Development of a three-dimensional unit cell to model the micromechanical response of a collagen-based extracellular matrix.

The three-dimensional microstructure and mechanical properties of the collagen fibrils within the extracellular matrix (ECM) is now being recognized as a primary factor in regulating cell proliferation and differentiation. Therefore, an appreciation of the mechanical aspects by which a cell interacts with its ECM is required for the development of engineered tissues. Ultimately, using these interactions to design tissue equivalents requires mathematical models with three-dimensional architecture. In this study, a three-dimensional model of a collagen fibril matrix undergoing uniaxial tensile stress was developed by making use of cellular solids. A structure consisting of thin struts was chosen to represent the arrangement of collagen fibrils within an engineered ECM. To account for the large deformation of tissues, the collagen fibrils were modeled as hyperelastic neo-Hookean or Mooney-Rivlin materials. The use of cellular solids allowed the fibril properties to be related to the ECM properties in closed form, which, in turn, allowed the estimation of fibril properties using ECM experimental data. A set of previously obtained experimental data consisting of simultaneous measures of the fibril microstructure and mechanical tests was used to evaluate the model's capability to estimate collagen fibril mechanical property when given tissue-scale data and to predict the tissue-scale mechanical properties when given estimated fibril stiffness. The fibril tangent modulus was found to be 1.26 + or - 0.70 and 1.62 + or - 0.88 MPa when the fibril was modeled as neo-Hookean and Mooney-Rivlin material, respectively. There was no statistical significance of the estimated fibril tangent modulus among the different groups. Sensitivity analysis showed that the fibril mechanical properties and volume fraction were the two input parameters which required accurate values. While the volume fraction was easily obtained from the initial image of the gel, the fibril mechanical properties were not readily available. Therefore the fibril mechanical properties were estimated in the leave-one-out cross-validation (LOOCV) analysis. The LOOCV analysis showed that the model was able to predict the ECM stress-stretch curve with an average mean squared error of 9.71 kPa(2). The three-dimensional architecture expands on previous continuum models and two-dimensional representations to provide a useful model for studying the hierarchical effects of ECM microstructure on cell function. This model can be used as a design tool to engineer the optimum microstructure for cells to function.