Computational design optimization of a SMA-based active steerable needle

*[email protected]; phone 1 215 204-7805

Computational design optimization of a SMA-based active steerable

needle Bardia Konha and Parsaoran Hutapea*a

aDept. of Mech. Engr., Temple University, 1947 N 12th street, Philadelphia, PA, USA 19122

ABSTRACT

Shape memory alloy (SMA) actuated needle is currently being developed to assist surgeons/physicians in their

percutaneous interventional procedures. The proposed active surgical needle can potentially compensate the possible

misplacements of the needle tip in the tissue benefiting from the improved navigation provided by the attached SMA

actuators. In this study finite element tools have been utilized in order to maintain an optimum design of the active needle

configuration. There are several parameters involved in the design affecting the active needle’s applicability and

maneuverability; among them are the length, diameter and the maximum residual strain of the SMA wires, the stiffness

and diameters of the surgical needle and the offset distance between the needle and the actuator. For analyzing the response

of the active needle structure a parametric model was developed in ANSYS. This model was linked to the automated

optimization tools for an improved design of the active needle. The most sensitive parameters affecting the active needle’s

steerability were found to be the offset distance and the length of the needle. Considering the results and the clinical

limitations, an improved design of the active needle was presented.

Keywords: Design optimization, shape memory alloy, active needle, biomedical applications, medical devices

1. INTRODUCTION

Active surgical needles are interested to be developed to assist surgeons and physicians in their percutaneous interventional

procedures. So many researchers have studied different methods to activate the surgical needles. For instance Tang et al. 1

used magnetic forces in order to help the navigation of the needle inside the body. In another work Ayvali et al. 2 utilized

pre-curved SMA wires on the needle body to provide external actuations. The wires, which were initially straight,

transform to a pre-curved shape when heated. Similarly, Ryu et al. 3 used internal laser heating of SMA wires to bend the

needle. The nonlinear beam deflection via actuation of a SMA wire was studied by Shu et al. 4. The Shape memory alloy

(SMA) actuated surgical needle of figure 1 was proposed by Konh et al. 5,6. This configuration of active needle 7,8

privileging from the attached actuators can potentially compensate the possible misplacements of the needle tip in the

tissue. As shown in the figure the needle can benefit from the improved navigation that is provided the attached SMA wire

actuators 9 reaching target locations.

Figure 1. Schematic of the active needle design.

The needle behavior inserted to the patient’s body has to be investigated to help understanding the active needles.

Mechanics of an active needle inside tissue was studied by Datla et al. 10,11 using an analytical approach. Also behavior of

a surgical needle within the tissue and the consequent probable thermal damage due to the existence of heating elements

were studied by in our previous work 12. The SMA wires are the active components of our design. Knowledge of SMA

material behavior is critical for the design and development of devices in which actuation capabilities of SMAs are utilized.

Therefore in depth studies on the characteristics of the wires are important. In the last two decades, some constitutive

models have been provided for SMAs based on quasistatic assumptions 13. One-dimensional (1D) thermomechanical and

actuation properties of SMA wires were discussed in 14,15, especially for actuation utilization. One of the most famous

models were suggested by Brinson 16. This model could predict the phase transformation of the wires coherently. Input

parameters to the Brinson model such as transformation temperatures and Clausius-Clapeyron coefficients (which are the

slopes of the lines where transformation starts and ends) and the Young’s modulus of austenite and martensite were

obtained from experiments. Prior to implementation of the model, the characteristic parameters should be determined

experimentally.

Many groups discussed the optimization of active systems for example a design optimization for an actuated robotic

catheter was done by Crews and Buckner 17. They implemented a free energy model into finite element analysis (FEA)

package, COMSOL for their optimization strategies. To dampen the structural vibration, Ozbulut et al. 18 optimized the

installation of a SMA wire based on a genetic algorithm. Although their works cover many aspects of structural analysis,

there are still some limitations such as SMA’s constitutive model and the computationally expensive run time. The inelastic

transformation strain of SMAs as an independent quantity has not been implemented in such methods; therefore a new

empirical curve at each modified design configuration was required.

In this study finite element tools have been utilized in order to maintain an optimum design of the active needle

configuration. There are several parameters involved in the design affecting the active needle’s applicability and

maneuverability. Among them are the length, diameter and the maximum residual strain of the SMA wires, the stiffness

and diameters of the surgical needle and the offset distance between the needle and the actuator. The best design

configuration was found using well-established methods and implementing appropriate tools. These tools were used in

optimization algorithm to perform a predictive analysis seeking the best configuration. For analyzing the response of the

active needle structure a parametric model was developed in ANSYS. This model was linked to the automated optimization

tools for improved needle designs.

2. FINITE ELEMENT MODEL

2.1. Optimization using finite element analyses

Engineering analysis tools were used to optimize the active needle configuration. Design optimization of structures with

active materials can be a challenging endeavor. The automated simulation process presented here made it possible to have

an efficient assessment of the structural response of our design. The thermomechanical behavior of SMAs needs to be

included in the analysis. The model shown in figure 2 was developed for FE analysis of the SMA actuated needle. The

strain response of the SMA wire was approximated while subjected to thermally actuation. To have a good approximation,

the strain response of the wires was evaluated at different stress levels to find their contraction range. For each constant-

stress level of each wire, three repetitive measurements were performed to ensure material stable behavior. This strain

response of the wire, transformation from martensite to austenite, was estimated by defining the thermal expansion

coefficient, α, as -0.0096/ºC. This value of α was producing the same strain response as the wire temperature rises from

austenite start to austenite finish temperature. The negative sign of α shows that by increasing the temperature above

austenite start the material goes through the smaller crystallographic shape of austenite phase. Element BEAM188 and

SOLID185 were used for the wire and the cannula, respectively.

Figure 2. Geometry and mesh of the SMA-activated needle generated in ANSYS; the design parameters are shown.

To improve the flexibility of the active cannula, the effects of influencing parameters were taken into account. These

parameters include the cannula’s diameter and Young’s modulus, the SMA wire diameter, its pre-strain and its offset

from the neutral axis of cannula. The finite element model explained above was used for explore of the effects of these

involving design parameters through the optimization process. A 100mm long SMA wire attached to the needle with a

stainless steel holder was considered for the primarily design. Once this task was accomplished, a large collection of

samples and a response surface based on the objectives and constraints is forming as a global overview. The design

optimization was performed aiming the maximum deflection of the active needle to ensure its enhanced maneuverability.

The best design parameters resulting in the highest needle deflection were found using the Multi-Objective Genetic

Algorithm (MOGA) with evolving choices of candidate points in their domain. This optimization algorithm starts from

an initial design point and iterates through the whole domain with the samples evolving genetically until the best case is

found.

2.2. Experimental evaluations of the FE model

In order to validate the finite element model, the prototype shown in figure 3 was developed. An aluminum hollow needle

(Din=0.88mm and Dout=1.59mm) was actuated and bent by a FLEXINOL SMA wire (purchased from Dynalloy Inc., Tustin,

CA, USA) while attached by a 18mm stainless steel holder. SMA wire with diameter of 0.20mm was selected as the

actuator component of the prototype. The SMA wire was stabilized prior to performance. The stabilization was done by

repeatedly actuating the wire at a constant stress level at a cyclic temperature until a consistent response is maintained.

The offset gap between the actuator and the main axis of the cannula was 7.0mm. The distance between the two ends of

the cannula was arranged precisely to leave a pre-strain of 5% on the SMA wire, assuring maximum contraction. Joule

heating method was used for heating the SMA wire. The amount of deflection was captured by taking pictures of the

deflected shape with a graph sheet on the background. A high speed camera (Fastec inline camera, Fastec Imaging, San

Diego, CA, USA) was used for this purpose and pictures were processed using the ImageJ software 1.45s (National

Institutes of Health, Bethesda, MD, USA).

Figure 3. Prototype of the active needle.

3. RESULTS AND DISCUSSIONS

This study consists of modeling, analysis and optimization of a SMA-based active needle using finite element tools. The

accuracy of our FE model was shown by validating with experimentations on the active needle prototype. The prototype

described in section 2.2 was used here for validation. The maximum deflection of the prototype was ensured by applying

enough amount of current. The vertical deflection of 27.0mm was observed while predicted 28.27mm by the FE model.

The difference of less than 5% was seen and thereby validated the FE model. This model while validated was linked with

the iterative structural assessments to perform the optimization analyses.

Figure 4. The best design candidates that gives the maximum deflection of the active needle.

In our design optimization, the maximum possible needle tip deflection was aimed for maximum flexibility while the stress

on SMA wire was kept smaller than a critical value. The input design variables were: εL as the maximum residual strain of

SMA wires with different diameters, DSMA as the SMA wire diameter, Doutcannula/Dincannula as the cannula’s outer and inner

diameters, the offset distance between the neutral axis of cannula and SMA wire, Doutholder/Dinholder as the outer and inner

diameter of the holder, th as the holder’s thickness, L as the total length of the needle and L1 as the holder’s length. The

total deflection of the needle tip (δtip) and the maximum stress (σmax) of all elements were taken as desired output variables.

The length of the SMA wire as well as the offset distance between the needle and the SMA wire were found to be the most

effective parameters on the needle deflection. The optimized design resulted in a maximum deflection of 45.84mm with a

118.64mm long SMA wire. The convergence achieved after 11 total iterations and 594 evaluations resulted in 6 best

candidates for the active needle design.

4. CONCLUSIONS

The MOGA method of optimization was performed in this article to find the best design of the active needle. This method

provides a refined approach seeking among all design points. 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. A

clinical issue has to be considered in the design to minimize tissue rupture while inserting the needle. The amount of

rupture is directly proportional to the maximum distance between the SMA wire and the cannula, which happens at the

needle’s mid length. Therefore, minimizing this gap will reduce the amount of rupture. This can be achieved by dividing

the length into several sections. To demonstrate this, a case study with two sections having half length of the SMA wire

was designed to investigate how much this gap can be decreased. The study showed 44.06mm deflection assuming two

sections compared to 45.84mm deflection of the past one section model. However, the gap decreased from 2.56mm to

1.47mm. This clearly showed that a less destructive active needle can be made by increasing the number of sections.

ACKNOWLEDGEMENT

This work is supported by the Department of Defense CDMRP Prostate Cancer Research Program (Grant # W81XWH-

11-1-0398).

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