Medical Engineering and Physics 37 (2015) 469–477

Contents lists available at ScienceDirect

Medical Engineering and Physics

journal homepage: www.elsevier.com/locate/medengphy

Design optimization study of a shape memory alloy active needle for

biomedical applications

Bardia Konh, Mohammad Honarvar, Parsaoran Hutapea∗

Department of Mechanical Engineering, Temple University, Philadelphia, PA 19122, USA

a r t i c l e i n f o

Article history:

Received 31 October 2014

Revised 5 February 2015

Accepted 28 February 2015

Keywords:

Active surgical needle

Shape memory

Actuator

Design optimization

a b s t r a c t

Majority of cancer interventions today are performed percutaneously using needle-based procedures, i.e.

through the skin and soft tissue. The difficulty in most of these procedures is to attain a precise navigation

through tissue reaching target locations. To overcome this challenge, active needles have been proposed

recently where actuation forces from shape memory alloys (SMAs) are utilized to assist the maneuverability

and accuracy of surgical needles. In the first part of this study, actuation capability of SMA wires was studied.

The complex response of SMAs was investigated via a MATLAB implementation of the Brinson model and

verified via experimental tests. The isothermal stress–strain curves of SMAs were simulated and defined as a

material model in finite element analysis (FEA). The FEA was validated experimentally with developed proto-

types. In the second part of this study, the active needle design was optimized using genetic algorithm aiming

its maximum flexibility. Design parameters influencing the steerability include the needle’s diameter, wire

diameter, pre-strain and its offset from the needle. A simplified model was presented to decrease the com-

putation time in iterative analyses. Integration of the SMA characteristics with the automated optimization

schemes described in this study led to an improved design of the active needle.

© 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

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. Introduction

To date, many biomedical devices have utilized the pseudoelastic

roperties of advanced, active and adaptive materials such as coro-

ary stents, eyeglasses and orthodontic wires [1]. The actuation prop-

rties of the active materials have also attracted a lot of attention,

specially in medical devices such as active cardiac catheters [2], ar-

ificial muscles [3] and cochlea implants [4]. Shape memory alloys

SMAs), well known smart materials, have become increasingly pop-

lar in various applications due to their ability to remember their

nitial shape. Their unique thermomechanical characteristics of pseu-

oelasticity, shape memory effect and biocompatibility have made

hem a suitable option to revolutionize many diagnostic and ther-

peutic biomedical tools [5]. The primary concept of active surgical

eedle (Fig. 1) was suggested by Konh et al. [6] where the feasibility

f using SMA wires to actuate the surgical needles was shown. The

MA wires, i.e., Nitinol wires in our design, supply bending forces to

he needle body to guide the needle through desired trajectories in-

ide the tissue. The active needle [7] provides several advantages such

s improvements in accuracy to reach the target locations, avoiding

ritical organs during insertion and minimizing trauma to patients.

∗ Corresponding author at: 1947 N. 12th Street, Philadelphia, PA 19122, USA.

el.: +1 215 204 7805; fax: +1 215 204 4956.

E-mail address: hutapea@temple.edu (P. Hutapea).

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ttp://dx.doi.org/10.1016/j.medengphy.2015.02.013

350-4533/© 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

The success of many needle-based interventions such as

rachytherapy, thermal ablation and biopsy highly depends on the

ccuracy of the needle placements at target locations. For improve-

ent of the accuracy of needle placement, many groups have tried

ariety of options to activate the needle. For example, Tang et al. [8]

sed magnetic forces in order to help the navigation of the needle

nside the body. Ayvali et al. [9] utilized pre-curved SMA wires on the

eedle body to provide external actuations. The electrical resistance

nd the fatigue behavior of SMA wires used as actuators have been

tudied by Meier et al. [10]. They developed a control loop based on

he electrical resistance feedback.

Material characteristics of SMAs (the actuators) are complicated

ue to the history dependent hysteresis relationships between the

aterials’ stress, strain and temperature. A large recoverable strain

f SMAs is due to the transformation between two major internal

hases known as martensite and austenite. The transformation tem-

eratures are known as Ms, Mf, As, Af, where M represent martensite,

austenite, while subscripts s and f shows the starting and finishing

oint of the transformation process, respectively. Several researchers

11–13] have developed mathematical models to predict the SMA’s

esponse. Brinson [14] developed a model that includes the transfor-

ation between twinned and detwinned martensite. This model was

ble to predict the SMAs’ pseudoelasticity and shape memory effects,

imultaneously. Also privileging from non-constant coefficients this

odel provided an enhanced accuracy with respect to the previously

470 B. Konh et al. / Medical Engineering and Physics 37 (2015) 469–477

Fig. 1. Schematic of the proposed active needle design.

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developed models [11,12]. Brinson model was used in this study for

its accuracy and consistency with our SMA wires.

In this study, optimized design of the active needle has also been

presented. The past design and developments of systems consisting

SMAs had been based on graphical design trial and error [15]. Auto-

mated tools of the commercial software (ANSYS) were used here to

develop a predictive algorithm to assess the active needle response.

The novelty of our design optimization study lies on the incorpora-

tion of smart materials in our system. Prior to constructing an opti-

mization algorithm, implementation of a constitutive model capable

of predicting the inelastic strain response of SMAs is necessary. The

inelastic response of SMA wires with different diameters was first

studied via both experimental and numerical approaches. Since the

material properties of SMA wires could be different due to different

manufacturing processes, details of the constitutive model have been

described in this work so that it can be used in assessments of any

other systems with active components.

In previous optimization studies with SMAs [16–19], the desired

dynamic properties were found by optimizing the placement of a

single wire component to eliminate the high stress regions. The ac-

tive material optimization was done by Main et al., and Seeley and

Chattopadhyay [20,21] using analytical and gradient based studies.

In other work, design optimization of a system with a SMA spring

was investigated by Dumont and Kühl [22] using genetic algorithm.

To overcome some limitations of previous studies, such as expensive

computational time and incorporation of SMAs’ constitutive models,

we present an automated optimization approach based on a simpli-

fied model that benefits from extensive experimental and numerical

studies on SMA actuators.

This work is organized as follows: Section 2 introduces the overall

analysis tools and methodologies utilized for modeling and optimiza-

tion. Section 3 describes the constitutive model of SMAs in detail in-

cluding the numerical and experimental studies. Section 4 describes

the FE model and the prototype developed for verification purposes.

Section 5 validates the 3D FE analysis of the active needle via the

experimental tests and suggests a simplified model as an alternative

Fig. 2. Engineering tools used to show the actuation cap

or optimization studies followed by evaluation of its accuracy. In

ection 6, the optimization methods are described along with the

roposition of the best possible design of the active needle. Finally,

he conclusions are briefly summarized in Section 7.

. Analysis tools to optimize the active needle

The methodology used for the first part of this study is shown in

ig. 2. The thermomechanical behavior of SMAs needs to be included

n the analysis since they are the most important components of the

tructure. Three experimental setups developed to study the complex

ehavior of SMAs are discussed in detail in Section 3. Numerical and

xperimental studies on SMA wires prior to the finite element anal-

sis ensured a coherent material model to be used in the FE model.

he isothermal stress–strain curves obtained from a MATLAB imple-

entation of Brinson model and provided as the material model for

he FE analysis. The detail of this constitutive model is explained in

he next section.

The process of design optimization is shown schematically in Fig. 3.

ur design objective targets the highest deflection of the active needle

hile considering the restrictions such as maximum stress, strain and

lastic deformation of different components. Using this approach dif-

erent design configurations were evaluated seeking the best design.

he iterative structural analysis was performed over the defined do-

ain of design parameters to reach the design objectives. The ANSYS

esign optimization module was used for this objective that is capa-

le of being linked to the ANSYS parametric design language (APDL)

odule of the software where the FE model was generated and run

he analysis automatically. The optimization process consists of an

PDL input file with all design parameters and the required output

arameters defined which was iteratively solved through the whole

omain.

. Constitutive model: formulation and numerical integration

.1. Description of the material model

SMAs show two different behaviors known as (i) shape memory

nd (ii) pseudoelastic effects. The shape memory is its ability to re-

over a large residual strain by rising up the temperature whereas

seudoelasticity is its ability to resume a high amount of strain upon

nloading in a hysteresis loop. Two major phases exist in these alloys

hich are known as austenite and martensite. Austenite is known as

he parent phase, which only exists at high temperatures. Only de-

reasing the temperature will result in a phase change into marten-

ite. The martensite phase exists in two different orientations which

re known as twined and detwined, with respect to its multiple vari-

nts and twins. The phase transformation between martensite and

ability of SMA wires in the active needle design.

B. Konh et al. / Medical Engineering and Physics 37 (2015) 469–477 471

Fig. 3. Analysis algorithm for design optimization, seeking the maximum steerability

of the active needle.

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Fig. 4. Typical phase transformation diagram of SMA wires.

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ustenite generally empower the SMA to recover a large amount of

train which is used for activating the needle device. The constitutive

rinson model is used to model the active needle and is described

n this section. Prior to Brinson, Liang and Rogers [12] suggested the

tress (σ ) to be related to three material functions: the modulus of

MA, D(ε, ξ , T), the transformation tensor, �(ε, ξ , T) and the ther-

al coefficient of expansion, θ (ε, ξ , T) as shown in Eq. (3.1). In this

quation ε, ξ and T are the green strain, the martensite fraction and

emperature respectively.

σ = D(ε, ξ , T

)dε + �

(ε, ξ , T

)dξ + θ

(ε, ξ , T

)dθ (3.1)

Eq. (3.2) shows the relationship between temperature and trans-

ormation stress for a SMA material, where ε is the transformation

train and �H is the enthalpy change between martensite and austen-

te phases at T0. Both phases should be in equilibrium under the

tress σ .

dσ

dT= −�H

T0ε(3.2)

In Brinson model [14] the martensite fraction was divided into two

rystallographic shapes known as stress induced (ξ s) and temperature

nduced (ξ T) as shown below.

= ξs + ξT (3.3)

Finally assuming non-constant material functions, Eq. (3.4) was

odified by Brinson to suggest the SMA’s constitutive material as

ollows.

− σ0 = D(ξ)ε − D

(ξ0

) + �(ξ)ξs − �

(ξ0

)ξs0 + θ

(T − T0

)

(3.4)

Young’s modulus, D, highly depends on the martensite fraction of

he material (Eq. (3.5)) where Dm and Da represents the modulus of

MA with 100% martensite and 100% austenite, respectively. Their

athematical definitions mean that they are functions of martensite

olume fraction.(ε, ξ , T

) = D(ξ) = Da + ξ

(Dm − Da

)(3.5)

The material function, θ (ε, ξ , T), is assumed to be constant due

o its relatively small value, while the transformation function was

escribed as a function of martensite fraction (Eq. (3.6)) where εL is

he maximum residual strain of the wire.

(ξ) = −εLD

(ξ)

(3.6)

Eq. (3.4) and the transformation cosine function were used to find

he behavior of our SMA wires in this study. All the input parameters

or Brinson model were collected from experimental tests to form the

tress–temperature diagram (Fig. 4), describing the regions in which

he transformation happens. Having the phase transformation dia-

ram formed, we were able to define an external function in MATLAB

or the phase transformation kinetics. The material properties for each

iameter of the SMA wires were provided to the code from experi-

ents. Then a marching approach was followed based on Eq. (3.4) to

ll the stress, strain and temperature matrices while the martensite

raction at each step was predicted by the external function. For our

E model the constant stress, constant strain and isothermal stress–

train responses were desired. Therefore, while iterating on Eq. (3.4)

ur convergence criteria was to have one of these parameters to re-

ain constant at all steps. The isothermal stress–strain curves then

ere used as material properties of SMAs for the finite element model

s illustrated in Fig. 2.

Understanding the resistance heating of the SMA wires is impor-

ant because they are being used as actuators in our system. An iter-

tive approach to estimate the variation of temperature in the SMA

ires considering the major heat mechanisms such as environmental

onvection, resistance heating and latent heat difference due to the

hase transformation can be found in [23]. The energy generated in

he wire is contributed by Joule heating and latent energy of trans-

ormation. Our experimental results at room temperature on a single

MA wire showed that 10–15 s was required to cool down from 70 °Co room temperature (22 °C) for different wire diameters.

.2. Constant-stress test

The configuration set up for the constant-stress experiment is

hown in Fig. 5(a). The SMA wire was hung vertically under uniaxial

ensile loading. The movement of the weight hanger was tracked by

linear variable differential transducer (LVDT) (HSD 750-500, Macro

ensor, Pennsauken, NJ) with a nominal range of ±12 mm. The SMA

ire was activated thermally by Joule heating using a programmable

C power supply (BK Precision 1696, Yorba Linda, CA). A 0.003 in

-thermocouple (Omega Engineering, Stamford, CT) was attached to

he SMA wire. The output signals of both the thermocouple and the

VDT were collected using SCXI-1321 terminal block (National In-

trument, Austin, TX). To ensure complete austenitic transformation,

he wires were heated up to 80 °C.

472 B. Konh et al. / Medical Engineering and Physics 37 (2015) 469–477

Fig. 5. Experimental setup for (a) constant stress and (b) constant strain tests.

Fig. 6. Geometry and mesh of the active needle created in ANSYS.

Fig. 7. Experimental setup for measuring the deflection of the active needle prototype.

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3.3. Constant-strain test

When thermally activated, the actuator contracts due to its higher

temperature and shorter length. The experimental constant-strain

setup is illustrated in Fig. 5(b). The SMA wire was activated using

Joule heating by applying current as a ramp function. Force response

of the SMA wire was measured using a 22.7 N load cell (Futek Advance

Sensor Tech, Irvine, CA). The load cell signal was collected using SCXI-

1314 DAQ system. Similar to the constant-stress experiment, wire

temperature was measured using the k-thermocouple. A linear stage

(Edmund Optics, Barrington, NJ) was used to set a specific pre-strain

on wires.

4. Structural behavior of the active needle

4.1. Finite element model

A 3D finite element model of the active needle (Fig. 6) was de-

veloped in ANSYS to predict the needle deflection while actuated by

the attached SMA wire. The cannula (representing needle) and the

wire were chosen to be 100 mm long, attached to an 18 mm diameter

and 0.83 mm thick stainless steel disc. Aluminum was chosen as the s

aterial for the cannula for its flexibility. The cannula’s inner and

uter diameter was 0.88 mm and 1.59 mm, respectively. A total num-

er of 32,442 nodes and 23,805 elements were used for the whole

ctive needle structure. Mesh has been refined in the areas of contact

etween the needle, holder and the SMA wire. In this model the ele-

ents’ birth and death was interested to form three load steps similar

o the real experiment (explained below). Considering that this op-

ion was not supported by LINK180 elements, SOLID65 elements were

hosen for both needle and the actuator.

The maximum contraction of the SMA wire depends on its initial

re-strain prior to actuation. Birth and death capability of ANSYS was

sed before increasing the wire temperature to set a certain pre-strain

n SMA elements. The solver consists of three steps: First, a tensile

ressure load was applied to the holder while all cannula elements

ere killed (removed from the structure) that resulted in tensile stress

n the needle. Then the cannula was inserted to the structure (making

he elements alive) and the tensile load was removed. These changes

long with the internal energy stored in the wire from previous step

esulted in an equilibrium position with tensile stress in SMA wire

nd a small compressive stress in the needle. Lastly, the wire tem-

erature was increased from room temperature to 80 °C (above As)

hat caused the SMA wire to contract and consequently bends the

eedle. Although, only the loading part is presented in this study, the

odel is able to predict the unloading stage of the wires as well. In

rder to model the unloading, another step should be included in the

olver which is similar to the first step where the SMA feels the can-

ula’s tendency to go back to its initial shape. Following this method,

loop can be formed in the FE model to show the SMA’s repetitive

oading-unloading behavior. Also, in order to assess the 1D Brinson

odel with our 3D model, a preliminary model of a simple cube with

nly four elements was developed. The expected strain response (5%)

as observed after the three steps of solutions, thereby showed that

rinson model is suitable for our FE model.

.2. Prototype experimentation

The structure shown in Fig. 7 was developed to validate the finite

lement analysis. The structure consisted of an aluminum hollow

annula (Din = 0.88 mm, Dout = 1.59 mm) actuated by FLEXINOL SMA

ires, nickel-titanium alloy (Dynalloy Inc., Tustin, CA) which were

ttached by an 18 mm diameter stainless steel holder. Two other can-

ulas with inner/outer diameter of 1.67/2.38 mm and 2.46/3.18 mm

ere also developed. The size of the needles used in conventional

urgeries (for example for brachytherapy) are in the range of 18 gauge

OD = 1.27 mm) which is comparable to the cannula’s diameter pre-

ented in this work. It should be noted that in minimally invasive

B. Konh et al. / Medical Engineering and Physics 37 (2015) 469–477 473

Table 1

Material properties of the SMA wire obtained from experiments and the structural design parameters and

their variation range.

Parameters Description Values Unit

SMA wire σ s Critical start transformation stress 130 MPa

σ f Critical finish transformation stress 170 MPa

EM Martensite Young’s modulus 32.5 GPa

EA Austenite Young’s modulus 90 GPa

εmax Maximum residual strain 0.05 1

Mf Martensite finish transformation 25.0 °CMs Martensite start transformation 31.0 °CAs Austenite start transformation 34.2 °CAf Austenite finish transformation 38.4 °CCM Clausius–Clapeyron coefficient 12.0 MPa/°CCA Clausius–Clapeyron coefficient 16.6 MPa/°C

Structure Ecannula Cannula’s Young’s modulus 70-200 GPa

Din/Dout Cannula’s inner/outer diameter 0.88/1.59 to 2.46/3.18 mm

DSMA SMA diameter 0.20, 0.23, 0.29 mm

σ p SMA pre-strain 0.01–0.05 1

A Offset between SMA and cannula 3.0–7.0 mm

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urgeries a minimized tissue puncture diameter is always desirable.

MA wires with diameters ranging from 0.20 mm to 0.29 mm were

sed as actuators. The SMA wires were stabilized prior to the instal-

ation in the prototype in order to maintain a consistent actuation

erformance. The constant stress setup (shown in Fig. 5(a)) was used

or this purpose. While stress was kept constant at 300 MPa, a cyclic

emperature was applied until the response is stabilized. The dis-

ussion on the differences between the initial and following loading

ycles can be found in our previous work [24]. The offset between

he SMA wire and the neutral axis of cannula was 7.0 mm. The offset

as maintained using a drilled hole on the holder. Prior to actuation,

fixed amount of pre-strain was set on all actuators. The distance

etween the collets was set in a way to maintain εtmax = 5% on each

MA wire diameters. The Joule heating method was used to actuate

he SMA wire. The amount of deflection was quantified by taking

ictures of the deflection with the background of a graph sheet. The

ictures were captured using a high speed camera (Fastec inline cam-

ra, Fastec Imaging, San Diego, CA) and are then processed using the

mageJ software 1.45 s (National Institutes of Health, Bethesda, MD).

The FE model was validated using three prototypes of different size

models of Table 1). A wide range of Young’s moduli were selected

or the cannula. The conventional needles are made of steel, carbon-

ber, titanium and Nitinol which their stiffness is in the selected

ange of this study. Table 1 also lists the material properties of SMA

ire of 0.20 mm diameter. The values were obtained experimentally

or a stress free SMA wire. Using these values the internal phase

ransformation can be predicted by the model.

Fig. 8. Comparison of (a) stress–temperature and (b) strain–temperature re

. Verification of the thermomechanical response with

xperiment

.1. Evaluation of thermomechanical behavior of SMA wires via

umerical and experimental approaches

In Fig. 8(a), the stress–temperature response of 0.48 mm SMA

ire simulated using the Brinson model and that determined

rom the constant-strain experiment was compared. The hysteresis

ehavior of the SMA wire in stress–temperature response is because

f the internal phase transformation which begins at different

emperatures (As and Ms) in the heating and cooling parts. The

ame trend was observed with the stress–strain curves which

s explained below. The mismatches could be explained by the

rrors encountered in measuring the transformation temperatures

nd Clausius–Clapeyron slopes, primarily resulted from difficulty

ith the current experimental setup, especially due to crimp and

hermocouple attachments. A thermal paste was used in this study

o have the best possible connection between the wire and the ther-

ocouple. However, another way which would potentially enhance

he temperature measurement is to use laser welding (short pulse)

n the joint area. In order to verify the material model’s accuracy with

NSYS, a FE model of the wire was developed in ANSYS. SOLID65

as chosen as the element type. A 100 mm long wire was subjected

o constant pressure at one end while fixed at the other end. The

ransformation to austenite happened when the wire’s temperature

as increased from room temperature (22 °C) to 80 °C at 140 MPa.

sponse of SMA wires obtained using Brinson model and experiment.

474 B. Konh et al. / Medical Engineering and Physics 37 (2015) 469–477

Fig. 9. Isothermal stress–strain curves for the SMA wire diameter of 0.20 mm; the

experimental tensile test results have been shown.

Fig. 10. Deflection of the needle using birth and death method in ANSYS.

Fig. 11. Maximum deflection achieved with a 0.20 mm SMA wire for three differ-

ent prototypes of Din/Dout as (a) 0.88 mm/1.59 mm, (b) 1.67 mm/2.38 mm and (c)

2.46 mm/3.18 mm.

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t

The model was compared with experimental results (Fig. 8(b)). The

final strain in the wire was predicted exactly the same using both

methods. The difference in the slope of the transformation region

could be explained by different response time of wires during the ex-

periment. The small size of the wire and the thermocouple and their

poor connection could also cause inaccuracies in the temperature

measurement, thereby some deviation to the numerical prediction.

The isothermal response of the 0.20 mm diameter SMA wire at

different temperatures is presented in Fig. 9. During the initial steps

of loading, the material shows a linear response upon applied stress.

However, after reaching a critical amount of stress, the material goes

through a phase transformation where a large strain and low stiff-

ness is observed. This sort of stress response is comparable to the

plastic deformation. Once transformation is complete, the material

gets stiffer and once again the linear response is observable (complete

austenite phase). At low temperatures (T < As), applying stress causes

the transformation from twinned to detwinned martensite. The de-

twinning process makes the multiple martensite variants convert to

a single variant, by the alignment of the habit planes with the axis

of loading and consequently a large amount of residual strain. This

large amount of strain at higher temperatures (T > As) is caused by

the transformation from austenite to martensite. For lower temper-

atures, the incomplete transformation leaves a large residual strain

in the material upon unloading. This residual strain can be recovered

by heating the material above Af. For temperatures lower than Af,

there would be a partial recovery due to the presence of both phases.

For the temperatures above Af (pseudoelasticity effect), the material

will recover completely. Also included in Fig. 9 is the experimental

stress–strain curve of 0.20 mm SMA wire. An Instron Mini-55 (Arti-

san Technology Group, Champaign, IL) tensile machine was used to

obtain the tensile curve at room temperature (22 °C). A displacement

control of 4 μm/s was applied and the stress response was captured

via a 10 N load cell. The mismatches can be explained by differences

in values assigned to the martensite Young’s modulus.

5.2. Verification of FE model with the prototype

The needle deflection obtained by the FE model is shown in Fig. 10.

Three prototypes with the configurations described in Section 4.2

were used to validate the FE model. The maximum deflection was en-

sured by setting the highest pre-strain condition (equal to the maxi-

mum transformation stain of 5%) and by applying enough current. For

the smallest (Din = 0.88 mm, Dout = 1.59 mm) and the medium size

(Din = 1.67 mm, Dout = 2.38 mm) cannula the maximum deflection of

27 and 18 mm, respectively, was observed (Fig. 11(a) and (b)). Also as

can be seen in Fig. 11(c) for the biggest size of cannula (Din = 2.46 mm,

Dout = 3.18 mm) the maximum vertical deflection of 14 mm was

aptured. Table 2 compares the deflection of different cannulas

ctuated by different SMA wires with the FE model predictions. The

ifference of less than 10% validated our FE model.

.3. Thermal expansion method as a simplified FE model

A simplified approach was used to develop a FE model of the SMA

ctuated needle. In this approach the strain response of the SMA wire

as approximated while thermally actuated above As. To have a good

pproximation the constant-stress experiment described above was

epeated for different stress levels to find the contraction range of

he wire (Fig. 12). This strain response of the wire was estimated

B. Konh et al. / Medical Engineering and Physics 37 (2015) 469–477 475

Table 2

The maximum deflection of active needle measured from prototypes and predicted by FE model.

Prototype Din = 0.88 mm, Dout = 1.59 mm Din = 1.67 mm, Dout = 2.38 mm Din = 2.46 mm, Dout = 3.18 mm

FE model using nonlinear stress–strain curves

SMA Test FEM %error Test FEM %error Test FEM %error

0.20 mm 27 28.27 4.70 18 16.32 −9.33 14 12.71 −9.21

0.23 mm 28 30.77 9.89 19 17.39 −8.47 15 13.22 −11.86

0.29 mm 30 34.92 16.40 21 21.08 0.38 17 15.56 −8.47

Simplified FE model explained in Section 5.3

SMA Test Simplified FEM Nonlinear FEM %error with test %deviation of two FEMs

0.20 mm 27 28.56 28.27 5.78 1.02

0.23 mm 28 31.43 30.77 12.25 2.14

0.29 mm 30 33.88 34.92 12.93 2.98

Fig. 12. Strain response of 0.20 mm SMA wire under different constant stresses.

b

E

r

t

t

w

α

α

6

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t

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s

c

p

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t

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Table 3

Parameters used for optimization study.

Input parameter Initial design point Lower bound Upper bound

εL (%) 5.00 4.50 5.50

DSMA (mm) 0.20 0.08 0.30

Doutcannula (mm) 1.50 1.30 2.00

Dincannula (mm) 1.00 0.50 1.29

Doutholder (mm) 15.0 10.0 20.0

Dinholder (mm) 5.0 4.5 6.0

Offset (mm) 7.00 2.00 8.00

th (mm) 1.00 0.90 1.10

L (mm) 100 80 120

L1 (mm) 1.00 0.90 1.10

w

w

(

b

w

T

m

m

w

m

t

m

1

a

a

i

e

d

w

A

l

i

v

y defining the thermal expansion coefficient, α, as shown in the

qs. (5.1) and (5.2). This value of α was producing the same strain

esponse as the wire temperature rises from As to Af. FE model with

he same geometry and dimension as described above was used in

his approach. Element BEAM188 and SOLID185 were used for the

ire and the cannula, respectively.

= H

As − Af

(5.1)

= −0.0096 ◦C−1. (5.2)

. Optimization of the active needle design

Iterative analysis tools presented in Section 2 (Figs. 2 and 3) were

tilized here to aid the design process. Several design variables were

aken into consideration to accomplish this task. In order to have a

ower computational time in the structural iterative assessments, the

implified model (presented in Section 5.3) was used instead of the

omplete FE model (presented in Section 4.1). Moreover, the sim-

lified model provides global results of deflections and forces with

easonable accuracies. Table 2 lists the deflection of the active needle

redicted by the simplified model compared with the first proto-

ype. It is also shown that the results of the FE model with nonlinear

tress–stress curves are very close (with less than 3% deviation) to

he simplified model. It should be noted that only the final deflection

f the structure can be trusted with the simplified model since the

onlinear hysteresis response of SMAs cannot be predicted by the

hermal expansion coefficient defined in this method. Assigning one

imensional element to SMA wire can lead to some degree of errors

n the amount of stress; therefore a 100% safety factor was consid-

red to avoid the plastic deformation. The objective in our design

tudy was to achieve the maximum possible needle tip deflection to

nsure the maximum flexibility while constraining the stress of SMA

ire to be less than a critical level. The input design variables selected

ere:

• εL: maximum residual strain of SMA wires with different

diameters• DSMA: SMA wire diameter• Doutcannula/Dincannula: cannula’s outer/inner diameter• offset: the offset distance between the neutral axis of cannula and

SMA wire• Doutholder/Dinholder: outer/inner diameter of the holder• th: the thickness of the holder• L: total length of the cannula• L1: holder length

The total deflection of the needle tip (δtip) and the maximum stress

σ max) of all elements were taken as desired output variables. The

aseline design point and the range of variation of each parameter

hich were used in our goal driven optimization study are listed in

able 3. Starting from the initial baseline design point we sought the

aximum needle tip deflection with the constraint that the SMA’s

aximum stress must be lower than 150 MPa. The optimization task

as done using two approaches: design of experiments (DOE) and

ulti-objective genetic algorithm (MOGA). It should be noted that

he selected bond for the offset makes the overall scale of the needle

uch larger than the conventional needles (which are in the range of

8 gauge � OD = 1.27 mm). In order to have a needle this small,

nother method for attaching SMA wires is preferable. Therefore

nother design was introduced by the same authors [25] to elim-

nate the collet component completely. In this work however, the

ffect of offset along with the other effective design parameters is

iscussed.

The DOE task, which is a non-iterative direct sampling method,

as performed by choosing 100 random possible configurations by

NSYS. The analysis showed that, among all input parameters, the

ength of the cannula and the offset distance are the most influenc-

ng parameters on the needle tip deformation. Fig. 13(a) shows the

ariation of needle tip deflection (the objective parameter) based on

476 B. Konh et al. / Medical Engineering and Physics 37 (2015) 469–477

Fig. 13. Optimization results from the DOE method. (a) Visualization of the objective parameter with variation of cannula’s length and offset distance and (b) five best candidate

design points.

Fig. 14. Optimization results from the MOGA method. (a) Visualization of the objective parameter with variation of cannula’s length and offset distance and (b) ten best candidate

design points.

r

D

o

D

v

a

p

i

o

i

c

e

t

s

i

these two sensitive parameters for all the 100 design points. The five

best configurations having the maximum deflection are shown in

Fig. 13(b).

The MOGA study was also performed that provided a more refined

approach to find the best design configuration. This optimization al-

gorithm started with the initial design point (Table 3) and iterated

through the whole domain with the samples evolving genetically un-

til the best case was found. The convergence achieved after 11 total

iterations and 594 evaluations resulted in 10 best candidates for the

active needle design which are shown in Fig. 14(b). Also among all

input parameters the offset, the cannula’s length and the cannula’s

outer diameter were shown to be the most influential parameters on

the needle tip deflection. The variation of the tip deflection based on

variations of the two sensitive parameters (the total length and the

offset) is shown in Fig. 14(a).

Table 4 compares the best candidate design points obtained

from DOE and MOGA methods. It was observed that almost similar t

esults were obtained using the two methods. The offset and the

SMA values show a deviation of 41 and 39%, respectively. It was

bserved that the values of the five best candidates suggested by the

OE method do not show a specific trend so that a certain converged

alue can be interpreted. Comparing the best five candidates of DOE

nd MOGA method leads to a more or less deviations within different

arameters. The calculation time using MOGA was lower because

terations were done using genetic algorithm, therefore less number

f assessments/iterations was required. This suggests that MOGA

s a preferred optimization method over DOE, because results were

onverged a shorter time.

As a clinical aspect, the tissue damage due to existence of heated

lements of actuators has to be investigated thoroughly. The degree

o which real tissue is damaged due to the heated SMA wires was

tudied using a phantom that shares the tissue’s thermal properties

n our previous work [26]. In most cases the tissue necrosis occurs at

emperatures above 50.4 °C as reported in [27]. The thermal damage

B. Konh et al. / Medical Engineering and Physics 37 (2015) 469–477 477

Table 4

Comparison of the optimized design points obtained from DOE and MOGA methods (all dimensions are in mm).

εL (%) DSMA Cannula Holder Offset th L L1 Maximum deflection

Dout Din Dout Din

DOE 4.68 0.15 1.36 1.09 16.44 5.46 4.37 0.92 118.54 1.06 45.93

MOGA 4.65 0.24 1.46 0.98 17.02 5.08 2.01 1.01 118.64 0.99 45.84

c

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w

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t

t

n

fl

o

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s

m

p

p

C

A

P

R

[

[

[

[

[

[

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[

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an be avoided by actuating the wires for a very short period of time

r by thermally insulating the wires.

. Summary

This study demonstrates the modeling, analysis and optimization

f a shape memory alloy actuated needle using finite element ap-

roach. The nonlinear, hysteretic dependent material model of SMAs

as defined as a multilinear function for the finite element software.

he accuracy of the finite element model was established by

xperiments. A design optimization study was also performed with

he objective of maximizing the needle tip deflection to ensure the

ighest steerability of the active needle. Suitable design parameters

ere presented using two different methods: design of experiments

DOE) and multi-objective genetic algorithm (MOGA). The length of

he SMA wire as well as the offset distance between the needle and

he SMA wire were found to be the most effective parameters on the

eedle deflection. The optimized design resulted in a maximum de-

ection of 45.84 mm with a 118.64 mm long SMA wire. The amount

f tissue damage due to the heating elements of actuators depends

n two factors: the actuator’s temperature and the time the tissue is

ubjected to heat. The propagation of the damage zone inside a ther-

al sensitive phantom due to the heated wires has been shown in our

revious study [26]. Insulation of SMA wires with a low conductive

olymer is under investigation by our group.

onflict of interest

None.

cknowledgment

This work is supported by the Department of Defense CDMRP

rostate Cancer Research Program (Grant # W81XWH-11-1-0398).

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