In the biomechanics literature, most of the experiments are conducted on soft tissues that have been dissected from the body. In these cases, ultimate stresses and strains are determined when the experimental specimens break.
Unfortunately, in the living organism, injurious loads and deformations may be significantly lower than those which tear or rip the tissue. In the experiments described in the following section, observations were noted of constriction of
blood flow and subsequent hemorrhage at quite modest levels of applied load- ing. The pressure loading on the inner wall of the intestine at which such injury was evident was often less than one-third that which caused the specimen to burst. So, clearly, the ultimate stress of these tissues is not a reasonable limit for benign interactions with an endoscopic robot. This research proposes three other measures for the prediction of injury.
Firstly, this analysis can predict the internal stresses that result from de- formations produced by the robot. This biaxial stress state causes the afore- mentioned injuries. So, one simple approach to limiting the impact of the robot on the intestinal wall is to determine a measure of the biaxial stresses that causes injury and prevent the robot's effects from exceeding those lev- els. Although it is not well motivated by these circumstances, the von Mises Stress is often used to predict the failure of solid materials. This criterion was developed to predict the failure of linearly modeled materials as a limit of the allowable strain energy of deformation. It is slightly more conservative than the common, maximum shear stress criterion (the Tresca criterion for yielding) in linear analysis. Nevertheless, it is the following measure of the biaxial stress state in the membrane:
A second ad hoc limitation on the acceptable levels of loading could be the magnitude of the normal traction applied to the inner surface of the intestine.
Villi line the intestine's inner surface, and large contact forces to these fragile structures can be injurious. So although this measure of the robot's impact on the intestine neglects the internal wall stresses within the membrane, care
must be taken to ensure that it remains at a benign level. Also, this interfacial contact loading could be measured directly using tactile sensors located on the robot's gripper segments. Since the experiments used only internal pressure to provide tractions on the intestine, the biaxial stress state that is produced in these experiments would be expected to differ significantly from that which results from action of robotic gripper segments. Nevertheless, the relative ease by which the normal traction is measured by a robot indicates that it should be considered in addition to more sophisticated measures of acceptable loading.
The last, proposed injury criterion for the small intestine actually was in- spired by the biomechanics experiments on living intestines. Since the mechan- ical behavior of the pigs' intestines were observed while their blood supply was intact, their health could be monitored qualitatively as well. This was critical to provide insights into the mechanisms of injury for these fragile membranes.
For loading conditions that seemed quite modest, that is, for internal pressures that measured at roughly one pound per square inch above atmospheric pres- sure (roughly 1.07 Atmospheres, absolute), the intestines' blood supply was constricted visibly. As may be expected, the larger vessels appeared to contain blood after the flow in the smaller ones was clearly nonexistent. This would suggest that a measure that predicts the collapse of smaller intestinal blood vessels may be a well motivated criterion for limiting the maximum loadings of the small intestine. In rubber elasticity theory (recall the assumption of incompressible material behavior
,
the stress state is typically reduced to the sum of two constituent tensors: the isotropic stress tensor and the deviatoncstress tensor. Since these materials exhibit zero dilatation, stresses that would otherwise tend to cause such volume changes can grow without impact on the deformation of the body. These stresses are often referred to as the isotropic
stress, or pressure, within the body. Generally, this term is removed from the stress tensor as it plays no role in the prediction of the deformations in rubber. However, in the case of the constriction of intestinal blood flow, this
"hydrostatic" pressure seems to play a very significant role. This pressure builds in the membrane surrounding the intestinal blood vessels. When this isotropic stress exceeds the local blood pressure, the capillaries and relatively thin walled veins will collapse under their external loading. Once this hap- pens, blood flow supplying the intestines is effectively shut down. By analogy, the external loading can "ring the blood out" of the membranes like water from a towel. This is evident as the pressure builds, and the natural color of the intestines vanish. "Color" returns as soon as the loading is removed, but it is not a desirable color. At this point the delicate tissues are bruised and hemorrhaging.) The isotropic stress tensor is a scalar multiple of the identity tensor, and this scalar is calculated to be one-third of the trace of the Cauchy stress tensor. For this intestinal modeling, the pressure is merely one-third of the sum of the meridional and circumferential stresses.