7 Prostate cancer is the second most common malignancy in American men . High -dose - 8 rate brachytherapy is a popular treatment technique in which a large, localized radiation 9 dose is used to kill cancer . Utilization of curvilinear catheter implantation inside the 10 prostate gland to provide access channels to host the radiation source is under 11 investigation by our group. To this aim, we have introduced an active needle to curve 12 inside the prostate conforma l to the patient’s specific anatomical relationship for improved 13 dose distribution to the prostate and reduced toxicity to the organs at risk (OARs) . This 14 work presents closed -loop control of our tendon -driven active needle in water medium 15 and air using th e position feedback of the tip obtained in real time from an ultrasound (US) 16 or an electromagnetic (EM) tracking sensor, respectively . The active needle consists of a 17 flexure compliant section to realize bending in two directions via actuation of two inter nal 18 tendons. The actuation system is developed using two Maxon motors programmed to pull 19 the two tendons at certain displacement s. An US or EM tracker sensor is used to track 20 the tip of the robotic tool in real time and provide position feedback to the con troller. 21 Tracking errors using US and EM tracker are estimated and compared. Results show that 22 the bending angle of the active needle could be controlled using position feedback of the 23 US or the EM tracking system with a bending angle error of less than 1.00 degree . It is 24 concluded that the actuation system and controller , presented in this work, are able to 25 realize a desired bending angle at the active needle tip with reasonable accuracy . 26 1. Introduction 27 1.1. Challenges associated with needle insertion tasks 28 Several minimally invasive diagnostic and therapeutic procedures rely upon needle 29 insertion techniques. The procedures’ success rate depends on accurate navigation of 30 the steerable needles and precise tip placement at target locations. Limited needle 31 actuation and flexibility inside tissue, movement of the target during needle insertion [1], 32 and inadequate visualization with the most practiced ultrasound (US) and magnetic 33 resonance imaging (MRI) inside of the patient’s body [2] are cited as common challenges 34 in manual or robotic needle placement. 35 An e xample of a minimally invasive procedure that benefits from accurate needle 36 placement is prostate brachytherapy. Prostate cancer is the second most common cancer 37 among men in the U.S. [3] with an estimated 288,300 new cases and 34,700 deaths in 38 2023 [4]. High -Dose -Rate (HDR) brachytherapy is an internal and temporary radiotherapy 39 method to remove cancerous tumors. Conventional HDR brachytherapy involves 40 placement of radiation sources close to the tumor using rigid, straight needles. Although 41 the conventional method has been promising [5]–[9] in terms of tumo r control, toxicities, 42 overall costs, and effectiveness (e.g., 5 -yr and 10 -yr distant metastasis -free survival 43 rates) [10]–[14], studies have reported side -effects such as edema in tissue, incontinence, 44 and impotence. The side effects are a result of excessive radiation and needle penetration 45 into sensitive organs such as the urethra, bladder, rectum, penile bulb, cavernous veins , 46 and neuro -vascular bundles. Also, use of HDR brachytherapy is limited in patients whose 47 pubic arch obstructs the transperineal path to the prostate, thereby interfering with needle 48 3 placement [15]. A study showed that the procedure was practical only for 24 out of the 40 49 patients studied due to pelvic bone arch interference [16]. Even a narrow pubic arch may 50 prevent proper implantation in a small prostate gland [17]. Known strategies to overcome 51 this problem such as oblique catheter insertion and pelvic rotation [18], [19] are not 52 optimal. Active tendon -driven needles [20] have shown promises to alleviate this concern 53 via their precise navigation in desired trajectories. 54 On another note, i mprecise catheter implantation oft en causes insufficient dos age to the 55 cancer and/or inadvertent radiation of the rectum, urethra, and bladder. The former 56 causes failure of treatment, while the latter results in adverse side effects like rectal 57 ulceration, incontinence, and dysuria (painfu l urination). Increased dose s to normal 58 structures is well correlated with increased toxicity after brachytherapy , and despite the 59 adoption of modern techniques, toxicity remains significant [21]. 60 Figures 1a & 1b show an US image of an anonymized patient’s prostate gland , where the 61 boundaries of the prostate are marked by a urologist. In conventional prostate 62 brachytherapy, needles are inserted in s traight trajectories (examples are shown in Figure 63 1a with dashed lines) usin g conventional straight and rigid needles ; however , conformal 64 to the patient’s specific anatomy (shown in the figure with small triangles) are curved 65 trajectories that are feasible to achieve using active flexible needles. Noting that most of 66 the cancer s are located at the peripheral zone of the prostate, placing radiation source(s) 67 in nearby areas (marked in Figure 1b via the curved access channels of the active 68 needles) is of great interest . In addition, active flexible needles provide the opportunity to 69 move away from organs at risk (OARs) such as urethra, bladder, and rectum and thereby 70 lower the risk of excess toxication. Figure 1b shows the prostate of the same patient 71 when deformed due to a needle insertion . The small triangles in both figures are used to 72 estimate the range of bending angle that an active needle should realize in a needle 73 insertion task (explained in Section 2.1). 74 Figure 1. Straight vs. curved trajectories for n eedle insertion inside (a) undeformed, and (b) deformed prostate. (a) (b) Straight Needle Prostate Capsule Active Flexible Needle Prostate Boundary 10 mm Rectum Radiation Sources 4 1.2. Background and related work 75 Researchers have been making efforts to introduce robotic needle insertion systems . For 76 instance, Gerboni’s group introduced a needle with high articulation by creating an 77 asymmetric tendon -actuated flexible section in one direction [22], while Chitalia’s group 78 has improved on the design by combining different notch patterns on a single needle [23]. 79 The group later proposes two distinct flexible sections along with a tendon -routing block 80 to minimize errors involving a misalignment issue [24]. Concerning efforts related to 81 imaging modalities, Kriger, et al. developed an MRI -compatible system with a hybrid 82 tracking method that eliminated the need for performing manipulator motions inside the 83 scanner while still reta ining accuracy [25] and Khadem’s group proposed a method to 84 estimate a passive needle tip’s trajectory using 2D transverse US images [26]. 85 Besides needle actuation, intraoperative tracking of the needle and tissue is of great 86 importance. Robotic closed -loop control of the needles navigating inside tissue relies on 87 the feedback of the needle tip positi on and/or the needle shape. Since the needles should 88 ultimately perform percutaneous procedures in nontransparent human tissue, vision - 89 based (camera) tracking is unrealistic. On the other hand, use of position/shape sensors 90 is not desired due to the small (meso -scale) size of the needle. Thus, US or MRI imaging 91 feedback are ideal candidates for needle tip and shape tracking; however, intraoperative 92 image acquisition and processing to have reliable feedback in real-time is challenging. 93 Recent research effor ts have introduced needle -tissue interaction models to predict the 94 needle behavior inside tissue. For example, a mechanics -based dynamic model was 95 introduced [27] to estimate deflection of a bevel -tip flexible needle while inserted into soft 96 tissues. In a later stu dy, a n overview of this dynamic model was presented with comments 97 about controllability of flexible needle insertions [28]. In another work [29], a needle 98 insertion model with mechanics of tissue rupture, and effect of insertion velocity on needle 99 force, tissue deformation, and needle work was presented. Another study in 2012 [30], 100 introduced a mechanics -based model for needle deflection with multiple bends during 101 insertion into soft tissue based on a Rayleigh -Ritz formulation. A later study in 2015 [31] 102 the beam theory was extended to develop a new mechanics -based dynamic model for 103 needle insertion in soft tissue. More recent works [32], [33] presented an estimator to 104 predict needle tip deflection and needle shape during needle insertion into soft tissue. 105 Finite element method s have also been developed to model needle -tissue interaction s 106 using a discretized model of the needle and tissue [34], [35] . A nonholonomic model for 107 steering flexible needles with bevel tips was developed in [36] for needle control with 108 actuations at the base of the needle. Another study in 2015 [37] presented an extension 109 to the kinematic bicycle model for bevel -tipped needle motion in soft tissue, accounting 110 for no n-constant curvature paths for the needle tip. The models are intended to be used 111 in model -based control of the needle while navigating inside tissue towards a moving 112 target. However, models are associated with errors, and could not be trusted without 113 additional sensory feedback and a proper controller. This work presents real -time and 114 reliable estimation of the needle tip to realize a closed -loop control of the needle 115 movement inside tissue. 116 5 Dexterity and visualization of robotic instruments are key factors in the procedure’s 117 success. Recent research has been focused on improving flexibility of the instruments as 118 well as sensing and visualization of the instruments inside the body . Examples of robotic 119 tools with improved flexibility include tendon -driven notched needles [41], [42 ], steerable 120 guidewires [43], continuum robotic tool [23], [44] , concentric tubes [45], [46] , and 3D 121 printed active flexible needles [47], [48] . To the best of our knowledge, none of the above - 122 mentioned active needles are specifically designed and developed for prostate 123 brachytherapy. 124 Several sensing and visualization techniques have also been developed to provide 125 feedback to the operating surgeon o f the robotic systems. Recent progress in sensing 126 and visualization of the robotic tools include US tip tracking [49]–[51], shape prediction 127 [52]–[54], Fiber Bragg Gratings (FBG) based force estimation and shape sensing [55], 128 [56] and shape memory alloy (SMA) self -shape and self -force sensing [57], [58] . Our 129 group has previously published works on needle actuation. In one work, we studied the 130 performance and interactive response of multiple distributed SMA actuators to manipulate 131 a 3D printed active flexible needle [59]. In another work, Karimi and Konh developed an 132 electrical resistance feedback contro l of multiple SMA actuators to control the movement 133 of a 3D steerable active needle [60] in a tissue phantom . 134 This work presents two tendon -driven active needles to achieve a robotic bidirectional 135 bending inside the tissue. The active needle consists of a flexure section, carefully 136 designed, for improved flexibility inside the prostate gland. The needle’s bidirectional 137 bending is realized via independent actuation of two internal tendons. A closed -loop 138 control framework is provided to use real -time US tracking in water medium and 139 electromagnetic ( EM) tracking in air as position feedback of the tool’s tip for closed -loop 140 control. Ultimately, the performance of the active needle in a water medium is evaluated 141 to assess if the US track ing system can provide reliable position feedback to the controller 142 for precise needle manipulation. 143 This manuscript is organized as follows: Section 1 provides an introduction about the 144 needle insertion tasks and their challenges (Section 1.1) , along with the background and 145 related works in this area (Section 1.2 ). Section 2 lays out our robotic and control methods 146 to improve the needle insertion tasks. Section 2.1 introduces our tendon -driven active 147 needle , while Section 2.2 and 2.3 cover the actuation system to manipulate the active 148 needle with US and EM tracking systems, respectively . Section 2.4 explains our closed - 149 loop control method for precise manipulation of the active needle . Section 3 summarizes 150 the results of the tendon displacement c ontrol in Section 3.1, and the active needle 151 response using the US and EM tracking systems in Sections 3.2 and 3.3, respectively. 152 Discussions and c onclusion s are outlined in Sections 4 and 5, respectively . 153 6 2. Materials and Methods 154 2.1. Robotic tendon -driven active needle 155 The design of the tendon -driven active needle is shown in Fig ure 2a. The active needle 156 was developed by carving a series of six small notches on each side of a superelastic 157 nitinol tube (Johnson Matthey, London, UK) . Schematic d imensions of each notch are 158 shown in Figure 2b with the corresponding values listed in Table 1 . 159 Two active needles were developed in this work using the following manufacturing 160 methods (i) ultraviolet (UV) laser cutter machine (Confluent Medical, Scottsdale, AZ) on 161 the nitinol tube with 1.49mm inner diameter (ID) and 2.00mm outer diameter (OD) shown 162 in Figure 2c, henceforth called the US Tool , and (ii) typical machining methods in lab on 163 the nitinol tube with an ID of 1. 60mm and OD of 2.00mm shown in Fig ure 2d, henceforth 164 called EM Tool. 165 The US tool was made with a width of 0.46mm and depth of 1.68mm with higher precision 166 offering more flexibility however at a high manufacturing cost. The EM Tool was fabricated 167 in the lab using a Dremel to create notches that are approximately 0.42mm wide and 168 1.33mm deep at low manufacturing cost. 169 The notches produce a flexure section , shown in Figure 2a, that allows for improved 170 flexibility of the active needle . Two holes (0.25mm in diameter) were made near the d istal 171 end of the flexure section for two tendons (0.10mm diameter SMA wires) to get attach ed 172 to. The tendons were looped in and out of the holes and completely fixed to drive needle 173 bending when pulled . 174 Figure 2. Schematic design of (a) tendon -driven active needle with (b) the notch dimensions fabricated on a nitinol tube using ( c) UV laser cutter (US Tool), and ( d) typical machining in our lab (EM Tool). Flexure Section (a) (c) Polyethylene terephthalate (PET) heat shrink cover 1.49mm ID 2.00mm OD (d) 1.60mm ID 2.00mm OD (b) Neutral axis 7 The flexur e section of the needle was sealed to prevent tissue penetration into the needle 175 tube and avoid tissue rupture. Shown in Figure 2c, t he flexur e section was cover ed (tight 176 fit) with a Polyethylene terephthalate (PET) heat shrink tube (13μm thickness). The PET 177 material is biocompatibl e and sterilizable with Ethylene oxide. We have tested the heat 178 shrink tube on the active needle when bent and inserted into phantom tissues to ensure 179 that it does not rip off during an insertion task [65]. The active needle including the covered 180 flexur e section is sterilizable. 181 The utmost expected angular d eflection of the active needle to realize a curved trajectory 182 inside prostate gland was estimated using Figure 1b, where a small radius of curvature 183 is desired inside a deformed prostate . The bending angles were marked in the figure with 184 small triangle s on the curve d trajectory, and the largest overall angular deflection of 50 185 degrees was measured . Methods to estimate the bending angle s of the two active 186 needles , developed in this work, are explained below . 187 The following equations are used to estimate the bending angle of the flexure section . 188 For the notches schematically shown in Fig ure 2b , the neutral bending axis can be 189 calculated using the following equation [66]: 190 𝑦̄=4(𝑟𝑜3𝑠𝑖𝑛3(𝜙𝑜)−𝑟𝑖3𝑠𝑖𝑛3(𝜙𝑖)) 3(𝑟𝑜2(2𝜙𝑜−𝑠𝑖𝑛2𝜙𝑜)−𝑟𝑖2(2𝜙𝑖−𝑠𝑖𝑛2𝜙𝑖)) (1) 191 where 𝑦̄ is the distance moved from the center of the tube, 𝑟𝑜 and 𝑟𝑖 are the outer and 192 inner radii of the tube, respectively, and 𝜙𝑜 and 𝜙𝑖 are found by the following equations: 193 𝜙𝑜=𝑎𝑟𝑐𝑐𝑜𝑠 (𝑑−𝑟𝑜 𝑟𝑜) (2) 194 𝜙𝑖=𝑎𝑟𝑐𝑐𝑜𝑠 (𝑑−𝑟𝑜 𝑟𝑖) (3) 195 where d is the notch depth. The bending angle for each notch can be estimated as: 196 𝜃𝑖=ℎ 𝑟𝑜+𝑦̄ (4) 197 where h is the height of the neutral axis for each, which in this work is equal to the height 198 of the cut ( t). Assuming that the total deflect ion is distributed equally among the six 199 notches, the bending angle of the whole flexible section could be found by multiplying the 200 bending angle of each notch by the number of notches. 201 Table 1. The dimensions of the notches for the two active needles developed in this work. Units are in mm. 𝑟𝑖 (𝐼𝐷) 𝑟𝑜 (𝑂𝐷) 𝑑 𝑡 US Tool 0.75 (1.49) 1.00 (2.00) 1.68 0.46 EM Tool 0.80 (1.60) 1.00 (2.00) 1.33 0.42 Dimensions of each notch for the two active needles are listed in Table 1. Using the 202 equations above, the a ngular deflection of each notch for the US Tool and the EM Tool 203 8 14.48 and 14.13 degrees, respectively. The overall angular deflection of the flexure 204 section s (six notches ) 86.88 and 84.78 degrees for the US and EM Tools, respectively , 205 which both surpass the expected angular deflection of 50 degrees for the active needle . 206 2.2. Actuation an d ultrasound tracking system 207 The actuation system designed in this work consists of a motor, gear box, and lead screw. 208 The tendon pulling force (F) to realize a specific bending on the flexure section when 209 bending inside tissue should be estimated experimentally. T he following equation is used 210 to calculate the amount of torque ( T) required to pull the tendon and consequently bend 211 the active needle, similar to lowering down a load on a lead screw: 212 𝑇=𝐹𝑑𝑚 2(𝑙+𝜋𝑓𝑑𝑚𝑠𝑒𝑐𝛼 𝜋𝑑𝑚−𝑓𝑙𝑠𝑒𝑐𝛼) (5) 213 where dm, l, f, and 𝛼 are the mean diameter of a single thread, tendon displacement, 214 coefficient of friction, and thread angle, respectively. To provide an example of 215 calculations for the active needle ( shown in Figure 1b ), we estimated that a maximum of 216 22N of force (tendon pulling force ) is sufficient to bend the needle inside the tissue. This 217 was estimated through needle insertion experiments in tissue phantoms with different 218 Young’s modulus [39] resembling prostate tissue. With this tension, an 8 mm diameter 219 lead screw, friction coefficient of 0.25 for threaded pairs of a steel and dry screw, and 220 thread angle of zero for square threads, the maximum torque was estimated as 0.41 N.m. 221 Upon torque es timation, a DC motor, gear, and a lead screw combination was selected 222 and purchased to develop a pulling actuation mechanism. To realize bi -directional 223 bending on the active needle, two similar tendon actuation mechanisms were developed 224 and installed to ha ve full control over needle bending. 225 The experimental setup to actuate the active needle at a desired bending angle and real - 226 time US tracking in water medium is shown in Fig ure 3a. The position of the tip is tracked 227 using the US machine, processed through a series of image processing commands , and 228 provided to the controller for appropriate control actions (explained later). 229 The actuation system to pull the internal tendons on the US Tool to realize a desired 230 bidirectional bending at the tip (shown in Fig ure 3b) consists of two motors , each 231 consisting of a 0.5W (Maxon Group, Sachseln, Switzerland) DC motor RE 8 Ø8 mm, 232 Precious Metal Brushes with an 8mm diameter lead screw drive (GP 8 S Ø8mm, Metric 233 spindle, M3 x 0.5), and an encoder (MR, Type S, 100CPT). 234 An L7 Linear Array US probe (CHISON Medical Technologies Co., Ltd., Jiangsu, China) 235 was used to track the tip of the active needle in real time in water medium. The active 236 needle was submerged in water with the US lying on the surface of the medium. For 237 proper sealing, the inner walls of the 3D printed box (made by Prusa i3 MK3 printer), 238 shown in Fig ure 3c, were coated with a silicone sealant (Gorilla Glue Co., Cincinnati, OH). 239 To prevent water from entering the needle tube , wood putty (Minwax, Cleveland, OH) was 240 used at the distal end surrounding the entry point of the needle . 241 9 Figure 3d shows the 2D plane of the US for tip tracking. The cross section of the needle 242 appears as a circular shape in the US images. The US images are obtained in real time 243 with a frame grabber, Epiphan Av.io HD. (Epiphan Systems, Ottawa, Canada) from the 244 ECO 5 (CHISON Medical Tech nologies Co., Ltd., Jiangsu, China) through the US probe. 245 Figure 3. Experimental setup to evaluate performance of the tendon -driven active needle in water medium consisting of (a) US tracking, (b) tendon actuation system to bend the flexure section in two directions, (c) active needle and US submerged in water bath, and (d) 2D US plane for tracking bidirectional movement of the active needle tip . Due to the artifacts observed in the US images while tracking the needle movement in 246 the water medium, a series of image processing techniques (Fig ure 4a) were performed 247 to obtain the 3D coordinates of the robotic tool in real time . Figure 4b shows an 248 unprocessed US image, while Figure 4c shows the processed image where region of 249 interest (RO I) is designated by the white box with the needle tip being marked with a red 250 circle. The script assigned a coordinate system for the y -z plane over the US image being 251 generated, using the pixel count as a basis for converting to millimeter scaling. 252 (a) (b) (c) (d) CHISON ECO 5 Ultrasound Maxon motors, gear box, and lead screw Tendons US probe tracking needle tip Water bath 10 Figure 4. (a) Image processing method showing (b) unprocessed US images with sources of noise, and (c) processed US images in real time. The tip is marked with a red circle. 2.3. Actuation and electromagnetic tracking system 253 Another method of tracking the needle tip position was developed in this work using two 254 3D Guidance Model 55 EM tracking sensors (Northern Digital Inc., Waterloo, Canada), 255 shown in Fig ure 5. The EM tracking system includes two sensors . The first and second 256 sensor s were installed inside the needle tube at the tip and the proximal end of the EM 257 Tool, respectively . The EM tracker reports displacement and rotation data, so the bending 258 angle at the flexure section of the active needle is measured directly through measur ing 259 the rotation of the distal sensor compared to the stationary proximal sensor. A similar 260 actuation system , using Maxon motors as explained above, was used to manipulate the 261 active needle. Manipulation and control were performed in the air. 262 Figure 5. Actuation and EM tracking system consists of (a) active needle , (b) EM sensors, (c) EM transmitter, (d) EPOS4 positioning control board s, (e) two Maxon motor s, and (f) power supply. (b) (c) (a) 11 2.4. Closed -loop control 263 This section presents our controller to man ipulate the tip of the active needle to follow a 264 desired trajectory and reach a target point in water medium and air. Figure 6 shows a 265 block diagram of our closed -loop control algorithm for US -based or EM -based method to 266 realize a desired bending angle at the active needle’s flexure section . The controller 267 communicates with the actuation system to realize appropriate tendon displacements via 268 actuation of the Maxon motors , and consequently realizes an angular deflection at the 269 flexure section of the active needle . The controller was programmed to force the flexure 270 section to follow an input desired bending angle function. The needle tip position obtained 271 by the US tracking system, or the tip and dis tal positions of flexure section obtained by 272 the EM tracking system were recorded in real time and used to estimate the angular 273 bending of the flexure section. The PID controller compares the input desired function 274 with the bending angle estimated obtained in real time from the US or the EM tracking 275 system to adopt appropriate control actions . 276 Figure 6. Scheme of closed -loop control method for realizing a desired bending angle at the flexure section of the robotic tool. 3. Results 277 3.1. Relationship between the t endon displacement and angular deflection 278 To characterize the flexure section , the tendons were linearly and independently 279 displaced at increments of 0.5mm. Images were taken of the flexure section at each 280 increment and the angular deflection was measured using ImageJ. Figure 7 shows the 281 relationship between the linear displacement of the tendon with the angular deflection 282 (bending) of the flexure section towards opposite directions (left and right). A second 283 order polynomial function was fitt ed to the data , shown in Figure 7, to model the 284 relationship between the tendon displacement and the angular deflection of the flexure 285 section. This relationship was used by the controller to make decisions on the tendon 286 displacement actions. 287 12 Figure 7. Relationship between angular deflection of the flexure section and the tendons’ linear displacement. 3.2. Closed -loop control with US tracking feedback 288 To evaluate the performance of the active needle as well as the capability of our US 289 tracking system to provide reliable feedback , the controller was set to realize a maximum 290 angular bending of 10 degrees in a water medium . The coordinates of the needle tip were 291 displayed on a computer running the US tracking scri pt and recorded for graphical 292 analysis post -experimentation. The coordinates were used to calculate the bending angle 293 of the flexure section in real time. Time was also recorded during the experiment. The 294 measured bending angle (output) , as well as the desired bending angle (input) 295 determined by the displacement function, were also recorded, analyzed, and compared . 296 Three different input bending angle functions of (i) step, (ii) sine, and (iii) triangle were 297 utilized for the flexure section to follow. The actual (green) and desired (red) bending 298 angle of the flexure section was compared (Figure 8a) and the corresponding absolute 299 difference (bending angle error) between the measured output and desired input was 300 estimated and plotted (Figure 8b). 301 13 Figure 8. Bending angle of the tendon -driven active needle : (a) calculated from the data collected by the US tracking system for the different input functions, and (b) corresponding absolute difference (bending angle error) with respect to time. Figure 9. Bending angle of the tendon -driven active needle: (a) calculated from the data collected by the EM tracking system for the different input functions, and (b) corresponding absolute difference (bending angle error) with respect to time. 3.3. Closed -loop control with EM tracking feedback 302 To test the capability of the EM tracking system, the same displacement functions of (i) 303 step, (ii) sine, and (iii) triangle were utilized for the needle tip to follow in the air . For 304 comparison, the di splacement function period was kept the same ; however , since the EM 305 (a) (b) (b) (a) 14 tracker was capable of measuring higher deflection angles, the maximum deflection angle 306 was set to 20 degrees. It was assumed that the difference in maximum angle would not 307 greatly inhibit the function of the controller since the period was sufficiently long. The 308 same method was used for data collection, analysis, and comparison. Figure 9a shows 309 the controlled response of the flexure section with respect to the input functions, while 310 Figure 9b shows the corresponding absolute difference (bending angle error) between 311 the measured output and desired input. 312 4. Discussion s 313 The EM tracking system produced similar position data to the US tracking ; however , there 314 was significantly more noise in the data. The angular deflection measurements with the 315 EM tracker fluctuated routinely around ±2 .0 degrees for very close data points, whereas 316 the US tracking measurements hardly fluctuated (±0.5 degrees ). 317 Table 2. Bending angle tracking error in closed -loop control of the active needle using the feedback received from US and EM Track ing systems . Units are in degrees. Input Function Tracking Method Min. Err or Max. Err or Mean Err or Sine US 1e-04 1.09 0.23 EM 6e-04 4.54 1.00 Triangle US 1e-04 1.42 0.21 EM 8e-04 3.97 0.96 Step (ignoring delay) US 4e-04 11.45 (2.33) 2.00 (0.27) EM 10e-04 22.91 (4.02) 4.51 (0.83) Table 2 lists the maximum, minimum, and mean error for each input displacement 318 function (i.e., sine, triangle, and step) using US and EM tracking systems . The controller 319 was able to realize a sine displacement function with mean error values of 0.23 and 1.00 320 degrees with US and EM tracking systems, respectively. Tracking the triangular 321 displacement function was done with 0.21 and 0.96 degrees of mean error values for the 322 US and EM tracking systems, respectively. It was however noticed that the actuation 323 system was incapable of producing a quick response for the step displacement function, 324 and thereby a delayed response. Due to the relatively slow ramp -up time, mean error 325 values were 2.00 and 4.51 degrees for the US and EM tracking systems, respectively. 326 The highest maximum absolute error was observed to be 22.91 degrees from the EM 327 tracking system following step function with the lowest coming from the sine function with 328 the US system (1.09 degrees). As a consequence of the high absolute error, the largest 329 mean error was also observed in the EM tracking step function with 4.51 degrees, and 330 the lowest mean error was 0.2 1 degrees from the US tracking triangle function . The 331 values in parentheses were estimated for the step function, when ignoring the delay 332 period where the motors are running significantly behind the step. Once the measured 333 angle was within the 10% of the desired step angle for the first time, data recording was 334 15 resumed. The average delay period using the aforementioned parameters was 8.43 and 335 9.69 second s for the US tracking and EM tracking systems, respectively . Ignoring the 336 delay period, tracking of the step function resulted in mean error values of 0.27 and 0.83 337 degrees for the US and EM tracking systems, respectively, which closely align to the 338 accura cies produced from the other displacement functions. 339 The mean error difference in tracking the desired bending angle of the active using the 340 US or EM tracking systems were 0.77, 0.75, and 0.56 degrees for the sine, triangle, and 341 step functions, respective ly. The US tracking system realized a more accurate tracking of 342 the active needle (average of 0.69 degrees improvement in accuracy) compared to the 343 EM tracking for the three input functions used in this work. The results show that the US 344 tracking system, s ubmerged in the water, provides reliable feedback to the controller to 345 realize a desired angular bending at the flexure section of the active needle with 346 reasonable accuracy. 347 5. Conclusion s 348 This work present s a closed -loop control of a bidirectional tendon -driven active needle in 349 water medium and air using US and EM tracking, respectively. It has been observed that 350 the b ending angle of the active needle, could be controlled using position feedback of the 351 US or the EM tracking system with corresponding absolute difference (bending angle 352 error) <±1 degrees , and thereby comparable precisions . Therefore, the controller has 353 been able to realize a desired bending angle at the flexure section of the active needle 354 with reasonable accuracy using the US tracking system. 355 The US tracking system developed in this work is similar to the tracking method typically 356 used in needle -based prostate interventions. It was shown that the controller is able to 357 realize a desired bending angle at the flexure section of the active needle using the 358 feedback of the US tracking system submerged in the water bath . This work takes the 359 first step towards utilization of active tendon -driven needles in prostate interventions, 360 where both the needle and the US are placed and function inside tissue. 361 Future work will focus on developing a closed -loop control to steer the a ctive tendon - 362 driven needle in a curved trajectory inside the prostate gland . Axial insertion of the needle 363 to reach targets deep inside the tissue is also among our future aims. Introducing linear 364 stages to the system will provide robotic movement to the U S probe and provide more 365 accuracy in tracking the needle tip in the event of larger tip displacements, which is often 366 seen in patients with large prostate glands. 367 6. Competing interests 368 None declared . 369 7. Funding 370 Research reported in this publication was support ed by the National Institute Of 371 Biomedical Imaging And Bioengineering of the National Institutes of Health under Award 372 16 Number K25EB030562. The content is solely the responsibility of the authors and does 373 not necessarily represent the official views of the National Institutes of Health. 374 8. Ethical approval 375 Not required . 376 9.