Needle-Tissue Interaction Forces for Bevel-Tip Steerable Needles

Sarthak Misra, Kyle B. Reed, Andrew S. Douglas, K. T. Ramesh, and Allison M. Okamura

Abstract— The asymmetry of a bevel-tip needle results in theneedle naturally bending when it is inserted into soft tissue.As a first step toward modeling the mechanics of deflectionof the needle, we determine the forces at the bevel tip. Inorder to find the forces acting at the needle tip, we measurerupture toughness and nonlinear material elasticity parametersof several soft tissue simulant gels and chicken tissue. Weincorporate these physical parameters into a finite elementmodel that includes both contact and cohesive zone models tosimulate tissue cleavage. We investigate the sensitivity of the tipforces to tissue rupture toughness, linear and nonlinear tissueelasticity, and needle tip bevel angle. The model shows that thetip forces are sensitive to the rupture toughness. The resultsfrom these studies contribute to a mechanics-based model ofbevel-tip needle steering, extending previous work on kinematicmodels.

I. INTRODUCTION

Needle insertion into soft tissues is probably the most com-mon invasive surgical procedure used for either therapeuticdrug delivery or tissue sample removal from deep within thebody. Inaccurate needle placement may result in malignan-cies not being detected during biopsy, radioactive seeds notbeing in the correct location to destroy cancerous lesionsduring brachytherapy, and traumatic or even fatal effectswhile performing anesthesia. Thus, for medical diagnosesand treatments, the needle must reach its intended target.But tissue inhomogeneity and anisotropy, organ deformation,and physiological processes, such as respiration and flow offluids, cause the needle to deviate from its intended path. Apossible method to mitigate needle targeting errors is to usea needle that can be robotically steered in the body to reachthe intended target.

Several groups have examined the use of roboticallysteered flexible needles through tissue [3], [8], [9], [16],[18], [19], [20], [21]. Planning such procedures requires anaccurate model of the needle-tissue interaction. One of themethods to steer needles through the body uses needles withstandard bevel tips that naturally cause the needle to bendwhen interacting with soft tissue [20]. This phenomenon isattributed to the asymmetry of the bevel edge, which resultsin bending forces at the needle tip. Ideally, a mechanics-based model of the tip forces would be used to predict needlebehavior based on information about geometry and materialproperties.

Several research groups have developed physics-basedneedle and soft tissue interaction models that are not specific

This work was supported by a National Institutes of Health grant (R01EB006435) and a Link Foundation fellowship.

The authors are with the Department of Mechanical Engineer-ing, The Johns Hopkins University, Baltimore, MD, USA 21218.{sarthak,reedkb,douglas,ramesh,aokamura}@jhu.edu

to bevel-tip needles [2], [6], [7], [11], [12], [15]. A summaryof these studies and other non-physics-based needle-tissueinteraction models is provided in [14]. In all these studies,the objective of the researchers was to develop models torender simulation of needle-tissue interaction for real-timeapplications without specifically focussing on the interactionforces at the needle tip. Experimental work has identifiedforces (due to puncture, cutting, and friction) developedduring needle insertion through tissue [13], [17]. Further,in [21] a kinematic model specifically for bevel-tip needleswas presented whose parameters were fit using experimentaldata, but this model did not consider the interaction ofthe needle with an elastic medium. None of these studiesfocused on relating the tip forces to the amount of needledeflection based on the fundamental principles of continuumand fracture mechanics.

In this research we study the effect of tissue material andneedle tip geometric parameters on tip forces. Using finiteelement (FE) simulations, we show the relationship betweenthe bevel angle and the forces generated at the needle tip.Using needle insertion experimental studies with gels andtissue, we extract the material properties. We incorporatethese physical values into an FE simulation. The FE modelincludes contact between the needle tip and tissue, and alsoincorporates a cohesive zone model to simulate the tissuecleavage process.

This paper is organized as follows: Section II presentsthe mathematical preliminaries required to obtain the tissueelasticity and toughness values. Section III describes the ex-periments to measure tissue elasticity and toughness. SectionIV provides details on the FE simulations and sensitivitystudies. Finally, Section V summarizes the work done andprovides possible directions for future work.

II. TISSUE ELASTICITY AND TOUGHNESS

The deflection of a bevel-tip needle is a function ofseveral parameters (Figure 1): the needle’s Young’s modulus(

E, units: Nm2

), second moment of inertia

(I, units: m4

),

µ

Gc

C10 u

ρ

E, I

α

Fig. 1. Schematic of a bevel-tip needle interacting with a soft elasticmedium.

Proceedings of the 2nd Biennial IEEE/RAS-EMBS InternationalConference on Biomedical Robotics and BiomechatronicsScottsdale, AZ, USA, October 19-22, 2008

978-1-4244-2883-0/08/$25.00 ©2008 IEEE 224

Fig. 2. Stresses acting on body under uniaxial compression, where thesolid and dashed lines represent the body before and after compression,respectively.

and tip bevel angle (α); the tissue’s nonlinear (hyperelas-tic) material property

(C10, units: N

m2

), rupture toughness(

Gc, units: Nm

), and coefficient of friction (µ); and input

displacement from the robot controller (u, units: m). Di-mensional analysis provides an organized method to groupdimensionally similar variables [5]. Thus, the radius ofcurvature of the needle (ρ , units: m) can be written as afunction, f , of these parameters

ρ = f

E, I,α︸ ︷︷ ︸needle

,C10,Gc,µ︸ ︷︷ ︸tissue

, u︸︷︷︸input

. (1)

Performing dimensional analysis and invoking Buckingham’sΠ theorem on this system results in the following Π-groups,for primary variables E, C10, and Gc:

Π1 =ρC2

10EGc

, Π2 =IC5

10EG4

c, and Π3 =

uC210

EGc. (2)

Thus, the non-dimensional form of (1), for some function,g, is given by

ρC210

EGc= g

(IC5

10EG4

c,

uC210

EGc,α,µ

). (3)

From (3) it is observed that the radius of curvature isdimensionally scaled by both the tissue elasticity (globalparameter) and also the tissue rupture toughness (local pa-rameter), which tells us that in additon to α and µ , theeffect of both of these parameters (C10 and Gc) needs tobe investigated. In this section, we present a mathematicalformulation to evaluate the tissue elasticity and toughness tobe incorporated in an FE simulation framework.

A. Tissue Elasticity

The deformation of materials under strains greater than1%-2% is described by the theory of nonlinear elasticity, andhyperelastic models are commonly used. For a hyperelasticmaterial, the Cauchy stress tensor, σσσ , can be derived froma strain energy density function, W [10]. There are variousformulations for the strain energy density function dependingon the material. The material parameters associated with the

Tissue

Needle

Force Sensor

L1

u

L2

F2

F1

u

L1

Fig. 3. Schematic describing the procedure to calculate the rupturetoughness of an elastic material during needle insertion.

hyperelastic model are experimentally derived using tensile,compression, shear, or biaxial tests. In this study, uniaxialcompression experimental data was used and it fit the Neo-Hookean model well.

In order to fit the experimental data to a nonlinear elasticconstitutive relation, we proceed to derive the stress-strainrelationship. For a body under uniaxial compression (Figure2), if y represents the position after deformation of a materialreference initially located at X, we can describe compressionby

y = λ1X1e1 +λ2X2e2 +λ3X3e3, (4)

where ei and λi, for i = 1 to 3, are the Cartesian basevectors and stretch ratios, respectively. From (4), the matrixof the deformation gradient tensor, F, for axisymmetric(λ1 = λ3 and λ = λ2) and incompressible

(λ1 = λ3 = 1√

λ

)materials is computed as

F =∂y∂X

=

1√λ

0 00 λ 00 0 1√

λ

. (5)

Using the Representation Theorem [10], σσσ for anisotropic, homogenous, and incompressible hyperelastic ma-terial can be derived as

σσσ =−pI+2{(

∂W∂ I1

+ I1∂W∂ I2

)B− ∂W

∂ I2B2}

, (6)

where I1 and I2 are the principal invariants, B is the leftCauchy-Green tensor, and p is the Lagrange multiplier (es-sentially a pressure). The Neo-Hookean strain energy densityfunction is given by

W = C10 (I1−3) , (7)

where C10 is a material parameter specific to the tissue. In(7), the principal invariant, I1, can be evaluated from B =FFT as

I1 = B : I =2+λ 3

λ. (8)

225

(a) The RSA II test sta-tion

(b) Plastisol (soft) gel (c) Plastisol (hard) gel (d) Porcine gel (e) Chicken breast tissue

Fig. 4. Tissue elasticity measurement performed on several materials via uniaxial compression tests using the RSA II, where 1© and 2© are the actuatorand load cell, respectively.

Fig. 5. Representative compressive stress versus strain curves for variousmaterials recorded using the RSA II.

The Lagrange multiplier, p, in (6) can be evaluated fromthe boundary condition

σ11 = σ12 = 0⇒ p =2C10

λ. (9)

From (5) and (7) we can compute B2 and ∂W∂ I1

, respectively,and using (6) and (9), the compressive stress, σ22, is com-puted as

σ22 =2C10

λ

(λ

3−1)

, (10)

where stretch ratio is, λ = 1− strain. (10) is used to fitexperimental stress-strain data to obtain C10.

B. Tissue Toughness

As the needle penetrates through material, the insertionforce during this phase includes the force to overcomefriction and resistance due to tissue elasticity, and the forceneeded to cut through tissue. Figure 3 provides a schematicrepresentation of the method we use to extract the toughness.A similar method has been employed to extract fracturetoughness during needle insertion in [4]. The insertion forcerecorded for some distance, L1, travelled by the needle is F1.The work done, divided by the needle cross-sectional area, A,to overcome friction and tissue resistance, and to cut through

elastic material

needle

force sensor

linear stage

servo motor(needle spin)

Fig. 6. Experimental setup used to robotically steer a flexible needle thoughsoft elastic materials and used for toughness measurement.

tissue, G f tc, is given by

G f tc =1A

∫ L1

0F1dL. (11)

Once the needle tip has completely passed through thematerial, there is no cutting force. The force recorded duringthis phase, for a distance L1 travelled by the needle, is givenby F2. The work done, divided by the needle cross-sectionalarea, A, to overcome friction and tissue resistance, G f t , isgiven by

G f t =1A

∫ L1

0F′2dL, (12)

where L2 is the length of the needle shaft within the materialand F

′2 = F2

L1L2

. In order to account for the differences infrictional force along the needle shaft when the needle tiphas completely passed through the material versus the casewhen the needle tip is interacting with the elastic medium,F2 is scaled by L1

L2. This scaling assumes that frictional force

varies linearly along the length of the needle shaft. The workdone per unit needle cross-section area, Gc, to rupture andcut through tissue, is the rupture toughness (effective) of thetissue and is given by

Gc = G f tc−G f t , (13)

where G f tc and G f t are calculated for various materials usingneedle insertion experiments.

226

(a) Plastisol (soft) gel (b) Plastisol (hard) gel

(c) Porcine gel (d) Chicken breast tissue

Fig. 7. Insertion force versus distance travelled by needle used for rupture toughness measurement. The representative snapshots show the needle tipinteracting and outside the tissue samples. Data collected in the windows during which the needle tip travelled L1 are used to calculate G f tc and G f t .

III. TISSUE PARAMETER ACQUISITION

Experimental studies on phantom tissues (gels) and realtissue were performed in order to obtain both tissue elasticityand toughness parameters. Specifically, we found the Neo-Hookean model material parameter C10 given in (10) andthe rupture toughness derived in (13). Experiments wereconducted with two variants of plastisol gel (soft and hardversions), porcine gel, and chicken breast tissue. All testswere performed at room temperature and the chicken sampleswere thawed from freezer prior to the experiments.

In order to obtain values for C10, uniaxial compressiontests were performed on the soft materials using a Rheo-metrics Solids Analyzer (RSA) II, as shown in Figure 4.Three 1 cm3 cube samples of each material were preparedand tested. The compression tests were performed at a strainrate of 0.001 s−1. Representative stress versus strain curvesfor various materials are shown in Figure 5. The experimentaldata were fit to the constitutive equation given in (10) toobtain C10, and Table I provides the mean values of thetissue elasticity for various materials. Linear elastic modelswere also fit to the experimental data and Table I gives themean values of the Young’s modulus, Etissue, for the variousmaterials.

In addition to tissue elasticity, the rupture toughness ofseveral materials were evaluated using the needle steeringrobot shown in Figure 6 [20]. The nitinol needle had a

diameter of 0.71 mm and a tip bevel angle of 55◦. Asthe needle penetrated through the material, the insertionforce was recorded using an ATI Nano 17 force sensor.The material toughness was evaluated for soft and hardversions of plastisol gel, porcine gel, and chicken breasttissue using the expression given in (13). Figure 7 showsthe insertion force recorded as the needle travels throughdifferent materials. The needle was driven at a constantinsertion velocity of 0.125 cm/sec and the length, L2, for allgels was 10.2 cm except for the chicken tissue, which was7.5 cm. Also shown in Figure 7 are representative snapshotsduring which the toughness measurements were made. Thelength of the window when the needle tip is interacting andoutside the tissue is given by L1. During the phase whenthe needle tip is outside the tissue and only the needle shaftinteracts with tissue, the insertion force is fairly constant.The rupture toughness for the various materials are providedin Table I.

TABLE IMEASURED MATERIAL ELASTICITY AND RUPTURE TOUGHNESS

PROPERTIES FOR GELS AND TISSUE.

Material C10 (kPa) Etissue (kPa) Gc (kN/m) tc (MPa)Plastisol (soft) 3.6 21.5 39.3 110.6Plastisol (hard) 4.0 24.2 46.8 131.8

Porcine 4.9 29.6 114.4 322.2Chicken 3.7 22.1 24.2 68.2

227

IV. SENSITIVITY STUDIES

The material parameters obtained from the experiments inthe previous section were incorporated into FE simulationsusing ABAQUS [1] in order to evaluate the forces at theneedle tip. Figure 8 shows the various forces acting onthe needle interacting with an elastic medium. The needleis subjected to compressive and frictional forces along itsneedle shaft, and forces due to tip asymmetry. In this paper,we investigate the effect of rupture toughness, bevel angle,and tissue elasticity on the forces at the bevel tip.

A. Sensitivity to Tissue Rupture Toughness

In order to simulate the interaction of the needle tipdeforming and rupturing tissue as it travels, we employ acohesive zone model (Figure 9). Cohesive zone modelingtechniques are commonly used to simulate interface failurein composite structures. The cohesive zone is a mathematicalapproach to modeling the fact that work must be doneto separate the two surfaces at an interface. This workis described in terms of a prescribed relationship betweenthe tractions, t, required to separate the surfaces and therelative strains, δδδ , of those surfaces. A detailed explanationof the numerical implementation of cohesive zone models ispresented in [22]; cohesive zone elements are placed betweenbulk elements, as shown in Figure 9(a).

The cohesive zone elements are placed between continuum(bulk) elements and are defined in a small region (1 mmlong and 0.072 mm wide) near the needle tip, as shownin Figure 10(a). In our FE simulation models, the cohesivezone is implemented using quadrilateral elements (ABAQUSelement COH2D4), while the bulk elements are a mixtureof quadrilaterals (ABAQUS element CPE4H) and triangularelements (ABAQUS element CPE3H). The bulk elementsare assigned the nonlinear material properties (C10) givenin Table I, in addition to having geometric nonlinearity. Asthe needle tip deforms the tissue and the cleavage process

Fig. 8. Distributed load (compresssive and frictional forces) acting on aneedle shaft as it interacts with an elastic medium. Inset: Forces acting onthe bevel tip, where P and Q are the resultant forces along the bevel edge.qx and qy are the resultant forces along the bottom edge of the needle tip.

Fig. 9. The cohesive zone model used to simulate tissue cleavage process.(a) A sketch depicting application of cohesive zone elements along the bulkelement boundaries, where tensile/compressive (normal) and shear strainsresult in deformation and rupture of the cohesive elements. (b) Lineartraction-separation laws where values for Kn, Ks, Gc, and tc are obtainedfrom experiments and given in Table I.

is initiated, the cohesive zone elements open up in orderto simulate this behavior. All of the cohesive elements usea traction-separation law (Figure 9(b)), which defines therelationship between the vectorial tractions (force densityvectors), t, and strains, δδδ , across the element. The tractionsand strains are given by

tc = Knδnen +Ksδses, (14)

where Ks, Kn and δs, δn are stiffnesses and strains in theshear and normal directions, respectively. The description ofthe deformation and the traction evolution in these elementsis governed by a linear traction-separation law, as shown inFigure 9(b). The damage evolution and subsequent cleavageof the tissue is given by the rupture toughness, Gc. In order todefine the traction-separation law, inputs to the FE simulationmodel are: Kn, Ks, tc, and Gc. We assume the stiffness in thenormal and shear directions are the same and given by theelastic modulus of the tissue, as provided in Table I, i.e.Kn = Ks = Etissue. Gc values are also provided in Table I. Forunit original constitutive thickness of the cohesive element,δc is taken to be the same order of magnitude as the diameterof the needle i.e. δc = 0.71 mm, so for Gc being the areaof the shaded region (Figure 9(b)), tc = 2Gc

δc. The frictionless

228

200 mm

100

mm

Displacement (mm)

(b)

(a)

100

mm

0.71

mm

0.35

mm

200 mm

Fig. 10. FE simulation setup used to model needle and tissue interactionfor a needle with 55◦ bevel angle and 0.71 mm diameter. The needle tipwas made of nitinol (E = 50 GPa, ν = 0.3). (a) The green border used tosignify contact surfaces and the elements in red are assigned to be thecohesive zone. (b) Magnitude of nodal displacement contour plot for theneedle tip penetrating the tissue.

contact surfaces and the cohesive zone are highlighted inFigure 10(a) with an applied displacement of 0.35 mm.

Figure 10(b) shows the contour of the magnitude of nodaldisplacement in the vicinity of the needle tip and cohesivezone. Also shown is the needle tip penetrating through thetissue elements and the initiation of cleavage. The tissue rup-ture process is simulated as the cohesive zone elements openup, which in turn is governed by the traction-separation law.The resultant tip forces in the axial and transverse directionsare given by Fx and Fy, respectively, where Fx = qx +P andFy = qy + Q. Figure 11 shows the variation in Fx and Fy asthe rupture toughness, Gc, and the material elasticity, C10,changes for the different tested materials. Gc and C10 variedfrom 24.22 kN

m to 114.4 kNm i.e. 372.3% change, and 3.57 kPa

to 4.93 kPa, i.e. 38% change, respectively. This resulted ina 38% (0.44 N to 0.61 N) and 260.2% (0.11 N to 0.39 N)

variation in Fx and Fy, respectively. Also, as seen in Figure11, changes in tip forces are dominated by the variations inGc, and not C10. The overall bending of the needle is dueto a combination of forces along the needle shaft and at thetip. The results of this study indicate that the tip forces areprimarily governed by the rupture toughness. But in order topredict the path the needle will follow, the structural stiffnessof the needle shaft needs to be included in the model.

B. Sensitivity to Needle Tip Bevel Angle and Tissue Elasticity

In addition to studying the effect of rupture toughness, FEcalculations were also performed to assess the effect of bevelangle and tissue elasticity. Figure 12 shows the simulationsetup with boundary conditions and input displacement. Alsoshown is an example FE mesh used for the study. Theassociated elements used in this study are a combinationof quadrilateral (ABAQUS element CPE8) and triangular(ABAQUS element CPE6 and CPE6M) elements. Unlikethe study presented in Section IV-A in which contact wassimulated between the needle tip and the elastic medium,here we model the tissue and needle tip as one body butassign different material properties to signify the needle andtissue.

To study the effect of bevel angle, α was varied from10◦ to 80◦, while the tissue Young’s modulus and Poisson’sratio were kept constant at Etissue = 25 kPa and νtissue = 0.45,respectively. In order to study the sensitivity of tip forces totissue elasticity, Etissue was varied from 10 kPa to 35 kPa withνtissue = 0.45 and α = 45◦. It should be noted that a variationin bevel angle entails changing the geometry of the model,and requries re-meshing the model, unlike the cases in whichthe elastic property of the tissue is changed. For all studies,needle tip Young’s modulus and Poisson’s ratio were set toE = 2× 1011 Pa and ν = 0.3, and the needle diameter was2 mm with applied displacement of 0.5 mm. Also, thoughthe constitutive behavior of the elements is linear, geometricnonlinearity of the elements has been incorporated. Figure13(a) provides the variation of the needle tip forces in theaxial (P, qx) and transverse (Q, qy) directions as bevel angleis changed. qx decreases in a nonlinear manner with increasein bevel angle, while P decreases to a minimum value atapproximately 35◦ and then begins to rise for increase inbevel angle. It is seen that Q monotonically decreases withincrease in bevel angle, while qy monotonically increases(decreases in the opposite direction) with increase in bevelangle. The trends observed for qx, qy, and Q could beexplained as follows: With the increase in bevel angle, forconstant needle diameter, the length of the bevel and bottomedges decrease and hence the sum of the nodal forces alongthese edges also decrease. In Figure 13(b), Q and qy linearlyincrease and decrease (increases in the negative direction)with increase in tissue elasticity, respectively. Also, P and qxincrease linearly with increase in tissue elasticity. The trendfollowed by the tip forces could be explained as follows:With the increase in Young’s modulus (linear elasticity), thetissue resistance increases and thus, the tip forces linearlyincrease for the same input displacement of 0.5 mm.

229

(a) Forces in the axial (x) direction. (b) Forces in the transverse (y) direction.

Fig. 11. FE simulation results for needle tip forces with variation in nonlinear material elasticity and rupture toughness.

Fig. 12. (a) FE simulation model for performing tip force versus bevelangle and tissue elasticity sensitivity studies. (b) Example FE mesh for a 20◦bevel angle where the elements within the red border have been assignedneedle material properties.

V. CONCLUSIONS AND FUTURE WORK

This study determined bevel-tip needle and tissue interac-tion forces using FE simulations. We demonstrated a tech-nique to extract physically relevant tissue properties (tissuerupture toughness and nonlinear elasticity) and incorporatedthem into a FE simulation model in order to simulate thetissue cleavage process.

Tissue properties for several materials were measuredexperimentally and the sensitivity of the needle tip forces

to these parameters were shown using FE simulations. Theneedle tip forces were observed to be sensitive to therupture toughness. A 38% variation in nonlinear materialelasticity did not produce significant changes in tip forces.For most applications, in which the needle would be steeredthrough soft tissue, large variations in tissue elasticity are notexpected. Further, sensitivity of needle tip forces to changesin the bevel angle were also studied through FE simulations.In general, smaller bevel angles resulted in larger axial andtransverse tip forces. Possible extentions to this work includerefining the toughness experiments and performing simula-tions with contact and cohesive zone models for various bevelangles. Also, including the needle shaft within the simulationmodel is essential to predict the needle curvature. Further,the validation of such FE simulation models which includethe complete needle-tissue interaction, both along the needleshaft and also at the bevel tip, is integral for planning needleinsertion procedures. Validation studies need to be done withindependent experimental data, where comparison metricsmight include needle insertion forces, tip deflection, or radiusof curvature. Currently there only exists a kinematic modelthat predicts the needle deflection for a user-defined positioninput [21]. The parameters of this kinematic model mustbe determined experimentally and are not related to needlegeometry or material properties. One of the primary goalswithin the domain of robotically steered bevel-tip needles isto have an analytical and/or simulation model that wouldtake inputs as the tissue and needle material properties,and needle geometry, and predict the interaction forces anddeflection of the needle. Our future work is to develop sucha model to estimate the bending needed to robotically steerneedles through tissue and also, to choose feasible clinicalapplications and optimize needle design.

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