Computational vademecums for real‐time simulation of surgical cutting in haptic environments

Summary A new method for the real-time simulation of surgical cutting in haptic environments is presented. It is based on the intensive use of computational vademecums, that is, a sort of computational parametric meta-model, which is computed offline and only evaluated online. Therefore, the necessary time savings are obtained, allowing for feedback responses on the order of kilohertz. Such a high-dimensional, parametric solution of the problem is computed by employing proper generalized decomposition for the offline phase of the method, along with X-FEM techniques for the incorporation of the discontinuities in the displacement field after cutting, in the online phase. A thorough description of the proposed method, along with examples of its performance in the simulation of corneal surgery, are provided. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  David Néron,et al.  A rational strategy for the resolution of parametrized problems in the PGD framework , 2013 .

[2]  J. Marsden,et al.  Dimensional model reduction in non‐linear finite element dynamics of solids and structures , 2001 .

[3]  S Niroomandi,et al.  Real‐time simulation of surgery by reduced‐order modeling and X‐FEM techniques , 2012, International journal for numerical methods in biomedical engineering.

[4]  Stefanie Reese,et al.  Proper orthogonal decomposition-based model reduction for non-linear biomechanical analysis , 2013 .

[5]  Lenka Jerábková,et al.  Stable Cutting of Deformable Objects in Virtual Environments Using XFEM , 2009, IEEE Computer Graphics and Applications.

[6]  Ai-min Hao,et al.  Real-time cutting method for soft tissue based on TLED algorithm , 2010, 2010 2nd International Conference on Computer Engineering and Technology.

[7]  Elías Cueto,et al.  PGD-Based Modeling of Materials, Structures and Processes , 2014 .

[8]  Siamak Niroomandi,et al.  Model order reduction in hyperelasticity: a proper generalized decomposition approach , 2013 .

[9]  Hervé Delingette,et al.  Soft Tissue Modeling for Surgery Simulation , 2004 .

[10]  Morten Bro-Nielsen,et al.  Real‐time Volumetric Deformable Models for Surgery Simulation using Finite Elements and Condensation , 1996, Comput. Graph. Forum.

[11]  F. Chinesta,et al.  A Short Review in Model Order Reduction Based on Proper Generalized Decomposition , 2018 .

[12]  S Niroomandi,et al.  Real‐time simulation of biological soft tissues: a PGD approach , 2013, International journal for numerical methods in biomedical engineering.

[13]  Christian Duriez,et al.  Real-time simulation of contact and cutting of heterogeneous soft-tissues , 2014, Medical Image Anal..

[14]  Alberto Cardona,et al.  A reduction method for nonlinear structural dynamic analysis , 1985 .

[15]  Icíar Alfaro,et al.  Computational vademecums for the real-time simulation of haptic collision between nonlinear solids , 2015 .

[16]  Jaydev P. Desai,et al.  Modeling Soft-Tissue Deformation Prior to Cutting for Surgical Simulation: Finite Element Analysis and Study of Cutting Parameters , 2007, IEEE Transactions on Biomedical Engineering.

[17]  Ted Belytschko,et al.  Cracking node method for dynamic fracture with finite elements , 2009 .

[18]  David González,et al.  Real‐time direct integration of reduced solid dynamics equations , 2014 .

[19]  T. Belytschko,et al.  Arbitrary branched and intersecting cracks with the eXtended Finite Element Method , 2000 .

[20]  E. H. van Brummelen,et al.  Discontinuities without discontinuity : the Weakly-enforced Slip Method , 2013, 1304.7810.

[21]  Sébastien Ourselin,et al.  High-Speed Nonlinear Finite Element Analysis for Surgical Simulation Using Graphics Processing Units , 2008, IEEE Transactions on Medical Imaging.

[22]  K. Miller,et al.  Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation , 2006 .

[23]  Karol Miller,et al.  Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation. , 2010, Computer methods in applied mechanics and engineering.

[24]  Hervé Delingette,et al.  Hepatic surgery simulation , 2005, CACM.

[25]  J. Fish The s-version of the finite element method , 1992 .

[26]  Elías Cueto,et al.  Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions , 2012, International journal for numerical methods in biomedical engineering.

[27]  A. Ammar,et al.  Space–time proper generalized decompositions for the resolution of transient elastodynamic models , 2013 .

[28]  A. Nouy A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations , 2010 .

[29]  P. Ladevèze,et al.  The LATIN multiscale computational method and the Proper Generalized Decomposition , 2010 .

[30]  Kari Karhunen,et al.  Über lineare Methoden in der Wahrscheinlichkeitsrechnung , 1947 .

[31]  David Néron,et al.  Virtual charts of solutions for parametrized nonlinear equations , 2014 .

[32]  G. Holzapfel,et al.  Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations. , 2008, Journal of biomechanical engineering.

[33]  B Calvo,et al.  Biomechanical modeling of refractive corneal surgery. , 2006, Journal of biomechanical engineering.

[34]  Francisco Chinesta,et al.  Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models , 2010 .

[35]  Marc Garbey,et al.  Multiscale mechanobiology modeling for surgery assessment , 2012 .

[36]  Christian Duriez,et al.  GPU-based real-time soft tissue deformation with cutting and haptic feedback. , 2010, Progress in biophysics and molecular biology.

[37]  Francisco Chinesta,et al.  On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition , 2010, Math. Comput. Simul..

[38]  Siamak Niroomandi,et al.  Accounting for large deformations in real-time simulations of soft tissues based on reduced-order models , 2012, Comput. Methods Programs Biomed..

[39]  Jernej Barbic,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2007) Flipping with Physics: Motion Editing for Acrobatics , 2022 .

[40]  Pedro Díez,et al.  An error estimator for real-time simulators based on model order reduction , 2015, Adv. Model. Simul. Eng. Sci..

[41]  Siamak Niroomandi,et al.  Real-time deformable models of non-linear tissues by model reduction techniques , 2008, Comput. Methods Programs Biomed..

[42]  Danny C. Sorensen,et al.  Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..

[43]  Adrien Leygue,et al.  The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer , 2013 .

[44]  M. Doblaré,et al.  FE2 multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition , 2013 .

[45]  Manuel Doblaré,et al.  Finite element simulation of arcuates for astigmatism correction. , 2008, Journal of biomechanics.

[46]  A. Ammar,et al.  PGD-Based Computational Vademecum for Efficient Design, Optimization and Control , 2013, Archives of Computational Methods in Engineering.

[47]  J. Marsden,et al.  Structure-preserving Model Reduction of Mechanical Systems , 2000 .

[48]  Karol Miller,et al.  Meshless algorithm for soft tissue cutting in surgical simulation , 2014, Computer methods in biomechanics and biomedical engineering.

[49]  Y. Maday,et al.  Results and Questions on a Nonlinear Approximation Approach for Solving High-dimensional Partial Differential Equations , 2008, 0811.0474.

[50]  Mariano Alcañiz Raya,et al.  Real-time deformable models for surgery simulation: a survey , 2005, Comput. Methods Programs Biomed..

[51]  Markus H. Gross,et al.  Interactive simulation of surgical cuts , 2000, Proceedings the Eighth Pacific Conference on Computer Graphics and Applications.

[52]  Siamak Niroomandi,et al.  Model order reduction for hyperelastic materials , 2010 .

[53]  Icíar Alfaro,et al.  Towards a pancreatic surgery simulator based on model order reduction , 2015, Adv. Model. Simul. Eng. Sci..

[54]  Elías Cueto,et al.  Real time simulation for computational surgery: a review , 2014, Advanced Modeling and Simulation in Engineering Sciences.

[55]  Adrien Leygue,et al.  Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices , 2014 .

[56]  Herve Delingette,et al.  Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation , 1999, IEEE Trans. Vis. Comput. Graph..

[57]  Jernej Barbic,et al.  Real-Time subspace integration for St. Venant-Kirchhoff deformable models , 2005, ACM Trans. Graph..