This work investigates the performance of a novel compliant needle for cutting tissue. The novel cutting geometry transfers axial vibration to transverse motion at the tip. The cutting edge of the geometry is defined in terms of the time-dependent inclination and rake angle. Finite element analysis was performed to determine the compliant geometry effect on the axial vibration modes of the needles. An ultrasonic transducer is used to apply the axial vibration. An ultrasonic horn was developed to increase the amplitude of vibration. Experiments were performed to determine the effectiveness of the compliant needle geometry. The motion of the compliant needle is measured with a stereomicroscope. The two compliant geometries developed transverse motion of 4.5 μm and 16.0 μm. The control needle with fixed geometry developed no measured transverse motion. The insertion force was recorded for two different compliant geometries and a control geometry inserted into a polyurethane sheet. The puncture force of the control needle with applied vibration and the two compliant needles was up to 29.5% lower than the control insertion without applied vibration. The compliant needles reduced the friction force up to 71.0%. The significant reduction of the friction force is explained by the compliant needles' ability to create a larger crack in the material because of their transverse motion.

## Introduction

Needles are commonly used in many minimally invasive procedures such as biopsy, drug delivery, brachytherapy cancer treatment, blood sampling, and many others [1]. Precise placement of the needle inside the body is needed for many of these procedures to be effective. Inaccurate placement of the needle is due to the flexibility of the thin needle and softness of the tissue [2]. The flexible needle deflects due to forces acting on the needle tip [3]. In addition to tissue being soft, the tissue is not rigidly fixed in place and is free to move. This is unlike traditional manufacturing where a workpiece can be rigidly clamped in place. This causes the tissue to deform and the target location to move from its initial position [4]. Lower insertion forces have been shown to reduce needle and tissue deflections [5,6].

Researchers have developed many methods to reduce needle insertion force. Needles with smaller diameters, as small as 100 μm, have been created [79]. However, these smaller needles cannot be used in procedures where a larger diameter is needed, such as tissue biopsy and placing of radioactive seeds as a cancer treatment. Another method to reduce the insertion force is to alter the tip geometry. Researchers have been developing needles with sharper tips that have been shown to cut with less force and cause less pain to patients [1013]. Dynamic insertion methods, changing how the needle is inserted into the tissue, have also been shown to reduce the insertion force of needles further. Increasing the insertion speed has been shown to reduce the insertion force into softer tissues such as liver and heart tissues [4,1416]. However, increasing the insertion speed has shown no effect on the insertion force into tough tissues such as skin [1719]. Another dynamic insertion method is applying vibration to the needle.

Vibration has been utilized in traditional manufacturing for decades. First proposed by Wood and Loomis in 1927 [20], it has since been used to machine many different materials and utilized in many different processes. Work has been conducted utilizing ultrasonic vibrations which can reduce and almost eliminate burr formation in drilling processes [21,22]. This shortens manufacturing time because a second process to eliminate burrs is no longer needed. It has also been shown that manufacturing time is reduced with the application of ultrasonic vibration [23]. The allowed feed rate of cutting is increased because vibration reduces the cutting and friction forces reducing heat generation and chatter. Another benefit to vibration cutting is an improved surface finish [2427]. Vibrational machining methods such as vibration-assisted nano-impact machining by loose abrasives have proven to be an effective method of performing targeted machining of hard and brittle materials [28]. Finally, vibration cutting has been shown to reduce the cutting force required [26,29,30].

Applied vibration has been shown to reduce the cutting forces during needle insertion similarly to during traditional manufacturing procedures. Yang and Zahn showed a reduction of insertion force of microneedles by applying axial vibration to the needle [31]. Huang et al. showed reduction in force of 27 gauge hypodermic needles by applying ultrasonic vibration with a piezoelectric actuator [32]. Utilizing vibration, Izumi et al. successfully designed a harpoonlike jagged microneedle imitating a mosquito's proboscis to reduce insertion force [33]. Begg and Slocum similarly tested the insertion force of lancet needles at varying vibratory parameters [34]. However, little work has been done to understand how cutting geometry and vibration can together reduce cutting forces.

This study focuses on the performance of a novel compliant needle designed to work with vibration. Compliant mechanisms use elastic deformation of the mechanism to transfer force or motion as opposed to linkages and joints used in traditional mechanisms [35]. They are used in microdevices, actuators, tools, and other areas as a way to reduce weight and number of parts needed for a design. Researchers have previously used compliant needles to aid in needle steering procedures by changing the deflection of the needle [3638]. The needles incorporate an actuation mechanism that bends the compliant needle to steer it through tissue. The compliant needles bend with less force than traditional needles making it easier to actuate the needle tip.

This study explores the use of a compliant geometry to reduce the cutting force of the needle. Experiments were performed in phantom tissue to determine the performance of the compliant needle. This paper defines the compliant geometry and the cutting edge geometry of the needle, describes the test setup and procedure used to test the geometry, presents the results from the experiments, and presents the conclusion from the work.

## Novel Compliant Needle

A novel compliant needle is designed in this study and utilizes a compliant geometry that uses applied axial vibration to change the cutting direction of the needle tip. The applied vibration causes the compliant geometry of the needle tip to move perpendicular to the insertion direction as shown in Fig. 1. This changes the cutting direction of the needle from parallel to the insertion direction to perpendicular to the insertion direction. The purpose of the change in cutting direction is to reduce the deformation of tissue in the insertion direction. For example, for prostate brachytherapy, the parallel insertion force has been found to rotate the prostate up to 13.8 deg, moving the target location from its original position [39]. The goal of perpendicular cutting is to reduce the total force necessary for insertion to improve needle position accuracy. This is accomplished by reducing both the puncture force in the parallel direction as well as the frictional force.

### Compliant Geometry.

To achieve the transverse cutting, the needle shown in Fig. 2 was designed and manufactured. Two slits are cut into the needle a distance D1 down from the tip offset a distance D2 apart. The slits are on opposite sides of the needle. The slits are cut to a depth H and with a thickness t. The needle has a radius r. The slits in the needle create a single-axis flexural hinge which allows the tip of the needle to move in the transverse direction with the application of axial vibration. Single-axis flexural hinges utilize geometry, a slender region of the structure, to allow the structure to rotate about one axis without the need of moving parts [40]. The needle is vibrated at resonance to achieve the greatest amplitude of vibration at the needle tip. The compliancy of the needle is used to modify the axial mode shape of the needle to incorporate transverse motion. Tcherniak similarly utilized compliant geometry to achieve the maximum displacement of a resonating structure [41].

Three compliant geometries are considered in this study. The needles' parameters can be seen in Table 1. For this study, only the distance from the tip D1 and the offset distance between the slits D2 were varied. The radius of all the needles was that of 18 gauge needle, 0.635 mm, which are commonly used in brachytherapy cancer treatment and biopsy. The slit depth, H, is 0.635 mm, the same the needle radius. The thickness, t, is 75 μm. The slits were cut into the needle with a wire electron discharge machine and are as wide as the wire used in the process. A control needle with no slits was utilized to compare to the effects of the compliant geometry.

### Cutting Geometry.

The needle tip was designed such that it could cut both parallel and perpendicular to the insertion direction. The needle tip is manufactured by grinding four planes. The tip geometry can be described by two angles: ξ and β. The manufacturing process is shown in Fig. 3. In steps 1 and 2, the needle is tilted and ground at an angle ξ. In step 3, the needle is rotated by β in each direction. In step 4, this process is repeated on the opposite side of the needle. This process results in the diamond style tip shown in Fig. 3. For all the needles used in this study, ξ = 10 deg and β = 20 deg.

Oblique cutting geometry is used in this study to describe the cutting geometry of the needle. Oblique cutting is utilized in manufacturing to characterize the cutting face of a tool and is defined by two angles: inclination and rake angles [42]. The definition of the inclination and rake angles of oblique cutting can be seen in Fig. 4. The cutting edges of a needle can be described by oblique cutting geometry. Moore et al. showed the dependence of the insertion force of a needle on the rake and inclination angles of the tip [43]. A high inclination angle cuts with a lower force.

In this study, the rake and inclination angles of the cutting edge are developed incorporating the dependence on the cutting direction. An XYZ coordinate system is created with the origin at the tip of the needle, the Z-axis is aligned with the axis of the needle pointing down the needle, and the X-axis aligned in the perpendicular cutting direction, as shown in Fig. 5. Parametric equations are developed to describe the edges of the needle tip in order to calculate the angles. The three edges of one cutting plane are labeled in Fig. 5. The parametric equations describing edge 1 are

$x=0y=ψz=ψ cos βcotξ$
(1)
where the parameter ψ varies from 0 to r. The parametric equations for edge 2 are
$x=r sin γy=r cos γz=r cos(γ−β)cotξ$
(2)
where γ is from 0 deg to 90 deg and is the radial angle describing the position along edge 2 with respect to the Y-axis. The parametric equations for edge 3 are
$x=ψy=0z=ψ sin βcotξ$
(3)

where the parameter ψ varies from 0 to r. Edge 3 is the cutting edge for this needle geometry.

The variable cutting direction can be described with the plane Pr which has a normal vector v in the cutting direction as shown in Fig. 6. The normal vector is v = {sin θ(t), 0, −cos θ(t)}, where θ(t) is the rotation of the cutting direction in the XZ plane with θ = 0 deg being parallel to the insertion direction and θ = 90 deg being perpendicular to the insertion direction. Due to the nature of the motion of the needle tip, the cutting direction θ(t) varies with time t. The tangent vector s of the cutting edge for this geometry (edge 3) is s = {−1, 0, −sin θ(t) cot ξ}. The inclination angle λ(t) in oblique cutting is defined as the angle between the plane Pr and the tangent vector of the cutting edge s as shown in Fig. 6

$λ(t)=arcsin| s • v |‖ s ‖ ‖ v ‖=arcsin | cos θ(t)sin βcotξ−sin θ(t) | 1+sin2βcot2ξ$
(4)

The rake angle α in oblique cutting is defined as the angle between the needle face Aγ and plane Pr measured in the plane Pn as shown in Fig. 7. The plane Pr is the defined as the plane with a normal vector in the cutting direction, v = {sin θ(t), 0, −cos θ(t)}, and Pn is defined as the cutting edge normal plane. The normal vector of Pn is the tangent vector of the cutting edge, s = {−1, 0, −sin θ(t) cot ξ}. The normal vector of the needle face Aγ is nγ = {sin β cot ξ, cos β cot ξ, −1}. The intersections of planes PnAγ and PnPr are vectors a and b, respectively, as shown in Fig. 7. The intersection vector of two planes is defined as the cross product of the normal vectors of the plane. a and b are defined as

(5)

$b=s×v={0, cos θ(t)+sin θ(t)sin βcotξ,0}$
(6)
The rake angle α, as shown in Fig. 7, is the angle between a and b
$α=arccos| a•b |‖ a ‖ ‖ b ‖=arccos| 1+sin2βcot2ξ |csc2ξ(1+sin2βcot2ξ)$
(7)
As evident in Eqs. (5) and (8), the inclination angle is dependent on the cutting direction of the needle, and the rake angle is independent of the cutting angle. The inclination angle and rake angle as they change with cutting direction are plotted in Fig. 8. For this geometry, the inclination angle (most efficient cutting geometry) occurs when cutting in the parallel direction.

## Finite Element Analysis of Compliant Needle

Finite element analysis was conducted to determine the motion of the needle tip. For this study, the needles will be vibrated with an ultrasonic transducer at 20 kHz. For the ultrasonic vibration to maximize movement, the axial resonance frequency of the needle must match the driving frequency: 20 kHz. To determine the length of the needle, the equation for longitudinal wave propagation through a homogeneous rod with variable cross section is used [44]
$−ddz[EA(z)dU(z)dz]=ω2ρ A(z) U(z)$
(8)

where E is the Young's modulus of the material, A(z) is the cross-sectional area of the rod at a given position z, ρ is the density of the material, ω is the resonant frequency of the needle, and U(z) is the axial displacement of the horn at a given position z. The needle used in the finite element analysis had a length of 130 mm. The needle is made of 304 stainless steel with a Young's modulus of 200 GPa, a Poisson's ratio of 0.29, and a density of 8000 kg/m3.

The boundary conditions of the needles are modeled as free–free where each end of the needle is free to move. Other researchers have also used free–free boundary conditions in modeling ultrasonic machining tools [45]. This is appropriate because the back of the needle is free to move with the horn. The transducer is rigidly mounted but the vibrational input occurs at a node where the transducer and horn meet. This free–free boundary condition generates a half-wavelength mode shape that has maximum amplitude of vibration at the ends of the needle. The free–free boundary condition also allows for the needle to be modeled by itself, shortening the computational time.

To determine the motion of the needle tip, a modal analysis study was conducted using ansys software (Canonsburg, PA). Ten-node tetrahedral elements were used to mesh the tip of the needle down to 0.5 mm below the bottom slit. Twenty-node brick elements were used to mesh the rest of the needle to reduce the number of elements needed and shorten computation time. The deformation results of the first axial mode of the control needle and three compliant geometries can be seen in Figs. 9(a)9(d). The contours represent the mass normalized X-direction displacement (transverse motion). To compare the displacements of each needle to the others, the transverse motion of the node at the tip of the needle was recorded. The mass-normalized displacement for the needles was compared because each needle had the same mass. The results, as shown in Table 2, show that the control needle has no motion in the transverse direction, as to be expected. The wider offset D2 provided more transverse motion, as did having the slits farther down the needle (larger D1).

## Experimental Procedure

Needle cutting experiments were performed to determine the effects of the compliant geometry on the insertion force. The experiment utilized three needles. The needles used were the control needle, compliant 1, and compliant 2 as outlined in Table 1. Compliant 3 needle was not used in the experimental study due to it breaking from the stress caused by the vibration. The 18 gauge needles were made of 304 stainless steel. Each compliant needle was inserted with an applied axial ultrasonic vibration of 20 kHz. The control needle was inserted with and without applied vibration. The needles had a length of 127 mm to match the resonance of the ultrasonic transducer. The needles were inserted at a constant rate of 1 mm/s into a polyurethane sheet of Shore hardness 40A and thickness 1.588 mm for five separate trials. The polyurethane was used due to its consistency. Ex vivo tissue cutting experiments can yield results with standard deviations up to 25% [43] making it difficult to determine meaningful conclusions. Polyurethane has been used in other studies to simulate skin dermis [46,47].

### Finite Element Analysis of Ultrasonic Horn.

For this study, an ultrasonic vibration is applied to the needle in the axial direction. An ultrasonic piezoelectric transducer is used to apply the vibration. The piezoelectric ceramics in the transducer have a very low actuation length. However, the actuation length can be amplified if the frequency of actuation is the same as the axial resonance of the transducer. Because of this, the ultrasonic transducers are limited to only being able to operate at one frequency. An ultrasonic horn can be used to amplify the vibration further.

An ultrasonic horn is a device which magnifies the amplitude of vibration, usually made from a high-strength material such as stainless and hard steels, titanium, and aluminum [48]. The ultrasonic horn is a tapered bar of variable cross section that connects to the transducer. The cross-sectional area of the input end (the end connected to the transducer) is generally larger than the area of the output end (the tool end of the horn). The length of the horn is determined by the axial resonance of the horn, usually a multiple of the half-wavelength of the system [45]. For the horn to work, the axial resonance of the horn must match the axial resonance of the transducer. To determine the length of the horn, the equation for longitudinal wave propagation through a homogeneous rod with variable cross section is used (Eq. (8)) [44].

Three main shapes of horns are used in industry: conical, stepped, and exponential, examples of such can be seen in Fig. 10. For this study, a stepped horn shape is used due to its ease of manufacturing. To reduce the stress in the horn, a short conical section is added in between the steps. The solution to Eq. (8) for a stepped horn is given by

$L=k1c4f+k2c4f$
(9)
where L is the length of the horn, c is the wave propagation speed of the material which is defined as $c=E/ρ$, f is the desired frequency of vibration, and k1 and k2 are correction factors. The correction factors can be assumed to be unity yielding [45]
$L=c2f$
(10)

The horn used in this study was made of 6061 aluminum for its high strength and manufacturability (Young's modulus E = 68.9 MPa and density ρ = 2700 kg/m3). The desired frequency of operation is 20 kHz. The approximate solution for the conical horn designed yields a length of 126.3 mm. To determine a more exact length, a finite element analysis was run utilizing ansys. Ten-node tetrahedron elements were used to mesh the three-dimensional horn geometry shown in Fig. 11(a). The boundary conditions of the horn can be assumed to be free–free to achieve the half-wavelength mode shape [45]. Using a modal analysis, the length of the horn was determined to be 128.3 mm to achieve the 20 kHz resonant frequency. Results of the analysis can be seen in Fig. 11(b).

The stepped horn was manufactured to the length specified in the finite element analysis and tested for its effectiveness. An optical probe (MTI Instruments, Albany, NY) was used to measure the displacement of the transducer with and without the ultrasonic horn attached. The displacement results are plotted in Fig. 12 for a 100 V peak-to-peak sine wave driving the transducer. The horn was able to increase the amplitude of the ultrasonic transducer by 477% compared to the transducer without the horn.

### Experimental Setup.

The experimental setup shown in Fig. 13 was utilized to perform the insertion tests. A linear motor (Dunkermotoren, Bonndorf, Germany) is used to insert the needles into the polyurethane at a constant rate of 1 mm/s. The force was recorded with a six-axis force sensor (ATI Industries, Apex, NC). A 20 kHz piezoelectric transducer (Honda Electronics, Toyohashi, Japan) applies axial ultrasonic vibration to the needle. The polyurethane is mounted between two plates to ensure constant boundary conditions for each trial.

## Results

### Compliant Needle Motion.

To determine the effects of the compliant geometry on the motion of the needles, the displacements of the tips were measured using a stereomicroscope (Zeiss, Oberkochen, Germany). Images were captured for each needle with and without vibration applied. The motion of the tip was determined by the ghost image in the capture, as shown in Figs. 14(b) and 14(c). Figures 14(a) and 14(b) show the needle tip of compliant needle 2 with and without vibration applied. The motion can be tracked by measuring the displacement of the reflected spots caused by surface textures shown in Fig. 14(b). The exposure time for the images was 10 ms. At 20 kHz frequency, this allowed for 200 cycles to be captured in each image, ensuring the capture of the full range of motion.

The motion was recorded for each of the three needles used in this study. The control needle only had motion in the axial direction of the vibration shown in Fig. 14(c) and Table 3. The ghost image only showed the reflected dots moving only along the axis of the needle. However, the compliant geometries had motion in both the axial direction and the transverse direction. The transverse motion is evident in Fig. 14(b) by the square pattern of the reflected dot's ghost image. Compliant needle 2 (slits farther apart) had more transverse motion than compliant needle 1 as shown in Table 3.

The motion of the tip caused by the vibration is neither pure axial or transverse. The square-patterned motion causes the inclination angle of the cutting to change with time. For the needles used in this study, the rake angle is 67.7 deg from Eq. (7). The inclination angle, calculated from Eq. (4), is 62.7 deg in the axial direction and 27.27 deg in the transverse direction.

### Force Results.

Force and position data were collected for each trial, as shown in the example plot (Fig. 15). The figure shows the insertion forces for the control needle with and without vibration and compliant needle 1 with vibration. The puncture force is the force at the first peak of the insertion plot. Prior to the peak, the needle is only deflecting the polyurethane, and no cutting is occurring. At the peak where the puncture force is recorded, a crack is initiated and the needle begins to cut through the material. The friction force is taken to be the force between the needle and the polyurethane once the needle tip has exited the polyurethane as shown in Fig. 15.

The puncture force and friction force were recorded for the control needle with and without applied vibration and also for the two compliant needles with vibration. The results are shown in Fig. 16. The results show a significant decrease in puncture force for the trials with applied vibration for both the control needle, 29.5% (ANOVA F-test p-value of 9.06 × 10−6), and the compliant needles, 18.8% and 14.1% for compliant 1 and compliant 2, respectively, (ANOVA F-test p-values of 5.38 × 10−5 and 0.015, respectively) compared to the control insertion with no vibration. The control needle with vibration added had the lowest puncture force. This could be due to the control needle having the largest axial amplitude of vibration. The puncture forces for the two compliant needles are insignificantly different from each other (ANOVA F-test p-value of 0.207).

The friction force between the needle and the polyurethane was reduced with the applied vibration for the control needle, 48.3%, and the two compliant needles, 71.0% and 68.4% for compliant 1 and compliant 2, respectively, (ANOVA F-test p-values all less than 0.001). Similar to the puncture force results, the friction force of the two compliant needles is insignificantly different from each other (ANOVA F-test p-value of 0.233).

To determine the cause of the decrease in friction force of the compliant needles to the control needle, the cracks created in the polyurethane from the needles were examined. The cracks from the control needle with and without applied vibration as well as the cracks from the compliant needle with and without applied vibration can be seen in Figs. 17(a)17(d), respectively. As shown, a larger, more complex crack is applied when the compliant needle cuts with vibration. The average crack lengths are shown in Fig. 18. The larger crack allows the needle to pass through the polyurethane without having to stretch the polyurethane as much as a smaller crack. This reduced stretching means that the normal force between the polyurethane and the needle will be reduced. A lower normal force will help to reduce the frictional force. This can explain why the frictional force was the lowest for the compliant needles. The texture created by the larger crack size may also influence the frictional force. Future studies are necessary to determine the effect of crack texture on friction.

## Conclusions

A novel compliant needle was presented in this paper. The compliant geometry utilized vibration to transform axial motion into transverse motion. The design of the needle was described, and a finite element analysis of its motion was performed. The variable cutting geometry of the needle tip was also defined. Experiments were conducted to determine the effectiveness of a novel compliant needle geometry at reducing insertion forces. The compliant needles were able to reduce the puncture force of the insertion by 18.8% and the friction force by 71.0% compared to the control needle without vibration. However, vibration applied to the control needle outperformed the compliant needles in reducing the puncture force but the compliant needles were able to reduce the friction force by the greatest amount.

Further design of the compliant and cutting geometries is needed to improve the performance of the compliant needles. This study presented evidence of the compliant geometry causing transverse motion of the needle tip. The transverse motion was shown to change the cutting mechanics of insertion by increasing and changing the shape of the crack created in the phantom tissue. The specific shape of the transverse motion and how this affects cutting force and crack shape will need to be explored in the future. Additionally, failure of the most complaint needle demonstrated that fatigue failure is a concern for this novel needle design. Future research will need to investigate how needle geometry parameters influence fatigue life to ensure that the compliant needle design can be safely utilized in needle insertion procedures.

## Acknowledgment

This material is based upon work supported by the National Science Foundation under Grant No. CMMI-1404916.

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