plane and assuming perfectly spherical beads, a correction factor (actual z distance / nominal z distance) of .448 was obtained.

Two regions of interest, containing two differently-shaped lacunae, were converted to 3-D datasets in PV-Wave. The datasets were thresholded, and a boundary filter was sequentially applied to lacuna and matrix voxels to reduce noise. The resulting boundaries of the lacunae were very similar to that seen visually in the original image. Remaining holes inside the lacunae boundary were changed to lacuna voxels. The lacunae were then aligned to the voxel axes, with the long axis in the y direction and the intermediate axis in the x direction.

The 3-D data sets were converted so the voxels had equal dimensions in the three axes. The matrix voxels were given a Young's modulus of 3.9 GPa and Poisson's ratio of 0.3, and the cell voxels a Young's modulus of 10 MPa and Poisson's ratio of 0.4. The data sets were analyzed using homogenization routines (Voxel Computing, Inc.). During post-processing, a strain of {1325,287,80} µe (1 µe=0.00001% strain) was applied such that the 1325 µe was along the long axis and the 287 µe along the intermediate axis of each lacuna. In a separate analysis, a uniaxial strain of 1000 µe was applied to each model in the long axis of the lacuna.

Results

The dimensions of the lacunae were 11.7 µm x 6.6 µm x 3.4 µm and 17.4 µm x 4.8 µm x 3.8µm. The volumes of the lacunae were approximately 2.8% and 1.7% of the analyzed model, respectively. The results from the first of these lacunae are shown in the figures below.

The major principal strains in the matrix of the first lacuna ranged from less than 1 to 9890 µe in the {1325,287,80} case, while the major principal strains in the cell were generally below 2000 µe. The average major principal strain in the model was 773 µe. The second lacuna, which was longer and thinner, had higher strains with a similar distribution.

There is some magnification of the strain around and in the cell, as shown by the voxels with major principal strains greater than the applied strain. This suggests that the geometry of the lacuna allows the cells to see a higher strain than that applied to the bone matrix at the trabecular level. In addition, the geometry of the lacuna does play a role in determining the magnitude of the strains in the cell and matrix, as demonstrated by the higher strains in the longer, thinner lacuna.

The methods presented here may be applied to estimate in situ osteocyte and matrix strain directly from confocal images of bone tissue. These methods could be used to compare strains in and around osteocytes in various bone types and pathological conditions.

Progress

This study is published in Barbara McCreadie's dissertation (2000).

Graph of maximum principal strain for the Half of first lacuna model

{1325,287,80} strain case with cell material removed

{1325,287,80} Strain Case -- Maximum Principal Strains

x-y plane x-z plane ( reported in µe)

Uniaxial Strain Case - Maximum Principal Strains

x-y plane x-z plane ( reported in µe)