Spatial periodicity in growth plate shear mechanical properties is disrupted by vitamin D deficiency

Abstract

The growth plate is a highly organized section of cartilage in the long bones of growing children that is susceptible to mechanical failure as well as structural and functional disruption caused by a dietary deficiency of vitamin D. The shear mechanical properties of the proximal tibial growth plate of rats raised either on normal or vitamin D and calcium deficient diets were measured. A sinusoidal oscillating shear load was applied to small excised growth plate specimens perpendicular to the direction of growth while imaging the deformation in real time with a fast confocal microscope. Local deformations and shear strains were quantified using image correlation. The proliferative zone of the growth plate bores the majority of the shear strain and the resting, hypertrophic and calcification zones deformed less. Surprisingly, we regularly observed discontinuous deformations in the proliferative zone in both groups that resembled cell columns sliding past one another in the direction of growth. These discontinuities manifested as regions of concentrated longitudinal shear strain. Furthermore, these shear strain concentrations were spaced evenly in the proliferative zone and the spacing between them was similar across growth plate regions and across control specimens. In contrast to the healthy controls, the vitamin D deficient growth plate exhibited larger variations in the size and orientation of cellular columns in the proliferative and hypertrophic zones. High strains were observed between columns, much as they were in the controls. However, the regular spacing of shear strain concentrations was not preserved, echoing the observation of decreased structural organization.

Fig. 1

(a) Posterior view of rat tibia prior to cutting along dashed line segments. (b) Mechanical test specimen. Tissue sections were trimmed to obtain a parallelepiped shaped plug of length approximately 3.5 mm anterior/posterior (x), 4 mm superior/inferior (y) and 1.5 mm medial/lateral (z). Ruler markings indicate 1 mm.

Fig. 2

(a) Confocal micrograph of tibial growth plate demonstrating the four major zones and (b) schematic of the shear testing apparatus. Zones are distinguished by chondrocyte size (smallest in the resting & proliferating zones, larger in the hypertrophic zones) and alignment (organized into columns in the proliferating and hypertrophic zones). Image size is 637 μm × 637 μm. All tissue images are shown epiphyseal side up.

Fig. 3

Shear strain and shear modulus of the growth plate as a function of distance from the metaphyseal chondro-osseous junction. 637 μm × 637 μm confocal micrographs of a control rat tibial growth plate (a) before and (b) after application of 10% shear strain, the arrow indicating the direction of applied shear. (c) Shear strain and (d) shear modulus profiles for tested samples (n = 5) as a function of distance s from the chondro-osseous junction. Specimens are represented by the same color trace in both (c) and (d).

Fig. 4

Transverse variation in induced shear strain γ_xy within the proliferative and hypertrophic zones. (a, b) Due to intercolumnar sliding, medial–lateral photobleached lines become discontinuous as growth plate is sheared. This slipping behavior results in large negative and positive shear strains between chondrons, as demonstrated by a map of γ_xy (c). (d) Averaging the γ_xy strain map of a single sample in the longitudinal direction produces a profile of strain as a function of transverse position, in which the bands of large positive strain observed in (c) manifest as regularly spaced peaks. (e) Average γ_xy as a function of transverse distance from the midpoint between the regions of slip for all (n=5) samples. Each curve in the plot represents the average of at least 5 traces from a single growth plate sample. Scale bars in (a, b) indicate 100 μm.

Fig. 5

Local concentrations of induced shear strain γ_xy in the control (left) and vitamin D deficient (right) growth plates. (a, b) Representative confocal images of growth plates from control and vitamin D deficient rats indicating the direction of loading for mechanical testing. Growth plates from animals with vitamin D deficient diets exhibit extensive disorganization, with a discontinuous structure and columns of chondrocytes aligned in varying directions that were not parallel to the axis of growth. (Bottom) Superimposed on confocal images are markers denoting regions of high strain: the red + indicate locations where γ_xy exceeds 1 standard deviation above the average strain for each image. The black arrows indicate the direction of applied shear. As before, all tissue images are shown epiphyseal side up. Scale bars indicate 250 μm. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

Fig. 6

Two dimensional fast Fourier transforms (2D FFT) of strain fields γ_xy of growth plates shown in Fig. 5 ((a) control, (b) vitamin D deficient). These maps show the frequency distribution in spatial patterns of induced shear strain. The maps have been normalized to have a sum of 1, such that pixel intensity corresponds to the relative weight of that Fourier component in the reconstruction. (a) The high-magnitude horizontal band indicates that the strain field is strongly periodic in the horizontal and aperiodic in the vertical directions. The bright peaks indicate a single characteristic spatial frequency. (b) The 2D FFT of the vitamin D deficient growth plates is more widely distributed than that of the controls. (c) Comparison of the primarily horizontal Fourier components of the 2D FFT. The control specimen has a maximum Fourier coefficient at 6 cycles in the analyzed area. Since the analyzed area was 676 μm for this image sequence, this corresponds to a spatial period of about 676 μm=6 = 113 μm. The primarily horizontal components of the vitamin D deficient specimen 2D FFT does not have such a distinct peak and is smaller overall, the Fourier components being much more diffusing in both spatial frequency and direction. (d) A dot plot showing the spatial periods corresponding to the largest Fourier components of each of the Control and Vitamin D deficient FFT’s. Dot size is proportional to the maximum value of that FFT, such that FFT’s with a single large characteristic peak (indicating a very regular periodic spacing of shear concentrations) are represented by larger dots while flatter FFT’s are represented by smaller dots. The spatial periods of the control are clustered between 50 and 150 μm and have larger peak Fourier components while the dominant spatial periods in the vitamin D deficient FFT’s are more widely distributed and have slightly smaller peak Fourier components overall.