Scientia Iranica B (2016) 23(1), 295{300

Sharif University of TechnologyScientia Iranica

Transactions B: Mechanical Engineeringwww.scientiairanica.com

A meshless method to simulate interactions betweenlarge soft tissue and a surgical grasper

Z. Saghaei Nooshabadia, E. Abdib, F. Farahmanda, R. Narimaniaand M. Chizaria,c;�

a. School of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9567, Iran.b. Institute of Microengineering, EPFL, CH-1015 Lausanne, Switzerland.c. Orthopaedic Research and Learning Centre, College of Engineering, Design and Physical Sciences, Brunel University London,

Uxbridge, UB8 3PH, UK.

Received 28 October 2014; received in revised form 30 December 2014; accepted 5 May 2015

KEYWORDSIntra-abdominal;Large deformation;Finite element;Meshless method.

Abstract. Realistic simulation of tool-tissue interactions can help to develop moree�ective surgical training systems and simulators. This study uses a �nite element andmeshless modeling approach to simulate the grasping procedure of a large intra-abdominalorgan, i.e. a kidney, during laparoscopic surgery. Results indicate that the accuracy of themeshless method is comparable with that of the �nite element method, with root meansquare errors in the range of 0.8 to 2.3 mm in di�erent directions. For the model presentedin this study, the computational cost of the meshless method was much less than that ofthe �nite element model.© 2016 Sharif University of Technology. All rights reserved.

1. Introduction

Laparoscopic surgery is a keyhole surgical or min-imally invasive surgical approach that has achievedan increasing popularity in clinical practice in recentyears. In contrast to open surgery that needs largeareas of cutting, laparoscopic surgery requires onlysmall perforation holes for the entry of optical andsurgical instruments into the body. With this typeof surgery, the damage to the surrounding healthytissue is minimum, which results in less infection andpostoperative pain. However, this type of surgeryrequires that surgeons be trained for blindsurgery,which requires undertaking operations under a di�erentenvironment. Most importantly, laparoscopic surgeons

*. Corresponding author. Tel.: +98 (21) 66165583Fax: +98 (21) 6600021E-mail addresses: zeynab saghaee@yahoo.com (Z. SaghaeiNooshabadi); elahe.abdi@ep .ch (E. Abdi);farahmand@sharif.edu (F. Farahmand);narimani@sharif.edu (R. Narimani);mahmoudchizari@yahoo.com (M. Chizari)

miss their direct vision and sense of touch over theoperating organs, as they watch the surgery site usingan optic system on a screen and perform surgery usinglong rod endoscopic instruments. So, it is necessary toprovide new methods for laparoscopic surgery traineesthat can enhance their skills in time and cost e�cientways. Surgical simulation systems provide virtualenvironments wherein trainees can practice surgeryrepeatedly at minimal cost.

Biomechanical modelling of soft tissue is a methodto simulate and compute force-displacement interac-tions between the laparoscopic tool and the tissue. Themethod can provide the visual and haptic feedbackneeded for training. Detailed modelling of biologicalorgans is complex, but it is essential to model suchorgans and, in order to model the biomechanicalbehavior of the organ, appropriate modelling tools areneeded. Although experimental study is a choice formodelling the organs, complicated techniques may berequired to measure the force-displacement character-istics experimentally [1]. There have been attemptsin the literature to simulate the mechanical interac-

296 Z. Saghaei Nooshabadi et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 295{300

tion of surgical tools and soft organs using di�erentmodeling techniques, e.g. Finite Element Method(FEM) [2-4], mass spring [5], and meshless method [6].FEM is a common method in modelling soft tissue,but it is computationally more expensive than themeshless method and thus not appropriate for realtime simulations. The meshless method, on the otherhand, is not as accurate as FEM, but is much faster.It is also suitable for real time simulations, due tothe fact that it does not need a mesh generationprocedure. This is particularly important for tissuewith complex geometry, as well as for easy handling of�nite strains and large displacements in a Lagrangianframework [7].

The aim of this study is to compare the e�cacy ofFEM and meshless techniques used for fast simulationof tool-tissue interactions. For a soft large organ,mechanical integration with a laparoscopic grasper wassimulated, and the accuracy and computational cost ofthe two techniques were compared.

2. Method

2.1. Geometry of the kidneyTo simulate interaction between a kidney and a la-paroscopic grasper, the three dimensional (3D) geom-etry of the kidney and grasper has to be measured.To measure the geometry of the kidney, a dummymodel of the kidney was produced using a moldmaking and casting technique, as shown in Figure 1(a).Polyurethane foam liquid, as instructed in open liter-ature (http://www.brickintheyard.com/), was used tomake the model. Possible shrinkage of the foam modelduring the molding process was neglected. The foammodel (Figure 1(b)) was then measured using a digitalvernier caliper. All measurement records were thenused to create a 3D geometrical model of the kidneyin SolidWorks (DassaultSyst�emes, Fr).

The size of the kidney model was about 30 �40 � 75 mm. A measurement was also taken from acustom made grasper, and its 3D model was created inSolidWorks software.

Figure 1. (a) A dummy model of the kidney produced byusing a mold made of polyurethane foam liquid. (b) Thegeometry of the kidney extracted from the solid foammodel. Small shrinkage of the foam model during themolding process was neglected.

2.2. Material propertyFor a clear comparison between the FEM and meshlessmodels, identical mechanical properties were de�nedfor both. To simplify the models, the mechanicalproperties of the kidney model were assumed to bean isotropic, homogeneous, incompressible materialwith linear elastic properties. The material propertiesof the soft tissue kidney were obtained from openliterature [8]. The density and Young's modulusof the kidney were assumed to be 1000 kg/m3 and20 kPa, respectively, and its Poisson ratio to be 0.495,considering the nearly incompressible behavior of thetissue.

No material was de�ned for the surgical grasperin the Finite Element (FE) model as the grasper waspresented using two parallel rigid plates. It is assumedthat the deformation of the grasper is negligible incomparison with the deformation of tissue under theapplied contact force.

2.3. Finite element methodAfter creating the 3D model of the kidney and grasperin SolidWorks, the �les were imported into Abaqus(DassaultSyst�emes, Fr) software. An interaction wasde�ned between the grasper jaws and the kidney(Figure 2(a)). It was assumed that the loading wouldbe directed from the grasper towards the soft tissue.A \general contact" with \�nite sliding" was used todescribe the interface between the grasper planes andkidney. A \penalty" contact method, with a frictioncoe�cient of 0.15 [9], was chosen to minimize thepenetration of the contacting node and elements at theinterface. The boundary conditions were applied tothe kidney model as zero displacements at the nodesof its top surface, which can present the e�ect ofsurrounding tissue. An external loading was appliedto the grasper planes to squeeze the kidney tissue atits contact zone. The contact pressure between thegrasper planes and the kidney tissue in a Z directionwas de�ned to increase from zero to a maximum ofa 0.02 MPa in 2 seconds. As there was a small gapbetween the grasper jaws and the tissue, a preforce wasapplied to the jaws to make sure they were in touchwith the tissue before applying the original loading.As the geometry of the model was complex, a dynamicexplicit procedure was used to solve the FE model. Thekidney's model was meshed using 1330 nodes and 6195elements type C3D4 (Figure 2(b)).

2.4. Meshless methodIn this study, the Element Free Galerkin (EFG) methodwas used to simulate the mechanical interactions ofthe kidney and the grasper. This method presents ahigh convergence rate and e�ciency for models withmoving interfaces [10]. The shape functions of theEFG method were constructed using the Moving Least

Z. Saghaei Nooshabadi et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 295{300 297

Figure 2. (a) The 3D geometrical model of the kidney and grasper jaws in Abaqus. (b) The mesh model of the kidneyincluding 1330 nodes and 6195 elements.

Squares (MLS) technique [11]. This approximationintroduces u(x) as a function de�ned in Eq. (1):

uh(x) =mXi=1

pi(x)ai(x) = pT (x)a(x); (1)

where p(x) are polynomial basis functions, m is thenumber of basis functions in the column vector, p(x)and a(x) are their coe�cients, which are functions ofthe spatial coordinates, x. In the current implementa-tion, a 3D linear basis function was utilized.

The shape functions were derived as below:

�(x) = PT (x)A�1(x)B(x); (2)

in which A and B are de�ned as:

A(x) = pTw(x)p; (3)

B(x) = W (x)pT ; (4)

and w(x) represents the weight function with a domainof in uence.

At the initial step, using the geometry importedfrom SolidWorks software, the nodes were requiredto make the general geometry of the kidney. Then,the e�ective domain was determined for each node,and quadrature cells and Jacobian and weight matriceswere generated. A 3D linear basis function and implicitintegration were used in the model. The algorithmwas implemented in Matlab (Mathworks, US). Allboundary conditions and external loadings applied tothe model were similar to those of the FE model.

Originally, 83 nodes were implemented in themeshless model and the displacement of these nodes

was considered the deformation of the model. But, inorder to make a comparison between the meshless andFE models, the displacements of the nodes similar tothe FE model were also determined. In order to �ndthe displacements of these points, a meshless solutionfor the nearest nodes was considered. Using an inter-polation procedure, for each node, a new coordinatesystem was calculated considering its location withinthe domain. Eq. (5) indicates the formulation used forinterpolation in one direction:

dx =

�nPi=1

widxi�

nPi=1

wi; (5)

where i denotes the number of nodes that have the min-imum distance from a chosen point, and w represents acoe�cient depending upon the distance from the pointto each neighboring node.

3. Results

3.1. FE modelThe results of the �nite element model and the meshlessmodel for total displacement of the nodal points werepost processed using Matlab, as shown in Figure 3. Thenode coordinates and element speci�cations were usedas input to create the model. The magnitude of thedisplacement vector for each node was calculated. InFigure 3, the colors show the level of displacement atthe model. For instance, the blue areas at the top of thekidney are indicative of minimum displacement, andthe orange areas at the bottom of the kidney specifythe areas with the largest displacements.

298 Z. Saghaei Nooshabadi et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 295{300

Figure 3. The 3D kidney deformation: (a) FEM method; and (b) meshless method. Dimensions are in millimeters.

Figure 3(a) shows the results of the �nite elementmethod for distribution of the displacements on thekidney. The largest deformation at the kidney occurredat the contact area with the grasper jaw, where thetissue was compressed. The maximum displacementwas about 10 mm in this area. There were alsoregions of large deformations on the lateral sides of thekidney, near to the contact site, where the tissue wasa�ected by the edges of the graspers. The maximumdisplacement was about 5 mm in this area. Nodisplacement was observed at the top of kidney, whichwas kept �xed in the �nite element model. The runningtime of the FE model, with 1330 nodes and 2621elements, was about 2 hours on a laptop computer.

3.2. Meshless modelThe results of the meshless model for the total dis-placements of 1330 points, equivalent to the nodes ofthe �nite element model, are shown in Figure 3(b).The displacements of these points were found using aninterpolation procedure from the meshless solution forthe initial 83 nodes. Again, maximum deformationswere observed at the contact areas with the grasperjaws, with a maximum displacement of about 7 mm.Also, the large deformation regions, at the lateral sidesof the kidney, similar to the FE model, were predictedby the meshless model. A maximum displacement of3 mm was observed in this area. No displacement wasfound at the top of the kidney, due to the boundaryconditions applied to the model. The computationaltime for preprocessing and generating the sti�ness andmass matrices of the 83 node meshless model was about23 seconds. Also, the computational time to solve themeshless model was about 10 seconds, and it took0.07 seconds to perform the interpolation procedureand �nd the displacement for the 1330 points.

3.3. Error analysisIn order to evaluate the accuracy of the meshless solu-tion, its results should be compared with the FE model

using a node by node approach. The displacementsobtained from both FEM and meshless methods forall 1330 nodes were compared. The general patternof the displacement distribution for the two modelswas in close agreement. There were some di�erencesin the results, which is thought to be due to nodescattering, the interpolation procedure and the domainof in uence. In addition, the distribution of the nodesin the meshless model was di�erent; fewer nodes in themiddle and more nodes at the bottom of the kidneywere distributed. Hence, the main di�erences werefound to be at the latter side of the kidney.

Considering x and y as the lateral and distaldirections on the kidney's surface, respectively, and zas the direction anterior to the kidney (Figure 1), thedi�erences of the nodal displacements were analyzed ateach direction. The maximum displacements predictedby the FE model in x, y, and z directions were 5.32,2.26, and 9.79, respectively. While the correspond-ing results for meshless model were 0.40, 1.55, and6.35 mm, respectively.

To verify the accuracy of the results, an erroranalysis operation was performed. The Root MeanSquare (RMS) errors were calculated for all 1330 pointsin x, y and z directions. The RMS errors are as follows:

(RMS)x = 1:6 mm;

(RMS)y = 1:0 mm;

(RMS)z = 2:8 mm:

4. Discussion

In order to use a computer simulation system to trainfor laparoscopic surgery, a fast and real time computerprogram is required. This study focuses on developinga biomechanical computer simulator that can evaluatethe interactions between a large intra-abdominal organ,i.e. a kidney, and a grasping instrument. Generally,

Z. Saghaei Nooshabadi et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 295{300 299

undertaking laparoscopic surgery is complex, since thesurgery is blind, and manipulation of the tissue isdi�cult. There is no direct visualization and feedbacksensing. Thus, the training models should provideappropriate visual and haptic display in real time.

Previous studies in the literature have often beenunable to simulate the grasping procedure of softorgans with high accuracy and feasible computationalcost. The �nite element model can provide a realisticpresentation of soft tissue deformations, but, the �niteelement procedure is normally slow with high compu-tational cost. Therefore, the �nite element methodcannot be considered for real time simulations [3].

The meshless method examined in the presentstudy is based on a set of scattered nodes that build thegeometry of the soft organ. With the meshless method,during the running process, there is no need to meshand re-mesh the geometrical model. This would beimportant when dealing with soft abdominal organswhere deformations may be quite large. W With anFE model, re-meshing of the object during the solutionprocedure may be required, due to the geometricalirregularity of the models.

The results of this study show that the meshlessmethod can provide reasonable accuracy with lowcomputational cost. Close agreement between theresults of the meshless model and those of the FEM wasobserved. The RMS errors for the displacements of thepoints in the meshless model were within an acceptablerange, based on FE references. As a general conclusion,it might be suggested that the meshless method isan e�cient computing technique for evaluating themechanical properties of soft tissue in a real timeprocess.

The results of this study suggest that the di�er-ences between the meshless model and FEM resultsdepend upon the node scattering pattern. In general,the high density distribution of nodes was at thecontact regions, and the low density distribution ofnodes was in other regions to reduce computationaltime. As a result, higher accuracies were obtained atthe regions in contact with the grasper jaws comparedto those regions located outside the contact interface.This feature of the meshless method can be used toadjust the accuracy at di�erent areas of the soft tissuemodel by applying appropriate distribution patternsfor the nodes. For instance, at the sensitive areas ofthe tissue, e.g. near the blood vessels or nerves, higheraccuracy can be obtained utilizing a higher densitydistribution pattern.

Finally, a simple innovative approach was pre-sented in this study to achieve a realistic and com-prehensive graphical representation of the deformedorgans from the results of the meshless model. Withinthe current meshless method, only displacement wascomputed. It is obvious that by increasing the number

of nodes, higher computational time would be resulted,which is not the aim of this study. Here, a limitednumber of nodes was used to solve the meshless modelin an acceptable time frame. However, after �nding thedisplacements of the nodes, it is possible to calculatethe displacements for a large number of points aroundthe geometrical model by employing an interpolationapproach. The algorithm used for the meshless modelwould be very useful when dealing with irregular,complex and large organ geometries.

5. Conclusion

This study suggests that the meshless method is ane�cient technique for real time computer modeling oflarge organs. For the model presented in this study, thecomputational cost of the meshless method was muchless (99.5% less) than that of the �nite element model.

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Biographies

Zeinab Saghaei Nooshabadi received her MS degreein BioMechanical Engineering from Sharif University ofTechnology, Tehran, Iran. Her research interest lies onmechanical and biomedical engineering.

Elahe Abdi received her BS and MS degrees in Me-chanical Engineering and Biomechanical Engineeringfrom Sharif University of Technology, Tehran, Iran, in2009 and 2102, respectively. She is currently at theInstitute of Microengineering at EPFL, Switzerland,where she is a doctoral assistant.

Farzam Farahmand received an MS degree in Me-chanical Engineering from the University of Tehran,Iran, in 1992, and a PhD degree in BiomechanicalEngineering from Imperial College of Science, Tech-nology and Medicine, London, UK, in 1996. He iscurrently Professor and Head of the BiomechanicsDivision in the Mechanical Engineering Department

of Sharif University of Technology, Tehran, Iran. Healso has a joint appointment in the Research Centerfor Biomedical Technologies and Robotics (RCBTR) inTehran University of Medical Sciences, Tehran, Iran,where he is head of the Medical Robotics Group.His research is focused on human motion, orthopedicbiomechanics and medical robotics. In his career, hehas developed several medical instruments and devicesand published numerous journal and conference pa-pers in di�erent �elds of biomechanics and biomedicalrobotics

Roya Narimani received her BS degree in Electri-cal and Electronics Engineering from California StateUniversity, Sacramento, USA, in 1980, and her MSdegree in Bioengineering from the University of Utah,USA, in 1982. She is currently an instructor in theMechanical Engineering Department of Sharif Uni-versity of Technology, and Director of the AppliedElectronics Laboratory. Her research is focused onbioinstrumentation and rehabilitation.

Mahmoud Chizari received MSc degree in Mechan-ical Engineering from UMIST, UK, and PhD degreein Bioengineering from The University of Manchester,UK, in 2005 and 2008, respectively. He completedhis PostPhD in Biosurgical Engineering with the Uni-versity of Aberdeen, UK, in 2011. He is currentlymember of the Orthopaedic Research and LearningCentre, where he is a lecturer in the Department ofMechanical, Aerospace and Civil Engineering at BrunelUniversity, London, UK. He is also Adjunct Professorin the Mechanical Engineering Department of SharifUniversity of Technology, Tehran, Iran.