1. Analysis of chondron deformation during
physiologic and hyper-physiologic compression of the growth plate
Bhavya B Vendra, Esra Roan, John L Williams
Department of Biomedical Engineering, University of Memphis, Memphis, TN, USA v
This study aims to characterize the chondron level deformation of growth plates under compression by measuring the change in chondron shape under increasing compression levels of physiological (20%) and hyperphysiological (30% and 40%) compressive strains.
Aim
Introduction
Methods
Bone Harvest and sectioning: Three-week old porcine ulnar bones were harvested and stored frozen at -20°C until use. The bones were cut into 4 mm thick samples (Fig. 2a) at 100 rpm using a diamond impregnated blade.
Growth plate thickness measurement: Samples were imaged with a stereomicroscope. The thickness of the growth plate from the epiphyseal border to calcified cartilage zone was measured using ImageJ software.
Staining: Growth plate nuclei were stained with Hoechst for 30 minutes and washed with phosphate buffered saline for 5 minutes.
Confocal Microscope: The growth plate was placed in a custom-built compression device (Fig. 2c) with one fixed plate allowing for an even compression and imaged transverse to the bone direction to obtain a stack of growth plate chondron images. The growth plate was then compressed to 20% of the growth plate height and held for 15 minutes to allow for stress relaxation. After imaging again the process was repeated at 30% and 40% growth plate compression.
Extended Depth of Field (EDF) plugin: EDF is a fusion algorithm that collects information from a stack of images with the same alignment and magnification, creating a single composite image (Forster et al., 2004). This composite image combines the in-focus information of all images in the sequence into a single in-focus composite image (Forster et al., 2004).
Analysis: Using ImageJ, chondron shapes were obtained by collecting several data points in the EDF images (Fig. 3a, 3b) and the curvature (k) of each chondron was measured by fitting an osculating circle and spline fitting each chondron and using a three point finite difference approximation of the curvatures to quantitatively measure the deformation (Fig. 2d). These curvatures were then converted to contour plots using JMP Pro 12 (SAS Institute Inc., Cary, NC) to create contour maps of the changes in curvatures (Fig. 3c).
The growth plate consists of a highly organized arrangement of chondrocytes within a tubular matrix called a chondron. It has been shown that compressing the growth plate caused internal deformations resulting in heterogeneous patterns of both tensile and compressive strains (Villemure et al., 2007). No study to date has examined how chondrons deform when the physis is compressed. b c a
Fig.1: Confocal images of three different 3-week porcine ulnar bone samples: a) Sample 1 has a V shaped mammillary process; b) Sample 2 has a continually sloped mammillary process; c) Sample 3 has an unevenly sloped mammillary process. Scale bars 100 mm.
1st cut
2nd cut
3rd cut
6th cut
5th cut
4th cut a c
Reserve zone
Proliferative zone
Hypertrophic zone
Calcified cartilage
Epiphysis
Metaphysis
Secondary center of Ossification b d
Fig.2: a) sketch of a porcine radius and ulnar bone depicting the bone sectioning, b) Histology of a growth plate sample, c) depiction of a custom built compression device with the top fixed platen and the moving bottom platen, d) method depicting the osculating circle and formula used to calculate the curvature (k) and the radius of curvature (R).
Results and Discussion a b c
< 0.002
<0.005
<0.008
<0.012
<0.015
>=0.015
Curvature, k (1/microns)
The mean radius of curvature (R = 1/k) of the chondrons decreased as growth plate compression increased from 0% to 20% strain (within physiologic levels).
Beyond 20% compression, the response varied depending on the shape of the mammillary processes (Fig. 4a).
The chondrons in the sample with a V-shaped mammillary process continued bending (decreasing R, increasing k) in direct proportion to the applied compression.
The chondrons in the two samples with a sloping mammillary process deformed by shearing laterally, thereby straightening the chondrons and relieving them from bending strains.
Differences in the mean radius of curvature were found for each of the three samples between each level of compression (p < 0.001).
The apparent random pattern of strains observed in previous studies may be explained by observation of the bending strains.
Chondron crimping was seen between 20% and 30% compression at the reserve/proliferative zone transition, suggesting high bending strains and stresses corresponding to a decreased radius of curvature R (or increased curvature k (Fig. 4b, 4c).
Fig.3: a) EDF image of Sample 1 at 20% compressive strain, b) digitized points to delineate the shape of the chondrons using ImageJ, c) contour plot of chondron curvatures (k =1/R) where darker red areas correspond to greater curvature k. a c b
References
Fig. 4: a) Plot of sample mean radius of curvature (R = 1/ k) in microns versus applied sample compressive strains. The mean radius of curvature decreased at physiologic levels of compression of 20%, but beyond physiologic compression it either continued to decrease or increased, depending on the shape of mammillary process; b) Sample 2 at 30% compressive strain when local crimping of the chondrons was observed; c) Enlarged section of chondron crimping at the reserve zone border.
Villemure et al. (2007) J Biomechanics 40, 149–156 ; Forster et al. (2004) Microscopy research and technique 65(1‐2),
Acknowledgements
We thank Lauren Thompson of the Integrated Microscopy center of the University of Memphis for training and help with the use of the confocal microscope and Drs. Randy and Karyl Buddington of the Nutrition Research Laboratory at the University of Memphis for providing the opportunity to obtain piglet tissue samples.