Pelvis

The pelvis was first developed within VIRTUAL https://projectvirtual.eu/ and was further enhanced within the SAFE-UP project https://www.safe-up.eu/.

Bones

Pelvis

The geometry of the bone is based on the statistical shape model developed by Brynskog et al. (2021) ¹. An all hexahedral solid and quadrilateral shell element mesh was created to enable future tissue based injury risk estimation. The thickness of the cortical shells were assigned to the average thickness of the nine subjects analyzed by Anderson et al. (2005) ².

For modeling the cortical bone of the pelvis, data from Kemper et al. (2008) ³ was used. Although it only includes males, it was the most appropriate source identified within our review. The average curve was created, based on all curves that were presented in the paper, according to the method described in Klug et al (2019) ⁴. The curve was also converted to true stress / strain.

The trabecular bone was modelled using a linear elastic material model, using the parameters described in Dalstra et al. (1993)⁵. The material parameters could be updated in the future. Currently the yield stress is a "dummy value" and the young modulus should be increased.

Joints

Hip Joint

Material and cross-section parameters for the human hip joint capsule ligaments, attaching the femur to the pelvis, were based on Hewitt et al. (2001) ⁶. In this study ligaments were obtained from 7 females and 3 males (50-99 yo), and the stress-strain behavior was described using an exponential function. The displacement rate in the tests was 0.04 mm/s

Properties of Hip ligaments according to 6		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

Based on the VIVA+ circumferential of the acetabulum (167 mm) and teh cross sectional area of eth acetabulum, the ligament was predicted to have a thickness of 1.87 mm.

$150+100+63=313 mm^2$

$313 mm^2 / 167 mm= 1.87 mm$

At the femoral end the ligament has a circumferential of 120 mm, resulting in a thickness of 2.22 mm

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

$267 mm^2/ 120mm = 2.225 mm$

The ligaments were modelled using MAT_ELASTIC. The average modulus of elasticity (80% of failure strain) from Hewitt et al. (2001) ⁶ was taken as young modulus (136.8 MPa)

A beam element from the femur head to the acetabulum 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) ⁸ 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, and thus the stiffness of 50N/5mm=10N/mm was given to the ligament.

Modelling of sacroiliac joint

To SI joint was simplified modelled using a single layer of solid elements, nodally connected to the sacrum and connected to the pelvis using a tied contact. Material constant for a one term Ogden material model was tuned to match the (compression and tension) results from Miller et al (1987) ⁹. The result of the tuned joint stiffness can be seen below.

Pubic Symphysis

The PS joint was simplified modelled using four layers of solid element. Material constant for a two term Ogden material model was tuned to match the results from Li et al. (2006)¹⁰, which are in turn based on Dakin et al (2000)¹¹. The results of the tuned joint stiffness can be seen below.

References

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1. Erik Brynskog, Johan Iraeus, Matthew P Reed, and Johan Davidsson. Predicting pelvis geometry using a morphometric model with overall anthropometric variables. Journal of Biomechanics, 126:110633, 2021. ↩

2. Andrew E Anderson, Christopher L Peters, Benjamin D Tuttle, and Jeffrey A Weiss. Subject-specific finite element model of the pelvis: development, validation and sensitivity studies. Journal of biomechanical engineering, 127(3):364–373, 2005. ↩

3. 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. ↩

4. 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. ↩

5. M. Dalstra, R. Huiskes, A. Odgaard, and L. van Erning. Mechanical and textural properties of pelvic trabecular bone. Journal of Biomechanics, 26(4-5):523–535, apr 1993. doi:10.1016/0021-9290(93)90014-6. ↩

6. John Hewitt, Farshid Guilak, Richard Glisson, and T. Parker Vail. Regional material properties of the human hip joint capsule ligaments. Journal of Orthopaedic Research, 19(3):359–364, may 2001. doi:10.1016/s0736-0266(00)00035-8. ↩↩↩

7. 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, 13(8):e0200952, aug 2018. doi:10.1371/journal.pone.0200952. ↩

8. 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, 27(8):989–995, aug 2009. doi:10.1002/jor.20852. ↩

9. J. A. A. Miller, A. B. Schultz, and G. B. J. Andersson. Load-displacement behavior of sacroiliac joints. Journal of Orthopaedic Research, 5(1):92–101, 1987. doi:10.1002/jor.1100050112. ↩

10. 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, 34(9):1452–1462, aug 2006. doi:10.1007/s10439-006-9145-1. ↩

11. 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, 123(3):218–226, dec 2000. doi:10.1115/1.1372321. ↩