Steedle Technical Report

CONFIDENTIAL - NOT FOR PUBLIC DISCLOSURE

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Abstract – This paper focuses on the design and development of

a telerobot for needle distal tip steering. Current image-guided procedures are operated manually and limited by targeting errors due to instrument misalignment, deflection and an inability to reposition the distal tip of the instrument after it has been inserted into the skin. These limitations result in suboptimal diagnosis and treatment for patients as well as excessive procedure times and radiation dose from medical imaging. To address this we are developing a telerobot capable of distal tip steering based on the concept of deploying a flexible pre-curved stylet from a concentric straight cannula. Analytical models were developed to understand what material properties are required to recover from the imposed strains and calculate the deployment and retraction forces required for moving the stylet relative to the cannula and were compared to experiments. The curved stylet was modeled as a curved beam on an elastic foundation in order to estimate its end-point defection when subject to a tangential cutting force. The analysis and experimental results were then used as design specifications for a telerobotic system that is capable of implementing the desired relative motions for the cannula and stylet so that a volume may be targeted by the distal tip of the stylet inside the body. The prototype system is designed to be made from largely plastic components and actuation is achieved using micro stepper motors. The proximal end of the cannula is attached to the distal end of a screw-spline that enables it to be translated and rotated with respect to the casing. Translation of the stylet relative to the cannula is achieved with a second threaded screw with a splined groove. The desired position of the distal tip is specified using a custom interface. A detailed evaluation of the system in ballistics gelatin is planned.

Index Terms—needle, steering, screw-spline, telerobot.

I. INTRODUCTION inimally invasive percutaneous procedures are routinely performed procedures for both the treatment and

diagnosis of disease. In medicine, percutaneous needle insertion pertains to any medical procedure where the skin is punctured with a rigid needle to access to inner organs or other tissue as opposed to an approach where surgery is performed to expose the inner organs or tissue. A biopsy involves the removal of cells or tissues for histological or chemical examination. The removed cells or tissue are generally examined under a microscope by a pathologist. An increasingly significant portion of percutaneous procedures are for the local treatment of disease in a minimally invasive manner. Tumor ablation is defined as the direct application of chemical or thermal therapies to a specific focal tumor (or tumors) to achieve eradication or substantial tumor destruction

[1]. Initially providing only palliative care, Radio Frequency Ablation (RFA) is now used for complete eradication of tumors in a variety of organs (e.g. lung, liver and kidney). Another rapidly growing area of treatment is brachytherapy where small radioactive seeds are deployed through a needle and implanted into the tumor. There are also a growing number of other procedures where material is injected to a targeted location in the body for structural or therapeutic purposes. Typically the procedures are performed under image-guidance such as computed tomography (CT), fluoroscopy, ultrasound and magnetic resonance imaging (MRI) that provide high resolution images of the patient anatomy. After a target is identified in the body a needle insertion point is chosen so as to avoid obstructing structures (such as ribs and blood vessels) and the needle is then manually inserted towards the target.

A. Technical Difficulty Physicians currently find it challenging to precisely place needles to the desired target due to the difficulty in manually aligning the needle along the desired trajectory, needle movement due to tissue tension, respiratory motion and limited supporting subcutaneous soft tissue to support the instrument. Further unwanted buckling of the needle as it is being inserted may result in the instrument taking a curved shape and thus deviating from the desired trajectory as it is inserted into the tissue. The needles are often quite long (10-20 cm) and inserted into a patient’s body and can exhibit significant deflection that causes it to deviate from its desired trajectory. The subsequent small angular errors result in large lateral displacements of the distal needle tip because the pivot point is at the skin surface. It is a summation of errors that results in the inability of the radiologist to place the distal tip of the needle to the desired target within even an order of magnitude of the sub-millimeter and sub-degree measurements from the CT display. Figure 1 illustrates how alignment errors and needle bending result in the needle not hitting the desired target.

Reorientation of the needle once inside the body is difficult, if not impossible, as there are forces from the tissue that resist the pivoting motion. Thus in order to reposition the distal tip of the needle once it is inside the body the radiologist has two options, they can try and overcompensate when realigning the needle or they can retract the needle and attempt to re-insert it along the correct trajectory. However, both of these approaches result in damage to the tissue that can be uncomfortable for the patient and lead to a variety of complications. Further, if the instrument is assumed to pivot about the skin surface it is difficult for the radiologist to predict movement of the distal tip of the needle inside the body

Telerobot for Needle Distal Tip Steering Conor James Walsh, Jeremy Franklin, Alexander H. Slocum, Julio Guerrero, Rajiv Gupta

M


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and any excess manipulation can lead to tissue damage and complications.

B. Clinical Consequences

Due to this difficulty in precisely placing needles and repositioning of their distal tip when inside the body, radiologists currently find it difficult to target lesions that are less that 10 mm in diameter and target multiple points of lesions. This results in a delay to diagnose cancer when the tumor size is small and apply precise local treatment to all points of a tumor while avoiding the surrounding anatomy. If a biopsy is required for diagnosis, often a patient is forced to wait for 3-6 months until the tumor is large enough so that it can be targeted. Some experienced physicians do choose to target smaller lesions but to achieve this, a large number of manipulations of the needle are required that results in increased tissue trauma, complication rates, x-ray dose and procedure times. While there are clear benefits to locally treating disease the number of procedures that can be performed in this way is limited. For example, current RFA probes only provide a static volume of coagulative necrosis. The probe is deployed at a single location to achieve a pre-determined (typically cylindrical, spherical or ellipsoidal) burn volume that includes the tumor. Due to the difficulty in placing the instrument precisely, often the physician is forced to take unnecessarily large treatment margins so as to avoid leaving part of the tumor intact. To generate large ablation volumes RF ablation systems have been developed that have three or more electrodes in parallel attached to a single probe handle. However it is difficult to keep all electrodes correctly spaced relative to each other and these systems often cause the tissue or tumor to be pushed out of the way as opposed to punctured. Another approach to achieve a larger burn volume with a single needle insertion through the skin is to have an umbrella like flock of electrodes deploy from the distal tip of the needle. To generate even larger or irregularly shaped ablation volumes multiple skin punctures are made with multiple probes to insert electrodes into different locations of the tumor so as to burn the entire extend of the tumor.

C. Need for Needle Distal Tip Steering In order to correct for these errors or to position the distal tip of the needle at multiple points within the body through a single skin puncture, it is desirable to reposition the distal tip

of the medical instrument while it is inside the body. For biopsy, an increased targeting capability and an ability to accurately target multiple locations within a single lesion would allow for higher diagnostic rates as well as a reduction in the procedure time and radiation dose for the patient. As well as correcting for targeting errors due to instrument deflection or tissue deformation, there is also room for a radical departure from the current methodology for local treatments such as radiofrequency ablation. Instead of a large diameter probe, or a probe with multiple electrodes, a very thin probe with a small burn volume could be inserted into the tumor and then robotically steered so as to raster-scan through the tumor after a single needle insertion through the skin. Such a system would enable treatment to be applied to multiple small but overlapping volumes allowing conformation to the tumor morphology, while avoiding important collateral structure. Finer treatment margins as well as the ability to treat multiple tumors, satellite lesions or tumors that cannot be accessed along a straight path are clear advantages of such an approach.

II. PREVIOUS WORK Various robotic and navigation systems have been developed to increase the accuracy of percutaneous needle placement. These systems generally consist of robots that mount on the CT scanner bed [2-4] or the patient [5-7] and provide some method for remote needle orientation and insertion. The majority of these manipulators provide a remote center of rotation so that the needle can pivot about the skin surface [8-10]. All of these systems use some combination of intra-operative CT images [2], pre-operative 3D imaging [2], static real-time fluoroscopy [2, 11] or tracking systems [12-14] for procedure planning and execution. The doctor typically controls them via joystick [2, 11] or a point and click interface that directly incorporates the medical images [3, 6]. In all cases some registration between the patient, robot and imaging coordinate systems is required. This can be performed automatically or semi-automatically with fiducial markers placed on the tools and patient [3, 5, 13-16] and in some cases these fiducial markers are tracked so as to provide motion compensation.

Although robotic systems have demonstrated the ability to improve the accuracy of needle placement, no telerobotic system has the capability to reposition the distal tip of the needle after the needle has been inserted through the skin and into the body. As mentioned previously, this may be used to correct for targeting errors due to instrument deflection or tissue deformation as well as target multiple points of a tumor for more effective diagnosis and treatment.

Research is ongoing to develop needle insertion strategies to minimize deviation of the needle from its desired path. Spinning of the needle as it is being inserted has been shown to reduce deflection [17]; however continuous spinning of a beveled needle may lead to tearing of tissue, resulting in increased trauma for the patient. Another approach that has been used by physicians is to rotate the needle by 180˚ a number of times during insertion causing the needle bevel to point in the opposite direction. This approach has been

Figure 1 - Sources of targeting errors in image-guided, percutaneous interventions


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automated with a robotic system where the amount of needle deflection was estimated using a model based approach from real-time force and moment data at the needle base (where it is gripped by the robotic manipulator) and the insertion depth [17]. The system worked by automatically rotating the needle 180˚ when the bending moment on the needle exceeded a predefined threshold before inserting it further.

An extension of minimizing needle deflection is that of needle steering. Currently, physicians attempt to steer standard needles by bending the part of the needle that is partially or fully outside the body so that it takes a curved trajectory when inserted. They also exploit the asymmetric bevel tip to cause the needle to “glide” to one side. These approaches do allow some needles to be steered; however, they are not very intuitive for radiologists and require reaction forces from the tissue; so controlling the needle motion is difficult. Mathis and Yankelevitz et al. developed a steerable needle that enables the radiologist to exert a curved shape on the needle [18]. The mechanism consists of a pivoting handle on the proximal end of the needle that is attached to its distal tip via four small steel bands. The radiologist can cause the needle to take a curved shape by manipulating the handle or joystick with his/her thumb. However, this device lacks accurate controllability; in particular, when it is already partially inserted into the body. Further, there is no locking mechanism to hold a particular curvature.

Various research groups are actively working on automating needle steering in order to improve its accuracy and controllability. The approaches that have been taken use bevel [19-21] and external [19] forces on the needle to cause it to bend so as to steer through the tissue. In [19], DiMaio and Salcudean formulated a needle Jacobian that described tip motion due to needle base motion and a tissue finite element model. They assumed that the needle was rigid compared to the tissue and that it was redirected by pulling on and angling the needle shaft outside the body. Although they demonstrated the ability to steer the needle, this approach involves the knowledge of the tissue material properties. Further, the large forces may result in tearing and significant damage to the tissue. Webster et al. considered a system where the needle was flexible relative to the tissue and thus does not displace a large amount of tissue in order to steer itself [20]. For this system, needle steering resulted from the asymmetric forces on the needle tip due to the bevel. They developed a variant of the three-degree-of-freedom nonholonomic bicycle model for steering needles with bevel tips. However, this approach also required knowledge of the material properties and involved fitting model parameters using experimental data from various tracked needle insertions into a phantom with homogenous material properties. This approach is unsatisfactory as multiple needle insertions would not be permitted clinically. Further, a large beveled tip and a small diameter needle are required to achieve a large working volume so this method is not suitable for larger diameter instruments.

A similar system is presented in [21]. The system inserts the needle and applies “duty cycling” to the rotation, i.e. rotating the needle in a spin-stop-spin-stop manner such that the bevel stops in the same orientation each time with longer stop intervals creating steeper curvature and longer spin intervals

creating a straighter trajectory. A kinematic model for needle steering using this method is presented in [22] and is based off the nonholonomic model for bevel needle steering presented in [20]. However, as mentioned earlier needle spinning will result in damage to tissue, only thin needles can be used and the same difficulties exist in finding the values of the model for controlling the motion. Salcudean et al. developed a device that enables multiple needle curvatures to be achieved by employing a stylet that is longer than the cannula so that up to 2 cm of the stylet tip (with a mild curve) can be selectively exposed [23, 24]. The extended curve essentially acts as an adjustable bevel on the tip of the needle. Motors provide actuation for the rotation and extension of the stylet with respect to the cannula. The steering direction is selected by rotating the stylet and the steering rate is selected by extending the stylet and exposing the curve. By withdrawing the stylet, the stiffer cannula straightens out the curve and the needle becomes approximately straight. A miniature two-axis analog joystick is mounted on the shaft of the device facing opposite the insertion direction so that the physician can firmly hold the device in his or their palm and manipulate the joystick with the thumb. This system also requires a thin flexible needle whose complete shaft can bend due to reaction forces from tissues and “follow” the steering tip.

It is clear that there are limitations with the needle steering strategies that have been employed to date; in particular, relying on knowledge of the material properties has obvious limitations. Material properties are inhomogeneous, vary with patients as well as across tissue layers. While these strategies offer the potential for steering around anatomic structures, a major limitation is that once the needle tip is placed at the desired point, it cannot be easily repositioned to a near by point. Instead of steering the entire needle length, another approach is to insert the needle along a straight trajectory (ideally) and then have a mechanism for repositioning the distal tip of the needle. Such a mechanism would be useful for targeting multiple points in a volume or for directing the needle tip around obstacles when a straight line trajectory can not be taken.

Two passive devices exist that accomplish this via an inner cannula made from a superelastic material with a preformed bend on the distal end that can be substantially straightened when retracted into a stiffer coaxial outer cannula [25, 26]. Needles based on these designs are now commercially available with the main application being for spinal based procedures such as vertebroplasty. Using these devices, materials (e.g. bone cement or ethalol) can be injected at multiples locations in a volume by rotating the inner needle about and inserting it along its axis. The needle can also be “steered” around obstacles; although only the distal portion so there are limitations as to how much steering can be achieved.

Despite the commercialization of products based on the concept of deploying a flexible pre-curved stylet from a concentric straight cannula, no analytical or empirical data exist to guide the design of new medical products. Further, the current systems require manual operation and the do not lend themselves to accurately targeting points in a volume. The work in this paper addresses these limitations through the characterization of a needle steering system based on the


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concept of deploying a curved stylet from a straight cannula and development of a telerobot capable of the relative motions required to position the distal tip of the stylet within multiple points in a target volume after a single needle insertion through the skin.

III. DESIGN CONSIDERATIONS In order to develop a needle steering system based on the

concept of straightening a curved needle inside a stiffer outer cannula it is necessary to understand how effectively a needle can be straightened, what materials and geometry can he used so that the material does not yield, what force/energy is necessary to straighten the curved needle and how the curved segment of the needle will deflect when it encounters forces during cutting or other operations. Figure 2 illustrates the concept of straightening a pre-curved flexible stylet inside a stiffer, concentric outer cannula. Upon deployment of the stylet from the distal tip of the cannula, the stylet will then take its preformed shape.

A. Material and Geometry Considerations From Figure 2 it is apparent that in being straightened the

curved portion of the stylet will undergo significant strains. These strains will depend of the radius of curvature and will be assumed to vary linearly along the cross section of the stylet, a reasonable assumption when the end radius is significantly larger than the diameter of the wire. The longitudinal strains in the stylet are inversely proportional to the radius of curvature and vary linearly with the distance y from the neutral axis

xyερ

= − (1)

The maximum strain will be located at the maximum distance from the stylet cross section. A review of medical procedures and physicians provided specifications on the stylet geometry and material properties. Nitinol and stainless steel were selected due to their biocompatibility and pre-existing use in the manufacture of needles for percutaneous interventions. Nitinol exhibits two material properties depending on its alloy, superelasticity and shape memory, which are used extensively in medical devices. Superelastic Nitinol can withstand strains of up to 6-10% with little to no yielding in conditions around the alloy’s Active Austenite Finishing Temperature. At high

stress, austenitic Nitinol is induced into a deformed martensitic crystal structure, allowing it to elongate with relatively constant stress applied to it. Nitinol is not stable at this temperature in its martensitic state, and will revert to austenite when the stress is relieved.

A subset of stylet geometries (diameters ranging from 0.5 – 1.0 mm and radii ranging from 10 – 40 mm) were chosen that would fit inside standard medical needle cannula ranging from 20 to 14 gauge. Based on these specifications the maximum strain for these ranges was calculated and is plotted in Figure 3.

It can be seen that for all cases the yield strain of stainless steel (0.2%) is exceeded, while Nitinol’s superelastic properties enable it to meet the requirements for the design specifications identified.

B. Force/Energy to Straighten the Curve If we assume that the curved beam is straightened by pulling it inside a rigid outer cannula then given that there will be some clearance between the outer diameter of the stylet and the inner diameter of the cannula then we can assume that the shape the stylet will take is shown in Figure 4 below.

Cantilever Beam Model

A simple cantilever beam model can be used to estimate the force required to straighten the stylet. The geometry of the curved stylet of radius, R, is shown in Figure 5.

Figure 3 – Predicted Wire Strain for Pre-Bent Wire Drawn into Straight Cannula

Figure 2 – Pre-curved flexible stylet and rigid outer cannula

Figure 4 – Model of stylet behaviour when stylet is fully retracted into cannula


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The maximum strain analysis results illustrated in Figure 3 show that for almost all geometries the Nitinol will surpass its transition strain (estimated to be 0.7%) and enter the superelastic zone. From the manufacturers data sheets (Fort Wayne Metals Inc.), the young’s modulus before the transitions strain was estimated as 75 GPa and the assumption was made that the loading plateau stress, σSE, remains constant at 517 MPa for the entire plateau up until a yield strain of 6%. The consequence of this is that as the stylet is straightened, there will be an increasing component of the cross section in the superelastic stress-strain region as illustrated in Figure 6. The radius of curvature of the stylet is ρ. As the stylet goes from straight to curved, the cross section will have an advancing superelastic front that will reach its maximum area when the stylet is fully inside the cannula. Thus, the stylet can be treated as a composite beam with ASE loaded with a constant stress of 520MPa, and areas A1 and A2 undergoing elastic deformation.

Superelastic Zone

Neutral Axis

Center ofCurvature

d

R ρ RSE

Y

Z

A relation between the location of the superelastic transition zone, RSE, and the neutral axis, R, can be identified based on the superelastic transition stress σSE in a curved beam with elastic stress distribution.

SESE

SE

R REk

Rσ

−= (2)

where k has a value of 1.1 when the bend radius is significantly larger than the wire diameter. The expression can be rearranged to give RSE as a function of R.

( )SE

se

REkREkσ

=+

(3)

For a given strain in the stylet, the location of the neutral axis, R, can be calculated using the principle of static equilibrium, and assuming that the stresses due to bending dominate. Thus the net axial force in the wire can be equated to zero yielding

2 2

2 2

2 ...2 2

2 ( )... 02 2

SE

SE

R

SE

R

d dy dy

Ek R y d dy dyy

ρ

ρ

σ ρ

ρ

⎛ ⎞ ⎛ ⎞+ − − +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

− ⎛ ⎞ ⎛ ⎞+ − − =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

∫

∫ (4)

Finding Effective Stiffness With values for R, composite beam bending theory is applied to find an effective stiffness, EIeff, for a beam that has a partially elastic, partially plastic (superelastic) stress distribution. Modeling the elastic region of the wire with Young’s Modulus E (75GPa), and the plastic (superelastic) region with a Young’s modulus of zero, EIeff can be obtained from

( )

222 2

2

22

SE

d

effd R

dEI Ey y dy

ρ− + −

⎛ ⎞= −⎜ ⎟⎝ ⎠∫ (5)

In equation (5) the effective stiffness at the structure’s maximum strain state is evaluated, i.e. for a straight beam bent to the initial radius of curvature of the stylet. It should be noted that for a few cases, the maximum strain in the wire was calculated to be less than the 0.7% transition strain of Nitinol and so the beam was consider as purely elastic and equation (5) was not used. Energy Analysis Assuming elastic deformation, the energy contained within a curved beam shown in Figure 5 is

2 2

0

12

MU dEI

πρ θ= ∫ (6)

The curved cantilever shown in Figure 5 will have a moment that varies along its length because it is subjected to the tangential force, F. Thus, the radius of curvature will also vary along its length. For an elastic-perfectly plastic (superelastic) beam, however, EIeff is dependent on the bend radius as shown in equation (5). Thus, EIeff is based on geometric and material properties that are not considered in this model. For the relative motions of the stylet and cannula being considered, the stylet is straightened by withdrawing it inside a cannula, while the distal end maintains its preformed curvature. We assume that because of this incremental straightened, starting at the proximal end and finishing at the distal end, that our assumptions for EIeff and R are a reasonable first order estimate. Due to the path dependent or dynamic nature of the problem future models could be developed to obtain a more

Figure 6 – Cross Sectional view of bending superelastic wire

Figure 5 – Curved beam geometry


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accurate estimation of the energy. .The bending moment, M, in the stylet is given by cosM FR θ= (7)

Substituting EIeff and M into the equation and integrating along the length of the curved beam, i.e. from zero to θ the energy is

( )

2 2 2

02 3

1 cos ( )2

1 sin 22 4

eff

eff

FU dEI

FUEI

θρ θ ρ θ

ρ θ θ

=

⎡ ⎤= +⎢ ⎥⎣ ⎦

∫ (8)

The end-point deflection, at θ, due to force F can be expressed as

sin( ) UF

δ ρ θ ∂= =

∂ (9)

Evaluating and solving for F yields

2

sin( )1 sin(2 )

2 4

effEIF

R

θθ θ

=⎡ ⎤+⎢ ⎥⎣ ⎦

(10)

Maximum deployment and retraction force Knowing F, the frictional force between the cannula and the bent stylet can be calculated based on the assumption that, in a cannula, a straightening force and its corresponding normal reaction force, also equal to F, are applied and supported at two points within the cannula (Figure 4). Thus

2

sin( )2 2

1 sin(2 )2 4

efffriction

EIF F

R

θµ µ

θ θ= =

⎡ ⎤+⎢ ⎥⎣ ⎦

(11)

The maximum deployment force is when the stylet is fully inside the cannula. Evaluating for a ninety degree bend, i.e at π/2

2

8 effdeploy

EIF

R

µ

π= (12)

Figure 7 shows that the stylet enters the cannula an incident angle, and therefore, a horizontal and vertical component of retraction force is expected.

d D

-(D-d) ρ ρ

θNormal

FN

To calculate the full retraction force required to draw a needle into the cannula, Fnh is calculated to sum with the friction force. To find Fnh, the angle of the normal force FN is found with the assumption that the wire maintains its radius of

curvature between the outer edge of the cannula and the cannula’s upper wall as shown.

2 2

sin( ) sin( )2

1 1sin(2 ) sin(2 ) tan arcsin 12 4 2 4

retract friction nh

eff effretract

F F F

EI EIF

D dR R

θ θµ

θ θθ θρ

= − −

= − −⎡ ⎤ ⎛ ⎞⎛ ⎞−⎡ ⎤+ + −⎜ ⎟⎢ ⎥ ⎜ ⎟⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎝ ⎠⎝ ⎠

The proceeding analysis was solved using Maple where first equations (3) and (4) were numerically solved to find R and RSE and then the values of Fdeploy and Fretract were calculated.

Experimental Analysis To validate the analysis, experiments were performed to determine the required forces for relative motion between a cannula and a pre-bent stylet. To achieve this, a fixture and procedure were first developed for manufacturing Nitinol stylets with varying wire diameter and bend radius. An experimental rig was then developed that enabled these stylets to be deployed from and withdrawn into a subset of stainless steel cannulas of various diameters.

The fixture, shown in Figure 8 maintained the Nitinol in its final desired shape through heating and quenching while providing minimal thermal resistance to ensure rapid quenching.

Upper Picture Frame

Upper Vent Plate

Outline Plate

Lower Vent Plate

Wire Locating Plate

Lower Picture Frame

The primary bars are 2.5–4X the thickness of the bar to maximize exposed quench area, while minimizing rig deformation. For experimentation, the cannulas were mounted in a custom-made needle testing fixture shown in Figure 9. The fixture was designed to (1) bolt to an ADMET universal testing machine, (2) hold a cannula rigidly and vertically, and (3) provide enough space for ballistics gel samples to be held under a cannula for future experiments. The cannula was held in a pin vice attached to the rig and a matching pin vice screwed into the load cell above the test fixture to hold the stylet.

Figure 8 – Nitinol Quench Fixture

Figure 7 – Forces on stylet as it enters the cannula

FnFnh


7

Cannula Chuck

Pre-BenNeedle

Cannula

System Fixture

Data were recorded for 48 permutations of cannula

diameter, wire diameter, and bend radius to identify trends across all three dimensions. At the beginning of each test the PC was set to record data and deploy the stylet at 7.5mm/sec, a cannula was flushed with Isopropyl alcohol and attached to the Needle Testing Fixture to let dry, and a stylet was cleaned by the experimenter with Kimwipes and Isopropyl alcohol. Figure 10 illustrates the force-time data for a .508 mm wire with a 30 mm bend radius in a 14 gauge cannula.

14-.508-30-7.5

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 5 10 15 20 25

Time (s)

Load

(N)

Series1Series2Series3Series4Series5

Stylet in Cannula

Stylet Deployment

Stylet Retraction

Stylet in Cannula

Starting from the left of the time axis, relative motion

between the stylet and cannula when the stylet was completely within the cannula produced a nearly constant force as measured with the load cell. As the stylet was deployed from the cannula the force was observed to decrease until it reached a level close to zero when the curved portion of the stylet was completely deployed. Some small force was still observed due to slight misalignment between the cannula and stylet. The direction of movement of the ADMET machine was then reversed and hence the sign of the force changes. Retraction of the stylet into the cannula resulted in an increasing force that reached a peak and then reduced to a steady state value that was of a similar value to that observed just before the stylet was deployed from the cannula as we expected.

Comparison to Analytical Model To examine trends in deployment and retraction force for varying cannula diameter, stylet diameter, and bend radius, the deployment force as a function of the various combinations of cannula diameter, stylet diameter and bend radius and the data for a 16G cannula is shown in Figure 11 and compared to the analytical model. The error bars on the experimental data represent the standard deviation between five experimental runs at each data point. Exponential curve fits are included in the plots to display trends so as to easily compare the experimental data to the analytical model.

Deployment Force of Pre‐Bent Needle in 16G Cannula

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25 30 35 40 45

Needle Bend Radius (mm)

Deploym

ent Force (N)

.508mm

.635mm

.838mm

.990mm

.508mm Analyze

.635mm Analyze

.838mm Analyze

.990mm Analyze

Expon. (.508mm)

Expon. (.635mm)

Expon. (.838mm)

Expon. (.990mm)

C. Deflection of the Tip of the Needle

When the stylet is deployed from the cannula inside the body it will experience a force tangential to its tip (assuming a symmetric beveled tip) due to cutting of the tissue. The force required to puncture a tumor is typically higher than the force to cut through healthy tissue. As such we desire the stylet to be designed to be sufficiently stiff so as to it does not deflect appreciably under the expected cutting forces of a particular tissue. The deflection of the end-point can be assumed to a measure of the performance of a stylet with particular material properties and geometry. We can estimate this by assuming that the cannula is grounded, the stylet is fully deployed and rigidly attached to the cannula at the exit point. In reality the deflection of the curved stylet is going to also be a function of the stiffness of the tissue that surrounds it and the tissue will act to limit its deflection. The effect of the tissue can be adding by considering the stylet as a beam on elastic foundation [27]. Figure 12 shows the model of the curved beam with the elastic foundation included. The differential element is also shown and the model assumes that the reaction forces in the foundation are normal to the axis of the beam and proportional at every point to the radial deflection, y, of the beam at that point. The reaction of the foundation per unit length of the beam, p, is given by p ky= (13) Since y is taken to act radially and oppose the deflection of the beam, a positive displacement, when the radius of curvature is

Figure 11 – Deployment Force vs. Bend Radius plots for .508mm-.990mm stylets with 10mm-40mm bend radii deployed through a 16G cannula at 7.5mm/sec

Figure 10 – Load vs. Time plot for 5 runs of .508mm stylet with 30mm bend radius deployed through a 14G cannula at 7.5mm/sec

Figure 9 – Needle Testing Fixture


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increasing, will result from a tangential force as shown in Figure 12 and the elastic medium will be assumed to be in compression. In this model the elastic foundation is also assumed to represent tensile forces to mimic tissue on the other side of the stylet. Equation (13) implies that the supporting medium is elastic. Organ tissue has been shown to have nonlinear material properties [28] but for small strains it can be assumed to be approximately linear with a young’s modulus of 100 kPa. As it essentially acts as a stiffening spring, this assumption will be conservative in estimating the end point stylet deflection.

The infinitesimal differential element is acted on by the shearing force, Q, normal force, N, bending moment, M and reaction force of the foundation pdx. From the conditions of equilibrium acting on the differential element we can derive

3

2 31dy dM d Mk

dx dxr dx− = (14)

and the differential equation of bending of a circular arch of radius of curvature r and flexural rigidity EI is

2

2 2d y yEI Mdx r

⎛ ⎞+ = −⎜ ⎟⎜ ⎟

⎝ ⎠ (15)

Combining these, the fundamental differential equation of bending of circular beams supported on elastic foundation is then

5 3

5 2 3 42 1 0d y d y k dy

EI dxdx r dx r⎛ ⎞+ + + =⎜ ⎟⎝ ⎠

(16)

which can be written in terms of θ

5 3

25 32 0d y d y dy

dxd dη

θ θ+ + = (17)

where

4

1r kEI

η = + (18)

This general solution for this equation is

( )

( )0 1 2

2 4

cos ...

... sin

y C C Cosh C Sinh

C Cosh C Sinh

αθ αθ βθ

αθ αθ βθ

= + + +

+ (19)

where C0, C1, C2, C3 and C4 are the constants of integration and

12

ηα −= and 1

2ηβ +

= (20)

The boundary conditions for the stylet in tissue with a the proximal end of the curved segment assumed to be grounded and a tangential force at the distal end yield five equations that can be used to solve for the five unknown integration constants

(0) 0y = (21)

(0) 0dydθ

= (22)

( ) 02Q π = (23)

( ) 02M π = (24)

( )2N Fπ = (25)

Based on a tissue cutting force of 3 N, this analysis yielded that the radial deflections of the end-points ranged between 0.5 and 2.5 mm. Targeting experiments are planned (see Future Work) to experimentally measure the end-point deflection of a stylet deployed from a cannula into ballistics gelatin.

IV. MECHANICAL DESIGN Based on the analysis and experimental data a prototype telerobotic mechanism using the principle of a pre-curved stylet concentric with a stiffer outer cannula was developed. The system is capable of axially advancing and rotating a cannula and axially advancing a stylet though the cannula. The telerobot was designed to be attached to an access cannula that is first placed close to the desired target volume as illustrated in .

The depth to which the access cannula is placed is typically 5-15 cm and the telerobot would be attached to the access needle via a standard medical leur-lock connector. An advantage of this approach is that the access cannula can be either placed manually by the physician or with the aid of a patient mounted robot such as Robopsy [29]; however, if placed manually, there must be a means of supporting the access cannula and the attached mass of the telerobot. Further, this approach also enables the system to be used within the size constraints of a medical imaging system as the overall height requirement is reduced by first placing the access cannula. Alternatively, the system could easily be attached to the end of a robotic arm that can perform the first gross insertion and in this case, no access needle is required.

The prototype system is shown in Figure 14 and is designed to be made from largely plastic components for CT

Figure 13 – Concept of attaching the telerobot to a pre-inserted access cannula and targeting multiple points in a volume through advancement and rotation of the components.

Figure 12 – Curved beam on elastic foundation and differential element


9

compatibility. Actuation of the system is achieved using micro stepper motors. The system height and diameter are 15 cm and 5 cm respectively with a weight of approximately 180 grams.

The device has a protruding cannula with a stylet with a

curved distal tip pre-assembled inside. The proximal end of the cannula is attached to the distal end of a screw-spline that enables it to be translated and rotated with respect to the casing. The screw-spline is a modified plastic ACME threaded screw that also has a splined groove along its length. Nuts 1 and 2 (that are driven by micro stepper motors through spur gears) engage the screw threads and spline respectively. Nut 1 has a bore that is threaded to match the lead of the screw and Nut 2 has a keyed feature that engages the spline. Translation of the stylet is achieved in a similar way in that it is a second ACME threaded screw with a splined groove. A keyed feature on the inside of the screw-spline mates with the splined groove to constrain it from rotating. Further, this key also causes it to rotate with the cannula as the screw-spline is rotated. The cannula and stylet both attach to the screw-spline and screw respectively via plastic threaded inserts that are bonded to the proximal end of the cannula and stylet. The length of the cannula and stylet are chosen so as to be positioned at the distal tip of the access cannula when the parts are connected via a standard medical leur-lock.

A. Transmission Selection The theoretical and experimental results of section III yielded the forces and torques required to withdraw a curved stylet into and deploy it from an outer cannula. Using these numbers and preciously reported results from measuring the force to advance a needle in tissue as design specifications, the appropriate motors and transmissions were then selected. When choosing a leadscrew it is important to determine the necessary torque to be applied so as exert sufficient axial force (i.e. for cutting through tissue and overcome friction between cannula and stylet), overcome frictional forces due to sliding contact between the threads and also any other friction forces arising from bearings. The general equation for calculating the

torque to raise a load is

sec

2 secm m

m

Fd l dT

d lπµ α

π µ α⎛ ⎞+

= ⎜ ⎟−⎝ ⎠

(26)

Where F is the desired maximum force, dm is the pitch diameter of the lead screw, l is the lead, µ is the coefficient of friction between the threads and α is the ACME thread angle (i.e. 29˚). Using a simple sliding test, the coefficient of sliding friction of Acetal on Acetal was found to be 0.2. The pitch diameter for each of the threaded profiles was obtained from a combination of size and strength constraints as discussed later.

The stepper motors selected for this application are 10 mm diameter (AM1020, Faulhaber Inc) and have a holding torque of 2.4 mNm. Knowing the lead of 1/16 inch (1.5875mm) for the cannula and stylet we can rearrange equation (26) to find the maximum axial force obtainable. This analysis suggests that it was necessary to also have a gear reduction between the motor shaft and the nut on the screw. Achieving a higher transmission ratio by choosing a lower lead would require a non-standard ACME pitch and further, is not effective as the efficiency of power transmission of the screw is proportional to the lead. If T0 is the torque achievable assuming no frictional losses due to sliding contact between the threads the efficiency, e, for power transmission with a screw is given by

0

2T FleT Tπ

= = (27)

The preferred option to increase the maximum achievable force was to use a planetary drive attached to the micro stepper motors and a further gear reduction between the gearhead pinion and nuts. The planetary gearhead that was chosen had a two-stage 16:1 reduction (10/1 from Faulhaber) with a rated efficiency of 80%. A further gear reduction of 2 between spur gears on the gearhead pinions and each of the screw or splined nuts had an estimated efficiency of 90%.

Use of a gear reduction between the motor output and screw

and spline nuts also meant that the stepper motor could be used to constrain the screw-spline from rotating during a commanded pure translation or during a deployment of the stylet. Further, use of this gear reduction improved the angular and linear resolution of the system as the step size for the motors is 18˚. During operation of the device the cannula and stylet will be activated independently. As such, it will be necessary for the cannula to retain its axial position when the stylet is being translated and vice versa. An inherent advantage

Figure 15 – Screw-spline drive components.

Figure 14 – Section view of the needle steering system..

Screw Nut Spline Nut


10

of using the ACME screws for achieving translation of the stylet and cannula is that they are non-backdrivable.

B. Strength Analysis As mentioned earlier the strength of the components also

determined the sizing of the mechanism as well as geometry constraints. In order to ensure that the structure could withstand the forces and torques exerted on it, an analysis of the stresses in the leadscrew and gears were calculated. The axial and radial loads on the nut and gearhead bearings were also calculated to ensure that the rated load capacities of the bearings were not exceeded. Cannula and Stylet Leadscrews The axial stress in a screw due to a load, F, is given by

24

( )r i

Fd d

σπ

=−

(28)

where dr and di are the root and inside diameter of the leadscrew respectively. Assuming a solid screw, the nominal shear stress in torsion, T, in the leadscrew is given by

316

r

Td

τπ

= (29)

Assuming a stress concentration of two, the vonMises equivalent stress can be calculated from

2 22* 3equivelentσ σ τ= + (30)

In Figure 16 a plot of σequivalent is shown as a function of root diameter (ranging from 5 to 12 mm) and applied axial force. It can be seen that the stress is always below the yield stress of Nylon of 60 MPa. Based on this analysis the root diameter for the stylet screw was chosen to be 5 mm to ensure a factor of safety of approximately 3.

Spline The keyed feature for each of the splined grooves on the stylet and cannula screws was sized to ensure that it would be able to withstand the shear stresses generated due to torque transmission which is given by

sheark

2Td A

τ = (31)

Where dk is the diameter where the key engages to transmit the torque. Spur Gears Spur gears transmit torque by generating forces between the gear teeth. Thus a torque transmitted at a pitch diameter, dp, results in a radial load, Fradial, on the shaft on which the gear is mounted, given by

radial2

p

TFd

= (32)

Further, a pressure angle φ, between the gear teeth generates a force that acts to spread the gears apart spread radial sinF F φ= (33)

Thus, to ensure that the gearhead shafts were not overloaded the spur gears on the motor pinion were placed directly in line with the bearings from the gearhead shaft. The plastic nut spur gears were also mounted in bearings that were embedded and glued into the plastic mounting plate. This ensures that the supporting structure and spur gears hubs would be sufficiently stiff so that the teeth would always remain engaged.

C. Component Sizing and Selection A functional requirement for the system was that it could be compatible with CT machines. As such, the system parts were designed to be constructed largely of plastic. Plastic parts do show up on CT images but because of their low density they do not cause shadowing artifacts. The stepper motors and planetary gearheads used for actuation will result in shadowing artifacts; although they were placed away from the central axis of the cannula and stylet so as to minimize distortion to the images. Another requirement was that the system should have sufficient travel so as to target a volume on the order of 125 mm3 while also being compact enough so as to fit inside the bore of an imaging machine. This requirement, along with the strength analysis discussed previously drove the sizing of the system.

A 6mm outer diameter lead screw was chosen axial movement of the stylet. This screw was concentrically nested inside an 11mm diameter hollow plastic screw-spline. The nuts for the screw and screw-spline were manufactured from off-the-shelf Acetal spur gears; 24 mm pitch diameter for the cannula screw-spline nuts and 22.5 mm pitch diameter for the stylet screw. The spur gear nuts for the screws were internally threaded with a 1/16 inch AMCE thread profile to match the screws. The spur gear nut for the spline had a slot broached into the inside diameter that allowed a small plastic 1.5 mm diameter key to be inserted as shown in Figure 15 previously. This key then engaged the splined groove on the cannula screw-spline. A similar slot was machined into the top of the screw-spline where an identical key was used to constrain the rotation of the stylet screw with the cannula screw-spline.

Stainless Steel spur gears with a pitch diameter of 12 mm (SDP-SI) were used to transmit power from the planetary gearhead to the plastic spur-gear nuts. A hubbed spur gear was chosen so that the gear teeth were placed in line with the sintered brass bearings in the planetary gearhead. A brass

Figure 16 – Equivalent vonMises stress in nylon screw as a function of root diameter and axial load

5 6 7 8 9 10 11 120

5

10

15

Root Diameter (mm)

Von

Mis

es S

tress

(MP

a)

Axial Force = 5NAxial Force = 10NAxial Force = 15NAxial Force = 20N


11

insert was placed inside the 5mm bore of the spur gear and a 2mm diameter hole was drilled out. The gear was attached to the gearhead shaft via a set screw that pushed up against a flat on the shaft. The motors were clamped to their respective mounting plates so to aid with gear alignment and repair. The design was such that the same plastic clamp could be used for each of the motors.

Ceramic bearings were used for attaching each of the nuts to their respective mounting plates (VXB Bearing Inc.). These bearings provided a compact non-metallic package with sufficient axial and radial loadings for the forces we found in Section III; however, they are brittle and expensive. Plastic ball bearings were also considered but they have significantly larger height and outside diameter for a given internal diameter as well as approximately an order of magnitude higher axial play. A cylindrical precision ground tube (McMaster-Carr) was used to house all of the components. The tube has an internal tolerance of ±0.0005” and so provides the secondary purpose of a guide way for the flanges of the cannula screw-spline assembly. In order to reduce friction between the flanges and inside of the casing, 4-48 spring plungers (McMaster) were threaded into the side of the flanges. Spring plungers provide a ball element at their tip that is attached to a spring and thus provide rolling contact on the casing for translation and rotation of the screw-spline stages. Side hole were machined into the casing to provide a means for attaching the mounting plate for the motors that drive the screw-spline as well as the top and base plates. A standard ¼-24 plastic leur-lock was threaded into base plate for attaching to standard medical needles for access to the target site.

V. CONTROL The current embodiment of the system is designed to be controlled based on open-loop command signals sent to the stepper motors. The appropriate kinematic equations were derived that relate the motor angular positions to the distal tip of the stylet. A simple user interface was developed that allows a user to specify a desired position within a volume.

As discussed earlier, in order to reposition the distal tip of the stylet within a volume requires that the cannula be translated and rotated relative to the casing and the stylet be translated relative to the cannula. A schematic of the cannula and stylet is shown in Figure 17 with the distal tip of the stylet defined in standard Cartesian and cylindrical coordinate systems. Position variables to represent the motions of the cannula and stylet are also shown. Here we outline the necessary equations for determining the appropriate motor commands to position to a point in a CT coordinate system.

The radius of curvature of the distal portion of the stylet, R,

is assumed to remain constant when outside of the cannula. The included angle between a line tangent to the tip of the stylet and the axis of the cannula is defined as θ (see Figure 12) and it is related to the stylet curvature and displacement by

szRθ = (34)

The total bend angle of an undeformed stylet is defined as θcurve with the total length being given by the arc length as

curve curve *l Rθ= (35) which is the limit for stylet displacement relative to the cannula. The relationship between the curved needle and general cylindrical coordinates can be solved to yield the forward and inverse kinematics. Forward Kinematics From Figure 17 it can be seen that in the ρ-z plane the position of the tip of the curved stylet is a function of the radius of curvature of the stylet, R, and the amount it is extended from the cannula, zs, and the axial position of the cannula with respect to the casing, zc. Thus, from simple geometry we can derive

(1 cos )szR Rρ ⎛ ⎞= − ⎜ ⎟⎝ ⎠

(36)

sin sc

zz z R R⎛ ⎞= + ⎜ ⎟⎝ ⎠

(37)

The angle between the positive x-axis and the ρ-z plane is simply the angle of rotation between the cannula and the casing.

cϕ θ= (38) Inverse Kinematics Rearranging equations (36), (37) and (38) the equations relating the actuated degrees of freedom to a desired end-point in cylindrical coordinates can be obtained.

( )1cos 1sz R Rρ−= − (39)

Figure 17 - Coordinate system and position variables for cannula and stylet


12

sin )sc

zz z R R⎛ ⎞= − ⎜ ⎟⎝ ⎠ (40)

cθ ϕ= (41) If a desired end-point of the stylet is first defined in Cartesian coordinates then this point can first be transformed to cylindrical coordinates before the cannula and stylet positions are calculated. Mechanism Control The next step is to determine the necessary commands to be sent to the motors to achieve the desired zc, θc and zs so as to position the tip of the stylet at the desired location. The screw-spline concept was discussed earlier in Section IV where either pure translation or rotation of the cannula requires control of both motors. Table 1 illustrates how the three modes of operation possible (translation, rotation and spiral) are obtained as well as how the screw and spline nut inputs relate to the output motions.

Input Cannula Movement Mode Screw Nut Spline Nut Translation Rotation

1ω 0 1 2

lv ω π= 0

1 2ω ω= 2ω 0 2ω

0 2ω 2 2

lv ω π= 2ω

The equations for calculating the desired stylet screw nut angle, φs, and the angles for the cannula screw, φss1, and spline, φss2, based a desired position for the cannula for a commanded translation are

1 /2

ss c gss

zlπφ = and 2 0ssφ = (42)(43)

And for a commanded rotation are 2 /ss c gφ θ= and 1 2ss ssφ φ= (44)(45)

and for a commanded translation of the stylet is

/2

s s cs

zlπφ = (46)

where lss and ls are the lead of the cannula screw-spline and stylet screw respectively.

VI. ELECTRONICS IMPLEMENTATION The drive electronics for the system are contained in a control box that would be located away for the patient on the CT bed. It is plugged into a standard 120 V wall outlet and connected via a USB cable to a laptop. Inside the box are off–the–shelf components; a USB stepper motor controller (ARCUS Inc.), power supply (Name) and four stepper motor drivers (Name). The controller allows the system to be actuated remotely from the CT control room. A prototype software interface was developed that allows the movement of the cannula and stylet to be controlled.

User inputs may be specified in cylindrical or Cartesian coordinates that are then converted into desired rotations and speed and sent to the controller which in turn sends step commands to the individual motor drivers. This interface will serve the purposes of validated that a volume can be targeted with the device.

VII. CONCLUSION & FUTURE WORK In this paper we have outlined developed a telerobot capable

of repositioning the distal tip of a percutaneous instrument, after it has been inserted into the body. The analysis and experimental models developed will enable the system to be easily scaled for other medical procedures. Medical imaging system such as CT provides very high resolution images and ultimately, these commands will come from a 3D planning interface that directly integrates the medical images in a similar manner to [30].

Evaluation of the system is planned so as to characterize the targeting accuracy that can be achieved. Figure 19 illustrates the designed experimental setup for evaluation of the system.

The cannula and stylet will be deployed to multiple points

into ballistics gelatin that is cast into a transparent container. A

Figure 19 - Experimental setup for evaluation of telerobot

Table 1 – Modes of operation of screw-spline mechanism

Figure 18 - Prototype User Interface for controlling all axes individually or prescribing a position of the end-point of the stylet in cylindrical or Cartesian coordinates


13

grid is imprinted onto the back of the container so that images of the stylet position can be experimentally captured and compared to the commanded position.

ACKNOWLEDGMENT The authors wish to express their sincere appreciation to the Center for Integration of Medicine and Innovative Technology (CIMIT) for supporting this project.

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Documents

Steedle Technical Report