Elastin is responsible for the rigidity of the ligament under shear and rotational stress: a mathematical simulation study

BACKGROUND: An accurate understanding of the mechanical response of ligaments is important for preventing their damage and rupture. To date, ligament mechanical responses are being primarily evaluated using simulations. However, many mathematical simulations construct models of uniform fibre bundles or sheets using merely collagen fibres and ignore the mechanical properties of other components such as elastin and crosslinkers. Here, we evaluated the effect of elastin-specific mechanical properties and content on the mechanical response of ligaments to stress using a simple mathematical model. METHODS: Based on multiphoton microscopic images of porcine knee collateral ligaments, we constructed a simple mathematical simulation model that individually includes the mechanical properties of collagen fibres and elastin (fibre model) and compared with another model that considers the ligament as a single sheet (sheet model). We also evaluated the mechanical response of the fibre model as a function of the elastin content, from 0 to 33.5%. Both ends of the ligament were fixed to a bone, and tensile, shear, and rotational stresses were applied to one of the bones to evaluate the magnitude and distribution of the stress applied to the collagen and elastin at each load. RESULTS: Uniform stress was applied to the entire ligament in the sheet model, whereas in the fibre model, strong stress was applied at the junction between collagen fibres and elastin. Even in the same fibre model, as the elastin content increased from 0 to 14.4%, the maximum stress and displacement applied to the collagen fibres during shear stress decreased by 65% and 89%, respectively. The slope of the stress–strain relationship at 14.4% elastin was 6.5 times greater under shear stress than that of the model with 0% elastin. A positive correlation was found between the stress required to rotate the bones at both ends of the ligament at the same angle and elastin content. CONCLUSIONS: The fibre model, which includes the mechanical properties of elastin, can provide a more precise evaluation of the stress distribution and mechanical response. Elastin is responsible for ligament rigidity during shear and rotational stress. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s13018-023-03794-6.