The performance of endovascular surgery is highly dependent on catheter stiffness, especially when navigating past tortuous anatomy. Stiff catheters lack the maneuverability of compliant catheters, but they provide necessary support for medical device delivery and intervention. Conversely, compliant catheters can easily navigate through the vasculature, but they are not stable enough for device delivery and intervention. Catheters vary in length, diameter, shape, and stiffness to accommodate various surgical situations. Although stiffness is of critical importance when considering catheter properties, biomedical companies offer no quantitative measure of a catheter’s bending rigidity. A method for determining bending rigidity would therefore allow surgeons to compare products and make informed decisions on which catheters to use in surgery.

Linear beam theory, also known as small deformation beam theory, is often used to determine beam stiffness. However, since catheters are made from soft, composite materials, they undergo large deformations when subject to relatively small loads, and the linear beam theory loses accuracy. A nonlinear formulation of Euler-Bernoulli beam theory was used to derive a nonlinear flexural rigidity equation. The nonlinear flexural rigidity equation was validated using finite element analysis. The analysis showed that nonlinear beam theory could accurately predict beam stiffness, even at very large strains, compared to linear beam theory which loses accuracy as strain increases.

A simple image analysis experiment was devised to obtain the necessary parameters to calculate catheter stiffness. Expired and used catheters, donated by Drs. Joshua Osbun and Mohammed Zayed, were used for experimentation. Each catheter sample was subject to two experimental treatments: one smaller applied external moment and one larger applied external moment. For each treatment, flexural rigidity was calculated from the linear and nonlinear theories. The consistency of both theories was measured as the percent difference between experimental treatments. Statistical testing was performed using a paired data T-test for difference between means.

For catheter samples with high variation in angular deflection between treatments (> 30°), the nonlinear beam theory was much more consistent than the linear beam theory for quantifying catheter stiffness (p < 0.01). Across all experimental data, there was not significant evidence to indicate that the nonlinear theory was more consistent at measuring flexural rigidity than the linear theory (p = 0.073 > 0.05). Finite element analysis shows that nonlinear beam theory predicts beam stiffness more accurately than linear beam theory across varying angular deflections. Since the data does not suggest statistical significance, the experimental procedure must be further refined before using nonlinear beam theory to quantify catheter stiffness. Possible sources of error and suggestions for future experimentation are discussed at the end of this paper.

Document Type

Final Report

Author's School

McKelvey School of Engineering

Author's Department

Mechanical Engineering and Materials Science

Class Name

Mechanical Engineering and Material Sciences Independent Study

Date of Submission