Functional grading of mineral and collagen in the attachment of tendon to bone

Abstract

Attachment of dissimilar materials is a major challenge because high levels of localized stress may develop at their interfaces. An effective biologic solution to this problem exists at one of nature's most extreme interfaces: the attachment of tendon (a compliant, structural "soft tissue") to bone (a stiff, structural "hard tissue"). The goal of our study was to develop biomechanical models to describe how the tendon-to-bone insertion derives its mechanical properties. We examined the tendon-to-bone insertion and found two factors that give the tendon-to-bone transition a unique grading in mechanical properties: 1), a gradation in mineral concentration, measured by Raman spectroscopy; and 2), a gradation in collagen fiber orientation, measured by polarized light microscopy. Our measurements motivate a new physiological picture of the tissue that achieves this transition, the tendon-to-bone insertion, as a continuous, functionally graded material. Our biomechanical model suggests that the experimentally observed increase in mineral accumulation within collagen fibers can provide significant stiffening of the partially mineralized fibers, but only for concentrations of mineral above a "percolation threshold" corresponding to formation of a mechanically continuous mineral network within each collagen fiber (e.g., the case of mineral connectivity extending from one end of the fiber to the other). Increasing dispersion in the orientation distribution of collagen fibers from tendon to bone is a second major determinant of tissue stiffness. The combination of these two factors may explain the nonmonotonic variation of stiffness over the length of the tendon-to-bone insertion reported previously. Our models explain how tendon-to-bone attachment is achieved through a functionally graded material composition, and provide targets for tissue engineered surgical interventions and biomimetic material interfaces.

Figure 1

Tendon-to-bone insertion connects two very different, hierarchical tissues. A schematic of the collagen fibers is shown above a cross-sectional view of the tendon-to-bone insertion. Collagen fiber dispersion increases from tendon to bone. Blue shading in the schematic views indicates the concentration of mineral within each fiber. The schematic is representative of the diffuse model shown in Fig. 2b.

Figure 2

(a) Properties of mineralized and nonmineralized collagen at the nanoscale were incorporated with experimental measures of mineral content and collagen orientation to model the tendon-to-bone insertion at the microscale. (b) Three fiber-level models of mineral accumulation were studied. (c) Details for finite element model (i and ii) for Monte Carlo simulations to estimate the stiffness of partially mineralized fibers, and boundary conditions applied in extension (iii) and shear (iv).

Figure 3

Relative concentration of mineral (i.e., apatite) estimated from RMS measurements, displayed as the ratio of the areas of the 960 Δcm⁻¹ PO₄ peak to the 2940 Δcm⁻¹ collagen peak, across the tendon-to-bone insertion. Approximate regions of tendon and bone are indicated.

Figure 4

Bounds and estimates for the axial elastic modulus (E) and axial-transverse shear modulus (G) of a partially mineralized fiber. Mineral stiffens fibers dramatically at volume fraction above the percolation threshold (ϕ ≈ 0.5), indicated by the arrows. Percolation occurs at lower volume fraction for regions of enhanced mineralization elongated parallel to the fiber axis.

Figure 5

(a) Alignment of collagen fibers is greatest (angular deviation is lowest) in tendon, and angular deviation is highest in the tendon-to-bone insertion. (b) The spatially varying elastic modulus of a hypothetical tendon-to-bone insertion containing no mineral. The decreasing fiber alignment leads to a rapid drop in tissue stiffness in the first few percent of the tendon-to-bone insertion.

Figure 6

Combination of decreasing collagen organization and increasing mineral content leads to a decrease in modulus followed by an increase in modulus.