An update on the constitutive relation of ligament tissues with the effects of collagen types

The musculoskeletal ligament is a kind of multiscale composite material with collagen fibers embedded in a ground matrix. As the major constituent in ligaments to bear external loads, collagens are composed mainly of two collagen contents with different mechanical properties, i.e., types I and III collagen. The constitutive relation of ligaments plays a critical role in the stability and normal function of human joints. However, collagen types have not been distinguished in the previous constitutive relations. In this paper a constitutive relation for ligament tissues was modified based on the previous constitutive relation by considering the effects of collagen types. Both the collagen contents and the mechanical properties of sixteen ligament specimens from four cadaveric human knee joints were measured for determining their material coefficients in the constitutive relation. The mechanical behaviors of ligaments were obtained from both the uniaxial tensile and simple shear tests. A linear regression between joint kinematic results from in vitro and in silico experiments was made to validate the accuracy of this constitutive relation. The high correlation coefficient (R2=0.93) and significance (P<0.0001) of the regression equation revealed that this modified constitutive relation of ligaments was accurate to be used in studying joint biomechanics. Another finite element analysis with collagen contents changing demonstrated that the effect of variations in collagen ratios on both joint kinematics and ligament biomechanics could be simulated by this constitutive relation.