Biometry-Based Concentric Tubes Robot for Vitreoretinal Surgery
Fang-Yu Lin, Christos Bergeles, Member, IEEE, and Guang-Zhong Yang, Fellow, IEEE
Abstract—Vitreoretinal surgery requires dexterous manoeu-vres of tiny surgical tools in the confined cavity of the human eye through incisions made on the sclera. The fulcrum effect stemming from these incisions limits the safely reachable intra-ocular workspace and may result in scleral stress and collision with the intraocular lens. This paper proposes a concentric tube robot for panretinal interventions without risking scleral or lens damage. The robot is designed based on biometric measurements of the human eye, the required workspace, and the ease of incorporation in the clinical workflow. Our system is suited to 23 G vitreoretinal surgery, which does not require post-operative suturing, by comprising sub-millimetre concen-tric tubes. The proposed design is modular and features a rapid tube-exchange mechanism. To grasp and manipulate tissue, a sub-millimetre flexible gripper is fabricated. Experiments demonstrate the ability to reach peripheral retinal regions with limited motion at the incision point and no risk of lens contact.
I. I NTRODUCTION
Vitreoretinal surgery requires dexterous manoeuvres near the retinal surface [see Fig. 1(a)]. The forces applied are at the borders of human perception , making it one of the most demanding minimally invasive surgical interventions. Several assistive robotic systems have been proposed. Hand-held devices aim to filter-out hand tremor and augment haptic perception for the surgeon –, while master-slave systems telemanipulate an ophthalmic surgery tool –.
In all proposed systems, a straight tool is inserted through the pars plana of the sclera [see Fig. 1(b)]. Tool pivoting may enlarge the entry incision and lead to wound leak and ocular hypotony . Peripheral retinal interventions present the additional risk of intraocular lens touch . Moreover, since the forces experienced by tool/sclera interactions are greater than retinal/tool interaction foces, there is risk of imperceptible retinal damage . Grounded robotic sys-tems employ Remote-Centre-of-Motion (RCM) constraints to minimise scleral stress but accidental damage to the lens and retina remains a possibility [see Fig. 1(b)]. Establishing RCM requires precise system calibration .
To address these issues, this paper proposes a teleoperated vitreoretinal surgical concentric tube robot ,  (see Fig. 1(c) and Fig. 2) for peripheral retinal interventions without scleral stress or intraocular lens touch risk, while simultaneously allowing foveal manipulations with limited proximal motion. The clinical motivation is retinal patholo-gies like retinal detachments or epiretinal membranes, which can also occur in the peripheral retina.
Fig. 1. (a) Vitreoretinal surgery is a multi-port procedure. The inlet show the arrangement of tools intraoperatively. (b) Straight instruments cann reach an increased workspace without risking contact with the intraocul lens or damage to the sclera. (c) The proposed instrument overcomes the limitations to reach A, B, and C without lens collision or distal motion.
Our approach shares similarities with , , which propose the combination of a straight tool and a pre-curved cannula that extends from its tip. That work demonstrates the increased intraocular dexterity provided by a pre-curved cannula that can rotate and retract within the outer tube. Manipulation, however, still relies on constrained motion around the fulcrum point. Moreover, since the outer tube is rigid, there is no shape flexibility.
The current paper introduces anatomy-specific vitreoreti-nal robot optimisation for immobility at the incision and reachability of peripheral retinal regions [see Fig. 1(c)]. The design leverages the stiffness ratio between the tubular components to cover a large workspace. The tubes comply to 23 G surgery, which requires no post-operative sutures . The system is based on modular actuation units arranged in cascade and share a rapid tube-exchange mechanism for intraoperative instrument switching. Finally, a submillimetre tendon-actuated gripper is designed and fabricated, and our preliminary prototype system is evaluated with experiments based on an eye phantom.
II. TUBE REQUIREMENTS AND DESIGN
Concentric tube robots can be designed based on anatom-ical and surgical task constraints ,  but this approach has not yet been followed in practice.
Fig. 2. This paper’s concentric tube robot comprising 2 tubes and a sub-millimetre gripper. The relative translation (φ) and relative rotation (α) of each tube control the shape and tip pose.
Fig. 3. (a) The biometric eye model. The gray area is the desired reachable workspace, and the red points the anatomical targets specified for optimisation. (b) The simulated workspace of the optimised concentric tubes in 2D. The dashed blue lines indicate a straight tool reaching the same peripheral regions. Contact with the intraocular lens at the location indicated with the semi-transparent circle, and scleral stress, could arise.
Fig. 4. (a) The inner tube (top) and outer tube (bottom), together with the stainless steel extensions. (b) The combined tube arrangement.
For the investigated clinical application, the combination of two super-elastic nitinol (NiTi) tubes is considered. A two-tube robot provides 4 degrees of freedom (2 per tube), which is in par with the capabilities of modern vitreoretinal surgery tools and robots. Finally, adding forceps with roll provides a 5 th degree of freedom. The limited availability of NiTi tubes with less than 23 G diameters requires their selection based solely on concentricity and limits the choice of wall thickness and stiffness. Hence, the dominant stiffness rule, i.e. that the curvature of the overlapping-tube regions is controlled by the stiffer (outer) tube (refer to the design guidelines of ), must be relaxed.More specifically, 23 G vitreoretinal surgery protocols specify a maximum diameter of dmax= 650 μm. Thus, the selected tube diameters are dNiTi,1o= 635 μm, and dNiTi,1i= 432 μm, for the outer, and inner diameters of the outer tube, respectively, and dNiTi;2o= 406 μm, and dNiTi;1i = 203 μm, for the outer, and inner diameters ofhe inner tube, respectively. The wall thicknesses result in astiffness ratio of DNiTi,1 to NiTi;2= 5:1, which is an additionaloptimisation contraint.
This paper uses the authors’ optimal robot design algo-rithm  to design concentric tubes for the human eye. The algorithm receives as input the anatomical constraints and the set of anatomical points that should be reachable, and estimates the optimal curvatures and curved lengths of the concentric tubes.
The biometric model used is from the work of Escudero-Sanz et al. , and is created from averaged population data. The biometric model’s parameters are given in Table I, where surface numbers correspond to annotations in Fig. 3(a). Thickness corresponds to the distance between succes-sive surfaces, and the radius of curvature and conic constant define the surface shape. Eye models for patient-specific robot designs can be created from MRI scans.
State-of-the-art ophthalmoscopy lenses allow observation of the peripheral retina for a field-of-view on the order of 100o, which is selected as the desired reachable workspace. Achieving this large workspace allows peripheral retinal operations through a single incision. Figure 3(a) shows the desired workspace shaded in gray. Points spaced out evenly on the retina were provided as surgical targets to the algorithm and are shown as red circles. Starting from straight tubes, the algorithmic design process resulted in curvatures and curved lengths that are shown in Table II and Fig. 4.
The workspace of the optimised tube set was simulated for 1; 000; 000 sets of uniformly-selected forward-kinematics variables, f(φ; α)g, as annotated in Fig. 2, using a discretised version of the torsionally-compliant kinematics of . The enerated 3D points were cylindrically rotated to be coplanar, and were clustered in regions of 0:2 mm x 0:2 mm. The resulting intraocular workspace, as a 2D slice, is shown overlaid with the eye model in Fig. 3(b). The reachable retinal field is 110o, respecting the surgical task require-ments. Additionally, Fig. 3(b) demonstrates that a straight tool (dashed line) would be unable to reach the peripheral retinal region without risking collisions with the intraocular lens or potentially cause scleral stress.
Curving the tubes follows the protocols established in the literature, i.e. embedding the tubes in an aluminum template, heating for 20 mins at 520oC, and rapidly water-quenching them at the end. The achieved curvatures are within 10% of the desired values (10 repetitions). Cutting the tubes into the appropriate length requires an Electric Discharge Machine (EDM). Wire-EDM achieves accurate cuts while retaining the tube concentricity.
Fig. 6. “Fixture” and its assembly with the tube and gear. This assembly slides into the modules, and the gears engage rotation and translation for each tube.
Fig. 5. (a) The skull, eye, and imaging system pose constraints to the design of the actuation mechanism. (b) CAD model , and (c) prototpye of the modular component of the concentric tube robot. A: anterior side, B: posterior side. The module connect by sliding them along the rails annotated with the green arrow, while the tubes connect by sliding them along the purple arrows.
The tubes are manipulated at their base. The particularities of NiTi, however, give rise to buckling and torsion for long tubes, effects particularly prevalent in the sub-millimetre scale. This necessitates keeping the NiTi-part of the tubes short, ideally as short as the algorithmically estimated curved length. Thus, transmission lengths that extend the tubes from torsionally rigid materials are required. Concentric straight stainless steel tubes are attached at the end of each NiTi tube. The stainless steel tubes used in this study are 18 G, and 21 G, for the outer, and inner, NiTi tubes, respectively, and are attached at the end of each NiTi tube, as shown in Fig. 4. The diameters of the stainless steel tubes are selected to allow for concentric insertion.
III. ACTUATION MODULE REQUIREMENTS AND DESIGN
This section discusses minimisation of robot footprint and innovations in modularity and tube exchange.
A. Robot Footprint Constraints
The skull and the imaging system pose constraints to the design of the actuating components. The commonly used F844-F40 from Leica Microsystems is shown in Fig. 1(a) with a vitreoretinal observation system, the BIOM®, attached. This system, shown in Fig. 5(a) in CAD to approx-imate workspace constraints, requires a working distance of 17:5 cm, which guides the actuation system design towards a thin and elognated actuation mechanism. The stainless steel tube extensions allow the use of a mechanism with such an aspect ratio; otherwise the torsion and buckling of NiTi tubes would make the approach prohibitive.
B. Robot Modularity
Concentric tube robot mechatronic actuation systems are characterised by increased unoptimised footprint. This paper proposes a miniature modular design instead. Each module provides 2 degrees of actuation, i.e. rotation, and translation of a single tube, and modules are connected in cascade. All modules share a common lumen through which the tubes are inserted. This design allows the increase of the overall degrees of freedom in parallel to the developments of the tools and their actuation demands. The design of the module is depicted in Fig. 5(b) and the built prototype in Fig. 5(c).
C. Rapid Tube-Exchange Mechanism
Even in vitreoretinal surgery, the surgeon may need to exchange tools to cover the intervention’s needs, as, for example, change between forceps, hook, etc. The developed actuator possesses a rapid tube exchange contraption, illus-trated in Fig. 6. The stainless steel extension of each tube is fastened to a “fixture”, which is annotated as “A” in the figure. Then, the “fixture”-and-tube arrangement is screwed to a shaft ending with a helical thread (annotated as “B”). As the helical thread is compressed, it secures the tube in place. A gear and two bearings (annotated as “C”) are tightly fitted with the thread to allow for rotation of the tube. Finally, the bottom of the bearing housing (“sliding mechanism”, annotated as “D”) is designed for connection to the modular unit. The mechanism engages the actuation unit’s gears via simple sliding in the port indicated as “tube connector” in Fig. 5(c). Figure 6 shows the tube-exchange assembly.
A low-budget prototype module based on 3D printing is created to test the design principles. DC motors of minimal diameter, d = 6 mm, and length, L = 20:8 mm, are selected (206 108, Precision Microdrives Ltd, UK). A rack-and-pinion system converts rotation of one motor to translation of the mechanism, i.e. translation of the mounted tube.
Fig. 7. Design and manufacture of flexible robot gripper. Red circles denote welding, while yellow circles denote glueing.
Fig. 8. The experimental setup: (a) the concentric tube robot, and (b) the rthogonal camera system.
Potentiometers (EVU-2AF30B14, Panasonic) are coupled to the motors and calibrated to rotation angles and distances using goniometers and calipers. The voltage measurements act as encoders for the revolute and translation actuators. The motors are controlled through LabView® in closed loop with respect to the output translation and rotation via a PID controller with parameters estimated using the Ziegler-Nichols’ method. The achievable steady-state error is on the order of 600 μm, which will be improved by integrating reliable motors with embedded controllers and encoders and eliminating 3D printed gears from the system. This modular unit is miniatured, measuring just 66 mm x 52:20 mm x 29:65 mm, with a linear travel range of 30 mm, corresponding to the diameter of the human eye.
IV. F LEXIBLE GRIPPER DESIGN
Most surgical instruments used in vitreoretinal procedures are straight and rigid. As a result, no end-effectors (e.g. for-ceps, cutters) can be directly used with our flexible snake-like robot. For grasping and peeling applications, sub-millimetre forceps need to be attached to the robot while respecting its shape-altering capabilities and the size constraints of 23 G vitreoretinal surgery.
The tip of the designed gripper comprises steel forceps, with a diameter of 300 μ m welded with a piece of 27 G stainless steel tube (outer diameter = 410 μm, inner diameter = 200 μm) with length of 1:5 mm. Then, a NiTi wire with a diameter of 150 μm is inserted and glued 1 with the stain-less steel tube. The stainless steel component is necessary because welding strength between steel (forceps), and NiTi (wire) is weak. The combination of welding and gluing, however, creates the necessary bond. It should be noted that the NiTi wire is significantly less stiff than the inner tube, and does not affect the overall shape. For this reason, the NiTi wire is not considered as a 3rd tube. Since the wire is “enclosed” in the inner tube, its deflection is constrained and it can be pushed. The forceps are actuated by extending a piece of overtube and forcing their jaws to close and grip. This is achieved by adhering a section of the 635 μm diameter outer tube at the distal end of the inner tube as an overtube transition. The forceps, placed to overlap with this transition tube, are actuated by pushing or pulling them against it. The NiTi wire can be used to rotate/roll the forceps, providing an additional degree of freedom to the robot for a total of 5. The complete gripper fabrication is detailed in Fig. 7.
V. EXPERIMENTAL EVALUATION
The complete prototype is evaluated for reaching pe-ripheral retinal regions without risking contact with the intraocular lens and with minimal promixal motion. The robot [see Fig. 8(a)] comprises actuation modules for each tube and the forceps. The eye phantom (Gwb International, Ltd.) that is our experimental test-bed is 30% larger than the average human eye to account for simplified optics. This eye is needed because its hand-painted retina showcases the robot reaching the peripheral region [see Fig. 9(a), (b)]. The curved length of the tubes is increased by 30%, with curvatures remaining the same. The elongated curvatures increase the reachable retinal surface/angle. The tubes were rotated and translated to sample their entire range of motion.
The motion of the robot is observed via an orthogonal camera system comprising two Thorlabs DCC3240C cam-eras mounted on linear translation stages. The cameras are calibrated assuming orthographic projection. The pixel size is 14:5 μm, which indicates the system’s 3D resolution. The robot’s distal component enters the image from the top, in a scenario simulating vitreoretinal surgery (see Fig. 8). The orthogonal camera system provides the 3D coordinates of the robot tip via triangulation. Gridded paper was positioned perpendicular to the cameras to assist in quantification.
Figure 9(c) overlays the eye model and sequential tube shapes to indicate the reachability of peripheral retinal tissue. These locations are reached by retracting the outer tube to increase the overall robot curvature while the inner and outer tubes’ precurvatures are aligned. These arrangements correspond to maximal deflections. The figure also depicts a straight tool, indicated by the dashed gray line, to demon-strate the increased risk of colliding with the intraocular lens when straight tools are used. From this experiment, it is also observed that the motion of the distal tube components, near the “pars plana”, is on the order of 1 mm for the entire range of motion, supporting the use of this technology for minimising scleral stress.
Fig. 9. (a) Reaching the central retina, and, (b) the peripheral retina of the eye phantom. Images taken through a Volk® Digital Wide Field Lens. (c) Control of the forceps to the peripheral retina is achieved while limiting stress on the entry point and minimising risk of collisions with the intraocular lens. A conventional forceps is overlaid, and a red circle denotes the potential collision. (d) The sampled workspace, where red x indicate the tracked configurations and blue x result from the rotational symmetry.
Figure 9(d) shows sampled points from the intraocular reachable workspace as red ’x’s. Accounting also for cylin-drical symmetry of the workspace (blue ’x’s in the figure), it is seen that the robot can cover a significant portion of the eye phantom’s retina. This retinal angle is in agreement with the simulations (see Sec. II), accounting for the discrepancy attributed to the increased curved tube lengths.
VI. CONCLUSIONS AND DISCUSSION
In this paper, a vitreoretinal-surgery specific concentric tube robot was presented. The suggested design achieves an extended workspace without risking collisions with the intraocular lens or scleral stress. The actuation mechanism was miniaturised and built on the principles of modularity and rapid-tube exchange. Further, a submillimetre gripper was designed and fabricated. Experiments validated the reachable workspace and potential of the proposed design for peripheral retinal interventions. This prototype robot will be improved with more so-phisticated actuation components, and further research on miniature ophthalmic surgery tools will be performed. The robot will be attached to a robotic arm for alignment with the entry incision. Finally, control algorithms will be investigated to achieve sub-50 μm tip control.
We gratefully acknowledge Oertli UK, Alcon UK, and Rumex USA, for donation of trocars, 23 G forceps, and 25 G forceps, respectively, and Petros Giataganas for his help in creating the experimental setup.
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