Stress amplification during development of the tendon-to-bone attachment

Abstract

Mechanical stress is necessary to sustain the mineral content of bone in adults. However, in a developing neonatal mouse, the mineralization of soft tissues progresses despite greatly reduced average mechanical stresses. In adults, these reduced loads would likely lead to bone loss. Although biochemical factors may partly explain these different responses, it is unclear how mineralization is initiated in low load environments. We present here the effect of morphometric data and initial modeling supporting a hypothesis that mechanical factors across several length scales amplify stresses, and we suggest that these stresses are of a level adequate to contribute to mechanical signaling for initiation of mineralization at the developing tendon-to-bone enthesis. A mineral gradient is evident across the insertion from the onset of mineralization. This grading maintains a constant size from early postnatal time points to adulthood. At the tissue level, this grading contributes to reduced stresses in an adult animal and to a minor elevation of stresses in a neonatal animal. At the cellular level, stress concentrations around mineralizing chondrocytes are enhanced in neonatal animals compared with adult animals. The enhancement of stresses around cells at early time points may serve to amplify and transduce low loads in order to initiate mineralization.

Figure 1

Schematic of the modeling approach to estimate the stress environment of developing tendon-to-bone enthesis at the rotator cuff of a mouse. The rotator cuff to humeral head insertion is modeled as a concentric ring model. Because the size of the enthesis (mineralized region and unmineralized region) is much smaller than that of the tendon and bone, and the size of the cells are comparable to the length of gradient region, an axisymmetric unit cell model (a spherical cell in the center of cylindrical extracellular matrix) was used to estimate the stress concentration at cell and matrix interface.

Figure 2

Schematic of the developing tendon-to-bone enthesis at the rotator cuff of a mouse. The graded mineralized region maintained a relatively constant thickness over time, increasing while the outer radius of the cortical bone (humeral head) and tendon length grew. The unmineralized “fibrocartilage” disappeared with age. Rings are drawn to scale.

Figure 3

Histologic tissue sections of the tendon-to-bone enthesis at the rotator cuff of a mouse, showing a steady decline in the size and volume fraction of chondrocytes with age. Time points: (a) P7, (b) P10, (c) P14, (d) P28. The black/dark areas indicate mineral, the cell nuclei are stained with dark blue, hypertrophic chondrocytes appear as white circles (see arrows in (a), (b), and (c)), and the purplish/pinkish areas indicate the presence of proteoglycans, which are characteristic of cartilage. Note that the cells remain spherical throughout, and start to organize into columns at later timepoints. Although Raman spectroscopic analysis clearly indicates a gradient in mineral at all timepoints (Schwartz et al. 2012; Wopenka et al. 2008), the graded transition zone is not visible by von Kossa staining at any timepoint, as this staining yields an opaque band with even a small level of mineralization. (5 μm thick sections, von Kossa and Toluidine blue staining, scale bar = 100μm, arrows: hypertrophic chondrocytes).

Figure 4

Development of the volume fraction of cells at (a) mineralized fibrocartilage (b) unmineralized fibrocartilage.The range of data indicates standard deviation (N=3). (c) Mean radius of cells as a function of age. Both the volume fraction and size of cells decrease with age. The fraction of cells decreases rapidly after 14 days in the mineralized region. The volume fraction is much larger in the mineralized region than in the unmineralized region at early development.

Figure 5

Estimated peak muscle stresses as a function of age. Peak muscle stresses increase with age, with the stress ratio between the P56 (maturity) and P7 (early post-natal) about 14.8. The range of data indicates standard deviation (N=3).

Figure 6

As the volume fraction and the size of cells decrease over time, the SCF decreases at the cell-matrix interface. The SCF was determined numerically using finite element simulations; a schematic axisymmetric unit cell model with mesh is shown.

Figure 7

The stress concentration at the cell-matrix interface decreased as a function of age. The stress field remained qualitatively similar over time, as shown in the contour of peak principal stresses.

Figure 8

The effect of the mineral gradient region on the macroscopic stress concentration at the tendon-to-bone enthesis is shown as a function of age. The gradient region did not change over time and the stiffness was adjusted for the volume fraction of cells using the results of the finite element analyses shown in Fig. 7. A schematic of the concentric ring model is shown above the plot.

Figure 9

The peak principal stress surrounding cells during early development are elevated to near adult physiologic levels through stress concentrations. The estimated peak principal stress did not change significantly from P10 onwards; only the difference between P7 and P56 was significant statistically, with the average value at P7 0.23 times of that at P56. At all time points, the peak principal stress was not different statistically from that at young adulthood (P28).