Real time simulation of inextensible surgical thread using a Kirchhoff rod model with force output for haptic feedback applications

Abstract

International Journal of Solids and Structures (ISSN: 0020-7683)Citation for the published paper: Wang, Z. ; Fratarcangeli, M. ; Ruimi, A. et al. (2017) "Real time simulation of inextensible surgical thread using a Kirchhoff rod model with force output for haptic feedback applications". International Journal of Solids and Structures, http://dx.doi.org/10.1016/j.ijsolstr.2017.02.017Downloaded from: http://publications.lib.chalmers.se/publication/248860 Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source. Please note that access to the published version might require a subscription.Chalmers Publication Library (CPL) offers the possibility of retrieving research publications produced at Chalmers University of Technology. It covers all types of publications: articles, dissertations, licentiate theses, masters theses, conference papers, reports etc. Since 2006 it is the official tool for Chalmers official publication statistics. To ensure that Chalmers research results are disseminated as widely as possible, an Open Access Policy has been adopted. The CPL service is administrated and maintained by Chalmers Library.(article starts on next page)International Journal of Solids and Structures 113-114 (2017) 192-208 Contents lists available at ScienceDirect a b s t r a c tWe discuss the dynamics of an inextensible thin Kirchhoff rod used in the modeling of surgical threads, and demonstrate a very efficient scheme to not only simulate the motion of the thread in real-time (up to 1 ms per frame) but also obtain the constraint axial forces which can be fed back to a haptic system. The numerical scheme is based on a family of schemes called geometric or discrete variational integrators guaranteeing that the momentum and energy are exactly conserved over long periods of time for conservative systems. Besides, we report on an efficient numerical procedure to handle the inextensibility of the thread through physically based Lagrange multipliers, as well as the internal dissipation of the thread. We have performed simulations to verify the capabilities of our model to conserve momentum and energy, accurately calculate the axial constraint forces along the thread for haptic feedback, and capture bending-torsion coupling leading to the formation of plectonemes. While many of the ideas are well known in the computer graphics community (especially in hair modeling), we have implemented several improvements for the specific purpose of speeding up the computations for developing physically based haptic interfaces for knot tying and suturing.

Visual Haptic Feedback for Training of Robotic Suturing

“…It is common in simulators to model the geometry of the suture thread with piecewise continuous geometry like line segments (Wang et al, 2017), (Qi et al, 2017), or cylinders with fixed radius (Hüsken et al, 2013). Because each geometry primitive is only locally continuous and not smooth, discretization artifacts will always occur.…”

On a nonlinear rod exhibiting only axial and bending deformations: mathematical modeling and numerical implementation

“…Non-sheareable rods have been deeply investigated from a theoretical point of view. However, there is a renewed interest with respect to their application in very dissimilar research areas such as the analysis of DNA molecules [5,43,44], motion prediction of human hair [7,26], dynamics of cables [8,12], mechanical analysis of Möbius bands [36], dynamics of drill strings [47], interactive simulations [40], bifurcation analysis of tethers [48], motion prediction of vortical filaments [13], stability of elastic knots [4,24], clambering plants [32], morphoelastic rods [29,37], stents and catheters [49], cooking-induced deformation of spaghetti [19] and others. Obtaining closed analytical solutions is in general not possible, mainly due to the complex nature of the governing equations.…”

A finite element method for simulating soft active non-shearable rods immersed in generalized Newtonian fluids

“…Well established procedures exist, together with academic and commercial codes, that approximate these models and provide meaningful solutions to the analyst. They are also useful in modeling microscopic phenomena, both in the solid realm (e.g., fiber-reinforced composites [1,2]) and in the soft-bio-matter realm (e.g., human hair [3,4], climbing plants [5], catheters and stents [6], DNA [7,8], cilia and flagella [9] and further biological applications [10]) that is the focus of this contribution.…”