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Abdominal Segment

Lumbar Spine

The development and validation of the lumbar spine is presented in detail in Iraeus et al. (2023) 1. Shortly, the vertebrae body was meshed with a high quality, all hexahedral solid and quadrilateral shell mesh to enable tissue based injury evaluation, see below.

L4-L5 FSU mesh example

An orthotropic material model based on Kopperdahl et al. (2002) 2 and Ulrich et al. (1999) 3 was used for the trabecular bone, while the cortical bone uses a anisotropic material model with material parameters based on Kohr et al. (2018) 4. The thickness of the cortical shells ranges between 0.51 and 0.82 and are based on Edwards et al. (2001) 5. The disc annulus ground substance, modelled with solids are based on Panzer and Cronin (2009) 6, while the annulus fibers are based on Cassidy et al. (1989) 7 and Holzapfel et al. (2005) 8. The Nucleus material properties (the nucleus beeing modelled using an Ogden material model) were tuned in compression to experiments by Asano et al. (1992) 9, Jamison et al. (2013) 10, Marini et al. (2016) 11 and Markolf and Morris (1974) 12.

The ligaments were modelled using (force-deflection) beam elements, with material properties based on Chazal et al (1985) 13, Mattucci and Cronin (2015) 14 and Nolte et al. (1990) 15. The upstretched length of the ligaments were tuned based on cut-down experiments by Heuer et al (2007) 16 and Jaramillo et al. (2016) 17. A end-user parameter 'LUMBFLEX' was introduced in the model to adjust the ligament initial slack. Set this to -1 to represent a standing person and to 0 to represent a person sitting in a vehicle seat.

A tissue based injury risk function was developed according to the recommendations in ISO/TR 12350:2013 by reconstructing 124 FSU tests published by Brinckman et al. (1989) 18, Duma et al. (2006) 19, Granhed et al. (1989) 20, Hutton and Adams (1982) 21 and Tushak et al. (2022) 22. The IRF takes the local z-strain (in compression) in the vertebrae trabecular bone as input, and can be seen below, and outputs the risk to sustain a compression fracture to the lumbar spine.

The IRF for compression fractures to the lumbar spine

Subcutaneous Fat Layer

The extent of the subcutaneous fat was adapted from measurements from multivariate regression maps Holcombe et al. (2014) 23

Internal Organs

The internal organs are modelled using a simplified (lumped) approach, with solid elements filling the abdominal cavity. Material properties are based on adipose tissue according to Naseri (2022) 24.

A CONTACT_TIED_NODES_TO_SURFACE_OFFSET (CID 600010) is used to connect the pelvic cavity soft tissue to the pelvis. The purpose of this contact is to prevent unphysical relative motion between the abdominal soft tissue and the pelvis.

References

  1. Johan Iraeus, Yash Niranjan Poojary, Leila Jaber, Jobin John, and Johan Davidsson. A new open-source finite element lumbar spine model, its tuning and validation, and development of a tissue-based injury risk function for compression fractures. In The international IRCOBI conference. 2023. ↩

  2. David L Kopperdahl, Elise F Morgan, and Tony M Keaveny. Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone. Journal of orthopaedic research, 20(4):801–805, 2002. ↩

  3. D Ulrich, B Van Rietbergen, A Laib, and P Ruegsegger. The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. Bone, 25(1):55–60, 1999. ↩

  4. Fiona Khor, Duane S Cronin, Brock Watson, Donata Gierczycka, and Skye Malcolm. Importance of asymmetry and anisotropy in predicting cortical bone response and fracture using human body model femur in three-point bending and axial rotation. Journal of the mechanical behavior of biomedical materials, 87:213–229, 2018. ↩

  5. W Thomas Edwards, Yinggang Zheng, Lisa A Ferrara, and Hansen A Yuan. Structural features and thickness of the vertebral cortex in the thoracolumbar spine. Spine, 26(2):218–225, 2001. ↩

  6. Matthew B Panzer and Duane S Cronin. C4–c5 segment finite element model development, validation, and load-sharing investigation. Journal of biomechanics, 42(4):480–490, 2009. ↩

  7. JJ Cassidy, A Hiltner, and E Baer. Hierarchical structure of the intervertebral disc. Connective tissue research, 23(1):75–88, 1989. ↩

  8. Gerhard A Holzapfel, CAJ Schulze-Bauer, G Feigl, and Peter Regitnig. Single lamellar mechanics of the human lumbar anulus fibrosus. Biomechanics and modeling in mechanobiology, 3(3):125–140, 2005. ↩

  9. Satoshi Asano, Kiyoshi Kaneda, Shinji Umehara, and Shigeru Tadano. The mechanical properties of the human l4–5 functional spinal unit during cyclic loading: the structural effects of the posterior elements. Spine, 17(11):1343–1352, 1992. URL: https://journals.lww.com/spinejournal/Fulltext/1992/11000/The_Mechanical_Properties_of_the_Human_L4_5.14.aspx. ↩

  10. David Jamison, Marco Cannella, Eric C Pierce, and Michele S Marcolongo. A comparison of the human lumbar intervertebral disc mechanical response to normal and impact loading conditions. Journal of Biomechanical Engineering, 2013. ↩

  11. Giacomo Marini, Harald Studer, Gerd Huber, Klaus Püschel, and Stephen J Ferguson. Geometrical aspects of patient-specific modelling of the intervertebral disc: collagen fibre orientation and residual stress distribution. Biomechanics and modeling in mechanobiology, 15(3):543–560, 2016. ↩

  12. Keith L Markolf and James M Morris. The structural components of the intervertebral disc: a study of their contributions to the ability of the disc to withstand compressive forces. JBJS, 56(4):675–687, 1974. ↩

  13. J Chazal, A Tanguy, M Bourges, G Gaurel, G Escande, Mm Guillot, and G Vanneuville. Biomechanical properties of spinal ligaments and a histological study of the supraspinal ligament in traction. Journal of biomechanics, 18(3):167–176, 1985. ↩

  14. Stephen FE Mattucci and Duane S Cronin. A method to characterize average cervical spine ligament response based on raw data sets for implementation into injury biomechanics models. Journal of the mechanical behavior of biomedical materials, 41:251–260, 2015. ↩

  15. Lutz Peter Nolte, MM Panjabi, and TR Oxland. Biomechanical properties of lumbar spinal ligaments. Clinical implant materials, advances in biomaterials, 9:663–668, 1990. ↩

  16. Frank Heuer, Hendrik Schmidt, Zdenek Klezl, Lutz Claes, and Hans-Joachim Wilke. Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle. Journal of biomechanics, 40(2):271–280, 2007. ↩

  17. Héctor Enrique Jaramillo, Christian M Puttlitz, Kirk McGilvray, and José J García. Characterization of the l4–l5–s1 motion segment using the stepwise reduction method. Journal of Biomechanics, 49(7):1248–1254, 2016. ↩

  18. Paul Brinckmann, M Biggemann, and DJCB Hilweg. Prediction of the compressive strength of human lumbar vertebrae. Clinical Biomechanics, 4:iii–27, 1989. ↩

  19. Stefan M Duma, Andrew R Kemper, David M McNeely, P Gunnar Brolinson, and Fumio Matsuoka. Biomechanical response of the lumbar spine in dynamic compression. Biomedical sciences instrumentation, 42:476–481, 2006. ↩

  20. Hans Granhed, Ragnar Jonson, and Tommy Hansson. Mineral content and strength of lumbar vertebrae a cadaver study. Acta Orthopaedica Scandinavica, 60(1):105–109, 1989. ↩

  21. WC Hutton and MA Adams. Can the lumbar spine be crushed in heavy lifting? Spine, 7(6):586–590, 1982. ↩

  22. Sophia K Tushak, John Paul Donlon, Bronislaw D Gepner, Aida Chebbi, Bengt Pipkorn, Jason J Hallman, Jason L Forman, and Jason R Kerrigan. Failure tolerance of the human lumbar spine in dynamic combined compression and flexion loading. Journal of Biomechanics, 135:111051, 2022. ↩

  23. Sven A. Holcombe and Stewart C. Wang. Subcutaneous Fat Distribution in the Human Torso. In IRCOBI Conference, 145–165. Berlin, Germany, 2014. ↩

  24. H Naseri. Calibration of adipose tissue material properties in ls-dyna. Report, Chalmers University of Technology, 2022. ↩