Finite element simulation of the catheter movement in transbronchial biopsy

Abstract

The paper presents a preliminary finite element simulation of the movement of a catheter in the bronchial tree. The analyses are done using an explicit dynamics approach, in which a simplified model is considered to test the convergence and applicability of the method. The first branch of the bronchial tree (trachea, the right main bronchus, and the left main bronchus) is simulated as a Y shaped tubular volume while the geometry of the catheter was reduced to a cylindrical straight beam. To mimic the real insertion of the catheter into the bronchial tree, a displacement of 250 mm (chosen to ensure that the catheter travels up to the end of the Y tube and more) was imposed onto the end of the catheter model. The main purpose of the analysis was to evaluate the displacements distribution in both the catheter and the tube and to evaluate the haptic feedback (the response that the surgeon or the robot receive due to mechanical interaction between soft tissue and the surgical tool) by extracting the reaction forces and correlating their values with the velocity of the catheter movement through the bronchial tree. It is shown that the maximum displacement within the tube model is about 0.042 mm, value which confirms that the displacements are very small, indicating that a linear elastic approach for the tissue behavior is acceptable. The total reaction force in the fixed support was found to be below 2.2 N, while on the catheter insertion point, it is below 1.2 N, values that indicate reasonable interaction and are consistent with the values reported in the literature. The values of the predicted stresses, obtained through the presented numerical analysis are also in the same order of magnitude with those found in other research reports, for a linear elastic behavior of the soft tissue. The analysis of the obtained results and comparison with other results found in the relevant scientific literature showed that explicit dynamics approach can be used as a tool for simulation of catheter movement through the bronchial tree. Forces of interaction between tool and tissue can be thus predicted, being useful for simulation of haptic feedback.