A Micro-3-Degree-of-Freedom Force Sensor for Intraocular Dexterous Surgical Robots

The continuum manipulator improves the intraocular robot ﬂ exibility during retinal surgery. Herein, a micro-3-degree of freedom (DOF) force sensor with a length of only 3.8 mm that can adjust the puncture angle during retinal vein cannulation (RVC) is proposed. Taking advantage of 3D printing technology, the optical ﬁ ber and injection line are embedded in the nitinol tube with ﬂ exible hinges to achieve integration of the force sensing and injection functions. A new ﬁ ber Bragg grating (FBG) con ﬁ guration method and linear decoupling algorithm are also proposed herein. Static calibration experiments demonstrate excellent resolution of the force sensor, of less than 0.072 mN for transverse force and 0.738 mN for the axial force in the range from (cid:1) 20 to 20 mN. The proposed sensor is installed on a newly developed actuator, and an ex vivo experiment is performed on pig cadaver eyes. The interaction forces at each stage of the RVC are recorded in detail for the ﬁ rst time, further con ﬁ rming the feasibility and effectiveness of the developed sensor for monitoring the RVC interaction forces.


Introduction
Retinal vein occlusion (RVO) is a serious ocular fundus disorder. Compared to vitreous surgery, RVC is a more effective procedure for RVO, in which thrombolytic drugs are injected into the blood vessels to dissolve blood clots. RVC is a difficult and risky microsurgical procedure, and few cases have been reported. [1] This is because the properties of the retina are heterogeneous and anisotropic. [2,3] When the needle is inserted, the puncture force may act on the vein wall, and the blood vessel can be easily deformed or double puncture occurs. [4] The desired angle between the needle and the tissue can determine the success of the puncture to reduce the deformation of the tissue deformation and prolong the puncture path. [5] The detection of puncture force is used to determine the instantaneous state of the vein wall as the vein is pierced. This should stop the needle at the correct depth in a timely and accurate manner to prevent further damage. The angle of insertion and puncture force are the two most important factors that ensure the safety and success of RVC.
To insert the needle at the desired angle, scientists usually use curved glass or metal microneedles for RVC. [6,7] Wei et al. performed a needle insertion experiment on a retinal model and discovered that the most suitable insertion angle is between 25 and 35°. [8] However, rigid instruments lack the ability to adjust the insertion angle according to the position of the needle tip. In contrast, the intraocular flexible manipulator has the advantage of local dexterity to adjust the posture of the microneedle at different needle insertion points to achieve an optimal insertion angle into the deformable tissue. [9,10] Meanwhile, due to the narrow space in the eye and some constraints on the joint structure of flexible manipulator, current flexible manipulators have less capability of effective force sensing. [11,12] Accurate measurement of puncture force is essential for the safety of retinal surgery. In particular, during puncture and tearing of the membrane, when the tissue structure ruptures, the axial force changes dramatically. [13] Therefore, it is necessary to develop a micro-three degree of freedom (DOF) force sensor that can be integrated into an intraocular flexible manipulator to optimize the puncture angle and measure the puncture force.
Current rigid retinal surgical instruments [14][15][16] with highsensitivity force sensors are designed with one of the fiber Bragg gratings (FBGs) suspended in the center of the nitinol tube to measure the axial force. In these sensors, the measurement of the axial force is affected by the transverse force so nonlinear decoupling is inevitable. At the same time, these force sensor designs limited the integration of the force sensor with the injection line because the hollow channel of the tube was occupied by one central FBG. To preserve the injection function, Zhang et al. [17] designed a 3-DOF force-sensing microneedle and used a linear relationship between the wavelength shifts of the different FBGs to decouple the axial force and temperature change. These sensors are rigid instruments with limitations in the flexibility of adjusting the posture of the instrument. The continuum manipulator improves the intraocular robot flexibility during retinal surgery. Herein, a micro-3-degree of freedom (DOF) force sensor with a length of only 3.8 mm that can adjust the puncture angle during retinal vein cannulation (RVC) is proposed. Taking advantage of 3D printing technology, the optical fiber and injection line are embedded in the nitinol tube with flexible hinges to achieve integration of the force sensing and injection functions. A new fiber Bragg grating (FBG) configuration method and linear decoupling algorithm are also proposed herein. Static calibration experiments demonstrate excellent resolution of the force sensor, of less than 0.072 mN for transverse force and 0.738 mN for the axial force in the range from À20 to 20 mN. The proposed sensor is installed on a newly developed actuator, and an ex vivo experiment is performed on pig cadaver eyes. The interaction forces at each stage of the RVC are recorded in detail for the first time, further confirming the feasibility and effectiveness of the developed sensor for monitoring the RVC interaction forces.
Force sensor-based FBGs are widely used in medical continuum robots and endoscopes to detect minimal contact forces in the confined space of the human body. [18] Gao et al. [19] designed a 3-DOF force sensor based on an FBG with parallel flexure hinges to detect the contact force during catheter ablation. Linear and nonlinear methods were applied to decouple the axial and transverse forces with a force resolution of less than 1 g. Deng et al. [20] proposed a miniature triaxial FBG sensor and a linear model based on a singular-value decomposition algorithm to estimate the contact force during ureteroscopy. Li et al. [21] designed a disposable FBG-based force-torque sensor for neurosurgery. An annular diaphragm structure made of 3D-printed elastomer was designed to increase the sensitivity to external forces. Lai et al. [22] designed a force sensor incorporated into a flexible endoscopic surgical robot that can sense the tensile and axial forces of a rigid surgical instrument. All of the above sensors share a common feature: they are built as a small force-sensing module and can be attached to the end of the flexible manipulator. Compared with other natural cavities of the human body, the space in the eye is narrower [23] and the tissue is more sensitive, [24] which requires high measurement accuracy and small flexible manipulators. In addition, reserving the drug pipeline in the center of the sensor may increase the complexity of the force sensor design.
In this study, we propose a micro-3-DOF force sensor that can be integrated into the flexible manipulator of an intraocular dexterous actuator for RVC tasks. A new linear algorithm was developed to reliably estimate the interaction forces, and a new FBG configuration was also proposed. The purpose of integrating the 3-DOF force sensor with a flexible jointed manipulator is to ensure that the needle insertion angle is adjustable and that the puncture force is effectively sensed. The RVC was performed on the ex vivo porcine eye, and the change in puncture force throughout the process was recorded for the first time by the proposed sensor to prove its manipulability in the intraocular environment, which will help to expand the practical applications of the proposed sensor.

Results and Discussion
2.1. Design of the Proposed Sensor Figure 1a illustrates the design concept of the new 3-DOF force sensor. The 3D microprecision components (BMF Precision Tech Inc., China) at both ends of the nitinol tube have thorough holes. Therefore, the fibers and injection line were inserted into the force sensor through the holes. Three fibers with a 2 mm FBG (diameter of 0.08 mm) were spaced 120°apart along the circumference of the hollow nitinol tube. The fourth fiber was cut off and part of it was reserved along with FBG4. The suspended FBG4 was not affected by stress changes. An injection line made of a polyurethane hose (Qiujing., Ltd, China) and stainless steel microneedle (Beichuangtianze., Ltd, China) was suspended through the middle hole in the center of the force sensor. All these parts are bonded with a medical adhesive.
Nitinol, which has a low Young's modulus (41 GPa) and biocompatibility, is an excellent strain-gauge material. The flexible part of the nitinol tube significantly weakens its stiffness. However, the deformation of the force sensor should be small when it is subjected to an external force. The ratio of the diameter between the fiber and the nitinol tube is nearly 1:10; therefore, the contribution of the optical fiber to the stiffness of the sensor cannot be ignored. The built-in structure of the optical fiber has greatly improved the overall strength of the sensor. Figure 2 shows the structure of the sensor assembly.

Principle of Measurement
The measurement principle based on FBG can be described as follows: when broadband light is sent into the FBG, part of the light with a specific wavelength (Bragg wavelength) is reflected by optical grating. [25] The relative shift of the Bragg center wavelength increases linearly with changes in stress or temperature. This relationship can be expressed as follows.
where λ is the Bragg center wavelength, Δλ is the wavelength shift, P e is the optical strain coefficient, ε is the strain of the FBG, α is the thermal expansion coefficient, ξ is the thermooptical coefficient, and ΔT is the temperature change. To solve the mapping relationship between the 3-DOF force applied to the sensor, the shift of the Bragg center wavelength λ i and the theoretical mechanical modeling of the sensor were developed. The sensor is simplified as a cantilever beam. [26] As shown in Figure 3, FBG1-3 produces strain as a result of the deformation of the flexible segment. The torsional angle θ caused by the transverse force can be expressed as follows.
where E is the equivalent elastic modulus of elasticity of the flexible segment and, I is the area moment of inertia. The plane of the transverse force is defined as H, and the arc corresponding to the projection of the FBGi onto the plane H is l flex FBGi . The corresponding radius of l flex FBGi is r i þ R, and the deformation of FBGi is r i θ tube . Figure 4 shows the configuration of the FBG sensors inside the nitinol tube. The injection line is placed in the center of the sensor. The direction of the transverse force F passes through the origin of the coordinates. For example, the center of FBG3 is projected to H. Then the distance between the origin of coordinates and the point B is r 3 . Therefore, r i can be expressed as follows where φ is the angle between the defined axis X and the line formed by FBG1 and the center of the circle. ϕ is the angle between the transverse force and the defined axis X. According to (3) and (4), the strain ε 0 i of FBGi caused by the transverse force can be expressed as follows.  www.advancedsciencenews.com www.advintellsyst.com where l i FBG is the length of FBGi inside the sensor. k is the equivalent total bending stiffness of the FBGs and flexible segment. The strain ε i z caused by the axial force can be expressed as follows.
According to (4) and (5), when an external force is applied to the needle of the sensor, the strain of FBGi ε i is expressed as follows.
To remove the influence of temperature on the wavelength of the FBGs, a suspended FBG is placed inside the sensor which is used to detect the wavelength shifts due to the change of external temperature. The wavelength shifts of FBG1-4 exhibit a linear dependence on the temperature change. The linear correlation coefficients γ 1 , γ 2 , γ 3 between the wavelength shifts of FBG1-3 and FBG4 with the same temperature change need to be solved experimentally. Therefore, when the external temperature changes, the mapping relationship between the wavelength offset value of the sensor and external force can be expressed as follows.
where τ ¼ Fl flex ð2l beam1 Àl flex Þr 2EIl FBG , which may differ from the theoretical linear model due to fabrication and assembly errors. The actual linear model is calculated in the following section using a calibration experiment in the following section.

Force Calibration
As mentioned earlier, the structure of the sensor is designed and a measurement model is created. As errors occur during the manufacturing and assembly process, the performance of the sensor must be tested through experiments. Experiments on temperature calibration, force calibration, repeatability, and temperature compensation were conducted to determine the performance.
The microneedles for RVC are usually less than 100 μm in diameter. To avoid damage to the tip during the calibration process, it is necessary to apply only a tensile force to the microneedle. As shown in Figure 5a, an experimental platform for a 3-DOF force sensor calibration was created. This experimental platform includes an FBG interrogator (SI155, resolution:1 pm, USA), a prototype sensor, a laptop computer (Lenovo, China), an X-Y-Z manual linear stage (travel range: 50 Â 80 Â 120 mm), a PI linear actuator (Q545, travel range: À13 to 13 mm, precision: 1 nm, Germany), two rotary stages, and several fixtures (material: aluminum alloy, processing technique: CNC, China). The prototype sensor was attached to the ends of the fixtures. The PI linear motor can drive the up and down movement of the sensor, and the positioning accuracy increases to 1 nm. The weight was suspended from the top of the needle tip. After manually adjusting the roll angle α and sweep angle β of the rotary stage, the direction of the force exerted by the weight on the sensor is changed. The gravity of the weight is F g , and the transverse and axial forces can be expressed as follows.
The weights were 0.5, 1, 1.5, and 2 g. For each weight, the sweep angle β ranges from 0°to 360°at 30°intervals, and the pitch angle α ranges from 90°to 30°at 20°intervals. The experiment was repeated three times, collecting data from 576 samples. During calibration, the experimental environment was windless and the room temperature was constant. There were 576 data samples of wavelength shifts and 3-DOF force records collected. Based on (7), the sensitivity matrix was calculated using the least-squares method, which can be expressed as follows.
According to the definition of the sensitivity of the force transducer, the maximum value of each column of the sensitivity www.advancedsciencenews.com www.advintellsyst.com matrix is the theoretical resolution of the corresponding component force. [27] The FBG interrogator has a resolution of 0.001 nm; therefore, the resolutions of the transverse forces F x and F y are 0.072 and 0.065 mN, respectively. The resolution of the axial force, F z , is 0.738 mN. [17] As shown in Figure 5b, the proposed force sensor has very good estimation accuracy for the transverse force, and the root mean square (RMS) error is 0.36 and 0.33 mN. The linearity error is 2.42 and 2.37. The maximum absolute residual error is less than 0.97 mN for F x and 0.95 mN for F y . The probability of a transverse force estimation error greater than 0.5 mN is very small. Because the axial stiffness of the sensor was higher than the transverse stiffness, the axial performance of the sensor was slightly lower. The RMS error was 1.51 mN. The linearity error was 8.5%. The maximum absolute residual error was 3.43 mN.

Repeatability
As shown in Figure 5c, a quartz plate was pasted to the 3Dprinted support. When the microneedle touched the quartz plate, the compressive forces generated were measured using an electronic scale (resolution: 0.0001 g). The purpose of this experiment was to investigate the consistency of the performance of the force sensor under different loads. In this repetitive experiment, four different weights ranging from 0.7 to 2.2 g were sequentially attached to the sensor. The angles set for roll angle α and sweep angle β were the same as those in the calibration experiment. However, the axial performance of the force sensor was tested by applying tensile forces, and compressive force tests were also performed in this experiment. The sweep angle β ranged from 0°to 360°with the 30°intervals, and the pitch angles α ranged from 60°to 30°at 30°intervals. When roll angle α was 30°and 60°, the PI actuator moved 0.02 and 0.01 mm downward, respectively. The experiment was repeated three times. A total of 939 samples were collected. The tensile and compressive forces were calculated using (9). The results of the repeated experiments are shown in Figure 5d. The experiments showed that the force sensor had good performance uniformity. For F x , F y , and F z , the RMS error is 0.39, 0.94, and 1.42 mN, the linearity error is 2.42%, 2.23%, and 9.27%, and the maximum absolute residual error is less than 0.97, 0.94, and 3.71 mN.

Design and Assembly of Intraocular Dexterous Actuator
The 2-DOF intraocular dexterous actuator was connected to the RCM mechanism, while the proposed sensor was integrated at the end of the flexible joint of the actuator. This actuator was designed to further validate the application and the ability of the sensor to monitor the puncture force. The microneedle was located at the end of the flexible manipulator to adjust www.advancedsciencenews.com www.advintellsyst.com the position and attitude of the puncture during surgery. As shown in Figure 6a, the actuator contains two servo motors: servo motor 1 (Maxon-347 727) and servo motor 2 (Satelles-ECU16024). Servo motor 2 drives the anterior sensor of the actuator to rotate around the Z-axis.
The intraocular actuator is based on a cable-driven mechanism. In general, a cable-driven mechanism that achieves one-DOF motion requires the symmetrical motion of two motors for synchronous traction. [28] To reduce the size of the actuator and avoid motion interference between the actuator and external equipment, we used a simplified push-rocker device. A schematic diagram of this mechanism is shown in Figure 6c. Servo motor 1 changes the length of the push rod via the lead screw to realize the rotation of the rocker around the rotation center. The cable is attached to both sides of the rocker at the same distance from the center of the rotation of the rocker, ensuring that cables 1 and 2 maintain the consistency of equal movement. The anterior segment of the actuator integrates the flexible joint and proposed 3-DOF force sensor with the microneedle. To achieve a large deflection angle with a limited joint size, a new flexible joint with a flexible joint length of only 1.2 mm was developed. As shown in Figure 6b, the flexible joint was composed of three CNC joints with convex grooves to ensure the stability of the flexible manipulator. The maximum theoretical bending angle of the flexible joint with a combination of the three joints was 60°. As shown in Figure 7, the flexibility of the actuator was tested in the eye. An eyeball model with a diameter of 24.5 mm was designed. Six points were selected for the eyeball model. The adjustment of the puncture angles and puncture points is achieved when the flexible manipulator and RCM work together, which shows good dexterity in the eye space.

Experimental Section
In this study, an eye surgery robot (ESR) system with an intraocular dexterous actuator and an RCM mechanism was used to perform RVC in the ex vivo porcine eye. This was the first time that the 3-DOF force generated during needle insertion was recorded. Figure 8a shows the experimental site, a microscope and monitor providing visual feedback, an actuator installed in the RCM mechanism, and a PC, which reads the touch operation information to provide instructions for the ESR. At the same time, the PC interprets the force feedback information from the 3-DOF sensor in real time through the FBG interrogator.
As shown in Figure 1b, the manipulator first entered the eye at the initial position and then adjusted the angle to move close to the targeted retinal vein according to the predicted insertion point to effectively reduce the excessive scleral incision caused by needle insertion. The actuator adjusted the posture of the flexible manipulator to achieve an appropriate puncture angle. The operator controlled the RCM manipulator by touch to gradually approach the needle tip to the puncture site. As the needle tip approached the puncture site and was ready for puncture, the interrogator began reading and transmitting the FBG wavelength data. As shown in Figure 8b,c, the change in the force of the needle tip during the insertion process was recorded by the proposed force sensor, and the puncture was analyzed in five phases. In the first phase, the needle tip gradually approached the puncture point, and the puncture point was adjusted so that the needle tip was in the center of the retinal vein. When the needle tip touched the surface of the vein, the force of the needle tip increased in the three directions of F x , F y , and F z , with values less than 4 mN. In the second phase, the needle tip reached  www.advancedsciencenews.com www.advintellsyst.com the puncture point and the operator controlled the RCM mechanism by touch to bring the insertion path of the needle in line with the original angle of insertion. When the axial force reached 9.745 mN, the upper layer of the vascular wall was punctured, and the axial force quickly decreased to 6.853 mN. However, the operator may not realize in time to stop the needle insertion until the needle tip goes deeper and touches the bottom layer of the vascular wall, and the axial force was at 10.02 mN when they stopped needle insertion. This led to the third phase where the operator adjusted the depth and position of the needle tip to prevent the bevel of the needle tip from blocking the drug when it reached the lower layer of the vascular wall. The contact force between the needle wall and the tissue during the adjustment resulted in an increase in F y . In the fourth phase, administration of the drug with a high-injection pressure caused deformation of the vascular tissue, which increased the traction force on the injection needle. At the same time, the fluid pressure generated by the injection pushed the needle in the opposite direction, so that the axial force Fz gradually increased with the fluid pressure.
In the fifth phase, the injection was completed, the needle was withdrawn, and the 3-DOF force on the needle tip gradually decreased to zero. Retinal vascular injection is a complex and challenging procedure. The blood vessel floats above the retina, and too large a needle entry angle can easily displace the vessel and increase the puncture force. [29,30] In addition, if the puncture force is too large, the microneedle can easily penetrate the upper and lower layers of the vascular wall simultaneously, resulting in retinal damage. Therefore, the perception of the correct insertion angle and force is very important for the safety of the RVC procedure. Due to the lack of effective depth information in the eye image, the 3-DOF force sensor is of great importance in providing feedback for robotic RVC tasks. On the one hand, force feedback is used to ensure that the force is applied within a safe range. On the other hand, force feedback is used to make decisions during surgery that require immediate responses, such as stopping and retracting the needle, rather than relying on human hands for control. The command is sent to the robot immediately based on the force information to avoid tissue damage caused by the delay in human action. In the future, dexterous actuators could perform more delicate procedures based on force information, such as pushing down and plucking, which would further increase the chance of successful surgery.

Conclusion
Compared to the straight rigid instruments of a surgical robot, a flexible manipulator has the advantage of accessing a larger intraocular workspace and being more flexible. [9,10] In this study, a 3-DOF force sensor with a length of 3.8 mm integrated at the end of the flexible manipulator is proposed to achieve an appropriate puncture angle and puncture force measurement for RVC.
In previous studies, researchers fabricated an intraocular force sensor by attaching FBG fibers to the surface of nitinol tubes with glue. [31] This bonding method easily leads to the failure of the FBG chirp. In addition, special clamps need to be customized during the assembly process to ensure the accuracy of positioning the FBGs. In another study [17] of a 3-DOF force-sensing microneedle, the suspended FBGs lack the protection provided by the adhesive coating, and the microneedle could be easily damaged by accidental contact. In contrast, our proposed force sensor could integrate the FBG fibers and injection line into the nitinol tube through microprecision 3D components. The configuration of FBGs improves the overall stiffness of the sensor under the condition that the force sensitivity is guaranteed, and the optical fibers are not damaged by accidental contact. FBG fibers are not only sensitive to sensors, but also provide internal support. Theoretically, we can design more flexible segments and choose thinner nitinol tubes and optical fibers to further improve the performance of the sensor.
The force sensor [14][15][16] with the FBG in the center has relatively high accuracy in measuring axial force. However, it requires a nonlinear method to fit the axial force, which is time-consuming and requires the acquisition of a large number of data samples. In addition, the FBG occupies a central position of the force sensor, which results in the inability to integrate the injection line. In our work, a reference fiber (FBG4) was configured to compensate for the wavelength offset caused by the temperature change. A linear algorithm is proposed to decouple the transverse force, axial force, and temperature. The calibration and repeatable experiment have shown that the estimated axial compressive force calculated using the sensitivity matrix (9) is highly accurate and can be calibrated with the tensile force. When the temperature changes, the wavelength offset values of the reference fiber and other fibers show a good linear relationship, which can compensate for the thermal drift caused by the temperature change in the range of human body temperature. He et al. [16] Gonenc et al. [15] Zhang et al. [17] Zhang et al. [32] This work www.advancedsciencenews.com www.advintellsyst.com