Relationship between tendon stiffness and failure: a metaanalysis

Abstract

Tendon is a highly specialized, hierarchical tissue designed to transfer forces from muscle to bone; complex viscoelastic and anisotropic behaviors have been extensively characterized for specific subsets of tendons. Reported mechanical data consistently show a pseudoelastic, stress-vs.-strain behavior with a linear slope after an initial toe region. Many studies report a linear, elastic modulus, or Young's modulus (hereafter called elastic modulus) and ultimate stress for their tendon specimens. Individually, these studies are unable to provide a broader, interstudy understanding of tendon mechanical behavior. Herein we present a metaanalysis of pooled mechanical data from a representative sample of tendons from different species. These data include healthy tendons and those altered by injury and healing, genetic modification, allograft preparation, mechanical environment, and age. Fifty studies were selected and analyzed. Despite a wide range of mechanical properties between and within species, elastic modulus and ultimate stress are highly correlated (R(2) = 0.785), suggesting that tendon failure is highly strain-dependent. Furthermore, this relationship was observed to be predictable over controlled ranges of elastic moduli, as would be typical of any individual species. With the knowledge gained through this metaanalysis, noninvasive tools could measure elastic modulus in vivo and reasonably predict ultimate stress (or structural compromise) for diseased or injured tendon.

Keywords: biomechanics; modulus; strain; stress; tendon.

Fig. 1.

Compiled data collected from literature search of 50 studies. Each data point represents the average mechanical behavior of a single group in each study. A linear relationship between elastic modulus and ultimate stress was observed in the compiled data (A) and in the healthy control tendon data (B). Linear curve fits were forced through the origin.

Fig. 2.

The ratio of ultimate stress to elastic modulus (estimate of ultimate strain) shows a decreasing trend with increasing elastic modulus (standard deviation shown). ANOVA analysis revealed this trend when the whole range of elastic moduli were considered (P = 0.0656), but post hoc analysis found no significance or trends between any pair of groups (P ≥ 0.11). The decrease in estimated ultimate strain is most pronounced in the lowest modulus values, which coincides with the smallest animals and also with groups that underwent more drastic treatments (i.e., genetic knockouts, allografts, etc.). Smaller specimen size may amplify potential edge effects, and more extreme treatments may further result in altered tendon behaviors.

Fig. 3.

A: mechanical properties of normal and healing (after transection- or collagenase-induced injury) tendon (15, 28, 31, 32, 67). Each data point represents the average mechanical behavior of a single group (i.e., control, “sham” surgery, or healing group) in each study. Tendons induced with an injury and subject to different healing protocols followed the same linear relationship as was observed before. B: details of two studies (28, 31). Control data points are solid, treatment groups are open. Linear curve fits were forced through the origin. Solid lines fit all data in the individual graph, and the trend from Fig. 1A is superimposed on each graph as a dashed line.

Fig. 4.

Mechanical properties of tendons grouped by age (A), genetics (B), allograft treatment (C), and in vivo mechanical environments (D). Each data point represents the average mechanical behavior of a single group in each study. Control data points are solid, treatment groups are open. Linear curve fits were forced through the origin. Solid lines fit all data in the individual graph, and the trend from Fig. 1A was superimposed on each graph as a dashed line. A: age (16, 23, 43): tendon specimens from a range of animal life spans. Rat specimens included youth (3 mo), adult (15 mo), and elderly (24 mo); horse specimens included very young (5 mo) and youth (11 mo); human specimens included adult (29–50 years) and elderly (64–93 years). B: genetics (48, 54, 59, 60): altered expression of interleukins, GDF-7, collagen, and decorin results in altered mechanical behavior, but decreases (or increases) in modulus remain strongly correlated to decreases (or increases) in ultimate stress. C3H/HeJ (C3H) and C57BL/6J (B6) animals are two inbred strains commonly used in skeletal structure function studies; C3H animals demonstrate larger collagen fibrils than B6 animals. “+/+” Indicates an animal that is homozygous positive for a gene, “−/−” indicates a homozygous knockout for that gene. C1TJ8 animals had a mutation at the collagen cleavage site that resulted in accumulation of collagen in the soft tissues, C1M8 animals had a mutation that inhibited collagen formation, which resulted in a 50% reduction in type I collagen. C: allograft treatments (35, 61, 63, 64): common allograft treatments including irradiation (gamma, electron beam) and cross-linking [gluteraldehyde, 1-ethyl-3-[3-dimethyl aminopropyl] carbodiimide (EDC)]. The density of data points prohibits labeling of each point, but combinations of irradiation and cross-linking were used. D: mechanical environment (29, 45, 46, 62, 72): environmental conditions of tendons were varied using stress shielding/immobilization/unloading or physical training methods. Mechanical effects of age and allograft preparation were highly linear. Effects of genetic alterations and differences in mechanical environment were less well defined.

Fig. 5.

Mechanical data extracted from studies on human tendon (, , , , –39, 42, 43, 53, 75). Whereas different tendons have different mechanical properties, they have the same ratio of ultimate stress to elastic modulus (ultimate strain).

Fig. 6.

Example predictions using data from studies investigating allograft preparations (A) (61) and Achilles tendon repair (B) (77). Two data sets demonstrate that the prediction methods work well over a range of scales and that the location of the control data point is inconsequential. Control data points are solid, treatment groups are open.

Fig. 7.

Estimations of ultimate stress on the basis of elastic modulus values collected in vivo. Ultimate stress values fall within the range observed among human data shown in Fig. 5.