Research Papers

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

[+] Author and Article Information
Alix C. Deymier-Black

Department of Orthopaedic Surgery,
Washington University,
St. Louis, MO 63110
e-mail: Alix.c.black@gmail.com

Jill D. Pasteris

Department of Earth and Planetary Sciences,
Washington University,
St. Louis, MO 63110
e-mail: pasteris@levee.wustl.edu

Guy M. Genin

Department of Mechanical Engineering and
Materials Science,
Washington University,
St. Louis, MO 63110
e-mail: Genin@wustl.edu

Stavros Thomopoulos

Department of Orthopedic Surgery,
Columbia University,
New York, NY 10032;
Department of Biomedical Engineering,
Columbia University,
New York, NY 10032
e-mail: sat2@columbia.edu

Manuscript received January 13, 2015; final manuscript received September 1, 2015; published online September 23, 2015. Assoc. Editor: Silvia Blemker.

J Biomech Eng 137(11), 111005 (Sep 23, 2015) (8 pages) Paper No: BIO-15-1012; doi: 10.1115/1.4031571 History: Received January 13, 2015; Revised September 01, 2015

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.

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Grahic Jump Location
Fig. 1

Multiscale structures of the tendon-to-bone enthesis. At the macroscale (left), the tendon attaches to the bone with a splayed geometry leading to a large insertion area. The microscale interface (right) is characterized by gradients in cell geometry (open circles, ovals, and diamonds), mineralization (high mineralization is gray and unmineralized is white), collagen orientation (thin lines) and composition. Of interest to this study is the gradient in mineralization between the mineralized and unmineralized fibrocartilage as well as the waviness of this interface.

Grahic Jump Location
Fig. 2

Posterior view of representative supraspinatus–humerus complexes for all of the species studied. Shown is the supraspinatus muscle attaching to the humerus via the supraspinatus tendon and humeral head.

Grahic Jump Location
Fig. 3

(a) μCT of the humeral head and supraspinatus tendon of a rabbit. The attachment area is highlighted in the dark opaque region. Thearrow indicates the measured humeral head diameter. (b) von Kossa stained histological section of the tendon-to-bone attachment. The interfacial roughness, which is highlighted by the dashed line, is measured by the peak height, 2A, and peak width, λ. (c) Plot of the 960/1003 Raman peak height ratio (representing relative concentration of mineral to collagen) as a function of position from the interface between mineralized and unmineralized fibrocartilage in a rat. The gradient in mineralization is approximately 30 μm long.

Grahic Jump Location
Fig. 4

Millimeter-scale features: (a) plot of humeral head diameter as a function of animal mass. The scaling factor was 0.38, indicating a near isometric relationship. Isometry of α = 0.33 is shown as a dotted line. (b) Plot of insertion area as a function of PCSA. The scaling factor was 0.84, indicating near isometric behavior. Isometry of α = 1 is shown as a dotted line. Ninety-five percent of confidence intervals are shown as dashed lines.

Grahic Jump Location
Fig. 5

Micrometer-scale features: (a) plot of A/λ as a function of PCSA. The insets show A and λ independently as a function of PCSA. Isometry of α = 0.5 is shown as dotted lines in the inset. The small scaling factors for A, λ, and A/λ indicate hypoallometry of the roughness. (b) Plot of the standard deviation of A/λ as a function of PCSA. The insets show standard deviations of A and λ independently as a function of PCSA. Isometry of α = 0.5 is shown as dotted lined in the inset. The small scaling factors of the standard deviation of A, λ, and A/λ indicate a hypoallometric relationship. (c) Plot of width of the mineralization gradient as a function of PCSA. The scaling factor was 0.12, indicating a hypoallometric relationship compared to the isometry (dotted line) of α = 0.5. Ninety-five percent of confidence intervals are shown as dashed lines.



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