Soft Tissue Ablation Model for Surgical Simulation by Applying a

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The authors applied two hypotheses, the maximum shear ... the real world, such as incision and dissection z1|. In invasive .... elasticity parameters in the FEM.
Advanced Biomedical Engineering 2 : 38-46, 2013.

Original Paper

Soft Tissue Ablation Model for Surgical Simulation by Applying a Combination of Multiple Hypotheses Naoto KUME,*, # Kana EGUCHI,* Koji YOSHIMURA,** Tomohiro KURODA,*** Kazuya OKAMOTO,*** Tadamasa TAKEMURA, Hiroyuki YOSHIHARA,*

Abstract This study aimed to provide a simulation model for virtual ablation of soft tissue, focusing on simulating soft tissue deformation and destruction. The authors applied two hypotheses, the maximum shear stress hypothesis and the crack stress hypothesis, to simulate soft tissue rupture progression based on stress distribution. This combination of hypotheses realizes dynamic definition of the direction of rupture progression. The proposed model also supports multiple sources of manipulation, i.e. two or more hands working on the tissue simultaneously, because the direction definition algorithm requires only the stress distribution of the entire object. The simulation model was implemented on a thin square board model. The first experiment evaluated the direction of rupture progression when the board model was expanded at two manipulation points. The second experiment compared the simulated crack progression with crack progression in a silicon rubber. The third experiment assessed the length of rupture progression resulting from the same force applied to different positions. The fourth experiment evaluated the effect of rupture direction related to pressures. The final experiment was conducted to estimate the calculation time required for the rupture model to run. The simulations revealed that final crack length is strongly affected by the preset crack length. A similar phenomenon occurs in real-world crack progression. Also, the direction of rupture progression is affected plausibly by manipulations. Therefore, the authors conclude that the proposed model accurately represents the dynamic ablation of soft tissue. Keywords : medical virtual reality, ablation, shear stress hypothesis, stress intensity factor. Adv Biomed Eng. 2 : pp. 38-46, 2013.

1. Introduction Virtual reality (VR) simulation is expected to facilitate training of invasive operations that are unrepeatable in the real world, such as incision and dissection 1. In invasive surgery, ablation is one of the surgeonʼ s most important skills 2. Ablation is frequently used to peel membranes one layer at a time until the target organ is visible. After ablation, the target organ is separated into certain anatomical units. Ablation is considered successful when a surgeon separates the target organ into the intended units, and is deemed failed when ablation extends to peripheral organs that could be damaged. This study was presented at the Symposium on Biomedical Engineering 2012, Suita, September, 2012. Received on July 27, 2012 ; revised on October 20, 2012, January 23, 2013, April 18, 2013 ; accepted on May 7, 2013. * Graduate School of Informatics, Kyoto University, Kyoto, Japan. ** Department of Urology, Graduate School of Medicine, Kyoto University, Kyoto, Japan. *** Division of Medical Information Technology and Administration Planning, Kyoto University Hospital, Kyoto, Japan.  Graduate School of Applied Informatics, University of Hyogo, Hyogo, Japan. # 506, Kyoto Research Park Dept. 9, Awatacho 91, Chudoji, Shimogyo-ku, Kyoto-city, Kyoto 600-8815, Japan.

Because the anatomical units of the target organ vary depending on the surgery type, there are no absolute criteria by which to evaluate the success or failure of ablation. In general, ablation is performed with two or more pairs of forceps, one used for maintaining tension and another used to progressively enlarge the rupture. From the physics perspective, the performance of ablation can be understood as two steps. The first pair provides stress on the tissue to maximize expansion, while the second pair generates rupture by creating additional stress on and around the membranes adhered to the target organ. In other words, two different types of stress conditions are integrated to cause soft tissue destruction. The integration is recursively counted according to the number of forceps. A surgeon is required to control both expansion and pressure for successful ablation. Accordingly, VR simulation of ablation for training purposes must simulate soft tissue conditions through all stages of the ablation process, including deformation, rupture generation and rupture progression. Deformation is caused by expansion. Rupture is generated by a combination of expansion and pressure from the second forceps. Rupture progression is also caused by both expansion and pressure. Moreover, these three phenomena should be presented in an integrated simulation model that is able to express simultaneous ruptures as well as sequential single ruptures.

Naoto KUME, et al : Soft Tissue Ablation Model

A theoretical explanation of soft tissue destruction and solid material fracture in ablation has not yet been established. In fracture mechanics, the rupture of materials is explained by two different hypotheses 3. One is the maximum stress hypothesis ; the other concerns the stress intensity factor. The maximum stress hypothesis, which is mainly dedicated to the explanation of rupture generation, defines the limit of deformation by stress distribution. The stress intensity factor, which is dedicated to the analysis of stress accumulation at the tip of a rupture, defines the direction of rupture progression. Several models of soft tissue destruction by ablation have been proposed. A conventional simulation model defines the rupture element beforehand so that deformation and rupture appear together in an integrated model 4. This model, however, does not provide dynamic calculation of rupture generation or rupture progression. Other conventional models that simulate each phenomenon independently have been proposed. A simulation model based on the maximum shear stress hypothesis provides the definition of deformation limit by the yield stress value for the finite element method (FEM) 5. When the principal stress of an element exceeds the yield stress, the element is defined as destroyed, so that the model achieves dynamic rupture definition by simulating deformation and rupture generation. The other simulation model, which is based on the stress intensity factor, provides the definition of the stress intensity around the crack tip so that the model can predict the direction and the size of the next rupture based on the stress delivered by a manipulation of expansion 6. Both of these simulation models achieve dynamic definition of rupture, but neither is able to simulate rupture generation and rupture progression sequentially. In addition, these models do not support multiple stress distributions caused by two or more manipulators. Therefore, an effective simulation of invasive operations should present soft tissue destruction arbitrarily so that the simulated result is later defined by the users as success or failure. Also, physics-based simulation such as FEM is required to analyze the stress distribution in the expanded soft tissue. Finally, the sequential phenomenon from deformation to rupture progression should be managed by a simulation model that integrates several hypotheses to present an invasive operation in the virtual environment. This study aimed to provide a simulation model and a method to define rupture generation and rupture progression based on multiple stress distributions. The authors propose an ablation model based on a combination of the maximum shear stress hypothesis and the stress intensity factor. This simulator allows the user to learn the amount of force that can be used in handling fragile tissues, as the model realizes virtual soft tissue tearing by multiple instruments. Internal artery ablation, the separation of the artery from the membrane, is particularly well suited to VR representation.

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2. Method The following is a proposed model for the simulation of ablation, which can also calculate three other phenomena in soft tissue ; deformation, rupture generation and rupture progression. Also, the transition from each state to the next should be determined according to the stress produced by the userʼs manipulations so that the model can accept two or more manipulations. Figure 1 illustrates the transition from each state to the next in the proposed model in the simplest case of a board model. The ruptured element is shown as a black triangle. The edge of the crack is highlighted by a star. The manipulation point is denoted by a black spot. Gray arrows show the direction of pressure, and black arrows pointing toward the right express the transitions through the stages of rupture. Figure 1 ( a ) illustrates the transition from deformation to rupture generation. When the deformation exceeds the preliminarily set threshold for each element, rupture develops as the element fractures. Figure 1( b ) shows rupture progression due to the pressure around the existing crack and the stress distribution caused by the deformation. Two different types of stress which are treated as different problems in theory can thus be addressed together in the model. Therefore, the requirements of the proposed model are as follows. 1. Physics-based soft tissue simulation of deformation and stress distribution. 2. Determination of rupture generation after the simulation of deformation. 3. Determination of the next rupture progression by combining the two different types of stress hypotheses. Soft tissue behavior in surgery should be simulated as far as possible, otherwise the simulation cannot mimic a situation that requires the user to choose the optimal manipulation. Therefore a physics-based simulation is required. Also, the simulation model should integrate deformation and destruction, so that the model is handled smoothly during the transition of phenomena. According-

Fig. 1 Transitions in soft tissue rupture. ( a )transition from deformation to rupture generation, or stage 1 crack growth. ( b )transition from rupture generation to rupture progression, or stage 2 crack growth.

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Advanced Biomedical Engineering. Vol. 2, 2013.

ly, the model should determine the threshold of deformation, so that the element that is over-stretched can be defined as destroyed. Needless to say, the threshold of deformation is related to the elementʼ s characteristics, which must be defined initially before the simulation begins. After defining rupture, the model should be able to visualize the rupture as a crack. As rupture grows, the crack is depicted as an increasing number of destroyed elements. Hence the model should manage the relation between destroyed elements. Here, from the viewpoint of micro-scale phenomena, the destroyed element constitutes a missing part, even though crack formation should follow the law of conservation of mass. From the viewpoint of macro-scale phenomena, on the other hand, the crack should have a smooth surface. Although the crack surface should be represented to make VR visualization more realistic, this study focuses on physicsbased rupture progression ; therefore the model treats each destroyed element as a missing part. During ablation, the surgeon uses at least two tools to manipulate the organ for expansion and pressure exertion. The use of two or more manipulators affects stress distribution in the organ. When manipulators perform only deformation, stress distribution follows the superposition principle. However, when the object has cracks and includes a stress singularity field, the stress distributions are treated as different phenomena in physics. Therefore, a method combining different theories to superpose multiple stress distributions is required, and one is proposed here.

3. Theory To fulfill the requirements of the model, the authors employ a conventional method5for modeling deformation and destruction, and also develop a method of combining two factors that determine the course of crack development. 3.1 Simulation process The proposed method integrates the calculations of deformation and destruction in a linked simulation process. Figure 2 illustrates the simulation process of the proposed model. The process consists of two simulation loops : deformation and destruction. During the period prior to initial crack development, deformation and stress calculation are based on FEM simulation as in the conventional model. The determination of destruction is based on the maximum shear stress hypothesis. If the shear stress on an element exceeds the yield stress threshold of the element, the element is determined to be destroyed. If the destruction of that element is the first instance of destruction, it can be treated as an instance of rupture generation. After rupture generation, the course of further destruction is calculated based on crack extension force, which depends on the stress intensity factor. Because the destroyed element can be treated as a minimum crack, the proposed model has to consider both the crack tip stress singularity and the subsequent yield

Fig. 2 Simulation process incorporating deformation and destruction. The proposed method is applied to the calculation of the stress intensity factor in the subpanel on the right side of the destruction panel.(MSS : maximum shear stress hypothesis, SIF : stress intensity factor)

stress threshold of the element. When no destruction is detected, the model loops back to the deformation process. After the initial rupture is generated, determination of the destruction process shifts to be based primarily on the stress intensity factor. The length and direction of the next rupture are determined based on the stress intensity factor. And the results are incorporated into the process by updating the elasticity parameters in the FEM. 3.2 Deformation and rupture generation The authors employ a conventional model based on FEM for the first and second requirements5. The conventional model can simulate soft tissue destruction by expansion, which is essentially self-destruction, because the conventional model calculates soft tissue stress distribution as well as deformation. FEM requires a stiffness matrix to calculate displacement. To achieve real-time simulation, an inverse matrix is prepared beforehand to accelerate the displacement calculation. Deformation of the tetrahedral finite element is calculated as displacement of the vertexes. Also, the element has elasticity constants such as Youngʼs modulus, Poissonʼs ratio, and threshold of yield stress. The model employs the maximum shear stress hypothesis to determine selfdestruction. When the stress exerted on the element being deformed exceeds the threshold, the model determines that the element has been destroyed. Here, deformation is treated as a linear function, and plasticity is omitted. After the element is determined to have been destroyed, Youngʼs modulus is updated to approximately zero, so that the destroyed element never affects subsequent deformation and stress distribution. Finally, the destroyed element is treated as a missing part of the object. The proposed model employs the FEM model to simulate physics-based soft tissue deformation as well as stress distribution. Also, the proposed model determines rupture generation based on a combination of the stress intensity factor with the maximum stress hypothesis.

Naoto KUME, et al : Soft Tissue Ablation Model

3.3 Combination of two hypotheses For the third requirement, the authors propose a method in which progression to the next rupture is determined based on the stress distribution of the whole object and the stress distribution of the area surrounding the crack tip. However, the two stress distributions are provided by different hypotheses. Therefore, the proposed model should solve the problem of how to interpret the normal stress distribution, which is calculated based on the FEM, and how to determine the stress intensity factor, which is used to calculate the accumulation of stress effect around the crack tip. In physics, the period prior to the first crack development is called stage 1 crack growth, and rupture progression is called stage 2 crack growth. Stage 1 can be analyzed based on the maximum shear stress hypothesis of continuum mechanics. However, even after a single rupture has developed in a continuum object, the entire stress distribution is changed, especially around the tip of the rupture, which is considered a stress singularity in fracture mechanics. To simplify these problems, the proposed method neglects the effect of twist force and plastic deformation, which affect real objects around the limit of expansion. The calculation of rupture progression based on direction and length is given by Equation 1, based on the stress intensity factor according to the Tresca yield criterion that is applied to the stress singularity at the top of the crack tip in fracture mechanics. K  θ θ  1+sin (1) r θ=  cos 2 2 2πσ  Here, r is the length of progression, θ is the direction of progression, σY is yield stress, KI(total) is the total stress intensity factor of mode I weight. Subscript I denotes that the equation holds for mode(I)weight defined as simple separation of opening without twist motion. The proposed model regards σY as the limit of deformation. KI(total) and θ should be known. KI(total) consists of three stress intensity factors provided by Equation 2. (2) K  =K  +K  +K   Here, KI(a) is defined as a function of the stress of the expansion force. KI(b) is defined as a function of the stress due to pressure along both sides of a crack surface. KI(c) is defined as a function of the force exceeding the balance between both sides of a crack surface. KI(a), KI(b) and KI(c) are illustrated in Figure 3. Because the superposition principle is fulfilled by the stress intensity factor, summation of the three provides the total tendency of rupture progression. KI(a) is given by Equation 3. a cos  βσ  πa (3) K  =F b Here, F is a constant given in a table, which is determined based on practical experimental results3. F is related to the ratio parameter a/b. a is the length of the current rupture, and b is the size of the ruptured object in the direction of the rupture. When the locations of manipulation points are known, a and b are defined so that the value of F can be obtained from the table. β is the angle between









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Fig. 3 Determination of the direction of rupture progression based on stress intensity factor.

the normal direction of the rupture and the normal direction of the stress caused by expansion. σ0 is the magnitude of the stress caused by expansion from infinite distance. From the equation, it can be said that KI(a) is determined by the rupture length a as well as the stress given by β. In the proposed model, the stress equivalent to σ0 obtained from the calculation of stress distribution at the deformation is used as σ0 in the calculation of the stress intensity factor. The model defines a as the length from the tip of the crack to the manipulation point where pressure is exerted. Therefore, the stress given by the maximum shear stress hypothesis is incorporated into the stress intensity factor so that KI(total) can be calculated based on these two different types of stress distribution. From the perspective of VR simulation, when a user changes the position at which he grasps the object in order to pull on it to another position, σ0 and β are recalculated. Moreover, when the user switches position in order to push the object, a and b are re-defined so that KI(total) of the stress singularity is re-calculated according to Equation 3. In addition, KI(b) determines the length of the next rupture, and KI(c) changes the direction θ. KI(c) is given by Equation 4. P (4) K  =  2πb' Here, P is the magnitude of the force exerted on the crack surface, and b' is the distance between the crack tip and the pressure position. In addition, KI(b) is given by adopting P(both side) which is calculated based on stress distribution, rather than P(one side)as in Equation 4. Finally, the length and direction of the next rupture are determined by the three vectors of the stress intensity factors. Overall, the proposed model represents ablation as a phenomenon consisting of a sequence : first deformation, then rupture generation, and finally rupture progression, from the perspective of physics.

4. Results The proposed method was evaluated and compared with the conventional method that calculates stress distribution5. Three simulations were compared. Because the conventional model calculates the vector of the crack direction based on the vector of stress distribution in the

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Table 1 Parameters of the simulation model. tissue

Young’ s modulus [MPa]

Poisson’ s ratio

yield stress [MPa]

soft tissue upper

5

0.4

2

soft tissue lower

8

0.4

4

sustaining tissue

500

0.4

200

neighboring area of the crack tip4, it is not possible to make a proper comparison based on physics between the vector calculation method and stress calculation method. A three-dimensional primitive board model was prepared, with different elasticity values on its upper and lower sides. The parameters of the board model are shown in Table 1. The first simulation compared the stress distribution and the determination of rupture progression. The second experiment compared the simulated crack progression with the crack progression observed in a real (not simulated)piece of silicon rubber. The third simulation observed rupture progression and length in response to different manipulations by changing the pressure position. The fourth simulation evaluated the direction of rupture progression in response to different pressures on the crack surface. In addition, supplemental evaluations were conducted to measure calculation time of rupture generation and rupture progression. The results of the first simulation are shown in Figure 4. Figure 4( a )is the conventional model5, and ( b )is the proposed model. The upper panel of each figure shows stress distribution, and the lower shows rupture progression. In all panels, simulation was counted in steps according to the number of ruptured elements. Each pair of figures in the ruptured model indicates the state of the ruptured model containing 5 to 10 fractures. White areas indicate no stress, and black areas indicate blank and fractured elements. Stress in the middle is indicated by various shades of red. The gray portions on the upper and lower sides of the model indicate an unbreakable area that is required to simulate expansion properly. If the unbreakable area does not exist, the manipulation point, which is modeled as a material point, is always the force accumulation point. In other words, the stress does not affect any other place but the manipulation point. Each fractured element is indicated by a black triangle. The top of the model is fixed. The three-dimensional board model is expanded downwards from the lower right, where the yellow dot indicates the manipulation point. The upper panels of Figure 4( a )and( b )depict the stress distribution during expansion. The lower panels of Figure 4( a ) and( b )depict the distribution of the fractured elements at each step of fracture. The results in Figure 4( b )show that the proposed model accurately expresses the stress singularity near the crack tip. Figure 5 compares the results of the rupture simulation in Figure 4( b )and actual rupture progression in silicon rubber. Figure 5 ( a ) is the simulation of

Fig. 4 Comparison of stress distribution and rupture progression in two simulation models.(Gray area represents hard frame while white area represents soft tissue. n is the number of ruptures.) ( a )the conventional model5 ( b )the proposed model

Fig. 5

Comparison of crack progression in simulation using the proposed model and in actual silicon rubber, in response to the same manipulation(downward expansion at the lower right side). ( a )simulation at the last step in Figure 4( b ) ( b )silicon rubber

expansion as shown in Figure 4( b ), and Figure 5( b )is a silicon rubber model. A 5-cm2 piece of silicon rubber with no significant plasticity was used. The top of the rubber was fixed, and a small crack was introduced in the middle of the right edge. Expansion was applied to the lower right side in a downward direction. The force f1 in the figure was not measured. The first stage of crack progression in Figure 5( b ), as shown by the area enclosed by the dotted line, is similar in shape to that in the simulation in Figure 5( a ). In both cases, the crack first heads upward then starts to go down. Because of the small number of elements involved in this comparison, further comparison of the crack progression is difficult at this point. The length and direction of crack propagation are defined by the length of the existing crack. Even though it is not easy to verify whether every parameter corresponds with that in the real material, it can be concluded that the current result show similarity, at least at the beginning of the rupture. Figure 6 illustrates the results of the third simula-

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Naoto KUME, et al : Soft Tissue Ablation Model

Table 2 Calculation times for rupture generation and rupture progression. A: conventional model[5] , B: proposed model; B1(expansion only)and B2 (expansion and pressure on crack surface). process

Fig. 6

Comparison of rupture progression with manipulation points in different positions. ( a )near the crack tip ( b )at a distant from the crack tip

A[sec]

B1 [sec]

B2 [sec]

stiffness matrix

1.43

1.40

1.41

stress-displacement matrix

9.37

9.33

9.70

inverse matrix

55.2

54.8

56.7

element update

3.44

3.48

3.62

total

69.4

69.0

71.5

Table 3 Calculation times to determine rupture element. A: conventional model [5], B: proposed model. process

A[sec]

B [sec]

0.03

0.03



2.81

comparison between threshold and stress on each element

0.00

0.01

matrix update

0.00

0.01



0.00

0.03

2.86

stress distribution stress intensity factor

crack length update total

Fig. 7 Comparison of rupture progression by three different manipulations of applying pressure on the surface of the crack. f1 is the force of expansion. f2 is the force on the crack. A is the initial state, B is stress distribution, and C is rupture progression. f1 is the same in all(a, b, c). ( a )upper side only ( b )balanced between upper side and underside ( c )underside only

tion, which assesses the length of rupture progression resulting from the same force applied to different positions. The manipulation point is indicated by a yellow sphere. The force is applied downward and upward, crossing the crack direction at a right angle. Because the simulation is an explicit FEM method, the length of the resulting crack is given immediately after the magnitude of the given force is known. The results indicate that when the distance between

crack tip and manipulation point is shorter, the manipulation will have a greater effect on the length of the next rupture. These results are theoretically correct based on the stress intensity factor3. Figure 7 illustrates the results of the fourth simulation, assessing the direction of crack progression when different forces are applied to the same position. The results indicate that when the normal direction of the force on the crack surface is the same as the normal direction of the expansion, the integrated stress distribution is increased. When these two directions are opposite, on the other hand, the stress distribution is decreased. Obviously, the direction of rupture progression is affected by the integrated stress distribution. Consequently, it can be concluded that by efficiently combining two hypotheses, the proposed model achieves simulation of ablation as a sequential phenomenon consisting of deformation, rupture generation and rupture progression. Moreover, the proposed model supports multiple manipulations, and is sufficiently accurate : the results on rupture progression are sufficiently convincing of the modelʼs similarity to the natural phenomenon. As a supplemental evaluation, the authors measured the calculation times of the proposed model and compared with those of the conventional model5. To achieve realtime simulation in a VR application, the calculation time should be minimized. Because of the computational complexity of basic FEM, inverse matrix preparation generally requires enormous resources. Table 2 shows comparisons of the calculation time between the conven-

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Advanced Biomedical Engineering. Vol. 2, 2013.

tional model 5 and the proposed model. Because the pattern of destruction affects the processes that are required, the calculation times of the proposed model in the case of expansion and in the case of expansion and pressure are measured. The hardware platform consisted of a Xeon 3.2 GHz dual processor with 4 GB RAM, and the operating system was Microsoft Windows XP 64 bit. The simulation model was implemented using a thin board model that had 1954 tetrahedral elements as in the previous experiments. The results indicate that there is no difference in the total calculation time, although the calculation of the stress intensity factor requires little additional time. The calculation time to determine an rupture element is also compared between the conventional model and the proposed model. Because the conventional model only compares the threshold yield stress of each element with the shear stress exerted on the element, the total calculation time is very short at 0.03 sec. The proposed model, on the other hand, needs to calculate the stress intensity factor and other factors affecting the crack length, therefore determination of the rupture element takes 2.86 sec on average. For further implementation of the proposed method in a VR simulator, accelerating the inverse matrix reconstruction will inevitably be required.

5. Discussion According to the results of our simulations, the proposed model successfully merges two hypotheses to determine element destruction based on stress distribution. Model behavior during manipulation is plausible. Rupture progression is affected by the direction of expansion as well as by the direction of pressure on the crack. Moreover, after the first crack has developed, both processes based on the two hypotheses work independently to determine rupture progression and threshold-based rupture generation. In other words, the model is capable of representing new cracks on the object after one crack has developed. This means that the proposed model concurrently processes multiple rupture generations and rupture progressions. Therefore, it can be concluded that the proposed model accurately simulates destructive soft tissue manipulation regardless of the number of manipulators. The simulated rupture progression indicates that the length of the crack is a determinant of the size of the next rupture. If the object has a crack already, crack propagation takes priority over rupture generation when an external force is applied. The likelihood of crack propagation increases proportionally with rupture length. Therefore, crack length management is crucial for accurate simulation, even though this determination is based on physics principles. For instance, if a user changes the location where pressure is exerted, the definition of crack length is also changed. As the location approaches the crack tip, the efficiency of the stress intensity factor is maximized so that the user needs minimum force to cause crack propagation. In that sense, mesh formation could be important to

improve the accuracy of the simulation. In general, mesh reconstruction requires complex computation for realtime simulation. A mesh-less FEM would contribute to solving these problems 7, 8. In addition, the elasticity parameter is adopted empirically based on existing simulations. Absolute values of elasticity parameters such as Youngʼ s modulus should be employed even though measurement technology is still insufficient 9. This structure modeling is also related to the problem of computational complexity. The results show that reducing computational complexity for inverse matrix reconstruction is crucial for real-time simulation by the proposed model. At least three means of improving this model should be pursued. The first is mesh size reduction. The second is parallel processing of the matrix reconstruction. The third is adoptive preparation of the matrix. For the first approach, mesh structure should be refreshed to minimize the number of elements after an element fractures ; otherwise a smooth crack surface cannot be represented. For the second approach, matrix reconstruction can be accelerated by increasing the speed of hardware such as GPU acceleration. For this study, the supplemental evaluation was carried out using a standard computer. For the third approach, if the fracture direction can be accurately predicted, the simulation can prepare an inverse matrix of the fractured model. These approaches are expected to solve the prime problem of computational complexity. Prior to application to a VR simulator, the proposed model should be evaluated for its similarity to real membrane behaviors. Stiffness, density, and anisotropy are the key features to be measured. Fiber structure data is also needed to improve anisotropic behavior, especially for fat-adhered membrane presentation. Also, development of a layered membrane model is required to represent buckle depth. These static parameters are required for this model to accurately represent organ ablation in a virtual operative field.

6. Conclusion This study aimed to provide a soft tissue ablation model for VR training. A soft tissue ablation model for VR should support the use of two or more pairs of forceps as well as simulating ablation caused by both expansion and pressure. In the simulation of ablation, rupture of soft tissue comprises three phenomena : deformation, rupture generation and rupture progression. Because each of these phenomena depends on a different hypothesis, the authors propose a method of combining the hypotheses with calculation based on stress intensity factor. Therefore, the model can determine rupture generation and rupture progression based on its own stress distribution. Three simulations were carried out to evaluate the accuracy of the methodʼ s representation of the ablation phenomenon. The results indicate that the simulation accurately represents the three hypotheses of fracture mechanics. Therefore, we conclude that the proposed model achieves an accurate depiction of rupture progression by integrating stress hypotheses to simulate ablation

Naoto KUME, et al : Soft Tissue Ablation Model

as a unified phenomenon. In addition, stress distributions generated by multipoint manipulators are successfully simulated. The future direction of this study will be shape management including vertex arrangement, which should enable visualization of smooth surfaces in the crack. Acceleration of the simulation is also needed for its realtime application in VR. The proposed model provides the basis for a soft tissue rupture theory ; therefore VR application can be achieved by applying measured simulation parameters to the model in the future. References 1.

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5.

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7.

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9.

Bruyns C, Montgomery K, Wildermuth S : A virtual environment for simulated rat dissection. In : Westwood, J., et al.(eds.) Medicine Meets Virtual Reality, IOS Press, Amsterdam, pp. 75-81, 2001. Aggarwal R, Moorthy K, Darzi A : Laparoscopic skills training and assessment. Br J Surg. 91(12), pp. 1549-1558, 2004. Anderson TL : Fracture Mechanics : Fundamentals and Applications, Third Edition, CRC Press, 2005. Cotin S, Delingette H, Ayache N : A hybrid elastic model allowing realtime cutting, deformations, and force feedback for surgery training and simulation. Visual Comput. 16, pp. 437-452, 2000. Kume N, Nakao M, Kuroda T, Yoshihara H, Komori M : FEM-based soft tissue destruction model for ablation simulator. Proc Med Meets Virtual Reality. 13, pp. 263-269, 2005. Arai R, Kuroda Y, Kagiyama Y, Kuroda T, Oshiro O : Realtime calculation method of topological change by localization and recording and playing approaches. J Virtual Reality So Jpn. 15( 1 ), pp. 93-100, 2010. Henriques A, Wünsche B, Marks S : An investigation of meshless deformation for fast soft tissue simulation in virtual surgery applications. Int J Comput Assist Radiol Surg. 2(suppl 1), pp. 169-171, 2007. Henriques A, Wünsche B : Improved meshless deformation techniques for plausible interactive soft object simulations. In : Computer Vision and Computer Graphics, Theory and Applications, Braz J et al.(eds) Communications in Computer and Information Science, Vol. 21, Springer, Berlin Heidelberg, 2009. Okubo K, Yoshimura K, Matsui Y, Kamba T, Ogawa O, Umeoka S : Preoperative prediction for hardness of perirenal fat tissue using CT attenuation value : Is it possible? The 29th World Congress of Endourology SWL, 2011.

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Naoto KUME Naoto KUME is an associate professor of Electronic Health Record (EHR) Research Unit, Department of Social Informatics, Graduate School of Informatics, Kyoto University, Japan. He received M.S. and Ph.D. degrees in informatics in 2004 and 2006 from Kyoto University, Japan. He became an assistant professor of Division of Medical Information Technology and Administrative Planning of Kyoto University Hospital, Japan, from 2007 to 2013. His current research interests include EHR, Personal Health Record (PHR) , Electronic Medical Record (EMR) , Distributed Systems, and Medical Virtual Reality. Kana EGUCHI Kana EGUCHI received M.S. degree in informatics in 2012 at Kyoto University, Japan. She works as an ICT researcher for several years. Her current research interests include Middleware, Virtual Reality, and Human Computer Interaction. Koji YOSHIMURA Koji YOSHIMURA is an associate professor of Department of Urology, Kyoto University Graduate School of Medicine, Japan. He is M.D. and received Ph.D. degree in medicine in 2007 from Kyoto University, Japan. He was an assistant professor of this department from 2004 to 2009, a junior associate professor (lecturer) from 2009 to 2011, and became an associate professor in 2011. His current research interests include epidemiology and mechanisms of lower urinary tract symptom, technical development of laparoscopic and robotic surgery, and medical virtual reality. Tomohiro KURODA Tomohiro KURODA is a professor of Division of Medical Information Technology and Administrative Planning of Kyoto University Hospital. He received B.S. degree in information science from Kyoto University, M.S. and Ph.D. degree in information science from Nara Institute of Science and Technology, Japan. His current research interests include Human Interface, Virtual/ Augmented Reality, Wearable/Ubiquitous Computing, and Medical/Assistive informatics.

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Advanced Biomedical Engineering. Vol. 2, 2013.

Kazuya OKAMOTO Kazuya OKAMOTO is an assistant professor of

Hiroyuki YOSHIHARA Hiroyuki YOSHIHARA is an emeritus professor

Division of Medical Information Technology

of Kyoto University and the director of EHR

and Administrative Planning of Kyoto Uni-

Research Unit, Graduate School of Informa-

versity Hospital, Japan. He received B.S., M.S. and Ph.D. degrees in informatics from Kyoto University, Japan. His current research interests include Medical Informatics, Artificial Intelligence in Medicine, and Rehabilitation Engineering.

tics, Kyoto University, Japan. He received B.E. degree in engineering science from Osaka University, M.D. and Ph.D. degree in medical science from Miyazaki Medical College, Japan. He was a professor of the Division of Medical Information Technology and Administration Planning of Kyoto University Hospital, and a member of executive board of Kyoto University Hospital from 2003 to 2013. His current research interest includes EHR, PHR, EMR, Mathematical Simulation, and Medical Informatics.

Tadamasa TAKEMURA Tadamasa TAKEMURA is an associate professor of Graduate School of Applied Informatics of University of Hyogo, Japan. He received B.S. degree in healthcare science from Osaka University, Japan, and M.S. and Ph.D. degrees in healthcare science from Osaka University. His current research interests include Natural Language Processing, knowledge engineering in Medicine, PHR, EHR, EMR, and Medical Informatics.