No 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 (R 2 min =0.9329, RM SE max =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.KEY WORDS-intestinal wall, hyperelasticity, fiber reinforcement, soft tissue modeling, robotic endoscopy, minimally invasive surgery.

We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions W that are explicit functions of the elastic deformation gradient F and initial stress τ , i.e. W := W (F, τ ). The restriction is a consequence of energy conservation and ensures that the predicted stress and strain energy do not depend upon an arbitrary choice of reference configuration. We call this restriction initial stress reference independence (ISRI). It transpires that almost all strain energy functions found in the literature do not satisfy ISRI, and may therefore lead to unphysical behaviour, which we illustrate via a simple example. To remedy this shortcoming we derive three strain energy functions that do satisfy the restriction. We also show that using initial strain (often from a virtual configuration) to model initial stress leads to strain energy functions that automatically satisfy ISRI. Finally, we reach the following important result: ISRI reduces the number of unknowns of the linear stress tensor of initially stressed solids. This new way of reducing the linear stress may open new pathways for the non-destructive determination of initial stresses via ultrasonic experiments, among others.

Tubular organs display a wide variety of surface morphologies including circumferential and longitudinal folds, square and hexagonal undulations, and finger-type protrusions. Surface morphology is closely correlated to tissue function and serves as a clinical indicator for physiological and pathological conditions, but the regulators of surface morphology remain poorly understood. Here, we explore the role of geometry and elasticity on the formation of surface patterns. We establish morphological phase diagrams for patterns selection and show that increasing the thickness or stiffness ratio between the outer and inner tubular layers induces a gradual transition from circumferential to longitudinal folding. Our results suggest that physical forces act as regulators during organogenesis and give rise to the characteristic circular folds in the esophagus, the longitudinal folds in the valves of Kerckring, the surface networks in villi, and the crypts in the large intestine.