Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues

TL;DR

This paper develops a new variational method to analyze the micromechanical behavior of hyperelastic fibrous tissues, specifically applied to human coronary arteries, showing strong agreement with finite element simulations.

Contribution

It introduces a novel variational estimate for tissue micromechanics that accounts for histology and fiber behavior, providing accurate analytical predictions.

Findings

Analytical expressions match finite element results.

Method effectively captures nonlinear and anisotropic tissue responses.

Applicable to modeling coronary artery mechanics.

Abstract

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting, close form expressions, are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method these predictions are compared with corresponding 3-D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations.