Bi-material attachment through a compliant interfacial system at the tendon-to-bone insertion site

Abstract

The attachment of tendon to bone, one of the greatest interfacial material mismatches in nature, presents an anomaly from the perspective of interfacial engineering. Deleterious stress concentrations arising at bi-material interfaces can be reduced in engineering practice by smooth interpolation of composition, microstructure, and mechanical properties. However, following normal development, the rotator cuff tendon-to-bone "insertion site" presents an interfacial zone that is more compliant than either tendon or bone. This compliant zone is not regenerated following healing, and its absence may account for the poor outcomes observed following both natural and post-surgical healing of insertion sites such as those at the rotator cuff of the shoulder. Here, we present results of numerical simulations which provide a rationale for such a seemingly illogical yet effective interfacial system. Through numerical optimization of a mathematical model of an insertion site, we show that stress concentrations can be reduced by a biomimetic grading of material properties. Our results suggest a new approach to functional grading for minimization of stress concentrations at interfaces.

Keywords: Enthesis; Material optimization; Stress concentrations; Tendon-to-bone attachment.

Fig. 1

The rotator cuff as viewed from the side (i.e., the lateral view). Tendons are shown in white, muscles in red, and bones in tan. The rotator cuff tendons (TM, I, S, and SS) wrap around the spherical humeral head (H) (left panel). Removing the overlying structures (A, B, C) and unwrapping the rotator cuff tendons reveals the axisymmetric geometry of the tendons and their bony insertions (right panel).

Fig. 2

Mathematical model of an axisymmetric insertion site stressed by an equibiaxial loading, p. Dimensions are representative of an adult human humeral head.

Fig. 3

Distribution of normalized radial stress for unmineralized, fully mineralized, and linearly graded model rotator cuff insertion site.

Fig. 4

The peak stress in an insertion with sigmoidal spatial grading in elastic moduli varied, as a function of weighting ω (cf. Eq. (3)), between that associated with a linear spatial grading and that associated with a sharp tendon/bone interface situated at the midpoint of the tendon-to-bone insertion site.

Fig. 5

Modulation of radial stress concentration factor in a homogeneous, “three band” model of tendon to bone attachment as a function of the moduli E_r and E_θ of the middle band. At each point in the contour plot, ν_rθ was optimized to minimize radial stress concentrations. Above the upper dotted line (upper left), the peak radial stress occurred at the tendon/insertion site interface or within the tendon; for the region below the lower dotted line, the peak stress occurred at the tendon/bone interface; at points in between, the peak stress occurred within the insertion site.

Fig. 6

Distribution of normalized radial stress in an insertion site optimized to minimize stress concentration factor. In both cases, the stress concentration was eliminated. Note that the irregular peaks in the blue line could not be controlled: the optimization criterion was not influenced by local peaks.

Fig. 7

The distribution of material properties for minimization of radial stress concentration factor contains a biomimetic compliant band between tendon and bone. Results for minimization of a multiaxial (hydrostatic) stress (not shown) are analogous. Allowing Poisson’s ratio to vary across the insertion site had strong effect on the optimum distribution of tangential elastic modulus, but little effect on the optimum distribution of radial elastic modulus.