Towards the Development of a SMA-Actuated MRI-CompatibleTendon-Driven Neurosurgical Robot

Mingyen Ho,Student Member, IEEE, and Jaydev P. Desai,Senior Member, IEEERobotics, Automation, and Medical Systems (RAMS) Laboratory, Department of Mechanical Engineering

Maryland Robotics Center, Institute for Systems ResearchUniversity of Maryland, College Park, MD, USA

Email: myho@umd.edu, jaydev@umd.edu

Abstract— In this paper, we present the design and devel-opment of a magnetic resonance imaging (MRI)-compatibletendon-driven robot to overcome the limitations of our previousminimally invasive neurosurgical intracranaial robot (MI NIR).In this prototype, the robot is made of plastic and the MRI-compatible shape memory alloy (SMA) actuators are placedaway from the robot. The robot has four revolute joints whichare placed orthogonally to have out-of-plane motion capability.Each joint is connected to a pair of antagonistic SMA springactuators through the tendon-sheath mechanism. Each SMAspring actuator can be controlled independently to actuatethe corresponding joint. A theoretical model and experimentalsetup have been developed to evaluate the recovery force of theSMA spring at different displacement and temperatures. Theexperimental results closely match the theoretical model and itshows significant promise for future development in this area.A series of MRI compatibility tests have also been performedto evaluate the MRI compatibility of the device and to assessthe degradation in image quality, if any, during actuation. Theexperimental results clearly demonstrate that the robot isMRI-compatible and it creates no significant distortion in the MRimages during actuation.

I. INTRODUCTION

Currently, the optimal treatment for most brain tumorsinvolves primary surgical resection to remove as much tumoras possible. However, due to practical difficulties in accessingthe tumor, especially those situated deep inside the brain,coupled with the lack of excellent imaging modality for intra-operative use, it is sometimes difficult to remove the tumorcompletely. As a result, the median survival for patientswith brain tumor is only 4-8 months [1]. In this paper,we present our work on the latest generation of MINIR toovercome the above limitations. MINIR is designed to beoperated inside MRI scanners and resect brain tumor bypositioning surgical auxiliaries, such as electrocuateryandsuction/irrigation systems, that liquefy tissue and wash outthe debris. MINIR will be inserted through a surgical corridordissected by the physician. Fig. 1 shows a schematic of theenvisioned function of MINIR and it will be controlled by aphysician with real-time MR images as visual feedback.

In the area of MRI-compatible surgical robots, severaldesign and actuation techniques have been explored. A MRI-compatible pneumatically actuated robot for breast biopsyis

This work was supported in part by the National Institutes ofHealth(NIH) grant R21 EB008796 and 2011 UMCP-UMB research seed grantprogram.

Tumor

MINIR Surgical corridor

Fig. 1. Envisioned function of MINIR.

currently being developed by Yanget. al [2, 3]. A MRI-compatible 6-DOF liver surgery manipulator actuated by ahydraulic system was built in [4]. The MRI-guided needle in-sertion robots manufactured using polyethylene terephthalate(PET) and actuated using ultrasonic motors were developedin [5, 6]. A review of MRI-compatible systems for image-guided interventions can be found in [7]. Although theserobots themselves are small, the actuation mechanisms usedin these robots are relatively large. This makes the use ofthese robots in MRI room challenging. Besides, some of therobots only have one DOF and cannot be used to reach thetarget which is not in the “line-of-sight”.

Among MRI-compatible actuation techniques, SMA actu-ators have received attention due to its high power density.SMA has a special ability to memorize its shape at alower temperature and recover large deformation on thermalactuation. When a deformed SMA spring is heated above thetransformation temperature, it tends to recover its original(memorized) shape and generate a significant force. Thisphenomenon is called the shape memory effect (SME). Therecoverable strain of SMA can be up to a maximum ofabout 8% [8] and it can generate significant forces duringphase transformation due to its three- to four-fold increase inYoung’s modulus in austenite phase compared to martensitephase [9]. Moreover, SMA has high corrosion resistance,small size, light weight and is noiseless when actuated, whichmake SMA a good actuator candidate for medical devices,such as [10].

In this paper, to evaluate the potential of using SMAsprings as actuators in a neurosurgical robot, we discuss the

design of the robot in section II and present the modelingof a SMA spring in section III. Section IV describes theexperimental setup and section V shows the experimentalresults of SMA spring characterization as well as the MRIcompatibility of the robot. Finally, in section VI, we makesome concluding remarks.

II. ROBOT DESIGN

A. Tendon-driven neurosurgical robot

The design of MINIR presented in this paper was modifiedbased on the features of our previous prototype [11]. Inthe previous prototype, we used tendon-driven mechanismto actuate the robot. However, a pulley is required for eachtendon and all tendons have to be under tension continuously.Furthermore, the pulleys occupy a significant amount ofspace in the robot and make the routing of suction/irrigationtubes and electrocautery wires difficult. Since MINIR is tobe inserted into the brain through a flexible surgical corridor,it is difficult to keep all tendons in tension. To overcome thislimitation, we re-designed the robot with the tendon-sheathactuation mechanism. The major advantage of tendon-sheathactuation mechanism is that it can be used to transmit forcesthrough a long, narrow and flexible route while taking upvery little space. For this reason, the mechanism is widelyused in several robotic areas, such as [12–14].

Tendon-sheath actuation mechanism consists of hollowtubes (usually helical coils) and cables routing through thetubes. The cable serves as the tendon and the hollow tubeacts as the sheath to guide the cable. When a tendon is pulledat one end, it moves inside the sheath and transmits forcesto the other end of the cable. In this paper, two antagonisticSMA spring actuators were connected to a pulley through thetendon-sheath mechanism for each joint, as shown in Fig. 2.

The robot contains a tip link, a bottom link, three cylin-drical links and four revolute joints as shown in Fig. 3.Each tendon is routed through a sheath which is used toguide the tendon through a curved path. The sheaths aremore rigid than the tendons and hence helps to kinematicallydecouple various joint motion. Each joint has an independentsingle degree of freedom controlled by a pair of SMA springactuators and the motion range of each joint was designedto be±60. The robot is 63.5 mm in length and the largestdiameter is 12.5 mm which is very close to the 11.5 mmsurgical corridor for some endoscopic brain surgery [15].

B. SMA spring actuation system

SMA is a good actuator material, however, the currentused for resistive heating can cause noise in the MR im-ages [16, 17]. In this paper, we used SMA spring actuatorsand tendon-sheath mechanism to design our new actuationsystem so that the actuators can be placed away from therobot and outside the patient’s brain. This design will notonly minimize the MR image noise but also prevent thedamage to healthy brain tissue caused by the heat generatedby the current in SMA actuators. The envisioned actuationsystem of MINIR is shown in Fig. 4 and the envisioned

SMA spring actuators SheathsTendons

Fig. 2. Antagonistic SMA springs actuation mechanism.

Fig. 3. Schematic of MINIR.

Fig. 4. Schematic of the envisioned system of MINIR.

electrocautery and suction/irrigation system is also shown inthe same figure.

III. SMA SPRING MODELING

A. Constitutive model of SMA

The nonlinear thermomechanical properties of SMA de-pend on many variables, such as: manufacturing process,dimension, pre-strain, stress level, temperature, annealingcondition, and thermomechanical history. Several constitu-tive models have been proposed to describe this uniquephenomenon. Among those models, Tanaka [18], Liangand Rogers [19] and Brinson [20] are commonly used toquantitatively predict and describe the thermomechanicalbehavior of SMA. Based on those tensile models, Tobushiand Tanaka [21] further used similar equations to describeSMA behavior under pure torsional load. Considering thereis a pure shear stress in the cross-section of a SMA wire. Thegeneral relation between shear stress,τ , and shear strain,γ,can be expressed as [9]:

τ = Gγ +Θ√3T +

Ω√3ξ (1)

whereG, Θ, T , Ω and ξ represent the shear modulus, thethermal expansion coefficient, temperature, phase transfor-

D

F

d'

d'

d#

ds

r

dx

L3

Fig. 5. Schematic of a spring.

mation coefficient and the martensite volume fraction ofSMA, respectively. In this model, the strain, temperature,and martensite volume fraction are assumed to be indepen-dent state variables. Assuming that the SMA is initially atroom temperature (ξ0 = 1) and the thermal expansion effectis much smaller than the phase transformation effect, theconstitutive equation of SMA under pure torsional load canthus be simplified as:

τ − τ0 = G(γ − γ0) +Ω√3(ξ − 1) (2)

B. Force-displacement relation of SMA springs

We assume that there is pure shear in the cross-section ofa SMA wire of a spring when the spring in under tension.Since the analysis of conventional springs is standard andavailable in most mechanical design text books, such as [22],only some important concepts will be mentioned here forcontinuity. The displacement of a spring can be computedfrom the deformation of an element in the spring as shownin Fig. 5. The length of the element isdx and the radiusof the spring wire isr. An external force,F , acting on thespring results in a pure shear stress,τ , in the element. Theshear stress causes a rotation ofdθ in the element and theshear strain,γ, can be defined as:

γ =ds

dx(3)

Based on the geometry of the element, we have:

ds = γdx = rdθ (4)

In the figure, we can see that the rotation,dθ, will contributeto the spring deflection in the vertical direction by an amountof dδ and it is given as:

dδ = Ldθsinϕ =Dγ

2rdx (5)

whereD is the diameter of the spring. The total deflection ofspring,δ, can be obtained by integrating the above expressionfor entire length of the spring and is given by:

δ =

∫dδ =

Dγ

2r

∫ πDN

0

dx =πD2N

2rγ (6)

whereN is the total number of active coils in the spring.According to [22], the shear stress,τ , in the spring causedby external force,F , is given by:

τ = ksFD

πr3(7)

F0F0

L /0

FF

L /0

Fig. 6. Schematic of the SMA spring recovery force analysis.

whereks is the Wahl correction factor, which accounts forboth the curvature effect and the shear stress correctionfactor.

For a specific SMA material, the phase transformationcoefficient (Ω) can be expressed as [19]:

Ω = −E(ξ)εL (8)

whereE(ξ) is the Young’s modulus andεL is the maximumrecoverable strain of SMA. The Young’s modulus of SMAvaries with temperature and is given by:

E(ξ) = EA + (EM − EA)ξ (9)

whereEM andEA are the Young’s modulus in the martensitephase and austenite phase, respectively. The shear modulus,G, can be computed using:

G =E(ξ)

2(1 + ν)(10)

whereν is the Poisson’s ratio and is about 0.3 for SMA [9].With the above equations, a thermomechanical behavior of

SMA can be modeled by substituting equation (6), (7), (8)and (10) into equation (2), which yields:

C1(F −F0) = C2E(ξ)

2(1 + ν)(δ− δ0)−

E(ξ)√3εL(ξ− 1) (11)

whereC1 andC2 are constants and defined as:

C1 =Dks

πr3, C2 =

2r

πD2N(12)

The above equation (11) can be used to describe the force-displacement (F ∼ δ) relation of a SMA spring.

C. SMA spring recovery force analysis

Consider a SMA spring attached to a force sensor at oneend and fixed at the other end, as shown in Fig. 6. Assumethat the initial force and displacement in the spring areF0

and δ0 at room temperatureT0. As the spring is heated totemperatureT (above transformation temperature), it startsto contract and causes the recovery force in the spring toincrease. In this paper, we assume that the stretch in thetendon is small and hence negligible and the recovery forceincreases fromF0 to F and the displacement changes fromδ0 to δ. The recovery force, displacement and temperatureare related according to equation (11). Since the two endsof the spring are fixed, the displacement of the spring willnot change (δ = δ0) when the spring is heated. As a result,equation (11) can be re-written as:

C1(F − F0) = −E(ξ)√

3εL(ξ − 1) (13)

25 30 35 40 45 50

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5Recovery force vs. temperature at different displacement (simulation)

Temperature (°C)

Forc

e (

N)

δ0 = 0mm

δ0 = 2mm

δ0 = 4mm

δ0 = 6mm

δ0 = 8mm

δ0 = 10mm

Fig. 7. Recovery force of the SMA spring at different temperatures anddisplacement (simulation).

The martensite volume fraction,ξ, is defined as the ratioof the total volume of martensite to the total volume ofSMA. This parameter is a function of shear stress andtemperature [21]. For heating transformation, the parametercan be expressed as:

ξ = ebAcA(As−T )+bAτ (14)

where (bA, cA) are constants defined by transformationtemperatures (As, Af ) respectively. Sinceξ is dependent onthe shear stress,τ , in (13), the recovery force,F , at giventemperatures and displacement should be solved numerically.

Since the desired motion range of each joint of MINIRis ±60 and the diameter of the pulley used for MINIRis 8 mm, the required displacement of each SMA springactuator is±5 mm. Therefore, we used 0 mm to 10 mmas the testing range of displacement in the SMA recoveryforce experiment. The transformation temperatures,As andAf , of the SMA spring were tested to be 30C and 45Crespectively. Fig. 7 shows the simulated recovery force ofa 6.22 mm diameter SMA spring (the diameter of the wirein the SMA spring was 0.76 mm) at different temperaturesand displacement. Based on the simulation results, the SMAspring can generate 2.4 N to 5.3 N of force at 50C, whichis sufficient for our application. Since the previous prototypeof MINIR can only generate 1.4 N of force [23], we can saythat the new MINIR has higher force exertion capability.

IV. EXPERIMENTAL SETUP

For the experimental setup design, we followed the sug-gestions of ASTM standard F2082-03. This standard de-scribes the standard procedures to test the transformationtemperatures of NiTi SMA. However, it can be easily ex-tended to perform the tests for displacement vs. temperatureand force vs. temperature by using a displacement sensorand a force sensor, respectively.

In this paper, we developed a PC-based system to test theperformance of the SMA spring as shown schematically inFig. 8. The system consists of a motor, a force sensor, athermocouple, a DC power supply, a PWM controller and adata acquisition card. The motor is used to stretch the SMAspring to the desired displacement and is equipped with a

A/D

D/A

SMA spring

Force

sensor

Motor with

encoder

PWM

DC

Thermocouple

Fig. 8. Schematic for SMA spring recovery force test.

rotary encoder. The force sensor is used to measure the re-covery force generated by the spring. A T-type thermocoupleis used along with thermally conductive paste to measurethe spring temperature. Thermally conductive paste has highthermal conductivity and high resistance, which is used toensure heat transfer while preventing electric noise. Weassumed that the electrical resistance of the SMA spring isconstant throughout the entire spring and that the temperaturedistribution in the SMA spring was homogeneous. The DCpower supply was used to heat up the SMA spring and aPWM controller was used to control the temperature in theSMA spring. The details of the PWM temperature controlscheme has been discussed in [16, 17]. All experimental dataand control signals were transferred to a PC through a dataacquisition card which has sixteen 16-bit A/D channels andfour 14-bit D/A channels with 15kHz sampling rate. Theentire experimental setup except the PC was put inside achamber to ensure stable measurements of temperature.

V. EXPERIMENTAL RESULTS

A. Motion test of MINIR

The goal of this experiment was to evaluate if the tendon-sheath mechanism and the SMA spring actuators can beused to actuate various joints of MINIR. We used fourSMA springs to actuate two links of MINIR as shownin Fig. 9. The experimental results showed that the twojoints of MINIR can be moved independently and repeatablemotion was observed. The motion range of each link was±45 and the maximum output force of each link wasmeasured to be 2 N when the SMA spring was heated to50C. It took about 4 seconds to heat the SMA spring to50C and 45 seconds to naturally cool it down to 30C.The entire neurosurgical procedure usually takes hours tocomplete, thus, the slow response of SMA is not a limitationin our application. In fact, the robot should move slowlyduring electrocauterization to ensure that the tumor has beencompletely and safely removed.

B. SMA spring recovery force test

In this experiment, the SMA wire was stretched to adesired length by a DC motor and then heated to specifictemperatures while the corresponding force readings wererecorded. The experimental setup is shown in Fig. 10 andthe experimental results of the recovery force vs. temperatureof a NiTi SMA spring at various displacement are shownin Fig. 11. In the figure, we can see that the SMA spring

TendonSheath TendonSheath

SMA springsMINIR Tendon

Fig. 9. The motion test of MINIR actuated by SMA spring actuators.

SMA spring

Motor with

encoderForce sensor

Thermocouple

Fig. 10. Experimental setup for SMA spring recovery force test.

20 25 30 35 40 45 50

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5Recovery force vs. temperature at different displacement (experiment)

Temperature (°C)

Forc

e (

N)

Exp. data (δ = 0mm)

Exp. data (δ = 2mm)

Exp. data (δ = 4mm)

Exp. data (δ = 6mm)

Exp. data (δ = 8mm)

Exp. data (δ = 10mm)

Predicted data (δ = 0mm)

Predicted data (δ = 2mm)

Predicted data (δ = 4mm)

Predicted data (δ = 6mm)

Predicted data (δ = 8mm)

Predicted data (δ = 10mm)

Fig. 11. Recovery force of the SMA spring at different temperatures anddisplacement (experiment).

can generate significant amount of force (up to 5.2 N) whenheated above the austenite finish temperature (45C in thiscase). Moreover, the results are repeatable and consistentwith the theoretical model presented in section III. Thisimplies that the recovery force–temperature–displacement re-lation of a SMA spring is predictable, and equation (11) canbe used as the governing equation for feedback control. Forexample, if the displacement,δ, is measured, the temperature,T , can be used as a feedback signal for force control. Thisis a very important observation since there are not manysensors that can be used in a MRI environment.

C. MRI compatibility test

In this section, we did experiments to show that MINIR isMRI compatible and causes no significant noise in the MRimages. In our experiments, we used gelatin to simulate braintissue and the MR images of gelatin was the ground truthfor comparison. To quantify the induced disturbance to theMR images, we obtained the signal-to-noise ratio (SNR) of

(b)(a)

Signal ROI

Noise ROI

Signal ROI

Noise ROI

Fig. 12. Static MR images: (a) Static MR image of gelatin and (b) StaticMR image after placing the MINIR in the MRI scanner.

Fig. 13. Dynamic MR images at: (a) 5th second (before actuation), (b)25th second (during actuation) and (c) 35th second (after actuation).

the images, where SNR is defined as the ratio of the meanpixel intensity of signal in a region of interest (ROI) to thestandard deviation of the pixel intensity of the backgroundnoise in a ROI. Fig. 12(a) shows the static MR image ofgelatin and the SNR was computed to be 168.4. We then putthe robot inside MRI and the tip of the robot is in contactwith the gelatin. Same settings were used to take another MRimage as shown in Fig. 12(b). In the image, no significantdistortion was observed and the SNR was computed to be160.5, which is only 4.7% lower than the ground truth. Theresults show that the materials we used to build the robotare not only MRI compatible but they also do not producea significant degradation in the signal.

Since we have confirmed that the robot is MRI compatible,the next step is to evaluate the effect of the current that isused to actuate SMA spring actuators. There were four SMAsprings used in this experiment and they were placed 200 mmand 300 mm from the gelatin (imaging ROI) respectively.During scanning, each SMA spring was actuated individuallyfor 5 seconds from the 11th second to 31st second and atotal of 111 MR images were taken during the 37-secondscanning period. Fig. 13 shows three dynamic MR images atdifferent instants of time. We then computed the SNR of eachimage to quantify the experimental results and the results areshown in Fig. 14. The average SNR before actuation wascomputed to be 133.0 and it dropped to 131.4 after actuation.The SNR only dropped by 1.2%, which implies that passingcurrent did not introduce significant noise in the MR images.Thus, we can conclude that these dynamic MR imagescan be provided as visual feedback for physicians whenperforming the surgical procedures. With real-time visualfeedback, physicians can remove the brain tumor completelywhile minimizing trauma to the surrounding healthy brainduring intracranial procedures.

0 5 10 15 20 25 30 35

SNR of dynamic MR images

Time (second)

Before actuation, Avg. SNR=133.0During actuation, Avg. SNR=131.4After actuation, Avg. SNR=133.2

0

50

100

150S

NR

Actuation starts Actuation ends

Fig. 14. Signal-to-noise ratio of dynamic MR images.

VI. CONCLUSION

In this paper, we have presented a new design of MINIRusing SMA spring actuators along with the tendon-drivenmechanism to actuate the various joints of MINIR. Theprototype overcomes several limitations of our previousprototypes [11, 16, 17] while having a larger range ofmotion, larger output force and better MRI compatibility.A theoretical model and experimental setup have been de-veloped to evaluate the performance of the SMA spring.The output force of the SMA spring can be up to 5.2 N,which is advantageous in our application. Moreover, themodel developed in this paper enables us to use temperaturefeedback to control the output force of the robot if thedisplacement of the SMA spring is measured. This will bevery important for our future research in this area. Finally,we demonstrated that MINIR is MRI compatible by takingMR images. The images show no significant image distortionand very limited SNR drop was observed. The current designof MINIR enables the possibility of using MR images asvisual feedback for physicians when performing surgicalprocedures.

In this prototype, we have not developed the bipolar elec-trocautery system since the primary goal of this paper was toevaluate the performance of the robot and the SMA springactuation system as well as the MRI compatibility of MINIR.In fact, we have already demonstrated the electrocauterycapability of MINIR in our prior work [23]. As part ofour future work we plan to use a MRI-compatible (E-Type)thermocouple [24] with a displacement measurement sensorcomprised of a fiber-optic setup, which will result in accuratecontrol of the individual joint motion of MINIR. Further-more, we also plan to provide MR images to the physicianto simultaneously evaluate the desired joint motion.

ACKNOWLEDGMENT

The authors would like to acknowledge Dr. Alan B.McMillan from University of Maryland, School of Medicinefor taking MR images.

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