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

Abstract

Abstract [Background] It is important to accurately understand the mechanical response of ligaments to prevent damage and rupture. Most mathematical simulation studies consider the ligament as a single uniform sheet or focus only on collagen fibers, ignoring the other major component such as elastin. We evaluated how elastin affects the mechanical response of the ligaments under stresses 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 fibers and elastin (fiber model) and compared with that considers the ligament as a single sheet (sheet model). We also evaluated the difference in mechanical response in the fiber model depending on the elastin content. [Results] Uniform stress was applied to the entire ligament in the sheet model, while strong stress was applied at the junction of collagen fibers and elastin in the fiber model. In the same fiber model, as elastin content increased, the stress and displacement applied to the collagen fibers during tensile and shear stresses decreased and the slope of the stress-strain relationship increased especially under shear stress. The stress required to rotate the bones at both ends of the ligament by the same angle increased with increasing elastin content. [Conclusions] The fiber model, which included the mechanical properties of elastin, could provide us more precise stress distribution and mechanical response. It was shown that elastin is responsible for the rigidity of the ligaments during shear and rotational stresses.