Haptic Manipulation of Virtual Materials for Medical Application


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1 Haptic Manipulation of Virtual Materials for Medical Application HIDETOSHI WAKAMATSU, SATORU HONMA Graduate Scool of Healt Care Sciences Tokyo Medical and Dental University, JAPAN ttp:// Abstract:  Te aptic and force display system is available for medical training despite some simple matematical models are required in order to realize various kinds of necessary environment. Our matematical model of mass, elasticity, viscosity and plasticity is applied to represent te various deformations of materials including teir destruction. We propose te metod for description of arbitral complicated forms of virtual organs and/or tools, introducing lattice planes for te construction and simple andling of virtual objects. Ten, we analyze te mutual interaction of virtual objects to clarify teir dynamical features. In consequence, we propose te new metods of kinetic process of contact and collision wit calculation of generating moments, wic yield te basic application of our metods to medical fields. KeyWords : Haptic and force display, Virtual material, Viscoelastoplastic model, Cutting tools, Deformation and destruction of objects 1 Introduction Pysical penomena ave been matematically described to clarify teir relating dynamics under te various kinds of conditions. However, tis kind of analysis as been sometimes purely matematical, and not used for te description of real time dynamic analysis because of computing restriction. Tat is, various penomena could not be treated simultaneously as a wole system to present teir dynamics even under te simple calculating condition. Meanwile, a force display system was useful to manipulate artificially realized environment, wic partly made it possible to feel dynamics as visual and aptic sense by te outside operation of virtual objects. [3,4,7]. But, te cutting of te objects was forced to perform in a restricted form of destruction, for wic we ave ever tried to use practically matematical model for te convenient calculation. Our recent tecnology of artificial reality as ensured te realization of various penomena as a wole[14,15]. Consequently, important pysical properties can be really taken into account in order to ave virtual experience and training in medical domain. Tat is, tis kind of tecnology is useful for te teme from te point of actual treatment of complicated systematic penomena. If we would apply te system to even unrealizable experience in simulated micro and macro spaces, tere would be still lots of difficulties practically from te various viewpoints. However, it is useful for suc temes, in wic aptic and force display systems are used as te one providing te experience by uman visual, aptic sense and so on [5,6]. Actually, we ave ever developed scissorstype[8,9], knifetype[13,14] and sawtype cutting tools wit teir control systems[16] and te matematical formulation of objects representing irreversible dynamics[16]. Considering te computing ability, te calculating time ave to be reduced by using appropriate matematical models, wic are accepted by users as smoot operation of going on time. 2 Syntesis of virtual material as viscoelastoplastic model 2.1 Development and improvement of model Te viscoelastic KelvinVoigt model was used for te dynamical representation of virtual objects [1,11]. Furter, extended distinct element metod was proposed[1], in wic rigid body was divided into teir certain size of portions beforeand. Aside from tem, a particle metod[2] was proposed, in wic liquid was represented by te mutual action of particle masses witin te definite distance among tem. It as ISBN:
2 been confirmed appropriate to describe fluid dynamics of destroyed objects represented by te set of a certain size of particles. However, tey are not always effective to represent te deformation and destruction of a rigid body. Tus, te syntesis of materials was extended to versatile ones wit plasticity in teir dynamic caracteristics beyond te elasticity. Te metod can realize te mutual action of objects, considering te collision of masses on te elements wic yield te kinds of destruction under te various conditions [14]. By te syntesis of concerning models in a virtual space, teir deformation and destruction including teir position and attitude are appropriately represented on te basis of pysical properties. 2.2 Needs of general matematical model Te pysically more appropriate reality could ave been described by te introduction of oter metods to realize te penomena, providing users wit teir actual experiences in a virtual space. However, te pysical and logical processes are not easy to describe exactly and precisely. Tus, it is reasonable to make analysis by extracting of substantial feature as our proposed metod [9,12,13]. By te way, in many aptic and force display systems, operational tools as rigid bodies ave been implemented, wic sometimes forced us to do unreasonable operation. Indeed, we proposed lots of utilities to medical system from te points of safety and etic problems, even if we would only apply te concerning systems as a pseudoclinical practice in need of education. Hereby, some internal organs and tools are syntesized reflecting sape and caracteristics by using te viscoelastoplastic model, and furter develop medical training systems by wic operational feeling is experienced reasonably wit aptic sense and reactive force on blood sampling and on cutting of brain tissues. Hereby, we sould be careful for te unnecessary tecniques to keep safety and to avoid etical problems, even if tey would be developed only for training. 2.3 Appropriate matematical description Virtual material is syntesized as a matematical model in order to represent its real time deformation and destruction in a virtual space. It is necessary to keep speedy calculation of all te state cange, because te operator as relations wit te cange of virtual materials at real time. In order to overcome suc difficulties, particularly in destruction wit its wole movement including structural cange, Honma and Wakamatsu introduced viscoelastoplastic model as a modified KelvinVoigt. In te basic tetraedron units, eac element as te modified KelvinVoigt model wit mass on eac apex. Tese elements are connected in a series and formed in an arbitrary sape, wic lead us to describe deformation and destruction due to te collision of te objects made of above materials. Tis kind deformation of objects is sufficiently enoug speedy calculated in a real time duration by using PC, wic is appropriate for te force display systems. 3 Matematical model of virtual material based on viscoelastoplasticity 3.1 Matematical explanation of pysically relating penomena As illustrated by Fig.1, stress and strain caracteristic curve of a material suc a metal is experimentally obtained concerning te expansion as indicated by solid lines [14]. In te case of te range witin limit of elasticity, a material as proportionally elastic deformation according to te applied force. Te limit of elasticity is a (a)yield point, beyond wic plastic deformation occurs by te furter stress wit never back to its original state as represented by te figure. From tis state, te stress is differently effective in nonlinear way corresponding to te exerting force, and it breaks after all on te limited point, namely (b)breaking point. Considering te force generation due to a different elasticity k 2 beyond te limit of specific elasticity, variable y p is defined as yielding distance ratio by using te ratio l/l of lengt l and mass L b p L y p l Stress Coefficient of elasticity k 2 (1) (2) (3) (b) breaking (a) yield point point Strain Coefficient of y ' 1 p b p 1 elasticity k 1 y p 1 Lengt corresponding to plastic strain l c Bauscinger effect l : Lengt of viscoelastoplastic element at time t L : Original lengt of viscoelastoplastic element l c : Lengt corresponding to plastic strain y p : Yielding distance ratio b p : Breaking distance ratio Pysical Value Approximate Value y p < l / L < b p y p y p ' Fig.1 Approximate representation based on te pysical property of material ISBN:
3 natural lengt L, and l/l at (b)breaking point is defined as breaking distance ratio b p (1< y p < b p ). If te force is taken off from te element wit te lengt between yielding ratio y p and breaking distance ratio b p, its lengt becomes sort according to specific elasticity k 1, but longer by l c tan natural lengt L, even if te force is taken off in tis case. Te state of an element, namely a modified 1dimemtional KelvinVoigt model is described by te picture on te superior region and by te explanation on te rigt region in Fig.1. Te lengt cange l c is a stretc lengt corresponding to plastic strain, were yielding distance ratio y p canges to y p ' = (l+l c )/L. For tis calculation of plastic strain related to stress, te metod as been proposed on te basis of broken line approximation as designated in te figure [14]. Te proposing model as strain according to Hooke's law, proportional to a given stress were te elastic constant is k 1. Beyond te limit of elasticity its elastic constant is regarded as k 2 proportional to stress. On te removal of te force in tis area, its lengt decreases by elastic constant k 1 proportional to te stress. It is remarked tat nonlinear cange of elastic constant from k 1 to k 2, in actual material, wit less or around natural lengt as Bauscinger effect, is not taken into account for te present discussion [14]. Tus, model of tetraedron unit does not completely correspond to actual caracteristics of material, but te virtual objects consisting of teir continuous arrangement can be syntesized by coosing appropriate pysical parameters to represent teir macro caracteristics. 3.2 Description of condition by matematical formulation In order to explain te broken line in Fig.1 matematically, te following dynamical kinetics are described in tree stages, taking into account te ratio of te lengt l /L of te element l and natural lengt L concerning t element at time t. <1> y p >l / L Tis is stress and strain of te element witin limit of elasticity and wen te stress is taken off from te unbroken element after te state beyond te limit of elasticity. In suc cases te strain is proportional to stress f wic is described by eq.(1) using own specific elastic constant k 1 and viscosity coefficient γ. f = k 1 ( l L lc ) γ dl dt (1) Hereby, l c is a stretc lengt by plastic strain. It is zero owever, if te element does not ave a ysteresis of stress and strain, but it is no longer zero, if tey are once beyond te limit of its elasticity. <2> y p <l / L < b p It is interpreted as te state of a concerning element around (a) yield point beyond te limit of elasticity. Te stress f is represented by eq.(2) using coefficient k 1 before aving reaced te yield point and using coefficient k 2 once on passing troug te yield point. f = k {( y p 1 ) L lc} + k ( l y pl ) γ dl dt (2) 1 2 After f is derived from eq.(2), variable y p as yielding distance ratio y p and plastic strain l c are substituted for y ' = l L andlc' = l L f k, respectively. 1 p <3>l / L > b p Te element is broken down in tis case, i.e. te stress f exposed to mass on te element is f = (3) were te connection coefficient η c = 1 canges to η c =, and dynamic state of te element is not calculated and displayed. 4 Virtual objects based on virtual materials on lattice planes 4.1 Arbitrary formation by te combination of matematical models As sown in Fig.2(a) a virtual material is syntesized by arranging tetraedrons consisting of masses and elements caracterized by te elasticity, viscosity and plasticity as illustrated by Fig.2(b). Te appropriate area covering anticipated objects are first given to fulfill its inside wit teir tetraedron units as aligns on planes. Tat is, virtual materials are arranged inside of te given envelop, in wic te cange in parameters of pysical properties can be easily described as nonuniformity of teir inner states. Te set of 2dimensional points on eac plane forms 1layer virtual material as described by (a) and (c) in Fig.2. In oter words, concerning layers of material on te plane are combined using elements wit te ones on next parallel planes. Te virtual object basically consists of virtual materials wit continuous regular arrangements of masses on te apexes of tetraedrons. Te arrangement forms a kind of lattice wit te straigt lines on te plane, wic are connected to te next one by te elements. If some parts of tetraedron units are expected out of te given area, te concerning masses on te elements are regarded not existing in te area. ISBN:
4 elasticity mass viscosity plasticity (b) elastoviscoplastic model (a) lattice plane Odd Layer Even Layer Connecting Edge Fig.2 Virtual material syntesized by te 2dimensionally continuous connection of tetraedron units on te settingup lattice plane ()original (3)disunion (1)restitution (4)crus (c) (2)crack (5)smas Fig.3 Classification of destructions after te collision of virtual materials to te floor Te syntesis of an object is explained on te basis of te equallydistance arrayed planes, on wic te parallel aligns of apexes are set. Terefore, it is possible to construct an arbitral form of object using virtual materials on lattice planes, on wic te apexes of tetraedrons actually mounted[9]. Even if te sape of object is complicated, te various sizes of lattice planes are set in every concerning section of te object in te same way. Te empty area after te above operation is regarded in existence of no material. 4.2 Te dynamical state of virtual objects obtained from virtual material According to Fig.3 we ereby mention te collision of () original spere illustrated falling down on te floor as an example. An object witin te limit of elastic deformation comes back to te (1)restitution form in an original state. Te states of objects are classified into five categories after te collisions of virtual spere to te floor including te state before te collision. Tat is, te plastic deformations of objects are largely classified into four states as (2)crack, (3)disunion, (4)crus and (5)smas. Hereby, te collision between masses is regarded as perfectly elastic, but as a wole, our metod does not represent perfectly elastic collision, because te elements contain viscosity and plasticity. Te ligt line represents te element wic moves witin te limit of elasticity given as initial condition. Te dark line represents not broken element beyond te limit of elasticity. Te (1)restitution is an illustration of sligt deformation by te stress after te collision. If y p is big enoug, te deformation is likely witin te limit of elasticity, tus te object tends to old te original sape, even after te colliding stress is taken off. Tat is, te object comes back to te original sape by its elastic stress, altoug deformation is observed in te process of collision. In te case of (2)crack, a certain site of te concerning spere will partly break down elements, wose stress are transmitted to te neigboring elements, causing furter deviation beyond te limit of elasticity but wit little destruction to keep its almost original sape. Tat is, te site of y p in greater tan te definite value as an exceeding strain beyond its elasticity. Incidentally te near site wit its easy impact propagation as te deviation beyond te limit of elasticity, so tat te relating elements may partly ave breaking damage. In te case of (3)disunion, some breaking occurs in a certain direction on a certain site of an object. In consequence, te spere divides into relatively big and small parts. Comparing wit te latter case of (5)smas, y p is a little bigger, even wit small difference between y p and b p. Tus, te definitely larger impact causes te state beyond te limit of elasticity. Te force impact propagates to some elements to ave mecanical effects in some rate of tem. On one side, it breaks tem in parts, but on te oter and some are not broken. Consequently, some sites break down by propagation of impact and te oter undestroyed ones witout propagation of stress are divided into several parts as illustrated in te figure. In te case of (4)crus, almost all te elements ave deviation from te limit of elasticity witout breaking down. Tat is, small y p wit relatively big difference between y p and b p, give te unbreakable ISBN:
5 caracteristics beyond te limit of elasticity, and it easily forms a kind of soft deformation as a wole. In (5)smas, te broken particles are largely stretced out and te spere objects are almost all fragmented into small scattering pieces. Te reason of above caracteristics is small y p wit a small difference between y p and b p, Tat is, te elements easily break down as a wole, even toug strains remain small, as tey readily ave strain beyond te limit of elasticity due to certain impact. 5 Representation of various objects consisting of virtual materials 5.1 Virtual objects in various state All possible forces exerted on masses are used for te dynamical calculation of previously mentioned models. Tereby, te mutual interaction of concerning parts of objects can be calculated as a wole, taking into account te collisions and/or cutting of teir elements as given by te positional relation of teir masses concerning virtual materials. To be more precise, outer masses of object are defined as ones to possibly collide wit eac oter. Tat is, te collision is tougt to occur wen te distance of masses becomes sorter tan te definite value. As tis metod is useful to compreend te mutual relation and interaction among objects in a virtual space, it is now rational to syntesize organs and tools by our previously mentioned virtual materials. 5.2 Relation of virtual organs and tools in various state In tis section, virtual organs and tools are mainly concerned, because it is necessary to cut open skins and teir neigboring area in some kinds of surgery, for wic scissors, knife and saw were developed as basic cutting tools depending on te situation. Indeed, Wakamatsu and Honma ave developed scissorstype, knifetype, sawtype tools and teir control systems for te joint use of suc file, cisel and rasp in training practice[6,7]. But te deformation and destruction of te tools temselves ad not been examined from teir availability in te aptic and force display systems, altoug tey ad to be considered from te various viewpoints of te caracteristics of teir tools. Tat is, for te use of above tools tere are still found problems in movements. Tat will be good discussions of te practical movement of operational tools, as tere are practically various surgical actions to organs in medical treatments In blood sampling, one of te most basic medical practices, skin area near blood vessel are in a kind of invasion process and te cutting of brain tissues are seriously invasive in te terapeutic operation. Te virtual operating tools ave dynamic interactions mutually wit te concerning organs according to teir matematical models on te basis of pysical properties of te site of action. Te invasive process by te system will be discussed in te next study. Hereby only te objects mainly wit te sapes of organs and tools are discussed, suc as blood vessel wit puncture needle and syringe and as brain wit knifetype tools in practice. 5.3 Objects in movement and deformation Internal organs are not easy to represent teir forms including pysical properties, because many different kinds of tissues suc as smoot muscle and striated muscle must be taken into account. In addition, teir matematical models may be very different to syntesize considering teir individual variations. However, it is practically possible to describe teir matematical outline, altoug tere must be required more calculation and operation, in order to display and feel reactive force resulting from mecanism of deformation and destruction of materials. Twist angle θ Center of axis 2n Sarpened angle θ 4n Diameter 2r Virtual object 1 Needlesape device Virtual object 2 Blood vessel Needle lengt l Swing angle θ 1n Point P Rotation angle θ 3n Fig. 4 Syntesis of puncture needle and blood vessel needle blood vessel (a) (b) Fig.5 Te virtual rigid puncture needle into blood vessel as tubular type objects ISBN:
6 Here, te objects are in appropriate sapes composed of te previously mentioned virtual materials in suitable areas. Teir concerning masses belonging to te same lattice plane are tereby continuously connected to form arranged segments between every regularly spaced planes. Te organs inclusive of pysical properties are generally classified into tubular, cavity or ollow type and solid type of tissues. Tus, in te process of deformation, cutting and perforation of te organs by te virtual operating tools, a blood vessel as a tubular organ and a brainlike spere as a solid organ were given by Fig.4(b) and Fig.6(b), respectively. Here, te sape and pysical properties are given by te parameters, wic do not always correspond to te actual caracteristics. In te present case, elastic coefficients are given smaller one to represent soft materials. 6 Modeling of organs and tools as virtual objects 6.1 Blood vessel and puncture needle by matematical model A blood sampling is one of te commonly necessary, but relatively simple tecniques for medical staff. Te concerning training is not sometimes enoug for te incidental action of sting and bite by te needle, for wic operators must get used to make progress in teir skill. For tis complementary use, some kinds of training system are expected to realize as aptic and force display systems. On blood sampling te edge of needle comes into te inner side of vessel by cutting te tissue. Ten, te blood is inspired troug needle into te syringe. However, necessary liquid model was not taken into account in te present study. Hereby, only te needle in contact wit puncturing site provides operators its state and relation to te skin and blood vessels. Te puncture needle for te blood sampling is syntesized as a tangential form of an edge on unsymmetrical tube as sown in Fig.4. Te state of tangential sampling needle are caracterized by swinging angle θ 1n, twist angle θ 2n, rotational angle θ 3n, sarpened angle θ 4n and diameter r, wic are all to move in an arbitrarily position and attitude in any place in a virtual space by a mouse operation. Te needle is in te present study considered as 1layer of continuous tetraedron rigid body wit a balance of te matematical model of blood vessel. Movement of point by mouseoperation Velocity of origin V 1 +Representative velocity of inner particle v 1 Representative velocity of inner particle v 2 Twist Rotation angle θ angle θ 3k 2k Swing Virtual object 3 angle θ 1k Knifesape device Virtual floor Virtual object 4 Brain (spere) Fig. 6 Relation between virtual knife and spere object knife (a) brain (b) Fig.7 Te cutting of brainlike spere as a solid object It is remarked tat 1layer of tetraedrons on a plane can be regarded as consisting of two complimentary layers, because te complementary empty area can be regarded as if it were filled wit new concerning tetraedrons. It is natural tat various diameter and layers of a needle is introduced according to te medical purposes. Hereby, teir necessary parameters are given as nearly corresponding to rigid body. Figure 4 illustrates te blood sampling using te syntesized needle by te operation of te mouse. Figure 5(a) is a skit of movement for a puncture of needle and (b) illustrates te relating view during te puncture. In tis simulation of blood vessel, parameters are cosen to caracterize relatively fragile ones. Tat makes sometimes a ole on blood vessel by little strain suc a sligt tremble on te operation, incidentally destruction of te edge of needle. Te edge of needle is realized not broken so tat te strain by te concentrated force may appear on te very edge of blood vessel. 6.2 Brain and knife by matematical model Virtual knifetype cutting tool is syntesized as platelike one as illustrated by Fig.6, consisting of 1layer of tetraedrons seen as teir complimentary 2layers. As a knife of metal as little cange of form comparing wit various elastic objects, we treat ere it ISBN:
7 as viscoelastoplastic model, taking into account tat its edge is sometimes broken on its operation. In order to provide te caracteristics of a rigid body, its elasticity was given as a bigger one, and teir masses were cosen from 1 to 1, times bigger tan te masses of virtual objects as internal organs. In addition, te parameters were given as tangential angle, twist, direction of knife, θ 1k, θ 2k, θ 3k, by wic its position and attitude are arbitrarily controlled by using a mouse in a virtual space. Tis discussion can contribute to a basic condition for te unification of aptic and force display system wit organs in order to design operational knifetype cutting devices. Figure 7(a) is a skit of movement for a cutting and (b) illustrates te relating view during te cutting. In te simulation of brain, parameters are cosen to caracterize relatively fragile ones. 7 Reactive Forces during te deformation and destruction Wen some virtual materials are processed by virtual tools, all te forces appear on corresponding colliding masses wit eac oter in our proposed models. Tus, te moment are calculated around arbitrarily setting point by te forces on masses and teir distance from te setting point. According to te attitude cange of operational tool wit relative position to te objects, te numbers of masses cange in every sampling time concerning wit teir relating collision. In addition, te forces exerted on te masses continuously cange according to operational speed and direction of te tools. Tus, even if te same object is operated by te same knifetype tool in te same way, te output moment is different according to te operational condition. Figures 8 describe te calculated moments around 3 axes, wic are sown as examples during te operation of Fig.5(b). In Fig.8, mutual interaction of needle and blood vessel due to its puncture operation is illustrated wit cutting moments around eac axis on te point cosen in a virtual space. Figure 8 give te resulting moments from blood sampling by operations of te syringe wit puncture needle. In te present case, te angle to te vessel is set to remain uncanged. However, te measured moments are different in eac operation because different operational conditions. If te operation is sufficiently enoug performed, tere appear muc fluctuations of canging components of forces and moments. Tis may be a Moment [Nm] around xaxis around yaxis 55 around zaxis Time [msec] Fig.8 Moment calculated from a set point in a virtual space on te operation in blood sampling wit slow speed. Moment [Nm] 11 around xaxis 11 around yaxis 11 around zaxis Time [msec] Fig.9 Moment calculated from a set point in a virtual space on te cutting of virtual brain wit slow speed in a vertical direction. reason wit numerical results wy a strange feeling of a pain and/or a foreign body at blood sampling are often experienced depending on te skill of medical staff. Figures 9 are skits of calculated moments of brainlike matematical model around x, y, zaxes on a set point in a virtual space, by cutting it by a virtual knife wit relatively speedy operation. Te cutting moment was observed as given by Fig.9, wen te knife moves in a vertical direction of te arrow along te plane as illustrated by Fig.7. Te figure explains tat te moment around yaxis increases, if te knife is lopsidedly inclined toward yaxis, and tat te one around xaxis increases, if te knife is inclined toward xaxis. 8 Discussion Te matematical model consists of reconstructed differential equations wit different parameters at any time. Tus, te deformation and destruction of te ISBN:
8 virtual materials are effectively represented at real time. We tougt tat every plane represented every surface of section of te object, te proposed metod is useful for te construction of te objects, especially in acquisition of slice pictures on every equallydistant plane. Tus, it is possible to syntesize virtual organs based on te form of teir actual ones from medical image. However, it is impossible to acquire pysical properties suc as density, elasticity, viscosity and plasticity from teir image data, tus, tese parameters ave to be determined from te experimental process. We mentioned tat te deformation and destruction related to te velocity and distance between arbitral two masses on te apexes and tat tere occurred perfect elastic collision, if te distance became less tan definite lengt. Tereby, te concerning coefficients of restitution cange according to te dynamics of te properties on te element. Suc mutual reaction could substantially well describe touc and collision of te virtual objects, resulting in basic cutting operation in te present study. Hereby, all of te reactive force exerted on te masses and te distance are taken into account for calculating moment, and te operator obtains te aptic and force feeling due to te reaction in accordance wit pysical properties of materials. In te present study two kinds of simulation were performed for anticipating medical training in te next occasion As for te first case, it is rater difficult to know te state of needle inserted into subcutaneous blood vessel. Its tecnical progress is very dependent on tactile sense troug syringe by te skill of medical staff. Tus, it is effective to offer tem te visualized information for te training situation. Tat is, our system does not enoug simulate te blood sampling at present, but it is our first step in suc simulation. As for te second case, it is sometimes important to take out te brain tissue as laboratory testing to make tissue specimen from brain tumor. For tis purpose it is sometimes necessary to cut off brain tissue by using te so called brain knife considering tat te proposed system will be a training macine. However, te practical pysical properties are not actually reflected to our syntesized system because of complicated anatomy and various tissues of brain, so tat we stand only in te very beginning as well as te former example. 9 Conclusion Te tetraedron units are applied to te basic structure of virtual organs and virtual tools by teir continuous arrangement in order to make aptic and force display systems for medical training. However, it is still difficult to formulate well matematical model of organs because it requires sometimes bigger and complicated database form for large size viscoelastoplastic models. Te metod was proposed on te basis of te combination of apexes set on te planes, and it was confirmed by simulation to contribute to te easy formation of an arbitral object wit general versatility. Practically, very basic models of blood vessel and brain were constructed to do some experimental tests by puncturetype and knifetype edged tools. Tese tools are represented as visual information of teir position, attitude and forms and for te calculation of reactive force at te same time. In any case, te process of deformation and destruction was well represented by te proposed metod at a critical point of pysical properties. Furtermore, it is also ensured to make various kinds of internal organs from te MRI image and to syntesize various tools readily. In consequence, it is possibly expected to construct medical simulator for training of surgery by using virtual entire body including various virtual internal organs wit a elp of aptic and force display systems. Hereby, also te parameters of te pysical properties of practical materials will be our important subjects for our furter study, wic supplies as our useful software libraries of virtual objects. Acknowledgment Te autors would like to express appreciation to te staff of Biopysical system Engineering laboratory at Tokyo Medical and Dental University for valuable discussion. References: [1]P.A. Cundall, O.D.L. Strack: "A discrete numerical model for granular assemblies", Geotecnique, No.29, pp.47 65, (1979) [2]E.G.Pavia, B.C.Roisin : "Modeling of oceanic fronts using a particle metod", J. Geopysical Researc, Vol.93, No.C4, pp (1988) [3] H. Wakamatsu, T. Imai: "Stereoscopic display of te inside image of rat brain by tree dimensional ISBN:
9 dissection metods", Int. Fed. Med. Biol. Eng., 29Suppl. Part1, p.123 (1991) [4] T. Imai, H. Wakamatsu: "Stereoscopic tree dimensional dissection of brain image by binocular parallax", Trans. IEE Jap., Vol.111C, No.6, pp (1991) [5]H. Wakamatsu, T. Imai, K. Okada: "Artificial realization of reactive force feeling on stereoscopic cutting of image of multilayer spere", Proc. 2nd Int. Conf. Image Process., pp (1992) [6] H. Wakamatsu, T.Imai: "Development of stereoscopic image cutting system wit reactive force feeling". Trans.IEE Jap., Vol.113C, No.9, pp (1993) [7] T. H. Massie, J. K. Salisbury: "Te PHANTOM Haptic Interface: A Device for Probing Virtual Objects", Symp. Haptic Interfaces (1994) [8] H.Wakamatsu: "Operational systems of stereoscopic cutting 3D virtual objects wit reactive feeling. Proc. IFAC 13t World Congr., Biomed. Control, ,(1996) [9] H. Wakamatsu, X. Zang, S. Honma: Teleoperational force display system in manipulation of virtual object using scissorstype cutting device", Proc. 3rd AsiaPacific Conf. Control & Meas., pp (1998) [1]K.Hirota, T.Kaneko: "A Study on te Model of an Elastic Virtual Object", Trans. Soc. Inst. Control Eng., Vol.34, No.3, pp (1998) [11]S. Honma, H. Wakamatsu, X. Zang: "Mecanics and Manipulation of Virtual Objects Represented by Viscoelastic Model", Trans. IEE Jap., Vol.119C, No.12, pp , (1999) [12]S.Honma, H. Wakamatsu: "Analysis of te Cutting Moment of Viscoelastic Material by a KnifeType Tool for Its Application to Force Display System", Trans. Soc. Instrum. Control Eng.", Vol.4, No.4, pp ,(24) [13]S. Honma, H. Wakamatsu: "Cutting Moment Analysis of Materials by te Saw for Force Display System", Trans. Virtual Reality Soc. Japan, Vol.9, No.3, pp (24) [14]S.Honma,H.Wakamatsu:"Realtime Representation of Destruction Process Considering Interaction between Two Virtual Objects", Trans. Soc. Inst. Control Eng., Vol.44, No.7, pp.668, (28) [15]S. Honma, H. Wakamatsu: "Cutting process of pysical models by a virtual knife based on an viscoelastoplastic model", National Convention Record IEE Japan, part 3, p.35 (326) (28) [16] S. Honma, H. Wakamatsu: "Unified Haptic System Using Tree Kinds of Cutting Devices for te Basic Use of Medical Application", Trans. IEE Jap., Vol.13C, No.1, (21) ISBN:
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