Under fast dynamic loading conditions (e.g. high-energy impact), the load rate dependency of the intervertebral disc (IVD) material properties may play a crucial role in the biomechanics of spinal trauma. However, most finite element models (FEM) of dynamic spinal trauma uses material properties derived from quasi-static experiments, thus neglecting this load rate dependency. The aim of this study was to identify hyperelastic material properties that ensure a more biofidelic simulation of the IVD under a fast dynamic compressive load. A hyperelastic material law based on a first-order Mooney-Rivlin formulation was implemented in a detailed FEM of a L2-L3 functional spinal unit (FSU) to represent the mechanical behavior of the IVD. Bony structures were modeled using an elasto-plastic Johnson-Cook material law that simulates bone fracture while ligaments were governed by a viscoelastic material law. To mimic experimental studies performed in fast dynamic compression, a compressive loading velocity of 1 m/s was applied to the superior half of L2, while the inferior half of L3 was fixed. An exploratory technique was used to simulate dynamic compression of the FSU using 34 sets of hyperelastic material constants randomly selected using an optimal Latin hypercube algorithm and a set of material constants derived from quasi-static experiments. Selection or rejection of the sets of material constants was based on compressive stiffness and failure parameters criteria measured experimentally. The two simulations performed with calibrated hyperelastic constants resulted in nonlinear load-displacement curves with compressive stiffness (7335 and 7079 N/mm), load (12,488 and 12,473 N), displacement (1.95 and 2.09 mm) and energy at failure (13.5 and 14.7 J) in agreement with experimental results (6551 ± 2017 N/mm, 12,411 ± 829 N, 2.1 ± 0.2 mm and 13.0 ± 1.5 J respectively). The fracture pattern and location also agreed with experimental results. The simulation performed with constants derived from quasi-static experiments showed a failure energy (13.2 J) and a fracture pattern and location in agreement with experimental results, but a compressive stiffness (1580 N/mm), a failure load (5976 N) and a displacement to failure (4.8 mm) outside the experimental corridors. The proposed method offers an innovative way to calibrate the hyperelastic material properties of the IVD and to offer a more realistic simulation of the FSU in fast dynamic compression.
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October 2011
Research Papers
Calibration of Hyperelastic Material Properties of the Human Lumbar Intervertebral Disc under Fast Dynamic Compressive Loads
Eric Wagnac,
Eric Wagnac
Laboratoire de Biomécanique Appliquée, UMRT 24 IFSTTAR-Université de la Méditerranée, Faculté de Médecine secteur Nord
, Boulevard Pierre Dramard, F-13916, Marseille,Cedex 20, France
; Biomedical Engineering Institute, École Polytechnique de Montréal
, P.O. Box 6079, Station Centre-Ville, Montreal, PQ, H3C 3A7, Canada
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Pierre-Jean Arnoux,
Pierre-Jean Arnoux
Laboratoire de Biomécanique Appliquée, UMRT 24 IFSTTAR-Université de la Méditerranée, Faculté de Médecine secteur Nord
, Boulevard Pierre Dramard, F-13916, Marseille, Cedex 20, France
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Anaïs Garo,
Anaïs Garo
Laboratoire de Biomécanique Appliquée, UMRT 24 IFSTTAR-Université de la Méditerranée, Faculté de Médecine secteur Nord
, Boulevard Pierre Dramard, F-13916, Marseille, Cedex 20, France
; Biomedical Engineering Institute, École Polytechnique de Montréal
, P.O. Box 6079, Station Centre-Ville, Montreal, PQ, H3C 3A7, Canada
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Marwan El-Rich,
Marwan El-Rich
Laboratoire de Biomécanique Appliquée, UMRT 24 IFSTTAR-Université de la Méditerranée
, Faculté de Médecine secteur Nord, Boulevard Pierre Dramard, F-13916, Marseille, Cedex 20, France
; Biomedical Engineering Institute
, École Polytechnique de Montréal, P.O. Box 6079, Station Centre-Ville, Montreal, PQ, H3C 3A7, Canada
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Carl-Eric Aubin
Carl-Eric Aubin
Biomedical Engineering Institute, École Polytechnique de Montréal
, P.O. Box 6079, Station Centre-Ville, Montreal (Quebec), H3C 3A7, Canada
; Research Center, Sainte-Justine Hospital, 3175 Cote Sainte-Catherine Rd, Montreal, PQ, H3T 1C5, Canada
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Eric Wagnac
Laboratoire de Biomécanique Appliquée, UMRT 24 IFSTTAR-Université de la Méditerranée, Faculté de Médecine secteur Nord
, Boulevard Pierre Dramard, F-13916, Marseille,Cedex 20, France
; Biomedical Engineering Institute, École Polytechnique de Montréal
, P.O. Box 6079, Station Centre-Ville, Montreal, PQ, H3C 3A7, Canada
e-mail address:
Pierre-Jean Arnoux
Laboratoire de Biomécanique Appliquée, UMRT 24 IFSTTAR-Université de la Méditerranée, Faculté de Médecine secteur Nord
, Boulevard Pierre Dramard, F-13916, Marseille, Cedex 20, France
Anaïs Garo
Laboratoire de Biomécanique Appliquée, UMRT 24 IFSTTAR-Université de la Méditerranée, Faculté de Médecine secteur Nord
, Boulevard Pierre Dramard, F-13916, Marseille, Cedex 20, France
; Biomedical Engineering Institute, École Polytechnique de Montréal
, P.O. Box 6079, Station Centre-Ville, Montreal, PQ, H3C 3A7, Canada
Marwan El-Rich
Laboratoire de Biomécanique Appliquée, UMRT 24 IFSTTAR-Université de la Méditerranée
, Faculté de Médecine secteur Nord, Boulevard Pierre Dramard, F-13916, Marseille, Cedex 20, France
; Biomedical Engineering Institute
, École Polytechnique de Montréal, P.O. Box 6079, Station Centre-Ville, Montreal, PQ, H3C 3A7, Canada
Carl-Eric Aubin
Biomedical Engineering Institute, École Polytechnique de Montréal
, P.O. Box 6079, Station Centre-Ville, Montreal (Quebec), H3C 3A7, Canada
; Research Center, Sainte-Justine Hospital, 3175 Cote Sainte-Catherine Rd, Montreal, PQ, H3T 1C5, Canada
J Biomech Eng. Oct 2011, 133(10): 101007 (10 pages)
Published Online: October 31, 2011
Article history
Received:
April 7, 2011
Accepted:
September 24, 2011
Online:
October 31, 2011
Published:
October 31, 2011
Citation
Wagnac, E., Arnoux, P., Garo, A., El-Rich, M., and Aubin, C. (October 31, 2011). "Calibration of Hyperelastic Material Properties of the Human Lumbar Intervertebral Disc under Fast Dynamic Compressive Loads." ASME. J Biomech Eng. October 2011; 133(10): 101007. https://doi.org/10.1115/1.4005224
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