Biomechanical behaviour of esophageal tissues: constitutive model and parameters identification

Esophagus is a cylindrical shaped biological structure with a lumen of variable diameter surrounded by a wall composed by four layers, as mucosa, submucosa, muscularis externa and sierosa. The mucosal layer is composed by connective tissue where thin collagen fibrils are organised according to a loose and random network. The submucosa is generally thicker then mucosa and is mainly composed of a dense network of thick collagen fibrils. Two collagen fibre sets, arranged in a criss-cross pattern, can be identified, running respectively in clockwise and anticlockwise helixes down the esophagus. Different values of the crossing angle the fibres form with the circumferential direction are investigated, showing a range between 35° and 60°. The muscularis externa is mainly composed of smooth muscle cells and can be subdivided into two layers according to the main direction of the muscular fibres. In the internal layer, the orientation is circumferential; in the external layer it is longitudinal (Fig. 1e). Finally, the sierosa is a very thin layer of loose connective tissue. Esophageal tissues, as most of soft biological tissues, are characterised by a complex mechanical response, because of strongly anisotropic configuration, coupled material and geometrical non-linearity, time-dependent behaviour. Specific constitutive models have been developed with the aim of investigating the biomechanical behaviour of soft biological tissues. A specific hyperelastic formulation is defined to approach the investigation of esophageal tissues. Constitutive parameters are evaluated by a comparative analysis of model results and data from mechanical tests. The comparison is performed according to stochastic optimisation proce-dures.