Abstract
Mathematically describing the mechanical behavior of soft tissues under large deformations is of paramount interest to the medical simulation community. Most of the data available in the literature apply small strains (<10%) to the the tissue of interest to assume a linearly elastic behavior. This paper applies a nonlinear hyperelastic 8-chain network constitutive law to model soft tissues undergoing large indentations. The model requires 2 material parameters (initial modulus, locking stretch) to reflect the underlying physics of deformation over a wide range of stretches. A finite element model of soft tissue indentation was developed and validated employing this constitutive law. Ranges of the initial shear modulus and locking stretches were explored based on values found for breast tissue [17, 25]. Results of the model are shown with a lookup table containing third order polynomial coefficient fits. This work serves as an initial method to determine the unique material parameters of breast tissue from indentation experiments.
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References
Anand, L.: A Constitutive Model for Compressible Elastomeric Solids. Computational Mechanics 18, 339–355 (1996)
Arruda, E.M., Boyce, M.C.: A Three-Dimensional Constitutive Model for The Large Stretch Behavior of Rubber Elastic Materials. J. Mech. Phys. Solids 41, 389–412 (1993)
Azar, F.S., Metaxas, D.N., Schnall, M.D.: A Deformable Finite Element Model of the Breast for Predicting Mechanical Deformations under External Perturbations. Journal of Academic Radiology 8, 965–975 (2001)
Boyce, M.C., Arruda, E.M.: Constitutive Models of Rubber Elasticity: A Review. Rubber Chemistry and Technology 73, 504–523 (2000)
Carter, F.J., Frank, T.G., Davies, P.J., McLean, D., Cuschieri, A.: Measurements and Modeling of the Compliance of Human and Porcine Organs. Medical Image Analysis 5, 231–236 (2001)
Cotin, S., Delingette, H., Ayache, N.: Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation. IEEE Transactions on Visualization and Computer Graphics 5, 62–73 (1999)
Delingette, H.: Towards Realistic Soft Tissue Modeling in Medical Simulation. IEEE: Special Issue in on Virtual and Augmented Reality in Medicine 86, 12 (1998)
Farshad, M., Barbezat, M., Flueler, P., Schmidlin, F., Graber, P., Niederer, P.: Material Characterization of the Pig Kidney in Relation with the Biomechanical Analysis of Renal Trauma. Journal of Biomechanics 32, 417–425 (1999)
Fung, Y.C.: Biomechanics: Mechanical Properties of Living Tissues, 2nd edn. Springer, New York (1993)
Han, L., Noble, J.A., Purcher, M.: A Novel Ultrasound Indentation System for Measuring Biomechanical Properties of in Vivo Soft Tissue. Ultrasound in Medicine & Biology 29, 813–823 (2003)
Hayes, W.C., Keer, L.M., Hermann, G., Mockros, L.F.: A Mathematical Analysis for Inden- tation Tests of Articular Cartilage. J. Biomechanics 5, 541–551 (1972)
Holzapfel, G.A.: Nonlinear Solid Mechanics: A Continuum Approach for Engineering. John Wiley & Sons Ltd., West Sussex (2000)
Hutter, R., Schmitt, K.-U., Niederer, P.: Mechanical Modeling of Soft Biological Tissues for Application in Virtual Reality Based Laparoscopy Simulators. Technology and Health Care 8, 15–24 (2000)
Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)
Kauer, M., Vuskovic, V., Dual, J., Székely, G., Bajka, M.: Inverse Finite Element Characteri- zation of Soft Tissues. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 128–136. Springer, Heidelberg (2001)
Kim, J., Tay, B., Stylopoulos, N., Rattner, D.W., Srinivasan, M.A.: Characterization of Intra-Abdominal Tissues from in Vivo Animal Experiment for Surgical Simulation. In: Ellis, R.E., Peters, T.M. (eds.) MICCAI 2003. LNCS, vol. 2878, pp. 206–213. Springer, Heidelberg (2003)
Krouskop, T.A., Wheeler, T.M., Kallel, F., Garra, B.S., Hall, T.: Elastic Moduli of Breast and Prostate Tissues under Compression. Ultrasonic Imaging 20, 260–274 (1998)
Miller, K.: Biomechanics of Soft Tissues. Med. Sci. Monit. 6, 158–167 (2000)
Ottensmeyer, M.P., Salisbury Jr., J.K.: In Vivo Data Acquisition Instrument for Solid Organ Mechanical Property Measurement. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 975–982. Springer, Heidelberg (2001)
Plewes, D.B., Bishop, J., Samani, A., Sciarretta, J.: Visualization and Quantization of Breast Cancer Biomechanical Properties with Magnetic Resonance Elastography. Physics in Medicine and Biology 45, 1591–1610 (2000)
Sarvazyan, A.P., Skovoroda, A.R., Pyt’ev, Y.P.: Mechanical Introscopy - a New Modality of Medical Imaging for Detection of Breast and Prostate Cancer. In: Eighth IEEE Symposium on Computer Based Medical Systems (1997)
Skovoroda, A.R., Klishko, A.N., Gusakyan, D.A., Mayevskii, Y.I., Yermilova, V.D., Oran-skaya, G.A., Sarvazyan, A.P.: Quantitative Analysis of the Mechanical Characteristics of Pathologically Changed Soft Biological Tissues. Biophysics 40, 1359–1364 (1995)
Szekely, G., Brechbuhler, C., Dual, J., et al.: Virtual Reality-Based Simulation of Endo-scopic Surgery. Presence 9, 310–333 (2000)
Timoshenko, S., Goodier, J.N.: Theory of Elasticisy. McGraw-Hill, New York (1970)
Wellman, P.S.: Tactile Imaging. In: Division of Engineering and Applied Sciences, p. 137. Harvard University, Cambridge (1999)
Wu, X., Downes, M.S., Goktekin, T., Tendick, F.: Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes. In: Eurographics 2001, Computer Graphics Forum, vol. 20, pp. 349–358 (2001)
Yeh, W.-C., Li, P.-C., Jeng, Y.-M., Hsu, H.-C., Kuo, P.-L., Li, M.-L., Yang, P.-M., Lee, P.H.: Elastic Modulus Measurements of Human Liver and Correlation with Pathology. Ultrasound in Medicine & Biology 28, 467–474 (2002)
Zhang, M., Zheng, Y.P., Mak, A.F.: Estimating the Effective Young’s Modulus of Soft Tissues from Indentation Tests - Nonlinear Finite Element Analysis of Effects of Friction and Large Deformation. Med. Eng. Phys. 19, 512–517 (1997)
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Liu, Y., Kerdok, A.E., Howe, R.D. (2004). A Nonlinear Finite Element Model of Soft Tissue Indentation. In: Cotin, S., Metaxas, D. (eds) Medical Simulation. ISMS 2004. Lecture Notes in Computer Science, vol 3078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25968-8_8
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DOI: https://doi.org/10.1007/978-3-540-25968-8_8
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