Allometry of the Tendon Enthesis: Mechanisms of Load Transfer Between Tendon and Bone

Abstract

Several features of the tendon-to-bone attachment were examined allometrically to determine load transfer mechanisms. The humeral head diameter increased geometrically with animal mass. Area of the attachment site exhibited a near isometric increase with muscle physiological cross section. In contrast, the interfacial roughness as well as the mineral gradient width demonstrated a hypoallometric relationship with physiologic cross-sectional area (PCSA). The isometric increase in attachment area indicates that as muscle forces increase, the attachment area increases accordingly, thus maintaining a constant interfacial stress. Due to the presence of constant stresses at the attachment, the micrometer-scale features may not need to vary with increasing load.

Next generation tissue engineering of orthopedic soft tissue-to-bone interfaces

“…These splayed fibrils transition from the uncalcified fibrocartilage region into large type I collagen fibers that make up the oriented fiber region of the enthesis. [31,43] Understanding native structure/composition should inform material selection for tissue engineering.…”

The concentration of stress at the rotator cuff tendon-to-bone attachment site is conserved across species

“…The effects of the normalized attachment length on stress concentration were studied over a broad range that encompassed the physiological range (0.001 < L a / R b < 0.02) observed in adult animals ranging from mice (0.03 kg) to pigs (40 kg) (Deymier-Black et al, 2015). In these studies, the normalized tendon length was held constant, with the value of L t / R b = 20 chosen as a baseline; this value represents the approximate ratio of the Achilles tendon length and calcaneus radius over a broad range of animals (Gàlvez-López and Casinos, 2012).…”

“…Finally, the data of Deymier-Black et al (2015) were input into the model to estimate how stress concentration varied across species (Table I). In the absence of data for the ratio of the length of the supraspinatus tendon to the radius of the humeral head, a scaling was used based upon the cross-species scaling relationship of Pollock and Shadwick (1994) for the Achilles tendon length and body mass, m : $${L_t}^a=63.7m^{0.34},$$ where L t a is in mm and m is in kg, and that of Gàlvez-López and Casinos (2012) for calcaneus radius and body mass: $${R_b}^c=5.45m^{0.36},$$ where R b c is in mm and m is in kg.…”

“…These relationships indicated that the ratio L t / R b is nearly independent of body mass. However, L a / R b scaled strongly with animal mass, m (Deymier-Black et al, 2015): $$m=6.91\times {10}^{-8}{true(\frac{L_a}{R_b}true)}^{3.23}$$ where m is in kg. This relationship enabled the establishment of a trend relating stress concentration to animal mass.…”

“…The current study follows recent investigations of the scaling of the supraspinatus muscle and the force it applies in relation to the geometry of the insertion into the humeral head (Mathewson et al, 2013; Deymier-Black et al, 2015). Volume and physiological cross-sectional area (PCSA) of the muscle scale geometrically across species, and the area of attachment at the humeral head scales to maintain constant nominal stress at the interface.…”