Design of an Optical Force Sensor for Force Feedback during Minimally Invasive Robotic Surgery J. Peirs, J. Clijnen, P. Herijgers, D. Reynaerts, H. Van Brussel, B. Corteville and S. Boone Katholieke Universiteit Leuven, Dept. of Mechanical Engineering, Celestijnenlaan 300B, 3001 Leuven, Belgium email:
[email protected] http://www.mech.kuleuven.ac.be
Summary: A 5 mm diameter tri-axial force sensor has been developed for minimally invasive robotic surgery. To define the required force range and resolution, a needle driver has been equipped with strain gauges, able to measure two force components perpendicular to the instrument shaft. In vivo-tests with different types of needles and tissue show that the required force range and resolution are respectively 2.5 N and 0.01 N. The new sensor is based on a flexible titanium structure of which the deformations are measured through reflective measurements with 3 optical fibres. It has a range of 2.5 N in axial direction and 1.7 N in radial direction. Keywords: force sensor, optical, surgery, force feedback Category: 10 (Applications)
1 Introduction The introduction of robots in minimally invasive surgery (MIS) of soft tissues can considerably enhance the accuracy of medical interventions. The instruments are mounted on robot manipulators (the slaves) controlled by the surgeon through ‘joysticks’ (the masters). In this way, the surgeon can perform the operation in a more ergonomic way and his hand movements can be scaled and filtered to remove trembling and to enhance accuracy. Furthermore, additional degrees of freedom can be added at the instrument tip to enhance dexterity [1]. An important problem is that the surgeon lacks tactile feedback. This can be solved by introducing small force sensors in the instruments that enable force reflection in the masters.
Sensitive element
Fig. 1. Needle driver with 2-component force sensor based on strain gauges.
voltages coming from both bridges. From this data it is possible to determine the sensitivity and offset of both bridges, and the orientation of the two strain gauge pairs with respect to each other and with respect to the jaws. The angle between the two strain gauge pairs is required to filter out the crosssensitivity between both sensing axes.
2 Force range measurements 2.1 Test set-up To be able to design the force sensor, the expected force range has to be specified. As few data can be found in literature [2,3], a test set-up was built to measure the forces occurring during suturing. Figure 2 shows a needle driver equipped with a 2component force sensor based on strain gauges. The 4 strain gauges are glued on the instrument shaft with 90° interval. Two opposing strain gauges form a half bridge measuring the X or Y component of the force at the tip. The Z component is assumed to be of the same order of magnitude. The strain gauges are connected to AC bridge amplifiers and sampled at 250 Hz. The instrument is calibrated by holding it horizontally, with a mass hanging at the tip. The instrument shaft is rotated 360° while measuring the
2.2 Measurement results Suturing tests were performed by a skilled surgeon on an anaesthetized rat. The forces required to push the needle through the tissue depend on the thickness and shape of the needle, and the tissue. Table 1 shows the six tested needle types. Figure 2 shows the peak forces for skin, muscle and liver tissue. Skin is clearly the thoughest tissue while liver is the softest. The highest and lowest peak forces are respectively 2.3 N and 0.2 N. These are forces required to puncture the tissue. Other manipulations like oscillatory motions of the needle used to test the strength of the tissue are much lower, sometimes as low as 0.05 N for liver.
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2.5
Force (N)
2.0
S = Skin M = Muscle L = Liver
Fx max (N)
Fy max (N)
1.5 1.0 0.5 0.0 S
M
L
S
6-0 3/8 circle
M
L
S
3-0 3/8 circle
M
L
3-0 Straight
S
M
L
3-0 1/2 circle
S
M
L
1 3/8 circle
S
M
L
1 3/8 circle
Tissue and needle type
Fig. 2. Peak force occuring during suturing of skin, muscle and liver tissue using different needles.
Figure 4 shows 2 possible configurations for each of the 3 sensing fibres. The first configuration is the simplest as it uses separate emittor and receiver fibres. In the second configuration the light is reflected back into the same fibre. An optocoupler has to be used to couple the emittor (LED) and receiver (photodiode) to the same measurement fibre. Maximum sensitivity is obtained when a 50/50-optocoupler is used. This means that 50 % of the emitted signal is coupled into the measurement fibre while 50 % goes to the reference photodiode. Similarly, the reflected signal is split equally into the emittor and receiver fibres. This means that maximally 25 % of the emitted light is sent back to the receiver (in the limit when 100 % of the light is reflected in the sensor). In the first configuration these ‘coupling losses’ do not occur, but high losses occur at the mirror. As the receiver fibre is located next to the emittor fibre,
Table 1. Types of needles used in the test. Size
Cross-section of tip
Shape
6-0 small
Circular
3/8 circle
3-0
Triangular
3/8 circle
3-0
Triangular
Straight
3-0
Circular
1/2 circle
1
Triangular
3/8 circle
Circular
3/8 circle
1
large
3 Sensor design 3.1 Specifications The sensor will be mounted at the tip of a 5 mm diameter instrument driver with two bending degrees of freedom [1]. This instrument driver has an internal channel of 2 mm diameter through which surgical instruments can be inserted. The sensor should have the same internal and external diameters. As the sensor will be mounted in front of the local degrees of freedom, it should be as short as possible. Three components (FX, FY, FZ) should be measured with a range of ±2.5 N and a resolution of 0.01 N (0.2 % of range). The radial forces act on the instrument tip, at a distance of 15 mm from the sensor front. The sensor should be biocompatible, sterilizable and robust.
Tool interface Reflective surface Flexibility
Optical fibres
Fig. 3. Working principle of the sensor: Three optical fibres measure the deformation of the flexible structure through the intensity of the reflected light.
3.2 Measurement principle A design based on optical fibres was chosen for reasons of safety as no leakage currents or interference signals can originate from it. Figure 3 shows the basic layout of the sensor. It consists of two parts connected by a flexible connection. The upper part is connected to the tool while the lower part is connected to the instrument shaft. Three optical fibres, arranged at 120° intervals in the lower part, measure the relative displacement between upper and lower part through the intensity of the reflected signal. The fibres are placed axially because bending them inside the sensor over 90° would violate the minimum bending radius.
Sensor
Emittor Receiver
Reference
Sensor Emittor Optocoupler
Receiver
Fig. 4. Two configurations for reflective position measurement with optical fibres.
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it can pick up only a small portion of the reflected light, which is far less than 25 %. An additional drawback is that this configuration requires twice as much fibres to be integrated in the sensor. Therefore, the second configuration is chosen. The sensing fibre can measure the perpendicular distance from the surface or the lateral distance from an edge of this surface, depending on the sensor design. Figure 5 shows the reflected signal for both types of displacement and combinations. The following components were used: Honeywell HFE4225 emittor, Honeywell HFD3228 receiver, 200 µm diameter sensor grade optical fibre with a numerical aperture of 0.37 (F-MBB, Newport). The emittor is fed with a 5 kHz sinusoidal signal with 1.7 V amplitude and 3.35 V offset. The receiver signal is filtered with a bandpass filter of 5 kHz and amplified. This amplitude modulation scheme removes drift and noise of sensor and amplifier. The sensitivity for lateral displacements is higher than for perpendicular displacements. Nevertheless, a perpendicular distance measurement on a continuous surface (not an edge) is preferred because it is influenced by only one parameter – the perpendicular distance – while an edge measurement is influenced by both lateral and perpendicular displacements. For the edge measurement this could be solved by designing a flexible structure that allows only lateral displacement, but then no axial forces could be measured with the same structure. For simplicity, perpendicular distance measurement on a continuous flat mirror is chosen with 3 fibres arranged at 120° interval as illustrated in figure 3. Axial forces cause identical displacements above all 3 fibres, while radial forces result in different or opposite displacements.
Faxial Fradial
Fig. 6. Basic geometry of the flexible structure. The axial and radial stiffness are decoupled by use of parallelograms.
3.3 Flexible structure The main problem in designing the flexible structure is that for most structures torque caused by the radial forces generates a much larger deformation than an axial force of the same magnitude. Therefore, the design tries to decouple the deformations caused by axial and radial forces, by using parallelograms as illustrated in figure 6. An axial force causes the thin horizontal beams to bend, while the thick vertical beams deform negligibly. For a radial force the opposite occurs: the vertical beams deform while the horizontal beams are mainly stressed longitudinally, a direction in which they have a high stiffness. The flexible structure consists of 4 identical parallelograms placed in an axisymmetric arrangement.
2.25 2
Voltage (Vrms)
1.75 1.5 1.25 1 0.75 0.5
Fig. 7. Flexible structure of the sensor. A scale in millimetres indicates the size.
0.25
Edge measurement
100
150
200
250
0 300
tanc e (µm )
100
300
Late ral d is
200
Table 2. Dimensions of the flexible structure. 400
500
600
0
Tube
r ula dic ) pen (µm P er tance s i d
Horizontal beams
Distance measurement
Vertical beams
Fig. 5. Reflected signal as a function of perpendicular and lateral distance between fibre and Si surface edge.
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Outside diameter
5 mm
Wall thickness
0.5 mm
Total length
8.85 mm
Thickness
125 µm
Length
67°
Smallest thickness
18°
Length
6.05 mm
The sensor is made of a strong titanium alloy (Ti6Al4V) because this material has a good corrosion resistance, superior biocompatibility, low Young’s modulus and high strength, high fatigue resistance, and good shock resistance. Figure 7 shows the final design and the machined structure. The structure is optimised using finite element calculations, resulting in the dimensions shown in table 2. The circular holes are starting holes for the wire-EDM process used to machine the slits. The EDM wire has a diameter of 30 µm. The square features located just above the upper holes are end stops protecting the sensor from axial overload. The vertical gap is 50 µm corresponding to an axial load of 2.5 N. The end stop in radial direction is the core: the gap between the core and the flexible tube is 85 µm and closes at a radial force of 1.7 N. Due to a production error, the horizontal beams have a thickness ranging from 81 to 199 µm, instead of the design value of 125 µm. These errors have a large influence on the sensitivity of the sensor as discussed in paragraph 5.
5 Calibration To calibrate the sensor, a short rod is fixed to its tip to act as a lever for applying torque. The length of the lever, 15 mm, corresponds to the distance from the instrument tip to the sensor front. The sensitivity matrix A between the applied forces Fi and the displacements di measured by the fibres is defined as follows: d Faxial fibre1 d fibre2 = A ⋅ FradX FradY d fibre3
The design and calibration values for the sensitivity matrix are (in µm/N): 6.8 114 8 − 10.4 . 19.2 − 18.9 Adesign = 6.8 − 14.3 − 3.4 Acal = 114 . − 9.4 − 11 4.5 15.4 6.8 8.7 16.5 17.9
These values can be converted to mV/N by multiplying them with the sensitivity of the optical system: 10.3 mV/µm. The design sensitivity matrix is not symmetric due to the 120° spacing between the fibres and the chosen coordinate frame. The calibrated sensitivity matrix shows large differences with the design values because of production errors. The resolution of the optical measurement system is 0.3 µm, corresponding to about 0.04 N.
4 Prototype Figure 8 shows different steps in the assembly process of the prototype. At the top, the core is shown with the optical fibres glued in position and the front surface polished. At the bottom, the flexible tube is placed over the core. Finally, the mirror (not shown) is glued in front of it with a gap of 100 µm between mirror and fibres. Similar optical components are used as for the measurements shown in figure 5.
Conclusion A 5 mm diameter optical force sensor for minimally invasive robotic surgery has been developed, based on specifications from in-vivo tests. It has a range of 2.5 N in axial direction, and 1.7 N in radial direction. Despite small fabrication errors, the prototype has proved the concept of the chosen sensor design.
Acknowledgement This research is sponsored by the Belgian programme on Interuniversity Poles of Attraction (IAP5/06: AMS) initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The authors assume the scientific responsibility of this paper.
References [1] J. Peirs, H. Van Brussel, D. Reynaerts and G. De Gersem. A Flexible Distal Tip With Two Degrees of Freedom for Enhanced Dexterity in Endoscopic Robot Surgery. In: Proc. Micromechanics Europe Workshop, pp. 271–274, Sinaia, Romania, 6–8 Oct. 2002. [2] J. Rosen et al. Surgeon-Tool Force/Torque Signatures - Evaluation of Surgical Skills in Minimally Invasive Surgery. In: Proc. of medicine meets virtual reality, pp. 1–10, San Francisco, CA, Jan. 1999. IOS Press. [3] I. Brouwer et al. Measuring in vivo animal soft tissue properties for haptic modeling in surgical simulation. In: Medicine meets virtual reality, pp. 69–74, 2001. IOS Press.
Fig. 8. The sensor during consecutive assembly phases. Top: core with optical fibres and polished front surface. Bottom: the flexible tube is glued onto the core.
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