Finite-Element Simulation of Soft Tissue Deformation

Size: px

Start display at page:

Download "Finite-Element Simulation of Soft Tissue Deformation"

Hubert Nicholson
6 years ago
Views:

1 Finite-Element Simulation for Soft Tissue Prediction. In: Lemke, H.U. et al (eds.): Computer Assisted Radiology and Surgery (CARS), Elsevier Science B.V., pp (2000) Finite-Element Simulation of Soft Tissue Deformation S. Zachow, E. Gladiline, H.-C. Hege, P. Deuflhard Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB) Takustr. 7, D-495 Berlin, Germany This paper will present our work on the simulation of soft tissue deformation within the context of maxillofacial surgery. Our approach is based on finite element methods on tetrahedral grids. These grids represent different tissue regions and are automatically generated with guaranteed topological correctness and scalable resolution from segmented 3D tomographic data. We describe the complete pipeline from creating 3D models of the patients anatomy, the surgical planning, and the numerical simulation of soft tissue deformation. As a result of our investigation we will assess our approach with a view to providing a complete planning and simulation system for clinical use. Key Words: soft tissue deformation, finite element method, FEM, human modeling, biomechanics, computer assisted surgery, CAS. INTRODUCTION With the expanding application of computer technology for the planning of complex surgical operations, the demand for highly reliable computerized models of the human anatomy has constantly increased. The ultimate goal is to accurately simulate surgical interventions on virtual patient models in view of better preparation, improved surgical outcome, and shorter operation time. Besides computer assisted planning of bone surgery, current research is directed to modeling soft tissue for e.g. the simulation of minimally invasive surgery or the planning of maxillofacial surgery. In any case sophisticated models and fast reliable numerical simulation open new prospects in surgical planning. In our work we focus on computer assisted cranio- or dento-maxillofacial surgery, respectively, to simulate the behavior of soft tissue with regard to natural jaw movement, surgical bone rearrangement, and muscle based mimics. 2. PREVIOUS WORK For more than a decade researchers have been investigating the possibility of providing planning systems for cranio- or dento-maxillofacial surgery, in order to supply additional planning criteria with regard to facial tissue deformation for surgery preparation. Numerous approaches {zachow,gladiline,hege,deuflhard}@zib.de, URL:

2 for the simulation of soft tissue behavior have been developed, varying from pure geometric deformation of C -continuous skin surface, to volume based deformation with either physically based mass-spring or finite element (FE) models [,2]. In the volumetric case, prismatic elements were often used for spatial subdivision [3,4]. For biological objects, however, tetrahedral elements are known to be better suited at less degrees of freedom, especially for large deformation models of soft tissue regions with complex geometries. Apart from the elements shape there is always a tradeoff between accuracy and computation time due to the size of the elements. 3. MATERIAL AND METHODS Although there were many publications on different approaches to this rapidly expanding field of work, we do not know of any planning system in clinical use, that enables the surgeon to perform her entire 3D planning with subsequent assessment of the soft tissue arrangement. On this account we are presently investigating all essential working cycles, and are in the process of implementing an integrated planning system for maxillofacial surgery, in cooperation with the clinic for oral- and dento-maxillofacial surgery in Munich. Our work is based on the multipurpose visualization system Amira as well as on the Kaskade FE toolkit, which both have been developed at our institute [5,6], and are also in use in various medical application domains [7,8]. 3.. Modeling Approach The major steps needed to create a useful model of the patients anatomy for surgical planning and simulation are as follows:. Import of medical image data (ACR-NEMA/DICOM or any proprietary format) 2. Image filtering for the reduction of noise or artefacts 3. Segmentation of different tissue regions with subvoxel accuracy [9] 4. Generation of a non-manifold surface model with correct topology [0] 5. Surface simplification with scalable resolution 6. Surface optimization with regard to the triangular shape 7. Generation of an unstructured tetrahedral grid on basis of the surface model 8. Optimization of the volumetric grid with regard to an FE simulation Figure shows such a model of a patient s head generated by Amira. This model has been used for our first feasibility study, since the data set was complete and of very high resolution. Although most of the modeling steps mentioned above can be performed automatically or at least semi-automatically with Amira, it takes a considerable amount of time to generate such a volumetric model of tetrahedral elements. Especially for accurate FE simulation the tetrahedra must meet certain criteria, avoiding poor elements (such as needles, caps or slivers) Surgical Planning The planning of surgical bone rearrangement requires two major steps to be possibly repeated several times until the desired result is obtained:. Splitting or cutting of bone segments (osteotomy) 2. Repositioning of bony structures

Figure : Visualization of a patient s head model created by Amira Almost all articles in the literature, regarding planning systems for maxillofacial surgery, only describe planar cuts of geometric

3 Figure : Visualization of a patient s head model created by Amira Almost all articles in the literature, regarding planning systems for maxillofacial surgery, only describe planar cuts of geometric models. Those cuts, however, are not necessarily adequate for the planning of complex osteotomies. We found just one article describing arbitrarily shaped bone cuts, but only on the segmentation level []. This approach, in turn, is not acceptable for surgery planning, since the process of model generation has to be repeated for different cuts. After determination and specification of the optimal osteotomy lines, the separated parts of the model must be interactively transformed under visual control, according to surgical guidelines concerning functional rehabilitation, symmetry, and for example the occlusion. The transformation must be quantifiable in terms of the rotational and translational parameters. Thus the simulation of bone rearrangement in combination with the skull model can act as a substitute to the conventional articulator (virtual articulator) Numerical Simulation In our first approach, for the simulation of a soft tissue deformation, we made the following three modeling assumptions:. a volumetric grid of regularly shaped finite elements, 2. a distinct mechanical behavior for each tissue type, 3. suitably assigned boundary conditions. It is well known from literature [2], that biological tissue is anisotropic, inhomogeneous, and has a nonlinear stress-strain relationship. In our study we primarily model such a tissue as a Hookean elastic solid with stress σ linearly proportional to strain ε σ i j C i jkl ε kl () where C i jkl is a tensor of rank 4 with 8 elastic coefficients. As we do not know the anisotropic mechanical behavior of soft tissue, we further assume that the material is isotropic so that equation () can be greatly simplified to σ i j E ε ik ν ν 2ν ε llδ ik (2) with ε ll tr ε and only two remaining independent, elastic constants, the POISSON s ratio ν and YOUNG s modulus E [3,4].

The boundary value problem (BVP) on this grid is given by prescribed displacements, induced by the rearrangement of bony structures or the contraction of muscle regions.

4 As described in 3., our calculation is based on a surface model of all tissue regions defining material boundaries (bone, fat, muscle, air etc.). The resulting volume grid consists of coupled subgrids, each belonging to a certain tissue type. The boundary value problem (BVP) on this grid is given by prescribed displacements, induced by the rearrangement of bony structures or the contraction of muscle regions. The resulting displacements u (a vector valued 3D function) in any point of the material can be found in linear approximation as a solution of the L AMÉ NAVIER partial differential equation (PDE) 2 ν F E u 2ν grad div u (3) where F is the density of all external forces. With the abscence of such forces, i.e. in static equilibrium, equation (3) becomes a quasi-geometric formulation u 2ν grad div u 0 (4) For the numerical solution of (4) fast finite element methods with adaptive grid refinement based on local error estimators are used, which will facilitate a robust approximation of the solution up to a user defined level of accuracy [5]. To solve the belonging linear equation system, standard PCG methods as provided by Kaskade are applied. 4. RESULTS AND DISCUSSION Figure 2 shows a first result of facial tissue prediction after simulated surgical rearrangement of the mandible. Figure 2: First simulated surgical rearrangement of bony structures Having generated a tetrahedral grid of the patient s anatomy, any bone rearrangement or muscle contraction applied to the model leads to a deformation of the skin surface in a straightforward manner (Fig. 3).

Figure 3: Simulation of jaw movement At the moment we are applying our methods to cranio-maxillofacial surgery data from a patient with a congenital mandibular hypoplasia.

Figure 4: Simulation of mandible distraction with soft tissue prediction All calculations were performed on an SGI Onyx II with 95 MHz Mips R0000 processors, using only one processor.

5. CONCLUSION We have demonstrated by our prototype planning system, that surgical osteotomy planning on the basis of tomographic data including soft tissue prediction with an FE approach may already

5 Figure 3: Simulation of jaw movement At the moment we are applying our methods to cranio-maxillofacial surgery data from a patient with a congenital mandibular hypoplasia. Our first simulation results are indeed encouraging as shown in Figure 4. Figure 4: Simulation of mandible distraction with soft tissue prediction All calculations were performed on an SGI Onyx II with 95 MHz Mips R0000 processors, using only one processor. For a grid of approximately tetrahedra and a given residual norm of 0 2 the entire numerical solution took about 5 minutes (70 80 CG iterations), which seems very acceptable for clinical use. 5. CONCLUSION We have demonstrated by our prototype planning system, that surgical osteotomy planning on the basis of tomographic data including soft tissue prediction with an FE approach may already lead to reasonable results. Even such a simple model of static elastomechanics as described in 3.3 allows a first qualitative judgement of the surgical outcome in view of facial tissue arrangement. From our first findings and the positive feedback of collaborating surgeons we see a very high potential in providing such a planning aid for clinical use. Future work will therefore be directed towards the development of intuitive planning tools including more elaborate mechanical models of biological tissue. In order to simulate sliding contact between bone and soft tissue as well as to handle obstacle problems, e.g. gingival or

6 teeth and oral mucosa, adaptive monotone multigrid methods must be incorporated [6]. In perspective we believe that the simulation of muscle based mimics (such as smile or even laughter) will be possible in our approach thus giving an additional and very valuable criteria for maxillofacial surgery planning. ACKNOWLEDGEMENTS We would like to thank Dr. Dr. Zeilhofer and Dr. Dr. Sader from the clinic for oral- and dento-maxillofacial surgery, Munich (Klinik und Poliklinik für Mund-Kiefer-Gesichtschirurgie der TU München, Klinikum rechts der Isar) for kindly providing us with adequate patient data. REFERENCES. Zachow, S.: Modellierung von Weichgewebe - Simulation von Deformation und Destruktion: (Modeling of Soft Tissue - Simulation of Deformation and Destruction, in German) Neue Möglichkeiten in der computergestützten Chirurgie. Medizinische Informatik und Bioinformatik, Shaker Verlag, Aachen (998) 2. Maurel, W. ; Wu, Y. ; Magnenat Thalmann, N. ; Thalmann, D.: Biomechanical Models for Soft Tissue Simulation. Esprit Basic Research Series, Springer-Verlag, Berlin - Heidelberg - New York (998) 3. Keeve, E. ; Girod, S. ; Kikinis, R. ; Girod, B.: Deformable Modeling of Facial Tissue for Craniofacial Surgery Simulation. In: Computer Aided Surgery, Vol. 3, No. 5 (998) 4. Koch, R.M. ; Roth, S.H.M. ; Gross, M.H. ; Zimmermann, A.P. ; Sailer, H.F.: A Framework for Facial Simulation. Technical Report #326, ETHZ, Switzerland (June 8, 999) 5. Stalling, D. ; Hege, H.C. ; Zöckler, M. et. al. Amira - An Advanced 3D Visualization and Modeling System, URL: 6. Deuflhard, P. ; Leinen, P. ; Yserentant, H.: Concepts of an Adaptive Hierarchical Finite Element Code. IMPACT Comp. Sci. Eng., pp (989) 7. Deuflhard, P. ; Seebass, M.: Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyperthermia. In: Choi-Hong Lai, Peter E. Bjørstad, Mark Cross and Olof O. Widlund (eds.), Procs. Eleventh International Conference on Domain Decomposition Methods, DDM-org Press, Bergen, pp (999). 8. Zachow, S. ; Lueth, T.C. ; Stalling, D. ; Hein, A. ; Klein, M. ; Menneking, H.: Optimized Arrangement of Osseointegrated Implants: A Surgical Planning System for the Fixation of Facial Prostheses. In Lemke, H.U. et al. (eds.), Computer Assisted Radiology and Surgery (CARS), Elsevier Science B.V., pp (999) 9. Stalling, D. ; Zöckler, M. ; Hege, H.C.: Interactive Segmentation of 3D Medical Images with Subvoxel Accuracy. In: Lemke, H.U. et al. (eds.), Proc. CAR 98 Computer Assisted Radiology and Surgery, pp (998) 0. Hege, H.C. ; Seebaß, M. ; Stalling, D. ; Zöckler, M.: A Generalized Marching Cubes Algorithm Based On Non-Binary Classifications. ZIB Preprint SC (January 997). Schutyser, F. ; van Cleynenbreugel, J. ; Schoenaers, J. ; Marchal, G. ; Suetens, P.: A Simulation Environment for Maxillofacial Surgery including Soft Tissue Implications. In Taylor and Colchester (eds.), Medical Image Computing and Computer Assisted Intervention (MICCAI), Springer, pp (999) 2. Fung, Y.C.: Biomechanics: Mechanical Properties of Living Tissues. 2nd edition, Springer-Verlag, Berlin - Heidelberg - New York (993) 3. Sarti, A. ; Gori, R. ; Lamberti, C.: A physically based model to simulate maxillo-facial surgery from 3D CT images. Future Generation Computer Systems 5 (FGCS), pp (999) 4. Ciarlet, P.G.: Mathematical Elasticity. Vol., Studies in Mathematics and its Applications (20), North-Holland (987) 5. Bornemann, F.A. ; Erdmann, B. ; Kornhuber, R.: Adaptive Multilevel-Methods in 3-Space Dimensions. Int. J. for Num. Meth. in Eng. 36, pp (993) 6. Kornhuber, R.: Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems. Teubner Verlag (997)

From Image Data to Three-Dimensional Geometric Models Case Studies on the Impact of 3D Patient Models

From Image Data to Three-Dimensional Geometric Models Case Studies on the Impact of 3D Patient Models Hans-Christian HEGE 1,2), Hartmut SCHIRMACHER 2), Malte WESTERHOFF 1,2), Hans LAMECKER 1), Steffen