Hyperelastic Model of Anisotropic Fiber Reinforcements within Intestinal Walls for Applications in Medical Robotics

Abstract

The development of an anatomically realistic model of intestinal tissue is essential for the progress of several clinical applications of medical robotics. A hyperelastic theory of the layered structure of the intestine is proposed in this paper to reproduce its purely elastic passive response from the structural organization of its main constituents. The hyperelastic strain energy function is decoupled into an isotropic term, describing the ground biological matrix, and an anisotropic term, describing the single contributions of the directional fiber-reinforcements. The response of the muscular coat layer has been modeled as a stiffening effect due to two longitudinal and circular muscular reinforcements. The contribution of the submucosa has been described from a uniform distribution of fibrillar collagen in a cross-ply arrangement. An experimental procedure has been proposed in order to characterize the passive response of porcine intestinal samples from planar uniaxial traction and shear tests. The experimental data have been non-linearly fitted in the least square sense with the results of the theoretical predictions. The mechanical parameters have been fitted with high accuracy (Rmin =0.9329, RMSEmax =0.01167), demonstrating the ability of the model to reproduce the mechanical coupling due to the presence of multiple directional reinforcements. The fundamental mechanical role of collagen morphology in the passive biomechanical behavior of intestinal wall is demonstrated. These results may drive a better understanding of the key factors in growth and remodeling of healthy and diseased tissue, together with numerous applications in robotic endoscopy, minimally invasive surgery, and biomedical research.