An “Optimal” k-Needle Placement Strategy Given an Approximate Initial Needle Position

Abstract

Abstract. In this paper we address the problem of finding an "optimal" strategy for placing k biopsy needles, given a large number of possible initial needle positions. This problem arises for example in guided, endoscopic needle biopsies, where the position of the endoscope's tip is known with some error. We consider two variations of the problem: (1) Calculate the smallest set of needles 1 , needed to guarantee a successful biopsy. (2) Given a number k, calculate k needles such that the probability of a successful biopsy is maximized. We formulate both problems in terms of two general, NP-hard optimization problems. Our solution to both problems is "optimal" with respect to the best approximative algorithm known for the respective NP-hard problem. For the latter problem there exists an approximative algorithm which requires virtually no implementation effort and is guaranteed to be within a factor of 1 − 1 e of the exact solution. For both variations of the problem we are able to provide success probabilities for each needle to the physician. We have implemented the approximative algorithm for the second variation. The resulting probabilities show that our approach can provide valuable decision support for the physician in choosing how many needles to place and how to place them.

A navigation system for flexible endoscopes using abdominal 3D ultrasound

“…Navigation systems for endoscopes mostly register the available endoscopic video with preoperative CT images (Gergel et al 2011, Brouwer et al 2012. An interesting approach was presented by Kukuk (2003) who used a real-time deformable model for flexible instruments inserted into tubular structures. A three-dimensional endoscopic ultrasound system with convex scanning echo endoscope to diagnose and navigate for endoscopic puncture provides another solution (Koizumi et al 2003).…”

2D/3D registration of endoscopic ultrasound to CT volume data

“…The idea of equipping the endoscope with an additional electromagnetic tracking system (EMTS), to provide new initial parameters when the image registration procedure is lost, was not successful either. Another interesting approach was presented by Kukuk (2003), who used a real-time deformable model for flexible instruments inserted into tubular structures. A 3D endoscopic US system with a convex scanning echoendoscope to diagnose and navigate for endoscopic puncture provides another approach (Koizumi et al 2003).…”