FEniCS implementation of the Virtual Fields Method (VFM) for nonhomogeneous hyperelastic identification

TL;DR

This paper introduces two novel algorithms, RE-VFM and NO-VFM, implemented in FEniCS, for efficiently identifying nonhomogeneous hyperelastic material properties in tissues, with potential clinical applications like tumor detection and glaucoma risk assessment.

Contribution

The paper proposes two new algorithms, RE-VFM and NO-VFM, for hyperelastic property identification, implemented in FEniCS, improving computational efficiency and accuracy in inverse elasticity problems.

Findings

Both methods accurately recover Young's modulus distribution within 5 iterations.

The algorithms are validated on models including bilayer, lamina cribosa, and spherical inclusion.

The methods show potential for clinical applications in tissue analysis.

Abstract

It is of great significance to identify the nonhomogeneous distribution of material properties in human tissues for different clinical and medical applications. This leads to the requirement of solving an inverse problem in elasticity. The virtual fields method (VFM) is a rather recent inverse method with remarkable computational efficiency compared with the optimization-based methods. In this study, we aim to identify nonhomogeneous hyperelastic material properties using the VFM. We propose two novel algorithms, RE-VFM and NO-VFM. In RE-VFM, the solid is partitioned in different regions and the elastic properties of each region are determined. In NO-VFM, 2 the distribution of elastic properties is completely reconstructed through the inverse problem without partitioning the solid. As the VFM requires to use virtual fields, we proposed an efficient way to construct them and implemented the approach in the FEniCS package. We validated the proposed methods on several examples, including a bilayer structure, a lamina cribosa (LC) model and a cube model embedded with a spherical inclusion. The numerical examples illustrate the feasibility of both RE-VFM and NO-VFM. Notably, the spatial variations of the Young's modulus distribution can be recovered accurately within only 5 iterations. The obtained results reveal the potential of the proposed methods for future clinical applications such as estimating the risk of vision loss related to glaucoma and detecting tumors.