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Pelvis

This section of the documentation is under development

This section is being updated

A preliminary version of the pelvis was developed within VIRTUAL https://projectvirtual.eu/ and is currently further enanced witin SAFEUP https://www.safe-up.eu/.

Bones

Pelvis

For modeling the cortical bone of the pelvis, data from Kemper et al. (2008) 1 is applied. Although it only includes males, it was the most appropiate source identified within our review.

We have derived an average curve from all curves that were presented in the paper according to the method descibed in Klug et al (2019) 2. It could be later on decided to exclude some curves for the average. The curve was converted to true stress / strain.

The trabecular bone is modelled as linear elastic material using the parameters descibed in Dalstra et al. (1993)3. The material parameters will be altered in the future - the yield stress is a "dummy value" only and the young modulus should be increased.

Work in progress:

  • The material model of the trabecular bone will be recailbrated
  • The cortical thickness of the cortical pelvis bone will be set to average nodal thicknesses based on data from Harris et al (2012)

Material properties for the pelvic ligaments are descibed in Hammer et al. (2013)4.

Joints

Hip Joint

For the pedestrian a proper modelling of the tensile force transferred from the femur to the pelvis has to be modelled. Material and crossection parameters for the human hip joint capsule ligaments attaching the femur to the pelvis are reported by Hewitt et al. (2001) 5 . Ligaments were obtained from 7 females and 3 males (50-99 yo) The stress-strain behaviour is described by an exponential function. The displacement rate in the tests was 0.04 mm/s

Properties of Hip ligaments according to 5 Superior iliofemoral Inferios iliofemoral Ischiofemoral
Crosssectional area [mm^2]
Acetabular 150 100 63
Middle 120 92 81
Femoral 99 89 79
Modulus of Elasticity at 80% of failure strain (MPa)
Acetabular 112.9 285.8 80.9
Middle 113.3 242.2 99.5
Femoral 76.1 139.3 82.1
average 100.7 222.4 87.5

As the circumferential of the acetabulum of the VIVA+ model is 167 mm - using the whole circumferential and using the sum of the crossectional acatbular area, we get a thickness of 1.87 mm for the ligament

150+100+63=313 mm^2

313 mm^2 / 167 mm= 1.87 mm

At the femuroal end the ligament will has a circumferential of 120 mm, resulting in a tickness of 2.22 mm

(99+89+79)=267 mm^2

267 mm^2/ 120mm = 2.225 mm

The ligaments were modelled with MAT_FABRIC. The average modulus of elasticity (80% of failure strain) from Hewitt et al. (2001) 5 was taken as young modulus (136.8 MPa)

TODO:

  • use curves from paper to calibrate C2. Look for prony series parameters. Use beams instead of shell?

A beam element from the femur head to the acetbulum was included to replicate the "ligament teres". It was modelled with a linear-elastic material model using the information from tests of Ito et al. (2009) 7 in which the femur was teared apart from the acetabulum parallel to the femur shaft with the hip being in a neutral position. Load-Displacement curves are provided up to 5 mm for a constant loading of 4 mm/s. Around 300 N were needed to move the femur 5 mm apart from the pelvis with intact hip capsule. 50 N were needed when the capsule was completely resected.

TODO:

  • simulated Ito experiments and recalibrate hip joint stiffness if needed

Modelling of sacroiliac joint

To model the stiffness of the sacroiliac joint, a part consisting of one layer solid elements is created between the sacrum and the ilium.

The material parameters are chosen based on Miller et al (1987) 8. Data is based on 7 males and one female aged between 59 and 74 years.

Stiffness (k) in direction: * superior: 157.2 N/mm * inferior: 267.0 N/mm * anterior: 107.3 N/mm * posterior: 187.9 N/mm * medial (lateral): 386.8 N/mm

The area of the joint was measured as 1424 mm^2 (1104-1913m^2). In the VIVA+ 50 F model it is slightly lower than the smallest measured area, being 1050 mm^2 on anterior and 1062 mm^2 posterior side. The average thickness of the outer face is 4.4 mm.

E = k * thickness/A

leading to the Young's modulus

  • superior: 0.655 N/mm^2
  • inferior: 1.113 N/mm^2
  • mean of superior and inferior = 0.884
  • anterior: 0.447 N/mm^2
  • posterior: 0.783 N/mm^2
  • mean of anerior posterior = 0.615
  • medial (lateral): 1.612 N/mm^2

As the appropiate stiffness will be mainly important in lateral impacts and only validation loadcases for this impact direction are available, a linear elastic material is chosen for the baseline model using a young modulus of 1.612 N/mm^2 The density is set to the same one as for the PS disk.

Work in progress:

  • The material parameters of the sacriliajoint are optimised to match experimets of Miller et al (1987) 8 for ine directions

The sacroiliac joint is connected with the ilium using a tied contact.

Pubic Symphysis

Material parameters for the PS were taken from Li et al. (2006)9 based on Dakin et al (2000)10.

Work in progress:

  • PS is recalibrated using target curves from Li et al. (2006)9

References

  1. Andrew R Kemper, Craig McNally, and Stefan M Duma. Dynamic tensile material properties of human pelvic cortical bone. Biomedical sciences instrumentation, 44:417–418, 2008. ↩

  2. Corina Klug, Florian Feist, Bernd Schneider, Wolfgang Sinz, James Ellway, and Michiel van Ratingen. Development of a certification procedure for numerical pedestrian models. In 26th International Technical Conference on the Enhanced Safety of Vehicles ESV, number 19-0310. 2019. ↩

  3. M. Dalstra, R. Huiskes, A. Odgaard, and L. van Erning. Mechanical and textural properties of pelvic trabecular bone. Journal of Biomechanics, 264\-5:523–535, apr 1993. doi:10.1016/0021-92909390014-6. ↩

  4. Niels Hammer, Hanno Steinke, Uwe Lingslebe, Ingo Bechmann, Christoph Josten, Volker Slowik, and Jörg Böhme. Ligamentous influence in pelvic load distribution. The Spine Journal, 1310:1321–1330, oct 2013. doi:10.1016/j.spinee.2013.03.050. ↩

  5. John Hewitt, Farshid Guilak, Richard Glisson, and T. Parker Vail. Regional material properties of the human hip joint capsule ligaments. Journal of Orthopaedic Research, 193:359–364, may 2001. doi:10.1016/s0736-02660000035-8. ↩↩↩

  6. Ingmar Fleps, William S. Enns-Bray, Pierre Guy, Stephen J. Ferguson, Peter A. Cripton, and Benedikt Helgason. On the internal reaction forces, energy absorption, and fracture in the hip during simulated sideways fall impact. PLOS ONE, 138:e0200952, aug 2018. doi:10.1371/journal.pone.0200952. ↩

  7. Hiroshi Ito, Yongnam Song, Derek P. Lindsey, Marc R. Safran, and Nicholas J. Giori. The proximal hip joint capsule and the zona orbicularis contribute to hip joint stability in distraction. Journal of Orthopaedic Research, 278:989–995, aug 2009. doi:10.1002/jor.20852. ↩

  8. J. A. A. Miller, A. B. Schultz, and G. B. J. Andersson. Load-displacement behavior of sacroiliac joints. Journal of Orthopaedic Research, 51:92–101, 1987. doi:10.1002/jor.1100050112. ↩↩

  9. Zuoping Li, Jorge E. Alonso, Jong-Eun Kim, James S. Davidson, Brandon S. Etheridge, and Alan W. Eberhardt. Three-dimensional finite element models of the human pubic symphysis with viscohyperelastic soft tissues. Annals of Biomedical Engineering, 349:1452–1462, aug 2006. doi:10.1007/s10439-006-9145-1. ↩↩

  10. Greg J. Dakin, Raul A. Arbelaez, Fred J. Molz, Jorge E. Alonso, Kenneth A. Mann, and Alan W. Eberhardt. Elastic and viscoelastic properties of the human pubic symphysis joint: effects of lateral impact loading. Journal of Biomechanical Engineering, 1233:218–226, dec 2000. doi:10.1115/1.1372321. ↩