2002
DOI: 10.1007/3-540-45787-9_42
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A Real-Time Deformable Model for Flexible Instruments Inserted into Tubular Structures

Abstract: In this paper we present an approach to the problem of modelling long, flexible instruments, such as endoscopes or catheters. The idea is to recursively enumerate all possible shapes and subsequently filter them according to given mechanical and physical constraints. Although this brute-force approach has an exponential worst-case complexity, we show with a typical example that in case of tubular structures the empirical complexity is polynomial. We present two approximation methods that reduce this bound to a… Show more

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Cited by 5 publications
(7 citation statements)
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“…There exists an initial position domain P ⊂ M, which is a set of possible initial locations for the endoscope, before needle placement. The endoscope is assumed to be given by the model described in [4], namely by a sequence of links, interconnected by joints. Letp ∈ P denote the real, but unknown position of the endoscope after insertion.…”
Section: Assumptionsmentioning
confidence: 99%
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“…There exists an initial position domain P ⊂ M, which is a set of possible initial locations for the endoscope, before needle placement. The endoscope is assumed to be given by the model described in [4], namely by a sequence of links, interconnected by joints. Letp ∈ P denote the real, but unknown position of the endoscope after insertion.…”
Section: Assumptionsmentioning
confidence: 99%
“…A typical example for such a procedure is a "transbronchial needle aspiration biopsy" (TBNA) [3], [4]. Traditionally this biopsy is performed by maneuvering a bronchoscope to a suitable site within the tracheobronchial tree.…”
Section: Introductionmentioning
confidence: 99%
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“…Physically inspired models, e.g. multibody systems composed of rigid links as in Kukuk et al, 9 require explicit modeling of contact forces. Finite-Element Modeling (FEM) can represent bending realistically, but is computationally expensive and requires knowledge-based constraints.…”
Section: Introductionmentioning
confidence: 99%
“…More elaborate solution involve additional hardware like magnetic tracking devices that are fixed on the endoscope tip and allow to track the position of the endoscope in real-time (Solomon [13]). Another solution is based on a physical model of the endoscope and additional measurements of insertion depth, rotation angle and bending angle, measured at the outside of the patient (Kukuk et al [11]). …”
Section: Introductionmentioning
confidence: 99%