Non-linear anisotropic elasticity for real-time surgery simulation

TLDR: A new deformable model based on non-linear elasticity, anisotropic behavior, and the finite element method is proposed that is valid for large displacements and improves the realism of the deformations and solves the problems related to the shortcomings of linear elasticity.

Abstract: In this paper, we describe the latest developments of the minimally invasive hepatic surgery simulator prototype developed at INRIA. A key problem with such a simulator is the physical modeling of soft tissues. We propose a new deformable model based on non-linear elasticity, anisotropic behavior, and the finite element method. This model is valid for large displacements, which means in particular that it is invariant with respect to rotations. This property improves the realism of the deformations and solves the problems related to the shortcomings of linear elasticity, which is only valid for small displacements. We also address the problem of volume variations by adding to our model incompressibility constraints. Finally, we demonstrate the relevance of this approach for the real-time simulation of laparoscopic surgical gestures on the liver.

Full text

HAL Id: inria-00072611
https://hal.inria.fr/inria-00072611
Submitted on 24 May 2006
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Non-Linear Anisotropic Elasticity for Real-Time Surgery
Simulation
Guillaume Picinbono, Hervé Delingette, Nicholas Ayache
To cite this version:
Guillaume Picinbono, Hervé Delingette, Nicholas Ayache. Non-Linear Anisotropic Elasticity for Real-
Time Surgery Simulation. [Research Report] RR-4028, INRIA. 2000, pp.21. �inria-00072611�

ISSN 0249-6399 ISRN INRIA/RR--4028--FR+ENG
apport 

de recherche
THÈME 3
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Non-Linear Anisotropic Elasticity for Real-Time
Surgery Simulation
Guillaume Picinbono — Hervé Delingette — Nicholas Ayache
N° 4028
Octobre 2000

Unité de recherche INRIA Sophia Antipolis
2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France)
Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65
 "!#$%'&)(*,+-!.0/132465879:&
582;7!
<>=?A@B@DC0=FEHGJIK?BLM?BN#OQPRNPTSVU9GMW3X'Y[ZGM@B?ANF\'G^]_]_G`Sba9?AL*cPR@DC0defRC'L*cFG
g$hjikmlnoqpsrMtul3v.w^xyt.z|{^r9hj{^k}kml~Dkwx%hz|rjl^
zkw^l33j{rjrj3l33jx{^rjrwz.uwrxl_
bvu{ltVjzjwjvul
w0{^vtlKv.l3x%hjl3v.x%hlr'^MJoxtu{vul^Kowl3
¡3¢£*¤j¥¢¦
psr>t.hjzKwvt.zx§|l^R¨Qlml3.xv.z0l©tuhjlm§w*t.l3tl3ªl3§|{^jkmlrMt.«{¬bt.hjlmkmz|rjzkw§§|®zrª*wuz|ª^l
hlwtuzxujvu^lv.uz|k©j§w*tu{^vjv.{t.{t'llª^l§{'l3®wt«p¯p°±²°1³^l´jvu{^j§lkµ¨z¶t.h·ux%h·w8uz|k}~
§wtu{v«ztuhl©jhuzx3w§km{l3§|zrj9{¬¸{¬¹t«t.z.ujl33±º[l©vu{^0{Mlw8rjl¨»jl¬¼{v.kwj§lkm{l§Fw^l_
{^rr{r~½§|zrjl_wv$l§wtuzxz|twrzu{t.vu{^jzx«'lhw¾ªz{v_wr9tuhjl¿rjz|tulKl3§|l3kmlrMtk}ltuhj{²±Qg$hjz$km{l3§²z
ª*w§|z¬¼{v§wv.lKz§w^xlkml3r^t%¨hjzx%hkml3wrzrwvutuzxj§wv$t.hw*t«z¶tzzrª¾wvuzwrMt¨z|tuh®v.l3u0l_xyttu{
v.{t%w*t.z|{^r±Qg$hjzjv.{'lvut8z|kmjv.{*ªl_Àtuhjlvul_w§zuk{¬Ft.hjll¬¼{v.kmwtuz{rwr®u{§ªl3Àt.hjljv.{§|l3km
v.l§w*t.l3tu{8tuhjluhj{^vt%x{kmzrj^${¬V§|zrjl3wvl§wtuzxz|t0¨hjzx%h®z{^rj§ª*w§z´¬¼{vukw§§z§w^xlkml3r^t%±
º[lw§{´wjjvul_utuhjlmjv.{§|l3k{¬¸ª^{§jkml©ª*wv.zw*tuz{r0>wz|r9t.{{^jvk}{l3§Fz|rx{kmjv.l3.zjz§¶~
z|tHx{^rtuv%wzr^t%±Ázrw§§|^¸¨Àll3km{rtuv%w*t.l9t.hjlv.l§lª*wrxl´{¬t.hjz}wjjv.{^w^x%h¬¼{v©tuhjlv.l3w§¶~Dtuzkml
uzkj§w*t.z|{^r{¬§wwvu{Mux{jzxujv.zxw§R^l3tujv.l3${^r9t.hjlK§|zªl3v3±
®ÃMÄRÅ.ÆÇ
£*È¡¦ÊÉ
jv.l3vu®uz|k©j§w*tuz{r²rj{r~½§z|rjl_wvl§wtuzxz|t²§wv.l}zj§wxlkmlrMt_²¿rjz|tulml§lkml3r^t
kmltuhj{²jl¬¼{v.kwj§lkm{jl§Dvul_w§|~At.z|kmljwrjz{tuv.{zrx{^k}vul_uuz|z|§z¶t8x{rtuv%wzrMt.3±


!²Ày

!3

 ©JJ79 ! 32 7´!




´F7:6)24´ 

!

¡


¦

wr«xltwvutuzx§l'rj{_xv.z|ª^{r§|l_«l3vurz|l3v.«ª^l§{j'lkmlrMt%Jjvu{tu{tM'll
uzkj§w*t.ljvblx%hz|v.jv.zlÀkmzrjzkmw§|l3kmlrMtbz|rª*wuzªlvb§|l$¬¼{^z|ljªl3§|{^j'

§

p¯p°±

rvu{^j§|i3kml
x§|$w¾ªl_xbxlÀl3rjv.lQl$zk§wtulvl_tF§w«km{§z.w*t.z|{^rjhz

MjlQjl3tuzuukm{3±¯{jv.{'{^u{r0
rrj{ªl3wk}{i3§|lÀ¬¼{^vukwj§|lV0wu¸v§

3§w^t.zxz¶t.¸rj{^r~D§zrj3wz|v.l_§|lQx{km'{vutul3k}l3rMtwrjzu{tuv.{'l
lt§wmkmtuhj{ljl33§|3k}l3rMt.$¿rz3±

QlKkm{i§lKv.l3tulKª*w§wj§lK'{jv§l3^v.wrj3j§wxl3kmlrMt.3xl

Mjzuz|^rjz|¿l¸l3rwvt.zxj§|zlv

M

z|§l3tFz|rª*wv.zwrMtwvv.{t.wtuz{r#±

QltutulÀjvu{^jv.z|tuQwkm§z|{^vulb§lÀvu_w§zukml
jl3¸j¬¼{v.kw*t.z|{^rblt¸vu_{^t¸§l3¸jvu{^j§ikml3¸§|z3Qw

m§|zkmz¶t%w*t.z|{^rQjl§

§wtuzxz|tu«§|zrj_wzvul^

Mjz'r

l_t
ª*w§wj§|l

^l80{^jv§l30ltuz|t.m3j§w^xl3k}l3rMt.3±>¯{0rj{^zrMtuv.l3.u{rw.zÀwjv.{j§ikml9jl8§w
ª*wvuzw*t.z|{^rjlª{^§|k}lKl3r·w*{^t.wrMt

8rj{tuv.lKk}{i3§|l}l3«x{^r^t.v.wz|rMt.l3

zrx{^k}vul_uuz|z|§z¶t.±Vrj¿r#
r{Àkm{^r^t.vu{^rb§ljz|l3r~D¬¼{rlxlttulwjvu{x%hjl0{^jv$§w©zkj§w*t.z|{^r8lr9tul3k}0Qv.l3§'jl«^l3tul3
x%hz|v.jv.zxw

ml3r§wwv.{^.x{^jz|lv§|l¬¼{^z|l^±
Ȃ
¢_¡
Å
¥
"!

¡¦É
zk§wtuz{r©jlÀx%hjzv.jvu^z|l^¾§wtuzxz|tuÀrj{r~½§z|rj_wzvul^¾v%wrj3j§w^xl3k}l3rMt.3*k}tuhj{l
jl3$§kml3r^t%$¿rjz3tulkmvu3l§Djwrjz{tuv.{jzlx{rMtuv%wzrMtul3$

zrx{^k}vul_uuz|z|§z¶t.±

Frequently asked questions

Q1. What are the contributions in "Non-linear anisotropic elasticity for real-time surgery simulation" ?

HAL this paper is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. 

Q2. ?

K{^r rj{^r ~½§|z rjl3w v l3§ w^ t.z x z¶t w r >w9¿ rjz|tul}l § l kml rMt kml tuh { #±KºJl©¿ v% t z|rMt.vu{ x l t.hjl©§ z rjl3w v«l3§ w^ t.z x z¶t ´tuh l { v.®w r ·z¶t% z|km j§ l ~ kml3r^t%w*t.z|{^r8tuh vu{^ j h t.hjl«¿ rjz|tul l § l kml rMt$kml tuh { # jw r 9¨Ql«tuhjl3r9hjz h §|z hMt$z¶t% À uhj{^v t%x { kmz rj ^