Implementation of a new constitutive model for abdominal muscles.

Background And Objective: Abdominal hernia repair is one of the most often performed surgical procedures worldwide. Numerical simulations of the abdominal wall mechanics can be a valuable tool to devise actions aimed at preventing hernia formation. A first step towards this goal is the development of consistent constitutive models for the tissues that form the human abdominal wall. In this study we propose, for each of the tissues involved, a new formulation of the so-called transversely isotropic hyperelastic model (TIHM).

Methods: We propose a new TIHM for the human abdominal wall tissues and we present a systemic view of the methodology that we have implemented in the present study. First we consider the mathematical background of the TIHM. The novelty of our formulation is that both the isotropic and the fiber contributions to the strain energy function are characterized exclusively by polynomial convex functions of certain invariant quantities. Then, we provide a detailed description on how the constitutive model is implemented into an open source finite element (FE) software. In our approach we use the specific interface provided by the MFront software to incorporate our TIHM formulation into the Code Aster FE solver. For each of the tissues considered, the values of the TIHM constants are adjusted by means of a numerical simulation of previous experimental data from tensile tests.

Results: We studied the following abdominal wall tissues: linea alba, rectus sheath, external oblique muscle, internal oblique muscle, transversus abdominis muscle and rectus abdominis muscle. Our formulation closely reproduces tensile test data for each tissue in the corresponding FE numerical simulation.

Conclusions: The new TIHM formulation is suitable for a future numerical investigation of the abdominal wall, which will in turn help us to assess the best zone to practice a colostomy. The methodology implemented in the present study can be easily extended in the future to develop and implement a TIHM for active muscles and/or a different type of constitutive model which might be suitable to characterize other tissues of biomedical interest.