3D Constitutive Model of the Rat Large Intestine: Estimation of the Material Parameters of the Single Layers

Several functions of the large intestine depend on its morphology and biomechanical properties. Since some classes of soft tissues have non-linear mechanical behavior, they may be modeled as hyperelastic materials applying the strain energy function. Moreover, as the arterial walls, the colonic walls are composed by collagen fibers characterized by an anisotropic behavior. It is known a mechanical model of artery that considered its walls composed of two cylindrical layers reinforced with fibers of collagen suitably oriented. Afterwards, it has been proposed a structure-based mathematical model for mechanical passive behavior of the rat colon, fitted to data obtained from inflation/extension tests that doesn’t subdivide the walls into layers. However, the wall of the rat large intestine is composed by four distinct layers, i.e. mucosa, submucosa, muscle layer and serosa. Thus, the aim of this paper is to identify a method for estimating the parameters of a computational model that considers each layer of the colonic walls. We use the Nelder-Mead nonlinear regression technique for minimizing the residual sum of squares between experimental data reported in literature and the outcomes of the proposed model. The estimated material parameters (\( {\text{k}}_{ 1} ,{\text{k}}_{ 2} ,c \)) are used to develop a 3D finite element model. Furthermore, we computed the components of the Cauchy stress over the colonic wall across each layer for different values of internal pressure and axial stretch.