Contribution of Fiber Undulation to Mechanics ofThree-Dimensional Collagen-I Gel

The collagen-I gel is extensively used as a scaffold material in tissue engineering due to its ability to mimic the extracellular matrix (ECM). In this study, the mechanics of collagen-I gel is investigated using a numerical model of three-dimensional collagen network. The resulted mechanical behavior was validated against the published experimental data. Results illustrated that fiber alignment was dominated in the low strain region, and its transition to stretching dominated phenomena at higher strain led to the strain stiffening of collagen gel. The collagen undulation at the microscopic level was found to delay the initiation of strain stiffening. 112 digitalcommons.unl.edu Fiber Undulat ion in Mechanics of Three-Dimensional Collagen-I Gel 113 collagen gel. The volume fraction is estimated by the product of the mass density of collagen in solution (ρc = 1 mg/ml) and the specific volume of collagen (vc = 0.73 ml/g).[8] Each line is modeled by beam elements with length equal or smaller than 2 μm which was proved to be the average length between crosslinks in collagen networks. [9] The diameter of each fiber is assumed to be 62nm corresponding to the collagen gel polymerized at 37° C and pH7.4.[2] To achieve the connectivity of the network, the crosslinks between lines were then generated when the distance between two nodes is less or equal than 800 nm. The isolated beam elements were then removed to reduce computational cost since they won’t take loading and contribute to the network stiffness. Initially, a total of 1934 collagen fibers are generated as shown in Figure 1(a). After crosslinking and removing the isolated elements, 2360 crosslinks were generated and the number of collagen fiber is reduced to 1130. Here we defined the crosslink density as the number of crosslinks per collagen fiber. In this case, the crosslink density is 2.09. The Young’s modulus of collagen fiber is defined as 50MPa which is also used in the study of Stein et al.’s[5] and close to the value 79MPa chosen by Stylianopoulos et al.[10] The crosslinks were assumed to have the same material property to collagen fibers. At the intersection points between crosslinks and collagen fibers, no sliding motion is allowed, which means all the displacements and rotations at the intersection point are fixed. Uniaxial tensile loading along the x-direction is applied and solved using nonlinear finite element analysis software ABAQUS 6.12 (Simulia, Providence, RI). The network strain is calculated by dividing the displacement by the cubic edge length (40 μm). The macroscopic stress is calculated by the total reaction force at the y-z plane divided by the cross-sectional area. The crosssectional area is estimated by the area of the single collagen fiber times the number of collagen fiber passing through that plane. In addition, the effect of thermally induced undulation is also investigated. To quantify the thermally induced undulation of collagen fiber, the straightness parameter (Ps) is introduced: