Stitching Path Planning using Circular Needles-TissueInteraction Model

Faezeh Heydari Khabbaz and Alexandru Patriciu∗†‡

Abstract

This paper presents a path planning algorithm forrobotic assisted stitching. The method uses a nonlinearmodel for curved needle - soft tissue interaction. Theproposed method can be used for autonomous roboticsuturing. The performance of the algorithm was as-sessed through simulations and experiments. The exper-imental results illustrate that the path planned curvedneedle insertions are fifty percent more accurate thanthe unplanned ones. The results also show that an openloop approach is sensitive to model parameters.

1. INTRODUCTION

Since the introduction of the suture in the 16th cen-

tury by Ambroise Pare, the approximation of tissue us-

ing needle and thread has been the cornerstone of surgi-

cal techniques; suturing is a fundamental surgical task

that any practitioner has to acquire. Poor suturing tech-

nique can result in sub-optimal outcomes in terms of

healing, infection, and cosmetics. On the other hand,

suturing is a repetitive and time consuming task being

thus amenable to automation using robotics.

Virtual reality simulators allow surgeons to train on

a large variety of surgical scenarios. Kuhnapfel’s re-

search [8] and software is directed towards the simula-

tion of realistic interactions between surgical tools and

the organs, which are modeled as deformable bodies

[8]. Gubert introduced a new method, based on comple-

mentarity constraints, for simulating virtual sutures in

soft tissues [14]. Webster et al. created a simulation for

suturing that is based on a 2D mass-spring model [3].

Several other groups have been working on the sutur-

∗This work was partially supported by NSERC and CFI†Faezeh Heydari Khabbaz is with the School of Biomedi-

cal Engineering, McMaster University, Hamilton, On, Canada

heydarf@mcmaster.ca‡Alexandru Patriciu is with the ECE Depart-

ment, McMaster University, Hamilton, On, Canada;

patriciu@mail.ece.mcmaster.ca

ing specific simulations [1, 2]. The research results re-

lated to support systems for surgical suturing are fewer

than those related to simulations. Nageotte et al. [6]

presented a kinematic analysis of the entrance and exit

bites involved in the stitching task. However, most of

previous works focused on surgical knot tying. For in-

stance, Kang and Wen [4] and Nagy et al. [5] employed

tele-manipulation with haptic feedback to perform this

task. Marshall et al. [7] analyzed the various steps in-

volved in the suturing task.

Suturing involves the following steps: 1) Identify

suitable entry and exit points for the suture needle. 2)

Grasp the needle, move and orient it such that the tip is

aligned with the entry point. 3) Entry and exit bites are

made such that the needle passes through the tissue. 4)

Create a suture loop to tie a knot. 5) Secure the knot

under proper tension. Reaching the desired exit point

may be challenging because it must be realized with-

out direct visual feedback. We aim to provide a system

to help the surgeons perform robotic assisted stitching.

Our objective is to perform automatic tissue piercing, or

propose an optimal needle trajectory to the surgeons. In

contrast to the previous reported results [6] the proposed

trajectory planner takes into account the deformation in-

duced in the tissue by the needle.

This work is a step toward a robotic-assisted sutur-

ing system. The desired needle path is based on a non-

linear computational model of the interaction between

tissue and curved needle. The method doesn’t use real

time deformation feedback during stitching. This ap-

proach has advantages and disadvantages. The advan-

tage is that the implementation is simple; it does not

require advanced sensors to record the position of the

tissue. The disadvantage is that it is sensitive to model-

ing errors.

The paper is organized as follows: Section 2 will

describe the curved needle - soft tissue interaction

model, section 3 describes curved needle path planning

approach and section 4 shows the results for the simula-

tions and experiments. The paper closes with a discus-

sion of the results and conclusion.

1134

Proceedings of the 2011 IEEEInternational Conference on Robotics and Biomimetics

December 7-11, 2011, Phuket, Thailand

2. Soft Tissue deformation Modeling

A comprehensive review of the needle-tissue in-

teraction models have been published by Abolhasani

[11]. Finite element models (FEMs) have been used for

modeling soft-tissue deformation in order to rigorously

capture biomechanical properties of biological tissues.

However, the computational demands of finite elements

are serious hurdles for real-time simulation. Although

numerical techniques are proposed in [9, 10] to signifi-

cantly reduce its computation, the consensus is that lin-

ear FEMs can be accurate, but are not always appropri-

ate for large deformations of soft tissue, or for real-time

simulation of large geometries.

Meshless methods, which do not require time-

consuming mesh generations for modeling the analy-

sis domain, are expected to become a key technology in

the next generation of computation methods. Therefore,

several meshless and gridless methods have emerged

and some of them were proposed for tissue deforma-

tion simulation [15]. In this work, we use a meshless

model that is derived using RKPM (reproducing Kernel

particle) method [12].

2.1. Tissue Model

Throughout the paper we used the following con-

ventions. The initial (un-deformed) coordinate is repre-

sented by uppercase X and the deformed configuration

is represented by lower case x = φ(X , t). The region oc-

cupied by the body in the initial configuration is ΩX and

it has the boundary ΓX . The deformed configuration is

Ωx with the boundary Γx. The directional derivative is

represented using comma notation; repeated indices in-

dicate a sum over the number of dimensions.

The tissue model is formulated as a boundary prob-

lem using nonlinear elasticity tools as follows. The

body is subject to body forces bi, boundary traction hi

on the natural boundary Γhix and boundary displacement

gi on the essential boundary Γgix . The task is to find

ui(X , t) such that

τi j, j +bi = 0 (1)

τi jn j = hi on Γhix

ui = gi on Γgix

with ni the outward surface normal in the deformed

configuration, u(X , t) = φ(X , t)−X is the material dis-

placement, and τi j is the Cauchy stress tensor computed

as

τi j =1

JFimSmnFjn;Si j =

∂W∂Ei j

(2)

where F is the deformation gradient, E is the

Green-Lagrange strain, W is the strain energy density

function and J is the determinant of the deformation

gradient J = det( ∂xi∂X j ). The variational version of the

equations 1 can be formulated as described in [13].

The integro-differential equation is discretized using a

mesh-less approach and used in an iterative method to

solve for the deformation.

In a reproducing kernel particle method the defor-

mation is defined using global interpolants. The inter-

polants can be seen as smoothed dirac functions cen-

tered in a certain body coordinates - particles locations.

Let’s assume that there are NP particles distributed over

the body. Each particle has an associated shape func-

tion NI(X) : ΩX → R. Then, the displacement can be

expressed as

ui(X) =NP

∑I=1

NI(X)diI

NI(X) = H(0)T M(X)−1H(

X −Xi

a

)φa(X −XI)ΔVI (3)

M(x) =NP

∑j=0

H(

X −XJ

a

)H

(X −XJ

a

)T

φa(X −XJ)ΔVJ

where XI is the coordinate of particle I, aIi is

the I’s particle dilation parameter in direction i, His the multidimensional basis function vector H(Y ) =[1,Y1,Y2, ...,Y nsd ], φa is the multidimensional kernel

function defined using B-spline functions and ΔVI is the

volume associated with the Ith particle.

2.1.1. Curved needle interaction. Usually, the sutur-

ing needles are rigid and have the shape of an arc-circle.

As the needle is pushed into the tissue it interacts with

it through friction force and cutting force. This is mod-

eled as fundamental boundary; the needle-tissue friction

and cutting forces are applied through this boundary. In

addition, the boundary motion has to be constrained to

the needle trajectory. In other words, the material has

to be constrained such that it doesn’t move across the

needle. The needle trajectory is described by a vector

of points qi; i = 1...Nn in the un-deformed body coordi-

nates; the needle trajectory (ΓN) is the continuous curve

defined by qi , for each point on this trajectory the fol-

lowing equations hold

F = FN(X)∗a0(X) (4)

|u(X)T ai(X)| = 0 (5)

‖ai(X)T τ(X)ai(X)−Ri(X)‖ = 0; i = 1,2 (6)

where FN(X) is the magnitude of cutting and fric-

tion force applied on the needle at point X . a0(X) is the

1135

tangent to the needle direction at point X , a1(X) points

towards the needle center, and a2(X) = a0(X)× a1(X)(a1 and a2 are orthogonal on a0). Ri represents the

magnitude of the reaction force between the needle and

tissue in direction ai and τ(X) is the stress at point

X. These conditions are inserted into the variational

form of equation 1 using Lagrange multipliers. Simi-

larly with the displacement, it will be assumed that the

Lagrange multipliers are linear combinations of kernel

functions. Using all this information, the following in-

cremental equation is obtained as

(KT (d) G(d)GT (d) 0

)(Δdr

)=

(Δf(d)

0

)(7)

where KT is the tangent stiffness matrix, and d is

the displacement

Δ f =(Δ f T

M)T

M=1...NFP;Δ fM ∈ Rnsd×1 (8)

Δ fMi =∫

ΩX

NM(X)bi(x(X))J(X)dΩ−∫

ΩX

∂NM

∂Xj(X)FikSk jdΩ+

∫ΓN

NM(X)FN(X)a0i(X)dΓN ; i = 1 . . .nsd

G = (GLM) ;L = 1 . . .NFP,M = 1 . . .NPN (9)

GLM = −∫

ΓN

ΨM(X)NL(X)∗(

a1(X) · · · ansd−1(X))

dΓN

Where nsd is the number of space dimensions

which in this work is 2, NFP is the number of points

along the needle trajectory and NPN is the number of

particles inside the body. Equations 7 to 9 provide a

means to implement an incremental solver for needle

insertion simulation. The general needle insertion algo-

rithm is presented in Algorithm 1.

The applied force is first distributed as friction

force along the needle; the friction force per unit length

is constant for a given material and needle. The remain-

ing force is assigned to the first segment of the needle

(needle tip) as cutting force. If the cutting force is larger

than a threshold assigned to the material in the neigh-

borhood, a new point is added to the needle points vec-

tor.

The new tip point (Xtn) has to satisfy two con-

straints; the distance to the needle center (O) equals

the needle radius (R) and the distance to the old nee-

dle tip (Xtn−1) equals the insertion step (IS). If we as-

sume that the circular needle rotates with a constant an-

gle θ for each insertion step, the insertion step length is

Algorithm 1 General Needle Insertion Algorithm

Initialize particles data

d ← 0

Choose insertion point and insertion step

Initialize Needle Points Vector �qInitialize insertion force to 0 fins ← 0

Initialize insertion force increment fincwhile tip of the needle is inside the body do

fins ← fins + fincrepeat

Distribute applied force on the needle segments

Find new displacement increments using equa-

tion 7

Update deformations, strains, and stresses

if (cutting force) > (threshold) thenadd one more point to the needle points vector

end ifuntil no new point is added

end while

IS = R×θ . The new tip position is computed by mini-

mizing the following cost function

C (Xtn) = (‖Xtn +u(Xtn)−O‖−R)2 + (10)

(‖Xtn −Xtn−1‖− IS)2

The cost function C is minimized using a

Levenberg-Marquardt algorithm. The starting point for

the optimization is provided by

X̃tn = Xtn−1+(cos(nθ)− sin(nθ))T ∗ IS; (11)

This computational model was used for path plan-

ning in robotic assisted stitching.

3. Curved Needle Path Planning

Given desirable initial and final positions, the task

is to find a feasible path between these two points. As

the needle advances through the tissue and the tissue

deforms, we may have under-bites; we need to adjust

the motion of the needle such that it compensates for

the deformation of the tissue. In this section we present

a path planning method for the robotic assisted stitch-

ing. In the experimental setup, the needle is held by the

robot using graspers. The robot follows the given trajec-

tory and inserts the needle toward the desired exit point.

The motion of the needle comprises two components;

a rotation around the needle center which provides the

insertion motion and a translation of the needle center

which changes the global needle position.

1136

We assumed that the tip of the needle is orthogo-

nal to the tissue at the entry point; exit and entry points

are on the same circle, we then wish to adjust the nee-

dle position during stitching such that the tip reaches

the desired exit site. The overall idea is that we try to

maintain constant the relative distance between the nee-

dle center and the exit point. Each time a new point is

added, the center of the needle is moved relative to the

displacement of the desired exit point such that the dis-

tance between new deformed exit point and center re-

mains constant. If the needle center adjustment results

in additional exit point motion this will be compensated

for in the next load iteration. The algorithm described

bellow runs each time a new needle point is added to

the trajectory.

Algorithm 2 Curved Needle Path Planning Algorithm

if new needle point is added thenFind the displacement of the desired exit point

u(Xexit) at time tnSet O(tn) = O(t0)+u(Xexit)

end if

The trajectory of the center of the needle (O(tn)),provides the necessary information for the motion of the

robot to perform a planned stitching task. Next section

shows the simulation and experimental results for dif-

ferent needle insertion tasks.

4. Results

The proposed path planning method was tested us-

ing a surgical ETHICON needle of type ”SH 1/2 Cir-

cle” with the radius of 8.88mm attached to a robotic ma-

nipulator. The object samples were made out of super

soft plastic by M&F Manufacturing. The object me-

chanical properties and needle-material interface prop-

erties were identified through a calibration procedure.

The properties of the hyper-elastic plastic mate-

rial were determined through a experimental procedure.

The object was deformed with a robot manipulator

while recording both the object deformation and inter-

acting forces. Simulations were then performed while

tuning object parameters until the simulated deforma-

tion matched the experimental deformation. Using this

algorithm for identifying the objects parameters leads

to values of 0.189151 and 0.147688 for the first (λ ) and

second(μ) Lame parameters respectively.

The needle-tissue friction and the cutting force was

measured through an experiment comprising two steps.

First, the needle was rotated in the air to record the force

sensor background noise. Second the needle was in-

serted into the object while recording the forces and to-

(a) (b)

(c)

Figure 1: (a) Curved needle insertion simulation with-

out path planning for 10cm×10cm object , (b) with path

planning (c) experiment.

ques applied to the robot end-effector. The difference

between these two recordings gives the force required

for inserting the needle into the body which it gives the

friction force. 6 sets of similar experiments performed

from different insertion points to measure the friction

force and the average result was 0.0602N/mm. Mul-

tiple simulations were performed to match as much as

possible the simulation and experimental result and the

penetration force was obtained to be 0.7N.

In the experiments we considered homogeneous

objects with the following dimensions 10cm × 10cm,

10cm× 5cm, 10cm× 4cm, 10cm× 3cm. For each di-

mension a needle insertion simulation was performed

in order to compute the desired needle center path for

robotic implementation.

4.1. Simulation setup

We set the parameters of the simulations according

to the measured experimental parameters. In each step

the needle rotates 0.08rad into the tissue. Figure 1- 4

shows simulations with the object size of 10cm×10cm,

5cm×10cm, 4cm×10cm, 3cm×10cm without and with

path planning. A cross in these figures shows the de-

sired exit point. In all of these simulations the object

has a fixed boundary at x = 10cm.

Table 1 shows results for those simulations. For

each simulation the error at the exit site is given be-

1137

(a) (b)

(c)

Figure 2: (a) Insertion without path planning for 5cm×10cm object , (b) with path planning (c) experiment.

(a) (b)

(c)

Figure 3: (a) Insertion without path planning for 4cm×10cm object , (b) with path planning (c) experiment.

(a) (b)

Figure 4: (a) Curved needle insertion without path plan-

ning for 3cm×10cm object , (b) with path planning.

Table 1: Simulation Results

Object size error before planning error after planning

10cm×10cm 1.89mm 0.01mm

5cm×10cm 3mm 0.05mm

4cm×10cm 3.58mm 0.02mm

3cm×10cm 4.35mm 0.01mm

fore and after path planning. Each time that the object

becomes smaller, it more deforms and the error at the

exit site becomes larger; however path planning algo-

rithm could effectively compensate the deformation of

the object and decreased the error to close to zero. The

computed trajectories were employed to programm the

robotic manipulator for the experiments.

4.2. Experimental setup

Figure 5 shows the experimental setup with de-

formable object and robot manipulator. The same sets

of experiments were performed as the simulation ones,

first one was with the 10cm×10cm object. Then it was

cut to 5cm×10cm, 4cm×10cm and 3cm×10cm to get

more deformations in next experiments. For each ob-

ject size, the unplanned and planned experiments were

performed at least 3 times to ensure the consistency of

the results for each object. The results were almost the

same in repeated experiments for each object size in our

range of measurement.

In the experiments, the robot was first positioned

such that the tip of the needle be on the desired entry

point. In unplanned ones, the robot manipulator just

rotates the needle into the tissue and follows a circular

trajectory. In the case of planned insertions, the robot

followed the trajectory which obtained from the corre-

sponding simulation and manipulated the position of the

center of the needle such that the tip is moved toward

the desired exit point.

Figure 1c- 3c shows the experiments for the

10cm × 10cm, 5cm × 10cm and 4cm × 10cm object.

Since the differences between unplanned and planned

insertions in these experiments are about a millimeter

and can not clearly depicted in pictures, just the un-

planned ones are shown. Figure 6 shows the experiment

for the 3cm×10cm object before and after planning. Ta-

ble 2 shows error at the exit site for these experiments

before and after planning and percentage of the error

reduction for each object size. These results show that

the path planning algorithm can guide the needle to the

desired exit point and prevents under-bites due to defor-

mation of the tissue.

1138

Figure 5: experimental setup.

(a) (b)

Figure 6: (a) Experiment without path planning for

3cm×10cm object,(b) with path planning .

5. Conclusion

The surgeon must often proceed the stitching by

trial and, in many cases, the desired exit point can only

be reached at the expense of large and undesirable de-

formations of tissues. As to assist the surgeons, we pro-

posed to compute a path for the circular needle through

the tissue and driving the needle towards the desired exit

point by changing the center of the needle during stitch-

ing to compensate for the displacement of the desired

exit point. This method can be implemented for robotic

assisted surgery. The proposed method for path plan-

ning uses a nonlinear model for the interaction between

tissue and circular needle. The work presented here is a

first modeling work which takes into account the global

deformation of thick tissues during stitching and sim-

ulation and experimental results indicate that the pro-

posed method reduces the error at the exit site.

Table 2: Experiment ResultsObject size unplanned error planned error reduction

10cm×10cm 0.80mm 0.35mm 56%

5cm×10cm 1.47mm 0.43mm 71%

4cm×10cm 2.69mm 1.18mm 56%

3cm×10cm 5.20mm 2.47mm 52%

References

[1] R. V. OToole, R. R. Playter, T. M. Krummel, W. C.

Blank, N. H. Cornelius, W. R. Roberts, and M. Raibert,

“Measuring and Developing Suturing Technique with a

Virtual Reality Surgical Simulator,” J. Amer. Coll. Surg.,vol. 189, no. 1, pp. 114−127, Jul. 1999.

[2] J. Phillips, A. Ladd, and L. E. Kavraki, “Simulated knot

tying,” in IEEE lnternational Conference on Roboticsand Automation, Washingon, DC, pp. 841−846, 2002.

[3] R. W. Webster, D. I. Zimmerman, B. J. Mohler, M. G.

Melkonian, and R. S. Haluck, “A prototype haptic sutur-

ing simulator,” Medicine Meets Virtual Reality, vol. 81

pp. 567−569, 2001.

[4] H. Kang and J. T.Wen, “EndoBot: a robotic assis-

tant in minimally invasive surgeries,” in IEEE Inter-national Conference on Robotics and Automation, pp.

2031−2036, 2001.

[5] I. Nagy, H. Mayer, A. Knoll, E. U. Schirmbeck, and R.

Bauernschmitt, “EndoPAR: An open evaluation system

for minimally invasive robotic surgery,” in IEEE Mecha-tronics and Robotics 2004 (MechRob), Germany, 2004.

[6] F. Nageotte, M. de Mathelin, C. Doignon, L. Soler, J.

Leroy, and J. Marescaux, “Computer-aided suturing in

laparoscopic surgery,” in Proceedings of the 18th Inter-national Congress on Computer Assisted Radiology andSurgery, Chicago, June 2004.

[7] P. Marshall, S. Payandeh, and J. Dill, “Suturing for sur-

face meshes,” in Proceedings of the IEEE Conference onControl Applications, Toronto, pp.31−36, 2005.

[8] U. Kuhnapfel, H. K. Cakmak and H. Maab, “Endoscopic

Surgery Training Using Virtual Reality and Deformable

Tissue Simulation,” Computers & Graphics, vol. 24, no.

5, pp. 671−682, 2000.

[9] M. Bro-Nielsen and S. Cotin. “Real-time Volumetric

Deformable Models for Surgery Simulation using Finite

Elements and Condensation,” in Proceedings of Euro-graphics, Computer Graphics Forum, Poitiers, France,

vol. 15, pp. 57−66, 1996.

[10] J. Berkley, S. Weghorst, H. Gladstone, G. Raugi, D.

Berg, and M. Ganter, “Fast Finite Element Modeling for

Surgical Simulation,” in Proceedings of Medicine MeetsVirtual Reality 1999, pp. 55−61, 1999.

[11] N. Abolhassani, R. Patel, and M. Moallem, “Needle in-

sertion into soft tissue: A survey,” Med. Eng. Phys., vol.

29, no. 4, pp. 413−431, May 2007.

[12] S. Li and W. K. Liu, “Meshfree and particle methods and

their applications,” Applied Mechanics Reviews, vol. 55,

no. 1, pp. 1−34, January 2002.

[13] R. W. Ogden, “Non-Linear Elastic Deformations,”

Dover Publications, 1997.

[14] CH. Gubert, CH. Duriez, S. Cotin and L. Grisoni,

“Suturing simulation based on complementarity con-

straints,” in Symposium on Computer Animation, 2009.

[15] A. Horton, A. Wittek, and K. Miller, ”A meshless to-

tal Lagrangian explicit dynamics algorithm for surgical

simulation,” Int. J. Numer. Methods Biomed. Eng., vol.

26, no. 8, pp. 977−998, 2010.

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