Tool Path Generation to Protect Soft Tissue with Multi ...

Tool Path Generation to Protect Soft Tissue with Multi-axis Milling Machine Taiga NAKANO1, Naohiko SUGITA1, Yoshikazu NAKAJIMA1, Takeharu KATO2, Kazuo FUJIWARA3, Nobuhiro ABE3, Toshifumi OZAKI3, Masahiko SUZUKI4 and Mamoru MITSUISHI1 1 School of Engineering, The University of Tokyo, Japan, [email protected] 2 Halley Valley Co., Ltd. 3 School of Medicine, Okayama University 4 School of Medicine, Chiba University Abstract: Tool interference causes damage to surrounding soft tissue in minimally invasive orthopedic surgery with a milling robot. The objective of this study is to avoid the collision of cutting tool with complicated shapes, and a novel approach of interference-free tool path generation is proposed: intraoperative modeling of tissues and interference-free tool path generation. A model is constructed by using a 3-dimensional optical position sensor. Based on the model, interference-free tool path is immediately determined by preliminary definition of evacuating direction. The effectiveness of the proposed method is evaluated with artificial models on the system that we have developed so far. Keywords: Interference-free, Tool Path Generation, Multi-axis Milling Machine, Bone Cutting

1.

Introduction Minimally invasive surgery, which is intended to enhance postoperative performance in artificial joint replacement, has been gaining public attention. In artificial joint replacement, the tool typically enters through the area opened by an incision and aligns with the shape of the artificial joint introduced to cut the femur and tibia (Fig. 1). Advanced bone processing technology is in demand because the precision of the installation of the artificial joint is dependent largely on the postoperative performance. Low invasion by means of minimal incision is required for the minimally invasive surgery dealt with in this study, in addition to the highly precise and efficient processing of the location of the artificial joint installation. Minimally invasive surgery, which is different from general artificial joint replacement, has many problems involved. The incision is narrow, causing not only a restriction of the operative view but also the tool invasion area and tool posture. In addition, the soft tissues to be protected are complex, and a wide range of bone cutting is required. This causes a problem of a drop in the precision of the bone cutting, as well as accompanying damage to the bio-tissues due to tool interference or work movement. As a result, postoperative performance depends highly on the personal skills of the practitioner. From the above, one may expect a support system that can perform minimally invasive surgery that is more stable in nature. Many support systems for orthopedic surgery, such as ROBODOC [1], have been developed, but none of them responds fully to minimally invasive surgery. In this study, we will work with problems of interference-free tool path generation specific to the surgery with a view to the protection of surrounding tissues.

Opening area

Femur

Tibia 30 mm

Anterior slope Anterior plane Posterior slope

Opening area Distal plane

Tibia plane

Posterior plane

(a) Opening area in MIS

(b) Resection planes

Figure1: Minimally invasive orthopedic surgery. Problems related to tool path generation without machine interference have been discussed in the metalworking field that uses multi-axis machine tools. Morishige et al. sought an interference-free tool position in a study utilizing configuration space used for a robot manipulator to avoid obstacles [2]. Jun et al. optimized the tool path [3] and Takeuchi et al. proposed a tool path generation method based on curved surface interpolation in the shape of the sweep of the tool [4]. Lauwers et al. proposed a tool path algorithm that avoided machine interference and that maximized the rejection rate of machined parts at the same time [5]. Hsueh et al. proposed a method that automatically generated the interference-free tool posture [6]. Ivanenko et al. optimized the tool path using the system of curvilinear coordinates [7]. Munlin et al. generated an optimized tool path that minimized calculation errors of inverse kinematics at the stationary point [8]. In this way, a multi-axis control processing system is capable of processing works from any desired posture and implementing the processing of works with a variety of shapes. In the case treated in this study, however, it is

impossible to completely avoid tool interference for a specific processing pattern with a complicated interference area, which makes it difficult to apply industrial CAM technology. Additionally, medical CAM seeks the quick generation of the tool path during surgery. The authors have proposed a method of tool path generation using the multi-axis processing system [9]. This method has not fully taken into consideration the problem of interference with soft tissues caused by minimally invasive surgery. Therefore, this study devises a new interference-free method of tool path generation for the purpose of minimizing contact with complicated soft tissues specific to minimally invasive artificial joint replacement and verifies the effectiveness of the new method through actual processing experiments. 2.

Materials and Methods

2.1 System Overview To verify the proposed method, we used the multi-axis bone cutting system we have developed. Figure 2 shows the main component and the motion transfer mechanism. The mechanism is characterized by (1) improvements in rigidity owing to the linear guide and circular guide elements, (2) the installation of a redundant axis (axis A), and (3) the agreed rotary center of the degree of rotary freedom. Taking into account the working area of the surgeon, the mechanism approaches from one side of the diagnosed leg. It assigns the opposite space as the surgeon’s working area. In the postures illustrated in Fig. 2, rigidity is 271 N/mm in the axial direction of U, 72 N/mm in the axial direction of V, and 65 N/mm in the axial direction of W. The redundant axis is placed at the tip of the robot, and it efficiently avoids obstacles, such as surrounding tissues, while minimizing changes in posture. The tool tip is immovable even while each axis (A, B, or C) is rotating, and it is capable of invading a joint while incurring no damage to the tissues if the tool posture is properly controlled.

V

2.2 System Drive Mechanism The processing system is installed with moving parts and axes in the order Z, B, C, W V, U, and A (Fig. 2(b)). The posture matrix and the tool center are represented by the following equations: Posture matrix

E = E

jθ1

⋅ E kθ 2 ⋅ E iθ 3

Tool center P = Li1 + C2j + E jθ ⋅ (Ci3 + Ck4 + E kθ 1

(1) 2

⋅ ( C 5j + L k6 + L 7j + Li8 + E iθ 3 ⋅ G 9 ))

(2)

where tool tip P is represented by rotation matrix E, variable vector L, fixed vector C, and face vector G. Each matrix and suffixes i, j, and k represent the operation in the area of U, V, and W, respectively. 2.3 Problem of Tool Interference in Minimally Invasive Surgery The following are the requirements of tool path generation in minimally invasive surgery. These requirements are different from those of general CAM for industrial use. (1) Cut bones over a wide area through a narrow opening (with an incision length of 70 mm) (Fig. 1). (2) The interference area is complicated in shape. The soft tissue involved, including tibia, muscles, ligaments, or nerves, and information on the position of these soft tissues are unknown until the intraoperative incision is made. (3) A tool path must be generated within a limited intraoperative time. This study attempts the following approach to the problems specific to medical CAM. First, it models the soft tissue from its intraoperative position information to specify the tissue as an interference area that the tool must not invade. Next, it uses the interference-free algorithm to generate a tool path that does not tamper with the soft tissue.

W U

C A

B

2.4 Proposed Interference-free Tool Path Generation

Z

(a) 7-axis milling machine V

W

C L 7 Lk6 Cj5 Ck4 Cj2 U Li8 B kθ2 E iθ3 A E k Ci3 Ejθ1 Z k G9 j Li1 i (b) Kinematics of milling machine j

Figure 2: Overview of system.

Method 2.4.1 Modeling of Soft Tissue Different from in industrial metalworking, as stated in the preceding section, the soft tissue that is an interference area to be processed has a complex shape in the bone cutting involved in orthopedic surgery. We modeled it in the form of the incision (area of the opening) that is a tool invasion area and the surrounding tissues (internal tissues) (Fig. 3). An optical, 3-dimensional position measuring instrument (Northern Digital, Inc., Polaris) is used to measure the position of the tissues involved, based on the following procedure. Use the measuring probe to determine, as a discrete

point group, a boundary area to the skin that represents the area of possible tool invasion. Find (λ , µ ,ν ) from a multiple linear regression analysis that minimizes a square error sum (Eq. (3)) to plane λx + µy +νz for the obtained point group ( x i , y i , z i ) in such a way that Eq. (4) is satisfied. Then, project the measured point group on the obtained plane of least squares and determine the open area from the convex hull calculation.

E = ∑ (λxi + µyi +νzi − 1)

2

(3)

i

∂E ∂E ∂E = = =0 ∂λ ∂µ ∂ν

Opening area Soft tissue

Femur

(4)

Sampled points

Tibia

Figure 3: Modeling of soft tissue. For the internal tissue, the measuring probe is used in the way described above to sample an area determined to be in danger if it receives contact by a tool. At this time, high-speed processing is prioritized and the internal tissue is defined as point group data. Specifically, sampling is done in such a way that the tip of the measuring probe comes to the target area and a sampled point group is defined as the interference area when tool interference is checked.

positions of the soft tissue are diverse, but the modeled shape can be understood to be tubular, in such a way that the opening is set as the upper surface, the cutting surface as the lower surface, and the internal soft tissue as the side, as in Fig. 4 (a). [b] Setup of default posture N-axis Since the center of the tubular shape can be the safe area, the direction of tool avoidance is preset toward its center if the tool interferes with the soft tissue. Specifically, the line that ties up each center of the opening and cutting surface is assumed to be the N-axis (Fig. A (a)). [c] Determination of the tool posture Point P on the N-axis for an optional cutting point on CL is determined by the following procedures. The posture that passes through point P, determined by the tool axis line, is assumed to be the interference-free tool posture at the cutting point. [c-1] Point P is virtually set to the infinite point on the N-axis to check interference. At this time, the tool posture is parallel to the N-axis (Fig. 4 (b)). If no interference is found, the tool posture is determined set as the default. If interference is found, the tool posture moves to [c-2]. The interface check is described in the following section. [c-2] Point P is set to the center of gravity of the opening to check interference (Fig. 4 (c)). [c-3] If interference is found at [c-2], point P is moved in steps below the opening area until no further interference is found (Fig. 4 (d)). If no interference is found at [c-2], point P is moved in steps above the opening area immediately before interference occurs. [c-4] If interference is unavoidable at [c-3], the tool posture is selected in such a way that the tool is inside the opening and point P is minimized. This possibly causes interference with the internal tissue to be restricted and avoids the burden imposed on the opening at the same time. Modeled soft tissue Opening area

2.4.2 Determination of Interference-free Tool Posture Two angle parameters represent the tool posture: a slope angle for normal vector of the processing surface and a revolution angle around the normal vector at one cutting point. It is therefore necessary to determine the interference tool posture parameters on all cutting points at the cutter location (CL). However, if the angle parameters are computed at all cutting points for the complicated interference area, as dealt with in this study, the amount of processing will be tremendous. It is difficult to generate the tool path in a limited intraoperative time using this method. The tool path generation method proposed in this study analyzes the shape of the interference area to restrict the direction of tool avoidance in advance if interference exists, which decreases the amount of processing to efficiently determine the interference-free tool posture. The following is a description of the proposed algorithm. [a] Shape analysis of the interference area As discussed in the preceding section, the shapes and

P=∞ (P // N)

N-axis

N-axis

Center of gravity

Cutting point Cutting surface

(a) Setup N-axis

(b) Default tool posture Tool posture

N-axis P

I

Cutting point

(c) Search of P-point

P

Cutting point

(d) Interference-free posture

Figure 4: Determination of interference-free tool posture. As follows from the above, the tool posture corresponds to the position of point P, which enables the issue involved in the search for the tool posture that avoids interference with the soft tissue to be the search at point P on linear line

N. This allows the efficient direction of avoidance of all cutting points on CL to be instantaneously determined by a simple calculation to find a straight line to link the centers of gravity of the opening and the cutting surface. In addition, a change in the tool posture from the default is minimized, which is done by setting the interference-free maximum point P as the tool posture. 2.4.3 Interference Check Method To efficiently check for the presence or absence of interference with the model soft tissue, this method checks if the tool can pass through the opening and then checks for interference with the soft tissue. Specifically, after checking if point of intersection I of the modeled opening area with the tool axis line is contained in the convex polygon or not in an interior and exterior manner, it checks interference using a distance to tool axis line for the internal tissue modeled by the point group. Interior and exterior checking uses vector {v i } toward each vertex of the polygon and optional vector a to set Eq. (5) as the internal condition (Fig. 5 (a)). The interference check for the internal tissue uses tool radius R, tool vector t , and vector {si } moving from the tool center to the point group of the internal soft tissue to set Eq. (6) as the noninterference condition (Fig. 5 (b)). ( v i × v i +1 ) ⋅ a > 0 　　 U 　　 ( v i × v i +1 ) ⋅ a < 0 　　 ( for ∀i )

(5)

∀

(6)

s j − (s j ⋅ t )t > R　　 ( for j )

v v

Soft tissue (Point model)

3

2

v

s －(s ・t) t

1

i

I

v

i

n

s

i

Opening area (Convex polygon model)

Tool

t (|| t || = 1) Tool center

I: Intersection point of tool axis with opening area

vi: Position vector of vertex of opening area

(a) Tool entry check

t: Normal tool axis vector si: Position vector of point modeled soft tissue

(b) Tool interference check

Figure 5: Interference check method. 3.

Experiments We evaluated the effectiveness of the proposed tool path generation method for the processing pattern specific to minimally invasive artificial joint replacement. Specifically, we used the processor for the multi-axis control bone cutting system mounted with an interference avoidance algorithm to automatically generate tool path data and do experiments on processing. We employed the same procedures for this purpose as those in actual surgery. In other words, we used a 3-dimensional position measuring instrument for the registration of a bone to be processed and then sampled the opening that was an

interference area and the internal tissue to generate NC. We carried out the processing experiment on total knee arthroplasty (TKA) and used a model bone fixed with clay simulating the soft tissue (Fig. 6 (a)). The clay model had a incision length of 70 mm, a major axis of 50 mm, and a minor axis of 30 mm. In the experiment, we used a ball end mill of φ8 at 4800 rpm with a tool feed speed of 800 mm/min.

Force sensor X 20 mm (a) Clay model

Y Z (b) Force sensor

Figure 6: Evaluation experiment with clay model. TKA cuts five surfaces (anterior plane, anterior slope, distal plane, posterior slope, and posterior plane) of the femur and one surface of the tibia (Fig. 1 (b)), but in this experiment, we applied the above-mentioned algorithm to the distal plane and posterior plane of the femur targeted for end mill tip processing to generate NC. In some cases, the processing pattern dealt with in this study may cause interference to be unavoidable. Thus, not only visual qualitative evaluation but also quantitative evaluation by measuring the contact force becomes important. However, a quantitative evaluation method for tool interference has not been established, and visual quantitative evaluation is usually used. We attempted to use a force sensor (Nitta, IFS-100M40A) mounted on the tool root for quantitative evaluation (Fig. 6 (b)). Specifically, taking into account the force of inertia due to the cutting force, gravity, and change in tool posture, a difference is calculated with force data during the operation of the system in accordance with the presence or absence of the clay model with the same NC and air cutter to calculate the contact force. The force sampling cycle is 5 Hz. In addition, we performed visual qualitative evaluation throughout the experiment using a human leg model that closely simulated actual clinical conditions. This leg model reproduces the skin, patella, ligaments, and soft tissue to be protected, in addition to the femur and tibia. Tool path data was automatically generated for the TKA distal end and posterior slope, according to the same procedures discussed above, to do processing experiments. The incision length was set to 70 mm. 4.

Results and Discussion The time taken to measure of the clay model was about 90 seconds, while the time taken for the PC (CPU: 2 GHz, Memory: 1 G bytes) to generate the tool path was about 5 seconds. This led to the determination of the tool path without any problems as surgery progressed.

120

120

90

90 Force [N]

Force [N]

To validate the proposed algorithm, we evaluated the contact force with the clay model during the processing experiment. Figure 7 shows the data acquired on the force during the cutting of the distal edge. Figure 7 (a) shows the force in the proposed tool path. For comparison, the force in the conventional tool path is given in Fig. 7 (b). For the conventional method, there was found to be a long period of contact with the soft tissue model in addition to a contact force of 60 N or more caused by contact with the tibia. On the other hand, for the proposed method, interference was avoided with the tibia and a contact force during interference was also largely reduced. Interference was found when the cutting surface had close contact with the soft tissue model while cutting the area with no clearance for the tool radius and when roughing moved to finishing. The cutting time was nearly double. Figure 8 shows how experiments were done using the human leg model. The time required was almost the same as that required with the clay model and almost no tool interference was visually confirmed. However, interference was partly confirmed with the root of the spindle and the robot arm. No bad cutting surfaces were observed in any experiment.

60

60 30

30

0

0 0

200

400 600

0

200

400 600

Time [sec]

Time [sec]

(a) Proposed method

(b) Previous method

Figure 7: Result of evaluation experiment.

cutting surface, causing interference to be unavoidable. (2) The interference of the spindle root was not taken into account. (3) The algorithm was not applied to the area while moving from roughing to finishing (4) A tool path generation error occurred due to a registration error. To resolve the situation described in (1) above, it is necessary to improve the proposed algorithm. One method is to preset a tolerance of the contact amount if tool interference is unavoidable and to generate the tool path within the tolerance. At present, the direction of tool avoidance is determined according to the surface to be cut and the center of gravity of the opening, which is based on a cylindrical approximation of the interference area. Thus, interference can be reduced greatly by taking into account the geometrical relation of the interference area to the cutting surface and opening to restrict the tool avoidance direction. We will extend the interference check method to the tool spindle to respond to (2). (3) is a problem that occurred because the present surgery system was required by its specifications to return to the default posture after roughing. We will extend the applicable range of the interference avoidance algorithm to include improvements in the specifications of the surgery system to respond to (3). With regard to (4), a registration error always occurs in the surgery system, and it is necessary to set extra clearance between the tool and the interference area based on the predicted registration error. The problem of the increase in the cutting time compared with conventional methods might be caused by an increased change in the tool posture due to interference avoidance. In particular, the processing system used in this study has some posture axes installed in the base side rather than the translation section, causing its posture change operation to be very slow. Since a change in the tool posture is indispensable for tool interference avoidance, it will be necessary to consider hardware improvements. 5.

(a) Front part of distal plane

(c) Front part of posterior slope

(b) Back part of distal plane

(d) Back part of posterior slope

Figure 8: Evaluation experiment with leg model. Some reasons why tool interference could not be completely avoided are as follows: (1) The soft tissue partly came into close contact with the

Conclusions This study proposes a new method of tool path generation which seeks to avoid interference with the complicated interference area specific to minimally invasive artificial joint replacement. As a result of using a processor for multi-axis control bone cutting devices that uses the proposed algorithm to do verification experiments using clay and human leg models, we obtained the following results. 1. We divided the soft tissue into the opening and internal tissue for modeling and proposed an interference check method in accordance with each of them. 2. We built up an interference-free algorithm that could obtain the modified direction of the tool posture in accordance with the shape of the model interference area, enabling the tool path to be generated in about five seconds. 3. For the processing experiment using the clay model, it

was confirmed that the method drastically decreased a spread of interference with surrounding tissues compared with conventional methods. A force applied to the surrounding tissues also decreased if interference was present. 4. For the experiment using the human leg model, it was shown that cutting that avoided the soft tissue was possible with a incision length of 70 mm, and that minimally invasive artificial joint replacement could be implemented. References [1] Taylor, R.H., Mittelstadt, B.D., Paul, H.A., Hanson, W., Kazanzides, P., Zuhars, J.F., Williamson, B., Musits, B.L., Glassman, E. and Bargar, W.L., 1994, An Image-directed Robotic System for Precise Orthopedic Surgery, IEEE Trans. on Robotics and Automation , Vol.10, No.3, pp.261-275. [2] Morishige, K., Takeuchi, Y. and Kase, K., 1999, Tool Path Generation Using C-space for 5-axis Control Machining, Transactions of the ASME, Journal of Manufacturing Science and Engineering, Vol.121, No.1, pp.144-149. [3] Jun, C.-S., Cha, K. and Lee, Y.-S., 2003, Optimizing Tool Orientations for 5-axis Machining by Configuration-space Search Method, Computer-Aided Design 35(6), pp. 549-566. [4] Morikawa, M., Ishida, T., Teramoto, K. and Takeuchi, Y., 2006, 5-Axis Control Tool Path Generation Using Curved Surface Interpolation, JSME International Journal, Vol.49, No.4 (C Series), pp.1209-1214. [5] Lauwers, B., Dejonghe, P. and Kruth, J.P., 2003, Optimal and Collision Free Tool Posture in Five-axis Machining Through the Tight Integration of Tool Path Generation and Machine Simulation, Computer-Aided Design 35(5), pp. 421-432. [6] Hsueh, Y.-W., Hsueh, M.-H. and Lien, H.-C., 2007, Automatic Selection of Cutter Orientation for Preventing the Collision Problem on a Five-axis Machining, International Journal of Advanced Manufacturing Technology (32), pp.66-77. [7] Ivanenko, A.S., Makahanov, S.S. and Munlin, M-A., 2004, New Numerical Algorithms to Optimize Cutting Operations of a Five-axis Milling Machine, Applied Numerical Mathmatics, 49, pp395-413. [8] Munlin, M. and Makhanov, S.S., 2004, Tool Path Generation, Simulation and Optimization of a Five-axis Milling Machine, IEEE Region 10 Conference, pp. 609-612. [9] Sugita, N., Genma, F., Osa, T., Nakajima, Y., Kato, T. and Mitsuishi, M., 2008, Toolpath Determination for Multi-axis Medical Machine Tool, Trans. Japan Soc. Mec. Eng., Vol. 74, No. 743 (C Series), pp. 1907-1913 (in Japanese).