Development of a Spiral Structure for an Active Catheter Overview of the Spiral Structure and Its Kinematic Configuration

Transcription

1 Development o a Spiral Structure or an Active Catheter Overview o the Spiral Structure and Its Kinematic Coniguration Yoshihiko KOSEKI and Noriho KOYACHI Tatsuo ARAI Mechanical Engineering Laborator Department o Engineering Science AIST, MITI Osaka Universit 1-2 Namiki, Tsukuba, Ibaraki Machikaneama-machi, Toonaka Japan Osaka , Japan Abstract We propose a special structure or an active catheter: a spiral structure. It consists o leible belt on which actuators, sensors, and/or control units are built. The belt is spiraled or put spirall around leible tube to work as a catheter. The actuators on one roll o the spiral move the net roll to realie the bending, twisting, and/or epanding motion o catheter. With this method, minute and complicated actuators, sensors, and circuits can be precisel machined with ver high densit, abricated and wired together in one continuous plane with silicon processes. The advantage o this method will be simple and high-densit abrication. In this paper, the overview and kinematic analsis o the spiral-structure active catheter are discussed and some tpes o active catheters are proposed. 1 Introduction These das, the surace micro-machining like silicon process has been developed to reduce the sie o circuits, sensors and actuators. Man researchers have proposed ideas o micro-machine. One possible applications o micro-machines is minimall invasive diagnosis and treatment, because such a small surgical device would minimie the surgical trauma. An active catheter is one o the strongest candidates or micro-machine application. Fukuda and Guo [1] proposed a wire-driven active catheter. Their catheter has advantages o eas control and simple structure, but has the disadvantage that the number o its DOFs (Degrees O Freedom) are limited to around 2 or 3 because the wires occup a large space and the conlict with each other. Lim s [2] and Kaneko s [3] prototpes are advanced with respect to multi-dof because control units are built-in close to the actuators and the koseki@mel.go.jp control the actuators independentl. A multi-dof catheter, which moves like snake, will etend the applications o the active catheter not onl to blood vessels o the brain and heart, but also to paranasal sinuses and nasotracheal brain treatments. However, one o the most signiicant problems or active catheters with built-in control units is that o assembling and wiring. Lim made each link separatel and assembled them with laser CVD. Kaneko proposed a MIF (Multi-unction Integrated Film), which is leible ilm on which control units and SMA (Shape Memor Allo) are mounted monolithicall but each MIF is not connected. The assembl and wiring problem is caused b the act that almost micro-machinings, e.g. deposition, etching, sputtering, and masking, are plane processes, so it is diicult to manuacture 3-dimensional objects. This means that a plane structure that can be easil transormed into a solid is advantageous or a micromachine active catheter. In net section, we propose a SS (Spiral Structure) or and active catheter because it can be easil transormed rom a plane to a tube. 2 Outline o Spiral Structure Basic and common ideas o Spiral Structures (SS) are eplained here. Fig. 1 shows one o SS (a 4-DOF tpe), and the other tpes will be discussed later. The SS consists o a leible belt. The space between the upper and lower sides o the belt is empt or elastic enough or both sides to move separatel. The belt is spiraled or put spirall around leible tube so that the upper side o the belt and the lower side o the net belt are united and move together. Both sides are connected b some actuators and these actuators generate the relative motion between both sides. For a 4 DOF tpe, 4 linear actuators are arranged or one roll o the belt. Combinations o

2 epanding and contracting motions o the 4 linearactuator generate 4-DOF motion: 2 bending, twisting and epanding. For eample, the catheter epands when all actuators epand. Actuator Control Unit Signal Conductor Power Conductor One Unit o Spiral Structure Figure 1: Spiral Structure Fig. 1 shows that control units are built-in or each actuator and are conducted with common signal lines. The control units open/close the gate o power suppl rom power conductor to actuator. I an sensors are necessar, the can be built-in in the same wa. The methodolog to build C-MOS circuits and SMA actuators on polimide ilm has been under development b Kaneko (See. [3]). The most striking eature o SS is that all elements are built in one continuous plane. This eature enables consecutive processes rom element manuacturing to assembl and wiring with conventional micro-machinings. It would result in miniaturiation o catheter and increase o actuators and sensors. In conventional methods, each element is processed separatel so the assembl is bottleneck o total processes. The SS can be used or an leible bar like endscope, orceps or balloon. 3 Kinematics o Spiral Structure In the ollowing sections, the kinematics o SS is analed to decide what kind o, how man and where actuators should be arranged per one roll. Here, we discuss not total DOF o catheter but DOF per one roll o spiral. We set ollowing 3 problems. In the ollowing, we modeled the spiral structure as clinder hollow. 1. How man DOFs a catheter has. To decide the number o actuators, it has to be known how man DOFs the mechanism has. The catheter has ininite DOF because it is so elastic and leible that an motion are possible i suicient loads are applied or an deormation can be detected however small it is. So we analed which motion ma occur with less orce. 2. How man DOFs are necessar. It is discussed what kinds o motion are necessar or conventional and new treatments. The catheter should be designed to meet it. 3. Veri how actuators work. The actuators, which are designed according to possible and requested motion don t alwas move as intended. The ormer two items are necessar condition but not suicient condition. 4 Possible DOF o Catheter Eq. 1 ormulates the relationship between eternal orces and displacement o tip o a tube. The matri K is a compliance matri, meaning the leibilit o object. As shown in Eq. 2, the K can be diagonalised with orthogonal matri T because it is smmetric. The reason wh with orthogonal matri is that the magnitude o power remains constant ( F 2 +F 2 +F 2 +M 2 + M 2 + M 2 = const ) and each vector is independent. In practice, some coeicients need be applied because orce and moment have dierent units. For simplicit, the values o T are not shown here, but onl plus or minus are shown. T = δx = T 1 t 1. t 6 λ 1... λ 6 λ 1,2 = a+b+ (a d) 2 +4b 2 2 λ 3 = c λ 4,5 = a+b (a d) 2 +4b 2 2 λ 6 = e = T F (2)

3 δx = δ δ δ δp δq δr = KF = a b a b c b d b d e F F F M M M a = 4l 3 3πE(r 4 2 r4 1 ) + b = 2l 2 c = d = e = πe(r2 4 r4 1 ) l πe(r2 2 r2 1 ) 4l πe(r2 4 r4 1 ) 2l πg(r2 4 r4 1 ) l πg(r 2 2 r2 1 ) (1) δ, δ, δ: Translation in,, ais, δp, δq, δr: Rotation around,, ais, F i : Eternal orces in i ais, M i : Eternal moments around i ais, E: Young s modulus, G: modulus o rigidit, r 1 : Inside radius, r 2 : Outside radius, l: length λ i means leibilit in t i direction (combination o orces and moments). Noting the dierence between λ 1,2 and λ 4,5, λ 1,2 are alwas larger than λ 4,5. In addition, according to numerical inspection, λ 1,2 λ 4,5. This act eplains that motion (a) in Fig. 2 occurs more easil than motion (b). F M F M ventricle o the heart, 1 DOF or stiness o twisting motion is necessar to resist aial torque. Toda s active catheter advances being pushed rom the back. It is dangerous when the catheter might break through the wall o vessel. Sel-propelling, like snake-like or inching motion might acilitate the insertion. So 1 DOF o epanding motion along the ais is useul. In this section, we conclude that 2-4 DOFs o movement are necessar according to its application. 6 Tpes o Spiral Structures (a) (b) Figure 2: Fleibilit o Tube 2 DOFs o δ, δ, δp and δq are negligible in comparison to 2 others (Notation o δ, et al., are shown in Eq. 1). There is another reason wh δ and δ are negligible. The rotational motion causes more displacement at a distant point. As or δ and δr, the leibilit depends on sie and shape, e.g. corrugated tube has more leibilit to δ. This analsis concludes that catheter has 2-4 DOFs. The discussions in the ormer sections lead that catheter has 2-4 DOFs and 2-4 o them must be actuated according to application and the rest o them must be constrained. We would propose 5 tpes o SS, 1 or 4-DOF, 2 or 3-DOF and 2 or 2-DOF as shown in Fig. 3. (a)4dof(d,dp,dq,dr) (b)3dof(d,dp,dq) (c)3dof(dp,dq,dr) 5 Required DOF o Catheter A micro active catheter has been demanded or the navigation o instruments in cerebral and cardiac vessel. The vessel guides the catheter, so active bending motion is needed at sharp corner and divergence. So 2 DOFs o bending motions are indispensable or active catheter. In tubular organ, like vessel, colon and urinar duct, the catheter is ree rom aial torque. I it were applied to non-tubular organ like paranasal sinuses (d)2dof(dp,dq) (e)2dof(dp,dq) Figure 3: Tpes o Spiral Structures The actuators proposed here are bending and linear ones. SMA is widel used as bending actuator. SMA is also used as linear actuator but luid actuator and ultrasonic motor would be able to be used in uture. 1261

4 (a) 4-DOF(δ, δp, δq, δr): This is a kind o parallel mechanism with linear actuators. One roll o spiral has 4 linear actuators. The combinations o epansions and contractions o actuators realie bending, epanding and twisting motions. (b) 3-DOF(δ, δp, δq): One roll o spiral has 3 linear actuators. When all o them contract, the catheter contracts. When one o them contracts, the catheter bends to the actuator. (c) 3-DOF(δp, δq, δr): One roll o spiral has 8 bending actuators. 4 o them bend outside and the rests bend so that the upper side slides along spiral. The ormer is bending motion and the latter is twisting motion. pitch =.1-2. r2= =.5(ied) dp (a) dr dq (b) (d) 2-DOF(δp, δq): This tpe bends in the same wa as (c) but doesn t twist. (e) 2-DOF(δp, δr): This tpe bends in the same wa as (b) but doesn t epand. For smmetr, this tpe shown in Fig. 3 has 4 linear actuators. So actuator moves contrar to opposite one. 7 Evaluation o Motions In this section, it is tested with FEM (Finite Element Method) how the catheter moves and what is the best coniguration o catheter. The reason wh the veriication is necessar is that an arrangement can not alwas generate required motion. For eample, i all actuators o (a) 4-DOF sta in parallel, the catheter doesn t twist. The conditions o FEM are shown in Table 1. FEM Program Problem Tpe Element Tpe Young s modulus Poisson s ratio Free Z88 developed b Dr. F. Rieg, German Normal (Not Hper-elasticit) Heahedron with 8 nodes 2.e-6 (that o rubber).46 (that o rubber) Table 1: Conditions o FEM The Young s modulus and Poisson s Ratio are speciied but the purpose o this analsis is not absolute evaluation o catheter motion but relative evaluation among dierent conigurations. So these values are not important. For the same reason, the values have no unit (usuall FEM program has no unit) and the outside radius r 1 is ied to.5 (diameter=1.). The inside radius r 2 and pitch o spiral l var rom.5 to.45, rom.1 to 2. respectivel (see Fig. 4). m=1 2 m=-1 (c) m=1 2 m=-1 (d) Figure 4: Boundar Conditions o FEM DOF(δ, δp, δq, δr) Fig. 5, 6, and 7 show the displacement o the tip o one roll in -ais, around - and -ais respectivel when one o 4 actuators eerts normalied orce 1.. So 4 values o displacements are plotted or ever radius and pitch. The results o displacement around -ais are not eactl the same as that o -ais but have the same tendenc, so the are omitted here. The displacements are divided b the pitch o spiral because the ratio o change is important. Each actuator is coordinated as shown in Fig. 4 (a). The normalied orces are applied oppositel at both sides o actuator. It can be said as a whole that the value o displace- 1 ment tends to ollow ( n rn 2 ) (n=2 or 4) (See the lower graphs o igures). As the pitch gets longer, the actuators becomes perpendicular and the vertical orce increases but the horiontal decreases (See the upper graphs o igures). So there is a trade-o between δr and the others DOF(δ, δp, δq) Fig. 8, 9, and 1 show the displacements in -ais, around - and -ais respectivel when one o 3 actuators eerts normalied orce 1.. So 3 values o 1262

5 d per pitch d per pitch 5e-7-5e-7-1e-6-1.5e-6-2e-6-2.5e-6-3e-6-3.5e-6-4e pitch o spiral -5e-7-1e-6-1.5e-6-2e-6-2.5e-6-3e-6-3.5e-6 r2=.5 r2=.15 r2=.25 r2=.35 r2=.45 pitch=.1 pitch=.5 pitch=1. pitch=2. -4e dr per pitch dr per pitch 2.5e-5 2e-5 1.5e-5 1e-5 5e-6-5e-6-1e-5-1.5e-5-2e-5-2.5e-5-3e-5 2.5e-5 2e-5 1.5e-5 1e-5 5e-6-5e-6-1e-5-1.5e-5-2e-5-2.5e-5-3e-5 r2=.5 r2=.15 r2=.25 r2=.35 r2= pitch o spiral pitch=.1 pitch=.5 pitch=1. pitch= Figure 5: δ per pitch o 4-DOF (δ, δp, δq, δr) Figure 7: δr per pitch 4-DOF (δ, δp, δq, δr) 1.5e-5 1e-5 5e-6-5e-6-1e-5-1.5e pitch o spiral 1.5e-5 1e-5 5e-6-5e-6-1e-5 r2=.5 r2=.15 r2=.25 r2=.35 r2=.45 pitch=.1 pitch=.5 pitch=1. pitch= e d per pitch d per pitch 4e-6 2e-6-2e-6-4e-6-6e-6-8e-6-1e-5-1.2e-5-1.4e-5-1.6e-5 4e-6 2e-6-2e-6-4e-6-6e-6-8e-6-1e-5-1.2e-5-1.4e-5-1.6e-5 r2=.5 r2=.15 r2=.25 r2=.35 r2= pitch o pitch pitch=.1 pitch=.5 pitch=1. pitch= Figure 6: δp per pitch o 4-DOF (δ, δp, δq, δr) Figure 8: δ per pitch o 3-DOF (δ, δp, δq) displacements are plotted or ever radius and pitch. Each actuator is coordinated as shown in Fig. 4 (b). The normalied orces 1. are applied oppositel at both side o actuator. The displacements are also divided b the pitch o spiral. The value o displacement tends to ollow 1 (r n 1 rn 2 ) (n=2 or 4) too (See the lower graphs o igures). As or pitch, the displacements convergent to constant value (See the upper graphs o igures) DOF(δp, δq, δr) The SMA, which memories bending motion eerts moment on the wall o catheter, so it is modelled as s are applied on both side o SMA and 2 on middle o SMA as shown in Fig 4 (c) and (d). The moment m = l is kept to 1. to normalie the load. Fig. 11 show the displacements around -ais when the bending moment is applied. This tpe has 4 ac- tuators or bending motion. The same results are obtained as or the others so the are omitted. The FEM indicates no twisting motion. As shown in Fig. 12, the counter moment cancel the bending motion because stiness o catheter is uniorm. So the lower side has to be reinorced to resist against the counter moment while keeping leibilit o the upper side. In practice, the leible belt should be stier than the tube which the belt is spiraled to. This analsis is one o uture works DOF(δp, δr) The results are the same as those o 3-DOF(δ, δp, δq), Fig. 9 and 1. So the are omitted here DOF(δp, δr) The results are the same as those o 3-DOF(δp, δq, δr), Fig. 11. So the are omitted here. 1263

6 1.5e-5 1e-5 5e-6-5e-6-1e-5-1.5e pitch o spiral 1.5e-5 1e-5 5e-6-5e-6-1e-5 r2=.5 r2=.15 r2=.25 r2=.35 r2=.45 pitch=.1 pitch=.5 pitch=1. pitch= e e-5 7e-5 6e-5 5e-5 4e-5 3e-5 2e-5 1e-5 9e-5 8e-5 7e-5 6e-5 5e-5 4e-5 3e-5 2e-5 1e-5 r2=.5 r2=.15 r2=.25 r2=.35 r2=.45-1e pitch o spiral pitch=.1 pitch=.5 pitch=1. pitch= Figure 9: δp per pitch o 3-DOF (δ, δp, δq) Figure 11: δq per pitch o 3-DOF (δp, δq, δr) 1e-5-1e-5-2e-5-3e-5-4e-5-5e-5-6e pitch o pitch 1e-5-1e-5-2e-5-3e-5-4e-5-5e-5 r2=.5 r2=.15 r2=.25 r2=.35 r2=.45 pitch=.1 pitch=.5 pitch=1. pitch=2. -6e Figure 1: δq per pitch o 3-DOF (δ, δp, δq) 8 Summar and Conclusions In this paper, we proposed the Spiral Structure or active catheter. We discussed its three kinematic problems: how man DOFs one roll o spiral has and should have and veriied how it works. According to this discussion, we concluded that it should have 2-4 DOF o 2 bending, epanding and twisting motions. So we proposed 5 tpes o Spiral Structure. We tested with the FEM how it works and what the best coniguration is. Then we also ound that it is necessar to increase the stiness o the lower side while keeping the leibilit o the upper side. 9 Future Works As mentioned in the introduction, our concept is that a plane structure, which can be easil trans- Figure 12: Delected shape o 3-DOF (δp, δq, δr) with aial moment ormed into 3-D object, is suitable or micro-machine. It is not main subject o our research to develop integrated circuits, sensors, or actuators. However, a simulation work is not suicient to prove whether our structure is useul or not. Now we are developing the prototpe o Spiral Structure. Reerences [1] T. Fukuda, S. Guo, et al., Micro Active Catheter Sstem with Multi Degrees o Freedom, Proc. o IEEE Int. Con. on Robotics and Automation, San Diego, USA, pp , 1994 [2] G. Lim, et al., Future o active catheters, Sensors and Actuators, A56, pp (1996) [3] S. Kaneko, et al., Monolithic Fabrication o Fleible Film and Thinned Integrated Circuits, Proc. o MEMS 97, Nagoa, Japan, pp (1997) 1264