Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation. (English) Zbl 1154.74045

Summary: We propose an efficient numerical algorithm for computing deformations of “very” soft tissues (such as the brain, liver, kidney etc.), with applications to real-time surgical simulation. The algorithm is based on finite element method using total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration. This choice allows for pre-computing of most spatial derivatives before the commencement of time-stepping procedure. We use explicit time integration that eliminates the need for iterative equation solving during the time-stepping procedure. The algorithm is capable of handling both geometric and material nonlinearities. The total Lagrangian explicit dynamics (TLED) algorithm using eight-noded hexahedral under-integrated elements requires approximately 35% fewer floating-point operations per element and per time step than the updated Lagrangian explicit algorithm using the same elements. Stability analysis of the algorithm suggests that due to much lower stiffness of very soft tissues than that of typical engineering materials, integration time steps a few orders of magnitude larger than what is typically used in engineering simulations are possible. Numerical examples confirm the accuracy and efficiency of the proposed TLED algorithm.


74S05 Finite element methods applied to problems in solid mechanics
74L15 Biomechanical solid mechanics
92C10 Biomechanics


Full Text: DOI


[1] Oden, Research directions in computational mechanics, Computer Methods in Applied Mechanics and Engineering 192 pp 913– (2003) · Zbl 1025.74503
[2] Carey, A unified approach to three finite element theories for geometric nonlinearity, Journal of Computer Methods in Applied Mechanics and Engineering 4 (1) pp 69– (1974) · Zbl 0286.73065
[3] Martin, Introduction to Finite Element Analysis: Theory and Application (1973)
[4] Oden, Finite Elements: Special Problems in Solid Mechanics (1983)
[5] Zhuang Y Real-time simulation of physically realistic global deformations 2000
[6] Picinbono, Non-linear anisotropic elasticity for real-time surgery simulation, Graphical Models 65 pp 305– (2003) · Zbl 1054.68165
[7] Hallquist, LS-DYNA Theoretical Manual (1998)
[8] Szekely, Modelling of soft tissue deformation for laparoscopic surgery simulation, Medical Image Analysis 4 pp 57– (2000)
[9] Belytschko, Computational Methods for Transient Analysis pp 1– (1983)
[10] http://www.ansys.com/services/documentation/manuals.htm
[11] ABAQUS, ABAQUS Online Documentation: Version 6.5-1 (2004)
[12] www.adina.com
[13] LS-DYNA, Keyword User’s Manual. Version 970 (2003)
[14] Belytschko, A survey of numerical methods and computer programs for dynamic structural analysis, Nuclear Engineering and Design 37 pp 23– (1976)
[15] Bathe, Finite Element Procedures (1996)
[16] Crisfield, Non-linear Finite Element Analysis of Solids and Structures pp 447– (1998)
[17] Miller, Constitutive modeling of brain tissue; experiment and theory, Journal of Biomechanics 30 (11/12) pp 1115– (1997)
[18] Miller, Constitutive model of brain tissue suitable for finite element analysis of surgical procedures, Journal of Biomechanics 32 pp 531– (1999)
[19] Miller, Mechanical properties of brain tissue in tension, Journal of Biomechanics 35 pp 483– (2002)
[20] Bilston, Large strain behaviour of brain tissue in shear: some experimental data and differential constitutive model, Biorheology 38 pp 335– (2001)
[21] Prange, Regional, directional, and age-dependent properties of the brain undergoing large deformation, Journal of Biomechanical Engineering 124 pp 244– (2002)
[22] Liu, Large deformation shear properties of liver tissue, Biorheology 39 (6) pp 735– (2002)
[23] Farshad, Material characterization of the pig kidney in relation with the biomechanical analysis of renal trauma, Journal of Biomechanics 32 (4) pp 417– (1999)
[24] Miller, Constitutive modelling of abdominal organs, Journal of Biomechanics 33 pp 367– (2000)
[25] Brewer JC Effects of angles and offsets in crash simulations of automobiles with light trucks 2001
[26] Kirkpatrick, Evaluation of passenger rail vehicle crashworthiness, International Journal of Crashworthiness 6 (1) pp 95– (2001)
[27] Cook, Concepts and Applications of Finite Element Analysis pp 367– (1989)
[28] Feng, A recurrence formula for viscoelastic constitutive equations, International Journal of Non-Linear Mechanics 27 (4) pp 675– (1992) · Zbl 0825.73204
[29] Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (1987) · Zbl 0634.73056
[30] Flanagan, A uniform strain hexahedron and quadrilateral with orthogonal hourglass control, International Journal for Numerical Methods in Engineering 17 pp 679– (1981) · Zbl 0478.73049
[31] http://msdn.microsoft.com/netframework
[32] Miller, Mechanical properties of brain tissue in-vivo: experiment and computer simulation, Journal of Biomechanics 33 pp 1369– (2000)
[33] Wittek, Patient-specific model of brain deformation: application to medical image registration, Journal of Biomechanics (2006)
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