Analysis of and mathematical model insight into loop formation in colonoscopy

The colonoscope is an important tool in the diagnosis and management of diseases of the colon; yet its design has not changed appreciably since it was first introduced to clinical practice 40 years ago. One of the ongoing challenges with this device is that the natural shape of the colon predisposes to loop formation by the scope during the examination. The result of this looping is that further insertion of the scope results in a larger loop size without any advancement of the tip of the scope. Looping thus causes pain in the patient, risks perforation of the colon, and results in incomplete examinations. In this article, loop formation is analyzed in terms of frictional force state and Kirchhoff's slender rod model in order to better understand the generic principle of loop formation. Next, a mathematical model of deformation of the colon with respect to external manipulation involving a number of variables involved in loop formation is constructed. Finally, a model of the motion of the scope relative to the colon when looping occurs is presented. The model has clinical significance for prediction of advancement of the tip of the scope when looping occurs. The mathematical model was then validated and verified using data available from the literature. Our models are an important starting point in the development of a novel device to overcome loop formation and result in increased patient comfort and an improved completion rate for colonoscopy procedures.