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Stat. Comput. Simulation</a> <a href="/?q=in%3A331327" title="Articles in this Issue">84, No. 6, 1280-1296 (2014)</a>. </div> <div class="abstract">Summary: Soft tissue warping is one of the key technologies in dynamic simulation of many surgical procedures, such as image-guided surgery, surgical navigation and structural/lesion localization. Previously, we proposed a force asynchronous diffusion model (FADM) for soft tissue warping simulation. The FADM works well if a lesion or an anatomical object has a convex shape. However, in some cases, this convex assumption is invalid. In order to remove this significant limitation, this paper presents an energy-based free boundary asynchronous diffusion model (EBFBADM) with three unique features. First, we utilize hexahedral voxels to represent the physical model of the surface triangular mesh and a regional proliferation algorithm to remove invalid voxels, simplify computation and improve realness in warping simulation. Second, we adopt the concept of free boundary to simulate soft tissue geometric characteristics more precisely during the warping process. Finally, we optimize the process of asynchronous diffusion by using the mechanical energy of mass point to achieve realistic soft tissue warping effects. Experimental results have shown that the EBFBADM improves performance in both computation and realness in surgical simulation.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7178417">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62P10" title="MSC2020">62P10</a> </td> <td class="space"> Applications of statistics to biology and medical sciences; meta analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62H35" title="MSC2020">62H35</a> </td> <td class="space"> Image analysis in multivariate analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60J60" title="MSC2020">60J60</a> </td> <td class="space"> Diffusion processes </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aimage-guided+surgery">image-guided surgery</a>; <a href="/?q=ut%3Aenergy-based+free+boundary+asynchronous+diffusion+model">energy-based free boundary asynchronous diffusion model</a>; <a href="/?q=ut%3Amechanical+energy">mechanical energy</a>; <a href="/?q=ut%3Aregional+proliferation+algorithm">regional proliferation algorithm</a>; <a href="/?q=ut%3Awarping+simulation">warping simulation</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">&times;</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1459.62209" data-ciurl="/ci/07178417" data-biburl="/bibtex/07178417.bib" data-amsurl="/amsrefs/07178417.bib" data-xmlurl="/xml/07178417.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07178417.pdf" title="Zbl 1459.62209 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1080/00949655.2013.810370" aria-label="DOI for “An energy-based free boundary asynchronous diffusion model for 3D warping of tissue dynamics”" title="10.1080/00949655.2013.810370">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ghali B. Algorithms for Nonlinear finite element-based modeling of soft-tissue deformation and cutting. Hamilton, Ontario, Canada: Electrical and Computer Engineering; 2008. [Google Scholar]</td> </tr><tr> <td>[2]</td> <td class="space">Schulze F, Bühler K, Neubauer A, Kanitsar A, Holton L, Wolfsberger S. Intra-operative virtual endoscopy for image guided endonasal transsphenoidal pituitary surgery. Int J Comput Assist Radiol Surg. 2010;5(2):143-154. doi: 10.1007/s11548-009-0397-8[Crossref], [PubMed], [Google Scholar]</td> </tr><tr> <td>[3]</td> <td class="space">Choi C, Kim J, Han H, Ahn B, Kim J. Graphic and haptic modeling of the oesophagus for VR-based medical simulation. Int J Med Robot. 2009;5(3):257-266. doi: 10.1002/rcs.256[Crossref], [PubMed], [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[4]</td> <td class="space">Alterovitz R, Goldberg KY. Jean pouliot and chow hsu. sensorless motion planning for medical needle insertion in deformable tissues. IEEE Trans Inf Technol Biomed. 2009 March;13(2):217-255. [Crossref], [PubMed], [Google Scholar]</td> </tr><tr> <td>[5]</td> <td class="space">Courtecuisse H, Jung H, Allard J, Duriez C, Lee DY, Cotin S. GPU-based real-time soft tissue deformation with cutting and haptic feedback. Prog Biophys Mol Biol. 2010;103(2-3):159-168. doi: 10.1016/j.pbiomolbio.2010.09.016[Crossref], [PubMed], [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[6]</td> <td class="space">Vytaras B, Jugal G. Estimating the common parameter of normal models with known coefficients of variation: a sensitivity study of asymptotically efficient estimators. J. Stat Comput Simul. 2007;77:663-681. doi: 10.1080/10629360600578221[Taylor &amp; Francis Online], [Web of Science ®], [Google Scholar] &middot; <a href="/1144.62019" class="nowrap">Zbl 1144.62019</a></td> </tr><tr> <td>[7]</td> <td class="space">Bryson S. Virtual reality in scientific visualization. Commun ACM. 1996 May;39(5):62-71. doi: 10.1145/229459.229467[Crossref], [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[8]</td> <td class="space">Chentanez N, Alterovitz R, Ritchie D, Cho L, Hauser KK, Goldberg K, Shewchuk JR, O&rsquo;Brien JF. Interactive simulation of surgical needle insertion and steering. ACM Trans Graph. 2009 August;28(3): 88-1-10. doi: 10.1145/1531326.1531394[Crossref], [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[9]</td> <td class="space">Si W, Yuan Z, Liao X, Duan Z, Ding Y, Zhao J. 3D Soft tissue warping dynamics simulation based on force asynchronous diffusion model. J Comput Animat Virtual Worlds (CASA 2011 Special Issue of JCVAW). 2011;22:251-259. [Google Scholar]</td> </tr><tr> <td>[10]</td> <td class="space">Shitan M, Heng LC, Padmanabhan AR. A new adaptive test for paired data for small to moderate sample sizes. J Stat Comput Simul. 2012;82:907-914. doi: 10.1080/00949655.2011.560850[Taylor &amp; Francis Online], [Web of Science ®], [Google Scholar] &middot; <a href="/1431.62198" class="nowrap">Zbl 1431.62198</a></td> </tr><tr> <td>[11]</td> <td class="space">Leon T, Ayala G, Gaston M, Mallor F. Using mathematical morphology for unsuper-vised classification of functional data. J Stat Comput Simul. 2011;81:1001-1016. doi: 10.1080/00949651003596099[Taylor &amp; Francis Online], [Web of Science ®], [Google Scholar] &middot; <a href="/1219.62102" class="nowrap">Zbl 1219.62102</a></td> </tr><tr> <td>[12]</td> <td class="space">Nesme M, Kry PG, Jerabkova L, Faure F. Preserving topology and elasticity for embedded deformable models. ACM Trans Graph. 2009 August;28(3):52-1-9. [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[13]</td> <td class="space">Kharevych L, Mullen P, Owhadi H, Desbrun M. Numerical coarsening of inhomogeneous elastic materials. ACM Trans Graph. 2009 August;28(3):51-1-8. [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[14]</td> <td class="space">Mosbech TH, Ersboll BK, Christensen LB. An efficient data-driven tissue deformation model. IEEE 12th International Conference on Computer Vision Workshops, Kyoto, Japan; 2009;1771-1777. [Google Scholar]</td> </tr><tr> <td>[15]</td> <td class="space">Faure F, Gilles B, Bousquet G, Pai DK. Spare meshless models of complex deformable solids. ACM Transaction on Graph. 2011 July;30(4):73-1-9. [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[16]</td> <td class="space">Barbic J, James D. Real-time subspace integration for St.Venant-Kirchhoff deformable models. ACM Transactions on Graph. 2005;24(3):982-990. doi: 10.1145/1073204.1073300[Crossref], [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[17]</td> <td class="space">Marchesseau S, Heimann T, Chatelin S, Willinger R, Delingette Hé. Fast porous visco-hyperelastic soft tissue model for surgery simulation: Application to liver surgery. Prog Biophys Mol Biol. 2010;103(2-3):185-196. doi: 10.1016/j.pbiomolbio.2010.09.005[Crossref], [PubMed], [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[18]</td> <td class="space">Zhu Y, Sifakis E, Teran J, Brandt A. An efficient multigrid method for the simulation of high-resolution elastic solids. ACM Trans Graph. 2010;29(2):16-1-17. [PubMed], [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[19]</td> <td class="space">Gilles B, Bousquet G, Faure F, Pai DK. Frame-based elastic models. ACM Trans Graph. 2011 April;30(2):15-1-12. [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[20]</td> <td class="space">Hecht F, Lee YJ, Shewchuk JR, O&rsquo;Brien JF. Updated sparse cholesky factors for corotational electrodynamics. ACM Trans Graph. 2012 October;31(5):123:1-13. doi: 10.1145/2231816.2231821[Crossref], [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[21]</td> <td class="space">Hildebrandt K, Schulz C, von Tycowicz C, Polthier K. Interactive surface modeling using modal analysis. ACM Trans Graph. 2011 October;30(5):119-1-11. [Web of Science ®], [Google Scholar]</td> </tr><tr> <td>[22]</td> <td class="space">Moll GP. 4D cardiac MRI segmentation and surface reconstruction. Masters Thesis, Department of Electrical and Computer Engineering, Northeastern University, Boston, MA; July 2008. [Google Scholar]</td> </tr><tr> <td>[23]</td> <td class="space">Gupta RC, Viles W. Statistical inference for the extended generalized inverse Gaussian model. J Stat Comput Simul. 2012;82:1855-1872. doi: 10.1080/00949655.2011.599530[Taylor &amp; Francis Online], [Web of Science ®], [Google Scholar] &middot; <a href="/1431.62455" class="nowrap">Zbl 1431.62455</a></td> </tr><tr> <td>[24]</td> <td class="space">Ziegelmann FA. Semiparametric estimation of volatility: some models and complexity choice in the adaptive functional-coefficient class. J Stat Comput Simul. 2011;81:707-728. doi: 10.1080/00949650903468193[Taylor &amp; Francis Online], [Web of Science ®], [Google Scholar] &middot; <a href="/1270.62066" class="nowrap">Zbl 1270.62066</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH&nbsp;Open. 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