Abstract
Faculty Adviser: Guy Genin
Geometric, kinematic, force, and material nonlinearity arise in manufactured products. Flexural rigidity, or relative stiffness of a beam, cannot be measured accurately for flexible, composite medical devices like catheters and sheaths using linear beam theory because they undergo high deformations when subject to relatively small loads. Surgeons depend on the relative stiffness of their catheters to determine the maneuverability of their devices. For neurovascular interventions, surgeons rely on stiffness to determine if their catheter can navigate arduous vasculature, especially around the aortic arch1. Navigation has become increasingly difficult as surgeons have adopted the transradial approach to neurovascular angioplasty procedures. In these procedures, surgeons must steer their guide catheter through the radial artery, across narrow bends through the subclavian artery, and around the aortic arch. It is unrealistic to consistently use particularly flexible catheters since they do not provide enough support to guide medical devices to the brain. To overcome this issue, surgeons pair flexible intermediate guide catheters with stiffer sheaths in a coaxial system. They navigate the guide catheter into position, run the stiff sheath over the guide catheter, and send more devices (microcatheters, stents, coils, etc.) through that system. Medical device companies now commonly design catheters with sections that vary in stiffness throughout the length of the catheter to help overcome these issues2. Although the relative stiffness of these devices are critical to the success of the procedure, stiffness values for these devices are unknown to surgeons. More generally, cardiovascular, peripheral vascular, and other general vascular surgeons experience similar difficulty in selecting catheters to navigate other arterial systems. Cardiovascular surgeons experience similar difficulty navigating bends through the aortic arch for different procedures. Beyond vascular surgery, flexural rigidity calculations are important throughout mechanical analysis, and these calculations become especially difficult for manufactured products with soft or composite materials. Previous studies have found flexural rigidity calculations of thin films for aerospace engineering3, of flat plates in mountains for geophysics4, of microtubules for cell biophysics5, and of jute fibers and yarns6. Euler-Bernoulli and Timoshenko beam theories provide relatively accurate approximations for beams under small deformations7. Applications of these theories are fitting to measure the flexural rigidity of catheters and other nonlinear systems. Beams with flexible materials undergoing large deformations require more complicated definitions to solve for flexural rigidity through deflection analysis. A nonlinear approach to beam theory does provide a more accurately measured flexural rigidity for high deformations than linear beam theory8. By applying the definition of curvature to the general equation for Euler-Bernoulli beam theory, the flexural rigidity can be calculated accurately. Other techniques have been applied to manufactured systems to measure mechanical properties of catheters and other medical devices9. Previous studies found the flexural rigidity of central venous catheters based on deflections10,11, which differs from the angle calculations used in this research. Another method from previous studies examines the buckling load of the device when the force is applied axially12,13. Yet another group compared stiffness between catheters based on the critical angle at which the catheter could physically bend14. These methods for measuring flexural rigidity are distinctly different from the technique used in this research, which instead measures the value based on the angle of rotation where the point load is applied. For measurement of manufactured products, the flexural rigidity can be calculated through image analysis paired with the nonlinear application of the general beam theory equation. Flexural rigidity can be found by examining the mechanical reaction of a fixed-free beam under a given load. This technique was tested using finite element analysis in COMSOL by measuring angles via displacements using the software applications and through image analysis of the deflection provided by the software. These values were compared to calculated flexural rigidity values, which are based on the elastic modulus and second area moment of inertia of the cross section. This strategy provides researchers with an accurate means to measure the flexural rigidity of medical devices like catheters that undergo large deformations under applied forces.
Document Type
Final Report
Class Name
Mechanical Engineering and Material Sciences Independent Study
Date of Submission
12-30-2019
Recommended Citation
Hartquist, Chase, "A Technique for Calculating Flexural Rigidity of Nonlinear Systems" (2019). Mechanical Engineering and Materials Science Independent Study. 110.
https://openscholarship.wustl.edu/mems500/110