Multiaxial mechanical behaviour of the passive ureteral wall: experimental study and mathematical characterisation

Abstract

There is a scarcity of data regarding the mechanical properties of the ureter, although this would facilitate our understanding of its physiology and pathophysiology, and the development of suitable biomaterials for replacement. There is hence an urgent need for multiaxial experimental data and methodical constitutive formulations, which we aim at presenting through this report. The zero-stress state of wall tissue, serving as the starting geometry for biomechanical analyses, was accordingly determined and the 3D passive behaviour of ureteral specimens, isolated from healthy rabbits, was studied under a physiologic range of finite inflation and longitudinal extension. Two most-commonly employed descriptors of soft tissue behaviour were chosen to fit the material response: the Fung-type strain–energy function (SEF) and its combination with a quadratic function. Both SEFs were tested in the thick-walled setting, with incompressibility enforced explicitly or via a Lagrange multiplier. The deformational response of the ureter exhibited an exponential and not the sigmoidal dependency on pressure that requests implementation of two-term SEFs. Indeed, the four-parameter Fung-type SEF resulted in reasonable fit of both the external radius and longitudinal force vs. lumen pressure data, and fitting accuracy was not improved when attempting the seven-parameter Fung-type or biphasic SEFs. There were also serious over-parameterisation problems with those models, favouring the implementation of the SEF with the smallest number of parameters. The material parameters optimised revealed significant mechanical anisotropy, with longitudinal properties being stiffer than circumferential ones under equibiaxial stress states. We conclude that ureter displays a nonlinear anisotropic mechanical response that is well-characterised by the four-parameter Fung-type SEF.

Keywords:

• phenomenological model
• inflation/extension testing
• anisotropic pseudo-elasticity
• strain–energy function

Acknowledgements

The author expresses his thanks to Michael Peroulis, MD for harvesting the specimens and to Spyridon Boussias, MSc for assistance with preliminary experiments.