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Bending stiffness variability between a deployable robotic laser osteotome and its insertion device

Bending stiffness variability between a deployable robotic laser osteotome and its insertion device DE GRUYTER Current Directions in Biomedical Engineering 2022;8(1): 138-141 Yukiko Tomooka*, Georg Rauter, Nicolas Gerig, Ryo Takeda, Philippe Cattin, and Manuela Eugster Bending stiffness variability between a deployable robotic laser osteotome and its insertion device https://doi.org/10.1515/cdbme-2022-0035 bone healing, functional cuts, and improved depth control [1]. However, lasers depend on robotic assistance when deep cuts Abstract: Varying device stiffness on purpose can provide are required. Such deep cuts were achieved by repeated accu- safety and performance improvements in interventions involv- rate laser movement across the same location [2]. In 2021, the ing flexible minimal-invasive surgical robotic devices. For ex- first laser osteotome called CARLO® (AOT, Basel, Switzer- ample, when flexible robotic devices are used for inserting land) was successfully released. However, procedures involv- minimal-invasive tools along curved paths into the knee joint ing CARLO® required exposing the bone in an open surgery for arthroscopy, a high device stiffness can allow precise path because direct access, i.e., line of sight, was necessary for laser following where desirable. In contrast, when the minimal- cutting. invasive flexible device has reached its desired location inside We aim to reduce the invasiveness of laser bone-cutting the patient’s body, decoupling the surgical tool (end-effector) by developing a robotic endoscope that guides the laser to the from the flexible robotic insertion device can be beneficial in bone without direct access, i.e., in a minimal-invasive man- avoiding transferring disturbances such as vibrations to the ner. Our first target applications are minimally invasive knee robot-patient interaction. In this paper, we investigate bend- arthroplasty and cartilage replacement surgery. Our latest pro- ing stiffness variability in dependence on the length of a flexi- totype [3] consisted of several subsystems, including a robotic ble supply channel. Our experiments have shown that bending endoscope for minimally invasive insertion with a miniature stiffness in fact decreases with the length of the supply channel parallel robot for accurate laser guidance mounted at its tip. but the highest stiffness connection is not sufficiently rigid and The miniature parallel robot could move the laser in 3 degrees we plan to implement a more rigid connection to allow precise of freedom and would attach to the bone surface to increase the path following during insertion. stability of laser positioning. The robotic endoscope housed a Keywords: Robotic surgery, supply channel, variable stiff- supply channel connected to the miniature parallel robot. This ness, parallel robot, robotic endoscope, minimally invasive supply channel held the laser fiber and flexible shafts required surgery, laser osteotomy. for the miniature parallel robot’s actuation (Figure 1). These flexible shafts were constructed of steel wire, wound into coils, alternately twisted in the right or left direction. 1 Introduction We have implemented a mechanism that allowed cou- pling/decoupling of the parallel robot from the robotic endo- Up to today, the standard for cutting bone in surgical proce- scope to minimize the transmission of external disturbances dures was mechanical devices, such as milling cutters, drills, to the parallel robot during laser guidance. The decoupling and saws. Laser osteotomy would have several advantages was not a complete mechanical decoupling, because the sup- over these mechanical tools for cutting bone, such as faster ply channel must remain connected to the parallel robot. Therefore, a flexible connection, i.e., the flexible supply chan- *Corresponding author: Yukiko Tomooka, BIROMED-Lab, nel, remained between the robotic endoscope and the paral- Department of Biomedical Engineering, University of Basel, lel robot (Figure 2). This flexible connection, i.e., the flexible Gewerbestrasse 14, 4123 Allschwil, Switzerland, e-mail: supply channel, could be modulated by adjusting the distance yukiko.tomooka@unibas.ch between the parallel robot and the distal end of the robotic en- Georg Rauter, Nicolas Gerig, Manuela Eugster, BIROMED-Lab, Department of Biomedical Engineering, University of Basel, doscope (see 𝑑 in Figure 1). This distance adjustment was ac- Allschwil, Switzerland tuated and controlled by the actuation unit. A strong coupling Philippe Cattin, CIAN, Department of Biomedical Engineering, of the parallel robot to the endoscope was reached by mini- University of Basel, Allschwil, Switzerland mizing the distance 𝑑 between the parallel robot and the distal Ryo Takeda, Laboratory of Deformation Control, Division of Me- end of the robotic endoscope, while a weak coupling (i.e., de- chanical and Aerospace Engineering, Faculty of Engineering, coupling) involved increasing the distance 𝑑. The purpose of Hokkaido University, Hokkaido, Japan Open Access. © 2022 The Author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 138 Y. Tomooka et al., Structural stiffness variability of a robotic laser osteotome Fig. 2: During insertion, the miniature parallel robot (2) was rigidly coupled to the robotic endoscope (1). After attachment, the minia- ture parallel robot was decoupled, and a connection remained via Fig. 1: Robotic system for minimally invasive laser osteotomy: the flexible supply channel (4). Our latest prototype consisted of a robotic endoscope (1) with a miniature parallel robot (2) mounted at its tip. These components were controlled by the actuation unit (3), which was placed on a serial robot for large-scale manipulation in the operating room. 2 Methods Because the supply channel was approximately rotationally a weak coupling was to minimize the transfer of disturbances symmetric, we measured one-dimensional bending stiffness and motions by proximal robot structures to the miniature par- in this first evaluation. We assumed that the mechanism only allel robot as soon as it was fixed close to the target tissue. In moves in one direction (𝑧). With this assumption, we defined the contrary, also motions of the patient or the miniature robot stiffness as during semi-autonomous laser osteotomy were not transferred 𝑘 = , (1) back completely to the robotic endoscope. The strong coupling 𝛿 of the miniature parallel robot (end-effector) to the robotic en- with 𝐹 being the force applied on the miniature parallel robot doscope was desired during device insertion and extraction to body in 𝑧-direction and 𝛿 the displacement of the body pro- enable device guidance even along curved insertion paths in duced by this force. a teleoperated manner. Thus, the flexible, compliant connec- The robotic endoscope (1) was oriented horizontally, tion could vary stiffness according to the current needs: pre- and the miniature parallel robot (2) was placed above a cise end-effector insertion/extraction (high stiffness and strong force/torque sensor (5) (Nano17 with calibration SI-12-0.12, coupling) along curved paths or semi-autonomous operation of ATI Industrial Automation, USA), which was mounted on the fixed end-effector during laser osteotomy with disturbance a manual translation stage (6) (PT1/M, Thorlabs Inc., USA) decoupling (low stiffness and weak coupling). Various strate- (Figure 3). gies have been proposed to achieve variable stiffness for endo- We performed measurements in four conditions scopic instruments. Examples include linkage locking mecha- (𝑑 = 3 mm, 𝑑 = 7 mm, 𝑑 = 13 mm, and 𝑑 = 17 mm). nisms [4] or granular jamming [5]. However, these strategies The first minimum condition (𝑑 = 3 mm) represented the require additional components at the instrument tip to modify state in which the parallel robot is coupled to the robotic en- the stiffness, which make miniaturization more challenging. doscope. The other three conditions represented decoupled Therefore, we propose a concept without additional compo- states. For each condition, we performed three repetitions of nents for stiffness variation. the measurement (runs i, ii, and iii). Each measurement con- The supply channel consists of several parts (flexible sisted of the following procedure: At first, the desired length shafts and optical fiber). Thus, it has a more complex structure of the supply channel (distance 𝑑) was set and verified by mea- than an elementary bending beam and is challenging to model surement with a Vernier caliper. Then, the force/torque sensor accurately. To better understand and exploit the advantages of was zeroed. The force sensor was moved with the manual an elastic, flexible supply channel that allows varying the stiff- stage until the sensor detected contact with the miniature par- ness of the connection between the insertion structure (robotic allel robot. Subsequently, the force sensor was moved using endoscope) and the robotic end-effector (parallel robot) , we the translation stage in four steps of 𝛿 = 2 mm. After each performed experiments to measure the bending stiffness of the step and a short initial settling time, we recorded an evaluation flexible supply channel in dependence of channel length (dis- time of 10 seconds. The measurement data was collected via a tance 𝑑). 139 Y. Tomooka et al., Structural stiffness variability of a robotic laser osteotome Fig. 3: Measurement setup to measure bending stiffness of the flexible supply channel (4) based on the force 𝐹 and displace- Fig. 4: Measured force 𝐹 for different displacements 𝛿 . The 𝑧 𝑧 ment 𝛿 . For description of the other labels refer to the manuscript different symbols refer to the different experiment conditions, i.e., text. distances 𝑑. The mean values over the three measurement runs are marked with a grey star and connected by a grey dashed line for each condition. Speedgoat real-time target machine (Speedgoat, Switzerland) at a sample rate of 1 kHz. The measurement data were analyzed using Matlab 4 Discussion r2020b (Mathworks Inc., USA). The bending stiffness was calculated according to Equation 1. 𝐹 was calculated as the We measured bending stiffness of the flexible supply chan- mean value of the force in the 𝑧−direction of the force sensor nel in dependence of four different channel lengths. The re- coordinate system measured during the 10 seconds evaluation sults showed the expected decrease in stiffness of the flexible time and 𝛿 was the manually set linear stage displacement. supply channel as the channel length, i.e., the distance 𝑑, in- creased (Figure 4). This result indicates that the effect of the external disturbances on the positioning of the laser can be re- 3 Results duced by increasing the channel length (distance 𝑑), i.e., by introducing a weak coupling between the parallel robot and The results showed that the bending stiffness of the flexible the robotic endoscope. supply channel decreased as the channel length, i.e., the dis- During insertion of the device into the patient, the parallel tance 𝑑, was increased (Figure 4). For more detailed values robot must be rigidly coupled to the endoscope to avoid a large refer to Figure 5 and Table 1. deflection of the flexible supply channel and thus buckling of the parallel robot. According to a previous study, the lateral Tab. 1: Resulting bending stiffness 𝑘. The minimum and maximum contact force during insertion of a rigid endoscope dummy into values for each distance 𝑑 are highlighted in bold. the knee of a body donor was in the range of 0−5 N [6]. We measured that the parallel robot displaced 8 mm under the lat- −1 Stiffness 𝑘 [N mm ] eral force (𝐹 ) of 1.2 N in the strongly coupled condition (𝑑 = Distance Run 𝑧 𝛿 = 2 mm 4 mm 6 mm 8 mm 3mm) (Figure 4). This result indicates that a displacement (𝛿 ) i 0.139 0.165 0.164 0.155 larger than 8 mm can be expected during the insertion of the 𝑑 = 3 mm ii 0.111 0.137 0.147 0.145 device into the knee. iii 0.099 0.127 0.137 0.139 Therefore, an additional mechanism to increase the cou- i 0.069 0.068 0.097 0.098 pling strength between the robotic endoscope and the paral- 𝑑 = 8 mm ii 0.057 0.067 0.081 0.090 iii 0.062 0.070 0.088 0.091 lel robot during device insertion will be required if a precise i 0.029 0.036 0.038 0.053 path following behavior is desired despite of inevitable inter- 𝑑 = 13 mm ii 0.033 0.041 0.043 0.057 action forces with the adjacent tissues. Possible concepts in- iii 0.033 0.041 0.040 0.055 clude granular jamming, which has also been proposed to vary i 0.040 0.036 0.034 0.040 the stiffness of joints [5], or inflatable balloons used in various 𝑑 = 17 mm ii 0.033 0.030 0.031 0.037 surgical applications (e.g., balloon catheters for angioplasty). iii 0.030 0.026 0.030 0.035 140 Y. Tomooka et al., Structural stiffness variability of a robotic laser osteotome 5 Conclusion We aim to minimize disturbances influencing the accuracy of the surgical instrument by decoupling the functional head of these surgical instruments (i.e., the parallel robot or other end-effectors) from the structures used for insertion (i.e., the robotic endoscope). We demonstrated that increasing the length of the flexible supply channel (distance 𝑑) decreased its bending stiffness. Therefore, it is feasible to reduce the prop- agation of forces. Further investigations considering damp- ing effects are necessary to evaluate the reduction of exter- nal disturbances’ transmission (e.g., vibration). In case higher stiffness of the system is desired such as during device inser- tion/extraction in a strongly coupled state, additional mecha- Fig. 5: The plot shows the measured force 𝐹 (grey) and mov- nisms to increase stiffness could be applied. ing average (1000 samples) smoothed values (black). The man- ual performed deflections 𝛿 are color-coded. Only one (sec- ond) experiment run out of three is shown for only one condition Acknowledgment: The authors gratefully acknowledge (𝑑 = 8 mm). The values for the other runs and conditions can be funding of the Werner Siemens Foundation through the MIR- found in Figure 4 and Table 1. The light grey vertical areas indi- ACLE project. cate the 10 seconds evaluation time. The colored lines indicate the calculated mean force values during the settling time labelled with Author Statement corresponding stiffness value 𝑘. The authors have no conflict of interest to disclose. We observed a deflection of the endoscope’s most distal joint during the experiments when a large force was applied to References the parallel robot. In the coupled state (𝑑 = 3 mm) the endo- scope’s most distal joint started to deflect at 𝛿 = 4 mm. For [1] Augello M, Deibel W, Nuss K, Cattin P, Jürgens P. Compara- the decoupled states, the endoscope’s most distal joint started tive microstructural analysis of bone osteotomies after cutting to deflect at 𝛿 = 8 mm. Thus, the measured displacements in by computer-assisted robot-guided laser osteotome and the coupled state also included a displacement of the robotic piezoelectric osteotome: an in vivo animal study. Lasers in Medical Science; 2018: 1471-1478. endoscope. Therefore, the actual bending stiffness of the flexi- [2] Burgner J. Robot-assisted laser osteotomy. Dissertation. ble channel could be higher than measured. Thus, to avoid de- Karlsruher Institute for Technology. 2010. flecting the device during insertion, it might also be required to [3] Eugster M, Robotic system for accurate minimally invasive stiffen the robotic endoscope’s joints. Such additional stiffen- laser osteotomy. At - Automatisierungstechnik; 2022:70:676- ing could be achieved by implementing joint breaks or series elastic actuation [7]. To measure the supply channel’s bending [4] Yagi A, Matsumiya K, Masamune K, Liao H, Dohi T. Rigid- flexible outer sheath model using slider linkage locking stiffness independently, the endoscope would have to be fixed mechanism and air pressure for endoscopic surgery. Med- during the measurement. In addition, the initial position of the ical Image Computing and Computer-Assisted Intervention parallel robot was set manually by observing the contact force (MICCAI); 2006:503-510. values. Therefore, a distance between the force sensor and the [5] Jiang A, Xynogalas G, Dasgupta P, Althoefer K, Nanayakkara parallel robot at the initial contact condition would have re- T. Design of a variable stiffness flexible manipulator with composite granular jamming and membrane coupling. In- sulted in a lower measurement force. This could have caused ternational Conference on Intelligent Robots and Systems the variation of the measured forces, i.e., the calculated stiff- (IROS); 2012. ness (Table 1) between the runs. Although the measured bend- [6] Eugster M, Zoller E, Fasel L, Cattin P, Friederich NF, Zam A, ing stiffness 𝑘 may include these influences, the reduction of et al. Contact force estimation for minimally invasive robot- the stiffness with increasing length of the flexible supply chan- assisted laser osteotomy in the human knee. Joint Workshop nel (distance 𝑑) shows the principle functionality of the decou- on New Technologies for Computer/Robot Assisted Surgery (CRAS) 2018. pling concept. [7] Fasel L, Gerig N, Cattin P, Rauter G. Control evaluation of antagonistic series elastic actuation for a robotic endoscope joint. Journal of Bionic Engineering; 2022:1-10. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Current Directions in Biomedical Engineering de Gruyter

Bending stiffness variability between a deployable robotic laser osteotome and its insertion device

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Abstract

DE GRUYTER Current Directions in Biomedical Engineering 2022;8(1): 138-141 Yukiko Tomooka*, Georg Rauter, Nicolas Gerig, Ryo Takeda, Philippe Cattin, and Manuela Eugster Bending stiffness variability between a deployable robotic laser osteotome and its insertion device https://doi.org/10.1515/cdbme-2022-0035 bone healing, functional cuts, and improved depth control [1]. However, lasers depend on robotic assistance when deep cuts Abstract: Varying device stiffness on purpose can provide are required. Such deep cuts were achieved by repeated accu- safety and performance improvements in interventions involv- rate laser movement across the same location [2]. In 2021, the ing flexible minimal-invasive surgical robotic devices. For ex- first laser osteotome called CARLO® (AOT, Basel, Switzer- ample, when flexible robotic devices are used for inserting land) was successfully released. However, procedures involv- minimal-invasive tools along curved paths into the knee joint ing CARLO® required exposing the bone in an open surgery for arthroscopy, a high device stiffness can allow precise path because direct access, i.e., line of sight, was necessary for laser following where desirable. In contrast, when the minimal- cutting. invasive flexible device has reached its desired location inside We aim to reduce the invasiveness of laser bone-cutting the patient’s body, decoupling the surgical tool (end-effector) by developing a robotic endoscope that guides the laser to the from the flexible robotic insertion device can be beneficial in bone without direct access, i.e., in a minimal-invasive man- avoiding transferring disturbances such as vibrations to the ner. Our first target applications are minimally invasive knee robot-patient interaction. In this paper, we investigate bend- arthroplasty and cartilage replacement surgery. Our latest pro- ing stiffness variability in dependence on the length of a flexi- totype [3] consisted of several subsystems, including a robotic ble supply channel. Our experiments have shown that bending endoscope for minimally invasive insertion with a miniature stiffness in fact decreases with the length of the supply channel parallel robot for accurate laser guidance mounted at its tip. but the highest stiffness connection is not sufficiently rigid and The miniature parallel robot could move the laser in 3 degrees we plan to implement a more rigid connection to allow precise of freedom and would attach to the bone surface to increase the path following during insertion. stability of laser positioning. The robotic endoscope housed a Keywords: Robotic surgery, supply channel, variable stiff- supply channel connected to the miniature parallel robot. This ness, parallel robot, robotic endoscope, minimally invasive supply channel held the laser fiber and flexible shafts required surgery, laser osteotomy. for the miniature parallel robot’s actuation (Figure 1). These flexible shafts were constructed of steel wire, wound into coils, alternately twisted in the right or left direction. 1 Introduction We have implemented a mechanism that allowed cou- pling/decoupling of the parallel robot from the robotic endo- Up to today, the standard for cutting bone in surgical proce- scope to minimize the transmission of external disturbances dures was mechanical devices, such as milling cutters, drills, to the parallel robot during laser guidance. The decoupling and saws. Laser osteotomy would have several advantages was not a complete mechanical decoupling, because the sup- over these mechanical tools for cutting bone, such as faster ply channel must remain connected to the parallel robot. Therefore, a flexible connection, i.e., the flexible supply chan- *Corresponding author: Yukiko Tomooka, BIROMED-Lab, nel, remained between the robotic endoscope and the paral- Department of Biomedical Engineering, University of Basel, lel robot (Figure 2). This flexible connection, i.e., the flexible Gewerbestrasse 14, 4123 Allschwil, Switzerland, e-mail: supply channel, could be modulated by adjusting the distance yukiko.tomooka@unibas.ch between the parallel robot and the distal end of the robotic en- Georg Rauter, Nicolas Gerig, Manuela Eugster, BIROMED-Lab, Department of Biomedical Engineering, University of Basel, doscope (see 𝑑 in Figure 1). This distance adjustment was ac- Allschwil, Switzerland tuated and controlled by the actuation unit. A strong coupling Philippe Cattin, CIAN, Department of Biomedical Engineering, of the parallel robot to the endoscope was reached by mini- University of Basel, Allschwil, Switzerland mizing the distance 𝑑 between the parallel robot and the distal Ryo Takeda, Laboratory of Deformation Control, Division of Me- end of the robotic endoscope, while a weak coupling (i.e., de- chanical and Aerospace Engineering, Faculty of Engineering, coupling) involved increasing the distance 𝑑. The purpose of Hokkaido University, Hokkaido, Japan Open Access. © 2022 The Author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 138 Y. Tomooka et al., Structural stiffness variability of a robotic laser osteotome Fig. 2: During insertion, the miniature parallel robot (2) was rigidly coupled to the robotic endoscope (1). After attachment, the minia- ture parallel robot was decoupled, and a connection remained via Fig. 1: Robotic system for minimally invasive laser osteotomy: the flexible supply channel (4). Our latest prototype consisted of a robotic endoscope (1) with a miniature parallel robot (2) mounted at its tip. These components were controlled by the actuation unit (3), which was placed on a serial robot for large-scale manipulation in the operating room. 2 Methods Because the supply channel was approximately rotationally a weak coupling was to minimize the transfer of disturbances symmetric, we measured one-dimensional bending stiffness and motions by proximal robot structures to the miniature par- in this first evaluation. We assumed that the mechanism only allel robot as soon as it was fixed close to the target tissue. In moves in one direction (𝑧). With this assumption, we defined the contrary, also motions of the patient or the miniature robot stiffness as during semi-autonomous laser osteotomy were not transferred 𝑘 = , (1) back completely to the robotic endoscope. The strong coupling 𝛿 of the miniature parallel robot (end-effector) to the robotic en- with 𝐹 being the force applied on the miniature parallel robot doscope was desired during device insertion and extraction to body in 𝑧-direction and 𝛿 the displacement of the body pro- enable device guidance even along curved insertion paths in duced by this force. a teleoperated manner. Thus, the flexible, compliant connec- The robotic endoscope (1) was oriented horizontally, tion could vary stiffness according to the current needs: pre- and the miniature parallel robot (2) was placed above a cise end-effector insertion/extraction (high stiffness and strong force/torque sensor (5) (Nano17 with calibration SI-12-0.12, coupling) along curved paths or semi-autonomous operation of ATI Industrial Automation, USA), which was mounted on the fixed end-effector during laser osteotomy with disturbance a manual translation stage (6) (PT1/M, Thorlabs Inc., USA) decoupling (low stiffness and weak coupling). Various strate- (Figure 3). gies have been proposed to achieve variable stiffness for endo- We performed measurements in four conditions scopic instruments. Examples include linkage locking mecha- (𝑑 = 3 mm, 𝑑 = 7 mm, 𝑑 = 13 mm, and 𝑑 = 17 mm). nisms [4] or granular jamming [5]. However, these strategies The first minimum condition (𝑑 = 3 mm) represented the require additional components at the instrument tip to modify state in which the parallel robot is coupled to the robotic en- the stiffness, which make miniaturization more challenging. doscope. The other three conditions represented decoupled Therefore, we propose a concept without additional compo- states. For each condition, we performed three repetitions of nents for stiffness variation. the measurement (runs i, ii, and iii). Each measurement con- The supply channel consists of several parts (flexible sisted of the following procedure: At first, the desired length shafts and optical fiber). Thus, it has a more complex structure of the supply channel (distance 𝑑) was set and verified by mea- than an elementary bending beam and is challenging to model surement with a Vernier caliper. Then, the force/torque sensor accurately. To better understand and exploit the advantages of was zeroed. The force sensor was moved with the manual an elastic, flexible supply channel that allows varying the stiff- stage until the sensor detected contact with the miniature par- ness of the connection between the insertion structure (robotic allel robot. Subsequently, the force sensor was moved using endoscope) and the robotic end-effector (parallel robot) , we the translation stage in four steps of 𝛿 = 2 mm. After each performed experiments to measure the bending stiffness of the step and a short initial settling time, we recorded an evaluation flexible supply channel in dependence of channel length (dis- time of 10 seconds. The measurement data was collected via a tance 𝑑). 139 Y. Tomooka et al., Structural stiffness variability of a robotic laser osteotome Fig. 3: Measurement setup to measure bending stiffness of the flexible supply channel (4) based on the force 𝐹 and displace- Fig. 4: Measured force 𝐹 for different displacements 𝛿 . The 𝑧 𝑧 ment 𝛿 . For description of the other labels refer to the manuscript different symbols refer to the different experiment conditions, i.e., text. distances 𝑑. The mean values over the three measurement runs are marked with a grey star and connected by a grey dashed line for each condition. Speedgoat real-time target machine (Speedgoat, Switzerland) at a sample rate of 1 kHz. The measurement data were analyzed using Matlab 4 Discussion r2020b (Mathworks Inc., USA). The bending stiffness was calculated according to Equation 1. 𝐹 was calculated as the We measured bending stiffness of the flexible supply chan- mean value of the force in the 𝑧−direction of the force sensor nel in dependence of four different channel lengths. The re- coordinate system measured during the 10 seconds evaluation sults showed the expected decrease in stiffness of the flexible time and 𝛿 was the manually set linear stage displacement. supply channel as the channel length, i.e., the distance 𝑑, in- creased (Figure 4). This result indicates that the effect of the external disturbances on the positioning of the laser can be re- 3 Results duced by increasing the channel length (distance 𝑑), i.e., by introducing a weak coupling between the parallel robot and The results showed that the bending stiffness of the flexible the robotic endoscope. supply channel decreased as the channel length, i.e., the dis- During insertion of the device into the patient, the parallel tance 𝑑, was increased (Figure 4). For more detailed values robot must be rigidly coupled to the endoscope to avoid a large refer to Figure 5 and Table 1. deflection of the flexible supply channel and thus buckling of the parallel robot. According to a previous study, the lateral Tab. 1: Resulting bending stiffness 𝑘. The minimum and maximum contact force during insertion of a rigid endoscope dummy into values for each distance 𝑑 are highlighted in bold. the knee of a body donor was in the range of 0−5 N [6]. We measured that the parallel robot displaced 8 mm under the lat- −1 Stiffness 𝑘 [N mm ] eral force (𝐹 ) of 1.2 N in the strongly coupled condition (𝑑 = Distance Run 𝑧 𝛿 = 2 mm 4 mm 6 mm 8 mm 3mm) (Figure 4). This result indicates that a displacement (𝛿 ) i 0.139 0.165 0.164 0.155 larger than 8 mm can be expected during the insertion of the 𝑑 = 3 mm ii 0.111 0.137 0.147 0.145 device into the knee. iii 0.099 0.127 0.137 0.139 Therefore, an additional mechanism to increase the cou- i 0.069 0.068 0.097 0.098 pling strength between the robotic endoscope and the paral- 𝑑 = 8 mm ii 0.057 0.067 0.081 0.090 iii 0.062 0.070 0.088 0.091 lel robot during device insertion will be required if a precise i 0.029 0.036 0.038 0.053 path following behavior is desired despite of inevitable inter- 𝑑 = 13 mm ii 0.033 0.041 0.043 0.057 action forces with the adjacent tissues. Possible concepts in- iii 0.033 0.041 0.040 0.055 clude granular jamming, which has also been proposed to vary i 0.040 0.036 0.034 0.040 the stiffness of joints [5], or inflatable balloons used in various 𝑑 = 17 mm ii 0.033 0.030 0.031 0.037 surgical applications (e.g., balloon catheters for angioplasty). iii 0.030 0.026 0.030 0.035 140 Y. Tomooka et al., Structural stiffness variability of a robotic laser osteotome 5 Conclusion We aim to minimize disturbances influencing the accuracy of the surgical instrument by decoupling the functional head of these surgical instruments (i.e., the parallel robot or other end-effectors) from the structures used for insertion (i.e., the robotic endoscope). We demonstrated that increasing the length of the flexible supply channel (distance 𝑑) decreased its bending stiffness. Therefore, it is feasible to reduce the prop- agation of forces. Further investigations considering damp- ing effects are necessary to evaluate the reduction of exter- nal disturbances’ transmission (e.g., vibration). In case higher stiffness of the system is desired such as during device inser- tion/extraction in a strongly coupled state, additional mecha- Fig. 5: The plot shows the measured force 𝐹 (grey) and mov- nisms to increase stiffness could be applied. ing average (1000 samples) smoothed values (black). The man- ual performed deflections 𝛿 are color-coded. Only one (sec- ond) experiment run out of three is shown for only one condition Acknowledgment: The authors gratefully acknowledge (𝑑 = 8 mm). The values for the other runs and conditions can be funding of the Werner Siemens Foundation through the MIR- found in Figure 4 and Table 1. The light grey vertical areas indi- ACLE project. cate the 10 seconds evaluation time. The colored lines indicate the calculated mean force values during the settling time labelled with Author Statement corresponding stiffness value 𝑘. The authors have no conflict of interest to disclose. We observed a deflection of the endoscope’s most distal joint during the experiments when a large force was applied to References the parallel robot. In the coupled state (𝑑 = 3 mm) the endo- scope’s most distal joint started to deflect at 𝛿 = 4 mm. For [1] Augello M, Deibel W, Nuss K, Cattin P, Jürgens P. Compara- the decoupled states, the endoscope’s most distal joint started tive microstructural analysis of bone osteotomies after cutting to deflect at 𝛿 = 8 mm. Thus, the measured displacements in by computer-assisted robot-guided laser osteotome and the coupled state also included a displacement of the robotic piezoelectric osteotome: an in vivo animal study. Lasers in Medical Science; 2018: 1471-1478. endoscope. Therefore, the actual bending stiffness of the flexi- [2] Burgner J. Robot-assisted laser osteotomy. Dissertation. ble channel could be higher than measured. Thus, to avoid de- Karlsruher Institute for Technology. 2010. flecting the device during insertion, it might also be required to [3] Eugster M, Robotic system for accurate minimally invasive stiffen the robotic endoscope’s joints. Such additional stiffen- laser osteotomy. At - Automatisierungstechnik; 2022:70:676- ing could be achieved by implementing joint breaks or series elastic actuation [7]. To measure the supply channel’s bending [4] Yagi A, Matsumiya K, Masamune K, Liao H, Dohi T. Rigid- flexible outer sheath model using slider linkage locking stiffness independently, the endoscope would have to be fixed mechanism and air pressure for endoscopic surgery. Med- during the measurement. In addition, the initial position of the ical Image Computing and Computer-Assisted Intervention parallel robot was set manually by observing the contact force (MICCAI); 2006:503-510. values. Therefore, a distance between the force sensor and the [5] Jiang A, Xynogalas G, Dasgupta P, Althoefer K, Nanayakkara parallel robot at the initial contact condition would have re- T. Design of a variable stiffness flexible manipulator with composite granular jamming and membrane coupling. In- sulted in a lower measurement force. This could have caused ternational Conference on Intelligent Robots and Systems the variation of the measured forces, i.e., the calculated stiff- (IROS); 2012. ness (Table 1) between the runs. Although the measured bend- [6] Eugster M, Zoller E, Fasel L, Cattin P, Friederich NF, Zam A, ing stiffness 𝑘 may include these influences, the reduction of et al. Contact force estimation for minimally invasive robot- the stiffness with increasing length of the flexible supply chan- assisted laser osteotomy in the human knee. Joint Workshop nel (distance 𝑑) shows the principle functionality of the decou- on New Technologies for Computer/Robot Assisted Surgery (CRAS) 2018. pling concept. [7] Fasel L, Gerig N, Cattin P, Rauter G. Control evaluation of antagonistic series elastic actuation for a robotic endoscope joint. Journal of Bionic Engineering; 2022:1-10.

Journal

Current Directions in Biomedical Engineering – de Gruyter

Published: Jul 1, 2022

Keywords: Robotic surgery; supply channel; variable stiffness; parallel robot; robotic endoscope; minimally invasive surgery; laser osteotomy

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