The Haptic Scissors: Cutting in Virtual Environments

Transcription

1 Te Haptic Scissors: Cutting in Virtual Environments A. M. Okamura, R. J. Webster III, J. T. Nolin, K. W. Jonson, and H. Jary Department o Mecanical Engineering Te Jons Hopkins University Baltimore, MD 118 {aokamura, robert.webster, jnolin, kate}@ju.edu, rjary@mtolyoke.edu Abstract Te Haptic Scissors is a device tat creates te sensation o cutting in virtual environments. Te scissors ave two degrees o reedom o motion and orce eedback, one or cutting (single blade rotation) and one or translation. An algoritm was developed to simultaneously display translational and cutting orces or a realistic cutting simulation. In previous work, we used iltered data rom cutting biological tissues to create aptic recordings o te cutting experience. Here, we consider two cutting models: one based on real tissue data and one tat is analytical. Te model based on real tissue is a segmented linear empirical model o te original data. Experimental results sow tat users cannot dierentiate between tese models and te aptic recordings created earlier. Te analytical model uses a combination o riction, assumed material properties, and user motion (position and velocity) to determine te displayed cutting orces. 1. Introduction Current simulations o biological tissues in surgical procedures are mostly, i not completely, visual wit regard to cutting. Tis work is motivated by te need or aptic display not only in poking and pulling surgical tasks, but also in grasping and cutting. Simulations o tissue cutting will likely be more realistic tan cadaver tissues, wic ave signiicantly dierent mecanical properties rom living tissues. Tese simulations will also be more practical tan pysical pantoms, wic cannot be reused. Also, aptic rendering o tissue cutting as te potential to reduce te need to sacriice animals or surgical training and dissection. Te work in tis paper is an extension o our previous work in te development o a single degree-o-reedom aptic scissor []. Tis original aptic scissor used aptic recordings, look-up tables o position vs. orce values rom real biological tissue cutting data, to display te orces. However, tis system was limited in realism or two major reasons: (1) te scissors did not translate during cutting, and () te aptic recordings did not take into account te context o user motion. Tese two problems limited our previous display to a single closing o te scissor blades. Cutting as also been explored in oter previous work. Te data used in tis paper was originally gatered by Greenis and Hayward. However, a Fourier analysis did not reveal a clear relationsip between orce and position, velocity, or oter dynamic interaction properties rom te data acquired [3,4]. In [7], a aptic simulation was created rom data acquired during cutting wit a single blade. Resolved-orce aptic devices, suc as te Pantom rom SensAble Tecnologies (Woburn, MA), ave been used to display external cutting orces o a single blade in surgical procedures (e.g., [1,5]). In addition, cutting wit scissors as been modeled, witout te display o internal cutting orces, in [6,8].. Te Haptic Scissors.1 Design Te current design o te aptic scissors is sown in Figure 1. Te scissors ave two degrees-o-reedom, one or cutting (rotational) orces, and one or translational orces. Te rotational degree-o-reedom as an angular resolution o.56 and a maximum torque output o 8 mnm, wic corresponds to a orce output o 7.58 N at Figure 1. Te two-degree-o-reedom aptic scissors.

2 Figure. Te aptic scissors and grapic display. te andle. Te translational degree-o-reedom as a resolution o.15 mm and maximum orce output o 159 N. (However, te cables are likely to slip beore te maximum orce is reaced.) A Maxon RE 5mm diameter/-watt motor (rotational) and a Maxon RE 35mm diameter/9-watt motor (translational) were used or actuation, bot wit HP HEDS 554 encoders or sensing. A PWM ampliier (5A-series, Model 1A8) rom Advanced Motion Control was used or eac motor. A Servo To Go card (Model ) was used to read te encoders, and a Measurement Computing card (CIO-DAS 16/1) was used or voltage/orce output. Te control computer was a Pentium III 8 MHz running Windows 98, and te development environment was Microsot Visual C++. Te grapic and aptic update rates were 5 Hz and 1 Hz, respectively. Te grapic display used an OpenGL NURBS scissor model, as sown in Figure.. Haptic Rendering o Scissor Translation Simultaneous rendering o cutting (rotational) and translational orces is necessary or realistic simulation o te cutting process. Te irst step is recognition o te direction o motion o te blades: opening or closing. Tis is determined by te sign o te angular velocity o te scissor blades. Because o noise tat would ave been seen in dierentiating te position obtained rom optical encoders, position data was passed troug a irst-order ilter wit a corner requency o 1 rad/sec beore dierentiation. Even wit iltering, owever, te system still exibited ringing or vibration eects at low velocity. Tis was because te orce output was suicient to move te scissors in te opposite direction, canging te sign o te velocity and consequently te direction o te output orce in a cyclical manner. Te issue was overcome and te system stabilized by creating a small linear orce rampdown band around zero velocity. Witin tis band, te cutting orce was multiplied by a scale actor proportional to te velocity. Tis scale actor decreased as zero velocity was approaced rom eiter positive or negative directions, and became identically zero wen velocity was zero. Te second step is collision detection, perormed to determine weter te cutting point on te scissors is intersecting te material. Figure 3 is a diagram o te scissors sowing te cutting point, x c, wit respect to te pivot point o te scissors. t( θ ) x c =, (1) sin ( θ ) were t(θ) is al o te widt o te scissor blade (wic canges along te lengt o te blade) and θ is te angle between te scissor blades. As an approximation, we assume tat te value o t canges linearly rom t max at te pivot to t min at te blade tips. Tus, t is calculated by: tan( θ ) ( ) θ tmax tmin + l t t( θ ) = tmax, () tan were l t, te lengt rom te pivot to te tip, is sown in Figure 3. I te edge o te uncut material is at a position x m wit Figure 3. Diagram o scissors and material to be cut, wit constants and variables used in aptic rendering.

3 respect to ground, a collision is detected i (x c + x s ) > x m. Wen a collision is detected, te cutting orce (generated by torque at te pivot), c, applied to te user is determined by one o te tree cutting algoritms presented in Section 3. Altoug data acquired rom instrumented scissors andles sow te orces displayed to te user, tey do not provide inormation about te state o te material. Tus, we deine a cutting tresold, max, above wic te material begins to cut away. Wen te cutting orce is below te tresold, te uncut material edge position, x m, remains uncanged. I te tresold is exceeded, te material edge position moves, maintaining x m = x c + x s. Translational orces are displayed as t = k x x x ), (3) t ( m c s were k t is te predeined stiness o te material in te translational direction. 3. Cutting Algoritms To analyze te sensation o cutting on te aptic scissors, we used tissue-cutting data acquired as described in [3,4]. We used data rom cutting noting (empty scissors) and tree rat tissues (liver, skin, and tendon) wit a pair o Metzenbaum scissors. We ave developed tree dierent metods or displaying te cutting data: aptic recordings, segmented empirical models, and analytical models. 3.1 Haptic Recordings Haptic recordings are implemented by replaying an angle to orce mapping o te acquired data on te aptic scissors. Te primary advantage o aptic recordings is teir computational eiciency (a simple lookup table can be used). A disadvantage is tat contextual inormation (e.g., velocity and grip orce) tat may aect te orce output is not considered. In contrast, analytical and empirical models are diicult to create, due to te complex material interactions tat give rise to orces during te cutting o biological tissues. However, tey provide a muc better undamental understanding o te scissor cutting activity. Current analytical models o tissue deormation and racture are nascent, and ave not been veriied by experimental data. Similarly, accurate empirically based models would require a signiicant data acquisition eort in order to caracterize te many parameters aecting cutting orces. To create te aptic recordings, te data was irst segmented and iltered. In eac set o te data sown in Figure 4, tere are several cuts, resulting in overlapping lines. Wen surgeons cut, a repetitive motion is used, and te scissors are never ully closed. Te data loops can be segmented into our pases: (1) opening scissors, () 3 1 Empty Scissors original data simulation data Skin switcing rom opening to closing, (3) closing scissors, and (4) switcing rom closing to opening. Te lower section o te plots, were te orce appears to remain relatively constant as te angle increases, corresponds to te opening o te scissors. Te upper section, were te orce luctuates more, corresponds to te closing o te scissors. At te let and rigt o te plots, te orces cange dramatically at a single angle; tese regions result rom riction wen te scissors are in te stiction state wile canging between opening and closing. Using tese aptic recordings alone, it is diicult to create a realistic simulation; we could not guarantee tat te users would maintain te scissor angles used in data acquisition. To provide orces or complete closure o te scissors, orces were smooted and te orce trend at te minimum angle was maintained to zero degrees. In addition, te tendon orces were scaled down to matc te real rat tissues available or comparison in []. Details o te aptic recording metod or single degree-o-reedom scissors (cutting/rotation only) are provided in []. Tat metod as been improved as ollows. A simulation using pure aptic recordings creates sarp discontinuities wen te scissors move between opening and closing. To create a smoot display o cutting orces rom te initial point o contact o te scissors wit te material until te scissors lose contact wit te material, a orce scaling metod was used. Consider te orce displayed to te user at te andle,. In a pure aptic recording, tis orce is calculated rom a lookup table open (θ) or close (θ), or opening and closing o te scissors, respectively, and linear interpolation is used to ind te orces corresponding to intermediate values o θ : Liver Tendon Figure 4. Data used or aptic recordings. Te original data was obtained rom instrumented Metzenbaum scissors wile cutting rat tissues. Te simulation data uses iltered data rom one closing o te scissors.

4 Force (N) Scissor Angle (degrees) open( θ ) = close( θ ) or or or θ& > θ& < θ& = Consider te quantity θ = θ θ switc, were θ is te current angle o te andle and θ switc is te angle at wic te user canges rom positive to negative velocity or vice versa. A constant scale actor k s is cosen so tat wen te scissors ave just canged direction (at angle θ switc ), θ k s =, and wen te normal look-up table orce is desired, θ k s = 1. Ten te orce output to te user at te andle is ( θ ) θ k s or θ k s 1 =, (5) ( θ ) or θ k s > 1 were (θ) is te lookup table value o orce at te current angle θ. Figure 5 sows ow tis scaling metod aects te aptic recordings. 3. Segmented Empirical Models θ switc original data scaled data Figure 5. Illustration o te orce scaling tecnique or smoot display o aptic recordings. Te segmented empirical model is an attempt to matematically model te data collected by cutting real tissues using a piecewise linear unction. Te goal o te model and associated experiment is to ascertain exactly ow complex a aptic representation o te scissor cutting orces must be. Te advantage o tis metod is its simplicity and adaptability. As can be seen rom Figure 6, raw data o scissor orces is not easily caracterized by a matematical unction. It is also not clear exactly ow accurately a good model must it te data. Te criterion we selected or tis was qualitative uman perception. Tat is, i uman users could not distinguis te dierence troug te eel o te aptic device, te model was considered to be acceptable. (4) To create segmented empirical models or eac kind o tissue as well as te empty scissors, te ollowing algoritm was used. First, te data rom eac complete cycle o opening and closing o te scissors was averaged wit te oter cycles to create an average data run. A userdeined piecewise linear it was applied to tis average using a sotware program developed or te purpose. Tis program plots te cutting data or te user and allows im or er to design a piecewise linear model by clicking on te plot at various points. Te resulting model is ten superimposed on te original data plot, allowing te user to see ow closely te model matces te data. Wen a qualitative visual inspection indicates a good matc, te resulting unction is displayed on te aptic scissors. To assess te success o tis modeling metod, an experiment was conducted using subjects wo ad experience cutting te same group o real rat tissues wit Metzenbaum scissors in []. Eac o te tree subjects was asked to compare te eel o a aptic recording to an empirical model or eac type o tissue. Te order o aptic display presentation (model or recording) was random, as well as te tissue order. Subjects were blindolded so tat te computer grapics and appearance o te aptic scissors did not aect te results. For eac type o tissue, te subjects were told wat kind o tissue tey were cutting and asked to determine i sample A or sample B elt more like cutting te real tissue. Te subject was allowed to reely manipulate te scissors. Tat is, tey could open and close te scissors as many times as tey liked, at watever speed tey desired, canging directions at watever angle tey preerred, etc. Tey were also allowed to switc back and ort between te two samples as many times as tey elt necessary. Te results are summarized in Table 1. As can be seen, aside rom te Blank case, tere was no tissue on wic every subject agreed. Additionally, eac subject said tat tey could eel extremely little i any dierence between te aptic recordings and te models, and ad a very diicult time making up teir minds. In te Blank case, it is probable tat users expect to eel linear orces (riction) wen tey open and close empty scissors, and tat te aptic recordings were inluenced by noise and/or oter actors in te data Table 1. Subject responses comparing te realism o te aptic recordings and te segmented linear model. Te display identiied as most realistic is listed or eac subject and tissue type. Tissue Subject 1 Subject Subject 3 Type Tendon Recording Recording Model Skin Recording Model Recording Liver Recording Model Recording Empty Model Model Model

5 3 Empty Scissors 3 Liver original data 1 simulation data Skin 3 Tendon Figure 6. Data used or te piecewise linear empirical models. collection process (e.g., orces not directly in te plane o te scissors motion generated inadvertently by te and o te experimenter) tat te empirical model does not include. Te piecewise linear models used or tis experiment are tose sown in Figure 6, demonstrating tat a small number o line segments ( to 7) is generally suicient. Figure 6 sows te data taken rom cutting real tissues overlaid wit te scissors closing empirical model. Note te visual similarity between tese plots and te aptic recordings sown in Figure 4. For te scissors opening segment o eac loop a rictional simulation model o scissors opening was displayed to te user. Tis model was equal to -½ te model or Empty Scissors (pictured above). All users agreed tat tis elt realistic. 3.3 Analytical Models Preliminary work on analytical modeling as been perormed to caracterize te eect o te canging cutting point on orces sensed at te andle. Te model presented ere is based on te assumption tat te orce required to cut te material (at te exact location o te cut) is constant. Tus, it is a simpliied model tat does not take into account te material variations present in biological tissues. Te orces elt by te user at te andle are assumed to be a summation o orces rom riction at te scissor pivot, riction at te scissor blades, and cutting orce at te cutting point x c. Te eect o torsional riction at te pivot point is computed rom a simple moment arm: p τ = l p, (6) were -p is te orce elt at te andle due to pivot riction, τ p is te torsional riction at te pivot, and l is te lengt o te scissor andle as sown in Figure 3. Blade riction arises rom a small contact area between te two blades. Te scissor blades are saped so tat tis area, approximated as a point, is te only source o blade riction. Te riction at te andle is = b b l x c, (7) were -b is te orce elt at te andle due to pivot riction, b is te riction at te blade contact point, and x c is te cutting point, as sown in Figure 3. Te orce necessary to cut a omogeneous material is assumed to be a constant, c. Tus, te orce elt at te andle is

6 teta (deg) Figure 7. Handle orces versus scissor angle or a constant velocity scissor closing (blank). = c c l x c. (8) analytical model. Tis would certainly yield insigts or basic researc in tissue modeling, and robot-controlled cutting. In uture work, more cutting data must be obtained. Tis data sould be acquired by a system wit controlled position, velocity, and grip orce. Furter improvements on te scissors interace itsel would include adding tilting (pitc) and steering (yaw) degrees o reedom to te scissors as a wole so tat tey could be rocked as a unit up and down and turned as cutting progresses. Acknowledgements Te autors acknowledge Paul Stemniski and Vanessa Cial or teir work in te design o te aptic scissors. Tis material is based on work supported by te National Science Foundation (grants IIS and EEC ), a Howard Huges Fellowsip, and a Department o Deense Fellowsip. Reerences A summation o tese tree orces provides te orce at te andle: = -p + -b + -c (9) A plot o te andle orces calculated in tis way is sown in Figure 7. Te discontinuities in te plot result rom te act tat te scissor blades do not actually cut at small angles, and at large angles te blades are no longer in contact. Te analytical model does not closely matc te recorded cutting data because several aspects, including te eects o user grip orce, inomogeneous tissue properties, and elastic orces in te tissue, are not modeled. However, it does capture te rise in orces at small angles, wic can be seen in te blank data rom Figure Conclusions and Future Work Adding translational motion/orces and context-based orce eedback to te aptic scissors as greatly improved te system by making te aptic interace eel muc closer to te experience o using real scissors. In addition, experiments comparing te segmented empirical models and aptic recordings veriied tat users o te aptic scissors could not dierentiate between a complex data recording and a simple piecewise linear model. Tis demonstrates tat models o cutting orces need not be very precise to eel real. Tus, or practical engineering purposes, it is probably not necessary to ormulate a precise model or cutting orces at all. A general idea o te proper sape o te curve or eac type o tissue is all tat is necessary or an adequate aptic rendering. However, a complete understanding o cutting wit scissors requires te development o a more complex [1] D. Biesler and M. H. Gross, Interactive Simulation o Surgical Cuts, Proceedings o Paciic Grapics, IEEE Computer Society Press, pp ,. [] V. Cial, S. Greenis and A. M. Okamura, On te Display o Haptic Recordings or Cutting Biological Tissues, 1t International Symposium on Haptic Interaces or Virtual Environment and Teleoperator Systems,, pp [3] S. Greenis, Acquisition and Analysis o Cutting Forces o Surgical Instruments or Haptic Simulation, Master s Tesis, Department o Electrical and Computer Engineering, McGill University, [4] S. Greenis, V. Hayward, T. Steen, V. Cial, and A. M. Okamura, Measurement, Analysis and Display o Haptic Signals During Surgical Cutting, Presence. (in press or December ) [5] K. Hirota, A. Tanaka, and T. Kaneko, Representation o orce in cutting operation, Proceedings o IEEE Virtual Reality, pp. 77, 1999 [6] C. B. Ho, M. A. Srinivasan, S. D. Small, and S. L. Dawson, Force Interaction in Laparoscopic Simulation: Haptic Rendering o Sot Tissues, Medicine Meets Virtual Reality, [7] M. Mavas and V. Hayward, Haptic Rendering o Cutting: A Fracture Mecanics Approac, Haptics-e, Te Electronic Journal o Haptics Researc ( Vol., No. 3, November, 1 [8] G. Picinbono, H. Delingette, and N. Ayace, Nonlinear and anisotropic elastic sot tissue models or medical simulation, Proceedings o te IEEE International Conerence on Robotics and Automation, vol., pp , 1.