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ORIGINAL ARTICLE
Toward high-speed 3D nonlinear soft tissue deformation
simulations using Abaqus software
Ashraf Idkaidek
1
•Iwona Jasiuk
2
Received: 7 July 2015 / Accepted: 8 September 2015 / Published online: 26 September 2015
Springer-Verlag London 2015
Abstract We aim to achieve a fast and accurate three-
dimensional (3D) simulation of a porcine liver deformation
under a surgical tool pressure using the commercial finite
element software Abaqus. The liver geometry is obtained
using magnetic resonance imaging, and a nonlinear con-
stitutive law is employed to capture large deformations of
the tissue. Effects of implicit versus explicit analysis
schemes, element type, and mesh density on computation
time are studied. We find that Abaqus explicit and implicit
solvers are capable of simulating nonlinear soft tissue
deformations accurately using first-order tetrahedral ele-
ments in a relatively short time by optimizing the element
size. This study provides new insights and guidance on
accurate and relatively fast nonlinear soft tissue simula-
tions. Such simulations can provide force feedback during
robotic surgery and allow visualization of tissue deforma-
tions for surgery planning and training of surgical
residents.
Keywords Computational surgery Nonlinear
constitutive model Numerical simulations Mathematical
models Robotics
Introduction
Robotic surgery allows surgeons to perform complex sur-
gical procedures using robotic arms. Advantages include
small incisions, which lead to faster patient recovery.
However, since surgeons have no direct contact with the
tissue, soft tissue resistance feedback is not directly
available. Modeling of soft tissue deformations under sur-
gical tools interaction can provide surgeons with valuable
insights into deformations of tissues during surgery. These
include information on the amount of force needed to
perform a given surgical task and visualization of defor-
mations. Such knowledge can also be used for surgery
planning and training of surgical residents.
Accurate soft tissue simulations must incorporate real-
istic material properties. Numerous experimental studies
have been done to characterize mechanical properties of
biological materials and organs, including liver. For
example, Kemper et al. [1] performed tension tests on a
human liver parenchyma at various loading rates to char-
acterize its viscoelastic and failure properties. This study
showed that the liver parenchyma is rate dependent, with
higher rate tests giving higher failure stresses and lower
failure strains. Also, Costin et al. [2] performed tensile tests
on fresh human samples of the liver parenchyma at several
loading rates.
Simulating soft tissue response due to surgical tools’
interaction using linear versus nonlinear properties leads to
large differences in force–displacement responses [3,4].
Several studies used linear elastic constitutive models, but
those generated results only for small deformations. For
instance, Chanthasopeephan et al. [5] simulated the porcine
liver cutting to enable fast haptics display using linear
properties. Delingette et al. [6] described the basic com-
ponents of a surgery simulator prototype using the linear
Electronic supplementary material The online version of this
article (doi:10.1007/s11701-015-0531-2) contains supplementary
material, which is available to authorized users.
&Iwona Jasiuk
ijasiuk@illinois.edu
1
Department of Civil and Environmental Engineering,
University of Illinois at Urbana-Champaign, 205 North
Mathews Ave, Urbana, IL 61801, USA
2
Departments of Mechanical Science and Engineering and
Bioengineering, University of Illinois at Urbana-Champaign,
1206 West Green Street, Urbana, IL 61801, USA
123
J Robotic Surg (2015) 9:299–310
DOI 10.1007/s11701-015-0531-2
elasticity theory and finite elements method (FEM). Bro-
Nielsen [7] presented the application of 3D solid volu-
metric finite element (FE) models to surgery simulation
using the linear elastic theory.
Soft tissue simulations have also accounted for nonlin-
ear material properties. For example, Grand et al. [8] used
average nodal pressure tetrahedral elements for better
handling of a volumetric locking numerical problem to
simulate soft tissue deformations. This method requires a
higher computational time compared to traditional FEM.
Kevin et al. [9] developed a real-time haptics-enabled
simulator for probing soft tissue using the FEM with a
nonlinear experimentally based constitutive law. This study
accounted for the soft tissue material nonlinearity but it did
not focus on generating fast simulations using 3D nonlinear
FE models. Ahn et al. [10] did a 3D simulation of inden-
tation of porcine liver and correlated it with experimental
results. The liver tissue properties were assumed to be
incompressible and nonlinear. Again, this study focused on
generating accurate simulation results without considering
a simulation time. Picinbono et al. [11] developed a sim-
ulator for laparoscopic liver surgery to enable fast haptics
display of cutting. He accounted for nonlinear elastic and
anisotropic material behavior using a simple hyperelastic
model. Wu et al. [12] proposed a real-time soft tissue
deformation analysis by using nonlinear FEM and adaptive
meshing techniques. The analysis included material non-
linearity, but no details were provided regarding a material
constitutive model used in their simulations.
Thus, the modeling of soft tissue deformations due to
interaction with surgical tools is a challenging and still
open research topic. Prior simulations idealized mechanical
properties and/or required long simulation times, as dis-
cussed above, which make them not fully suitable for
robotic surgery and other medical implementations.
In this paper, we address this problem by simulating the
deformation of a porcine liver under a surgical tool while
accounting for problem nonlinearities: contacts, large
deformations, and nonlinear material properties. More
specifically, we investigate the effects of the implicit ver-
sus explicit analysis schemes, mesh size, and element type
on the computational time and accuracy of results. Results
obtained from this study provide guidance on accurate and
efficient algorithms for soft tissue simulations.
Methods
Porcine liver MRI scanning
The porcine liver was scanned using magnetic resonance
imaging (MRI) with 0.9 mm
3
resolution. The MRI scan
was performed at the Beckman Institute at University of
Illinois at Urbana-Champaign. It generated multiple IMA
type files, and Simpleware software was used to generate
the 3D volume geometry and the FE models. The scanned
liver dimensions were 277 mm 290 mm 53 mm:
(Fig. 1a, b).
Soft tissue nonlinear constitutive model
To model a nonlinear behavior of the liver tissue, a
hyperelastic model involving the Ogden strain energy
potential [13,14], available in Abaqus, was used, as shown
in Eq. 1:
U¼X
N
i¼1
2l
a2
i
kai
1þ
kai
2þ
kai
33
þX
N
i¼1
1
Di
Jdel 1
2i
;
ð1Þ
where kirepresent the deviatoric principal stretches, J
el
is
the elastic volume ratio, Nis the order of the polynomial,
and li;ai, and Diare material constants. In this study, a
third-order polynomial form of the Ogden model was used
to represent the liver material properties based on tensile
loading tests reported by Kemper et al. [1]. These test
results presented Second Piola–Kirchhoff stress versus
Green–Lagrange strain. Engineering stress versus engi-
neering strain are needed as inputs for the Abaqus software.
Therefore, these test results were converted to the appro-
priate form based on solid mechanics principles. Since soft
tissues are considered roughly incompressible materials
with Poisson’s ratio in the range between 0.45 and 0.49
[15], the Poisson ratio of 0.48 was assumed in this study.
Finally, the Abaqus software used these inputs to calculate
the Ogden model material coefficients.
Finite element analysis: preprocessing
FE analysis problem was defined by applying translational
boundary condition constraints on the liver bottom nodes
(Abaqus has no rotational DOF for C3D4, C3D8, and
C3D8R elements) as shown in Fig. 1d. A surgical knife,
tapered toward the bottom at 0.54 degrees with a rounded
0.1 mm radius tip (Fig. 1c), was modeled using first-order
hexahedral elements and elastic properties of steel. Note
that representing the surgical tool as a rigid surface did not
give noticeable difference in a simulation speed. This is
because the simulation time was mostly taken by contact
and soft tissue deformation calculations. The analysis
involved applying the 10-mm vertical displacement to the
knife as shown in Fig. 1e.
Six different FE analysis models were developed: two
models were built using hexahedral elements while the
other four were built using tetrahedral elements (Fig. 2).
Each FE model was developed with the relatively constant
300 J Robotic Surg (2015) 9:299–310
123
average element size (no local refinement or adaptive
meshing) to generate a fair simulation time comparison.
Abaqus solvers and simulation time
As background information, Abaqus offers implicit and
explicit solvers. The implicit algorithm provides accurate
results when solving quasi-static problems [16]. On the
other hand, achieving equilibrium is a challenge due to
problem complexity (knife-tissue contact, large deforma-
tions, and soft tissue nonlinear properties) [16].
The explicit solver was developed to model high-speed
events. No energy dissipation is expected when solving a
soft tissue deformation problem due to its quasi-static
nature [16]. Therefore, performing this type of analysis
using an explicit solver should be acceptable as long as the
model internal and external energies are comparable. The
major advantage of using an explicit solver over an implicit
solver is that the simulation will always converge. This is
because the explicit solver depends on time steps without
the need to keep checking if an equilibrium is achieved. On
the other hand, the explicit solver requires a high compu-
tational time when compared to implicit solver. To over-
come these issues two approaches were used:
•Increase load rate This artificially increases the mate-
rial strain rate by the same load rate factor. To preserve
Fig. 1 Liver 3D volume
geometry and 3D finite element
model. aLiver geometry top
view. bLiver geometry side
view. cSurgical tool (knife)
cross section. dFinite element
model boundary conditions; all
highlighted nodes (in red) are
restrained in all translational
directions (Abaqus has no
rotational DOF for C3D4, C3D8
and C3D8R elements). eLiver
finite element model and the
surgical knife
Fig. 2 Liver finite element (FE)
models. aISO view of the liver
geometry, bFE model built
using 841,146 first-order
hexahedral elements. cFE
model built using 358,390 first-
order hexahedral elements. dFE
model built using 899,153 first-
order tetrahedral elements. eFE
model built using 237,060 first-
order tetrahedral elements. fFE
model built using 116,371 first/
second-order tetrahedral
elements
J Robotic Surg (2015) 9:299–310 301
123
a quasi-static response, it was noticed that the impact
velocity should be less than 1 % of the material wave
speed.
•Apply mass scaling Here, the stable time increment
increases by a factor of fwhen the material density is
artificially increased by a factor of f
2
as shown in Eqs. 2
and 3below.
The increase in the load rate and/or mass scaling will
reduce the Abaqus explicit simulation time significantly
but inertia forces need to be insignificant to insure accurate
results.
There are two ways to perform mass scaling when using
the explicit solver, fixed mass scaling and variable mass
scaling [16]. In this study, the variable mass scaling was
used, where scaling was adjusted based on simulation
behavior during the step to control Abaqus explicit simu-
lation time.
The Abaqus explicit algorithm requires the following
time increment condition to insure a stable and accurate
solution [16]:
Dt1
pvmax
;ð2Þ
where vmax is the FE model highest natural frequency.
The highest natural frequency depends on the time taken
by a dilatational stress wave to cross the smallest element
in the FE model. Therefore, the element stable time
increment is equivalent to [16]:
DtLe
Cd
;ð3Þ
where Leis the characteristic element length, Cdis the
dilatational wave speed =ffiffiffi
M
q
q,Mis the P-wave modu-
lus =Eð1vÞ
ð1þvÞð12vÞ,Eis the Young’s modulus, vis the Pois-
son’s ratio, qis the material density.
Results and discussion
FE simulation speed results, using an implicit solver, are
summarized in Table 1. All iterations were performed
using the Abaqus version 6.13 and 32 cores (2.9 GHz and
64 GB RAM each). Direct solver was used for all the
implicit analyses to preserve the results accuracy.
Reduced integration was used for models with hexahe-
dral elements because traditional hyperelastic hexahedral
elements were not able to achieve equilibrium with
acceptable tolerance. Even though reduced integration
hexahedral elements converged better compared to tradi-
tional hexahedral elements, the static (implicit) nonlinear
FE analysis did not achieve a full convergence due to large
deformations and soft tissue material nonlinearity. There-
fore, a quasi-static implicit FE analysis was considered. It
was noticed that achieving equilibrium using a quasi-static
implicit scheme is better than a static implicit scheme for
this kind of analysis. On the other hand, it requires more
simulation time and yet it is challenging to fully converge.
Resolving an implicit simulation convergence problem was
not considered in this study to be able to make a fair
comparison between different solvers’ ability to complete
such simulations.
Table 1 Simulation speed comparison using Abaqus implicit solver (X=2:03:33 =hh:mm:ss)
Iteration number Iteration description Element type Number of nodes Number of elements Max. vertical displacement
Running time
1 Quasi-static Hex. first-order elements 997,796 841,146 6.21 mm,
54.80X
2 Quasi-static Hex. first-order elements 433,092 358,390 6.82 mm,
4.69X
3 Static Tet. first-order elements 226,875 899,153 1.47 mm,
0.58X
4 Quasi-static Tet. first-order elements 226,875 899,153 9.03 mm,
4.71X
5 Static Tet. first-order elements 67,893 116,371 2.58 mm,
0.31X
6 Quasi-static Tet. first-order elements 67,893 116,371 2.58 mm,
0.28X
7 Quasi-static Tet. second-order elements 179,686 116,371 7.49 mm
3.07X
8 Quasi-static Tet. first-order elements 95,307 237,060 8.01 mm,
X
Bold values indicate faster simulation iteration using implicit solver
302 J Robotic Surg (2015) 9:299–310
123
As shown in Table 1, the use of the Abaqus implicit
solver did not lead to the 100 % completion of any of the
iterations, even when employing a quasi-static algorithm
and regardless of the element type. The Iteration 1 used a
FE model with 841,146 first-order hexahedral elements, the
simulation only completed 62 % of the analysis and it was
extremely slow. Therefore, a coarser FE model was con-
sidered (iteration 2), but it was able to complete only 68 %
of the analysis in about 10 h. Due to a long simulation
time, tetrahedral elements were used. Static and quasi-
static simulations were performed, respectively (Iteration 3
and iteration 4, respectively); both iterations used FE
model with 899,153 first-order tetrahedral elements. The
static simulation was able to complete close to 15 % of the
analysis. On the other hand the quasi-static analysis com-
pleted 90 % of the analysis but simulation time was rela-
tively high. To further reduce the simulation time, a coarser
mesh was considered (116,371 tetrahedral elements) and
three iterations were performed: static analysis using first-
order elements (iteration 5), quasi-static analysis using first
Table 2 Simulation speed comparison using Abaqus explicit solver (X=02:31:32 =hh:mm:ss)
Iteration
number
Iteration
description
Element type Number of
nodes
Number of
elements
Explicit
analysis time
Mass scaling Max. vertical
displacement
Running time
1 Double precision Hex. first-order elements 997,796 841,146 0.1 No 5 mm
42.29X
2 Double precision Tet. first-order elements 226,875 899,153 0.1 No 10 mm
33.4X
3 Double precision Tet. first-order elements 95,307 237,060 0.1 No 10 mm
14.14X
4 Double precision Tet. first-order elements 67,893 116,371 0.1 No 10 mm
10X
5 Double precision Tet. first-order elements 67,893 116,371 0.05 No 10 mm
3.88X
6 Double precision Tet. first-order elements 67,893 116,371 0.1 dt=1.5 910
-7
10 mm
0.52X
7 Double precision Tet. first-order elements 67,893 116,371 0.1 dt=1.0 910
-7
10 mm
0.73X
8 Double precision Tet. first-order elements 67,893 116,371 0.1 dt=0.9 910
-7
10 mm
1.4X
9 Single precision Tet. first-order elements 67,893 116,371 0.1 dt= 0.9 310
27
10 mm
X
10 Double precision Tet. first-order elements 67,893 116,371 0.1 dt=0.5 910
-7
10 mm
1.28X
Bold values indicate faster simulation iteration using explicit solver
Fig. 3 Abaqus explicit model
energy response (iteration 6 and
iteration 7). aIteration 6 model
energy response using Abaqus
explicit and mass scaling with
minimum dt=1.5 910
-7
.
bIteration 7 model energy
response using Abaqus explicit
and mass scaling with minimum
dt=1.0 910
-7
J Robotic Surg (2015) 9:299–310 303
123
and second-order elements (iteration 6 and iteration 7,
respectively). Due to the coarse FE model, using first-order
elements was not enough to achieve convergence even
when using a quasi-static algorithm. On the other hand,
using second-order elements allowed to complete close to
75 % of the simulation, but simulation time was still rel-
atively high. The finer FE model with 237,060 first-order
tetrahedral elements was able to complete 80 % of the
analysis in 2 h and 3 min (iteration 8). Therefore, this
iteration was considered best among all eight iterations
performed using the implicit solver. This iteration is
marked in bold in Table 1.
FE simulation speed results, using the explicit solver,
are summarized in Table 2. All iterations were performed
using the Abaqus version 6.13, double precision (except
iteration 9), and 32 cores (2.9 GHz and 64 GB RAM each).
Explicit solver fully completed all iterations simulations.
Based on these results, using hexahedral hyperelastic ele-
ments and explicit scheme requires extremely long time to
complete a simulation. On the other hand, using tetrahedral
Fig. 4 Implicit and explicit
solvers simulations results.
aImplicit versus explicit solvers
reaction force results—FE
model with 237,060 first-order
tetrahedral elements and 95,307
nodes. bImplicit solver
results—8 mm vertical knife
deformation and Mises stress
distribution. cExplicit solver
results—8 mm vertical knife
deformation and Mises stress
distribution. dModel
deformation under 10 mm
vertical knife displacement
304 J Robotic Surg (2015) 9:299–310
123
hyperelastic elements, one can solve the problem relatively
fast while preserving the results accuracy.
Simulation times of iterations 1–5 were relatively high
(no mass scaling was used) while the simulation times of
Iterations 6 and 7 were relatively low. On the other hand,
both iterations results were considered inaccurate because
both models experienced high dynamic response due to a
high element stable time increment (dt), where a model’s
kinetic energy was relatively high compared to a model’s
internal energy (Fig. 3). The iterations 8 and 9 were
similar except that the iteration 8 was completed using a
double precision while the iteration 9 was completed
using a single precision. Both iterations provided similar
results in terms of accuracy, but the iteration 9 was 40 %
faster compared to the iteration 8. Using the mass scaling
with element stable time increment less than 0.9 910
-7
did not improve results accuracy. On the other hand, it
increased the simulation time (iteration 10). Iteration 9
was completed in 2 h and 31 min using the Abaqus
explicit solver. This was a relatively short time compared
to other iteration analysis times. Therefore, the iteration 9
was considered best among all ten iterations performed
using the explicit solver. This iteration is marked in bold
in Table 2.
The force versus displacement results using implicit and
explicit solvers are close as shown in Fig. 4. When the
explicit solver was used, a reaction force oscillation was
noticed due to a dynamic behavior. Therefore, the Butter-
worth filter was used to eliminate such oscillation. The
inertial reaction response showed a slight difference
between the implicit solver result and the explicit solver
result due to an explicit solver dynamic effect. This dif-
ference is considered acceptable because it is not affecting
the overall liver response or von Mises stress distribution
as shown in Fig. 4.
Abaqus implicit solver was able to accurately simulate
the nonlinear liver deformation under surgical tool vertical
displacement in a relatively short time. However, the
analysis convergence was always a challenge. Therefore,
using a fine mesh is essential for the simulation to com-
plete. Abaqus explicit solver was also able to complete the
simulation with similar accuracy compared to the implicit
solver and without going through the simulation conver-
gence problem. On the other hand, it required higher
simulation time compared to the implicit solver, which was
compensated by increasing the load rate and using mass
scaling.
Table 3in Appendix provides a summary of the analysis
scheme effects on the simulation speeds and convergence.
In addition, Figs. 5,6,7,8,9,10,11, and 12 in the
Appendix show the liver deformation and Mises stress
contours due to surgical knife pressure at various
displacements. Also an animation video is available as
Supplementary Material.
Conclusions
This study provides guidance on how to simulate soft tis-
sue deformations under surgical tools displacement (and
resulting pressure), while taking into account problem’s
nonlinearity and soft tissue constitutive nonlinear model, in
a relatively short time, using the Abaqus implicit and
explicit solvers. Accurate results were obtained using first-
order tetrahedral elements with relatively fine mesh in a
relatively short time. Therefore, using first or second-order
hexahedral elements or second-order tetrahedral elements
would not necessarily improve results accuracy but would
increase the simulation time.
Both implicit and explicit analysis schemes are capable
of solving the problem in comparable analysis times while
preserving results accuracy. On the other hand, solving the
problem using implicit static or quasi-static algorithms is
very challenging to converge.
In this paper, we simulated soft tissue deformation under
a surgical knife in a relatively short time. Because this
study depends on iterations simulation time comparison, 32
Central Processing Units (CPUs: 2.9 GHz and 64 GB
RAM each) were used for all iterations even though the
current computing power is capable of using many more
CPUs. Therefore, the shortest simulation time reported in
this study is expected to be many times faster when using a
supercomputer and/or introducing graphics processing unit
(GPU) capabilities.
Acknowledgments The authors would like to acknowledge help of
research scientist Ryan Larsen for performing liver MRI scanning at
the Beckman Institute at University of Illinois at Urbana-Champaign.
We would also like to thank Dr. Richard H. Pearl from OSF Saint
Francis Medical Center in Peoria, IL, and Dr. T. ‘‘Kesh’’ Kesavadas
from University of Illinois at Urbana-Champaign for helpful
discussions.
Compliance with ethical standards
Disclosure of potential Conflicts of Interest Authors AI and IJ
declare that they have no conflict of interest.
Research Involving Human Participants/Animals All applicable
international, national, and/or institutional guidelines for the care and
use of animals were followed.
Informed consent Not applicable.
Appendix
See Table 3and Figs. 5,6,7,8,9,10,11, and 12.
J Robotic Surg (2015) 9:299–310 305
123
Table 3 Simulation time and convergence comparison (For mesh density information, please see Tables 1and 2)
Element
types
Algorithms
First-order Hex
element
First-order reduced integration Hex
element
Second-order Tet element First-order Tet
element
a
First-order Tet
element with
mass scaling
Static
implicit
algorithm
Simulation time is
relatively slow
Simulation time is relatively slow Simulation time is
relatively acceptable
Simulation time
is relatively
acceptable
Simulation
convergence is
extremely
challenging
Simulation convergence is extremely
challenging
Simulation convergence
is extremely
challenging
Simulation
convergence
is extremely
challenging
Quasi-static
implicit
algorithm
Simulation time is
extremely slow
Simulation time is extremely slow but
better than using fully integrated
first-order Hex element
Simulation time is
relatively slow
Simulation time
is relatively
acceptable
Simulation
convergence is
extremely
challenging
Simulation convergence is extremely
challenging but better than using
fully integrated first-order Hex
element
Simulation convergence
is acceptable
Simulation
convergence
is acceptable
Dynamic
explicit
algorithm
Simulation time is
extremely slow
Simulation time is extremely slow Simulation time is
extremely slow but
relatively faster than
using Hex elements
Simulation time
is slow
Simulation
time is
relatively
acceptable
May encounter
convergence
challenges due to
high loading rate
b
May encounter convergence
challenges due to high loading rate
b
Simulation convergence
is not an issue
Simulation
convergence
is not an issue
Simulation
convergence
is not an
issue
a
A model built with first-order Tet elements is expected to be relatively finer than a model built with second-order Tet elements
b
When using the explicit solver, a model built using fully integrated hyperelastic Hex elements has a better chance to converge than a model
built with reduced integration hyperelastic Hex elements
Fig. 5 Liver deformation and Mises stress contours at 1.5 mm vertical displacement due to surgical tool (knife) pressure
306 J Robotic Surg (2015) 9:299–310
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Fig. 6 Liver deformation and Mises stress contours at 2.5 mm vertical displacement due to surgical tool pressure
Fig. 7 Liver deformation and Mises stress contours at 3.5 mm vertical displacement due to surgical tool pressure
J Robotic Surg (2015) 9:299–310 307
123
Fig. 8 Liver deformation and Mises stress contours at 5.0 mm vertical displacement due to surgical tool pressure
Fig. 9 Liver deformation and Mises stress contours at 6.0 mm vertical displacement due to surgical tool pressure
308 J Robotic Surg (2015) 9:299–310
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Fig. 10 Liver deformation and Mises stress contours at 7.0 mm vertical displacement due to surgical tool pressure
Fig. 11 Liver deformation and Mises stress contours at 9.0 mm vertical displacement due to surgical tool pressure
J Robotic Surg (2015) 9:299–310 309
123
Liver response under surgical tool (knife) pressure ani-
mation video is available as supplementary material.
References
1. Kemper AR, Santago AC, Stitzel JD, Sparks JL, Duma SM
(2010) Biomechanical response of human liver in tensile loading.
Ann Adv Automot Med 54:15–26
2. Untaroiu CD, Lu Y-C, Kemper AR (2013) Modeling the
biomechanical and injury response of human liver parenchyma
under tensile loading. In: IRCOBI conference
3. Misra S, Okamura MA, Ramesh KT (2007) Force feedback is
noticeably different for linear versus nonlinear elastic tissue
models. In: 2nd Joint EuroHaptics conference and symposium on
haptic interfaces for virtual environments and teleoperator sys-
tems, vol 6
4. Shi Hongjian, Farag Aly A, Fahmi Rachid, Chen Dongqing
(2008) Validation of finite element models of liver tissue using
micro-CT. IEEE Trans Biomed Eng 55(3):978–984
5. Chanthasopsephan T, Desai JP, Lau ACW (2005) 3D and 2D
finite element analysis in soft tissue cutting for haptic display. In:
12th International conference on advanced robotics (IEEE Cat.
No. 05TH8813), pp 360–367
6. Delingette H, Cotin S, Ayache N (1999) A hybrid elastic model
allowing real-time cutting, deformations and force-feedback for
surgery training and simulation. In: Proceedings computer ani-
mation, pp 70–81
7. Morten B-N, Stephane C (1996) Real-time volumetric deform-
able models for surgery simulation using finite elements and
condensation. Comput Graph Forum 15:57–66
8. Joldes GR, Wittek A, Miller K (2009) Non-locking tetrahedral
finite element for surgical simulation. Commun Numer Methods
Eng 25(7):827–836
9. Lister K, Gao Z, Desai JP (2009) Real-time, haptics-enabled
simulator for probing ex vivo liver tissue. In: 31st Annual
international conference of the IEEE engineering in medicine and
biology society. EMBC, Minneapolis, pp 1196–1199
10. Ahn B, Kim J (2007) An efficient soft tissue characterization
method for haptic rendering of soft tissue deformation in medical
simulation. In: Frontiers in the Convergence of Bioscience and
Information Technologies (FBIT ‘07), pp 549–553
11. Picinbono Guillaume, Delingette Herve, Ayache Nicholas (2003)
Non-linear anisotropic elasticity for real-time surgery simulation.
Graph Models 65(5):305–321
12. Xunlei Wu, Downes Michael S, Goktekin Tolga, Tendick Frank
(2001) Adaptive nonlinear finite elements for deformable body
simulation using dynamic progressive meshes. Comput Graph
Forum 20(3):349–358
13. Umale Sagar, Deck Caroline, Bourdet Nicolas, Dhumane Parag,
Soler Luc, Marescaux Jacques, Willinger Remy (2013) Experi-
mental mechanical characterization of abdominal organs: liver,
kidney & spleen. J Mech Behav Biomed Mater 17:22–33
14. Gao Zhan, Lister Kevin, Desai Jaydev P (2009) Constitutive
modeling of liver tissue: experiment and theory. Ann Biomed
Eng 38(2):505–516
15. Fung YC (1981) Mechanical properties of living tissues.
Springer-Verlag, New York
16. Commercial software Abaqus V6.13 theory guide. http://www.
3ds.com/products-services/simulia/support/documentation/
Fig. 12 Liver deformation and Mises stress contours at 10.0 mm vertical displacement due to surgical tool pressure
310 J Robotic Surg (2015) 9:299–310
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