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An adaptive-remeshing framework to predict impact-induced skull fracture in infants


Infant skull fractures are common in both accidental and abusive head trauma, but identifying the cause of injury may be challenging without adequate evidence. To better understand the mechanics of infant skull fracture and identify environmental variables that lead to certain skull fracture patterns, we developed an innovative computational framework that utilizes linear elastic fracture mechanics theory to predict skull fracture as a first step to study this problem. The finite element method and adaptive-remeshing technique were employed to simulate high-fidelity, geometrically explicit crack propagation in an infant skull following impact. In the framework, three modes of stress intensity factors are calculated by means of the M-integral using the commercial analysis code, FRANC3D, and are used as measures of crack driving force. The anisotropy of infant skulls is represented by means of a transversely isotropic constitutive model and a direction-dependent fracture-toughness locus. The ability of the framework to predict impact-induced fracture patterns is validated by comparison with experimentally observed fracture patterns from the literature.

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  1. Asgharpour Z, Baumgartner D, Willinger R, Graw M, Peldschus S (2014) The validation and application of a finite element human head model for frontal skull fracture analysis. J Mech Behav Biomed Mater 33:16–23

  2. Bojtár I, Gálos M, Scharle A (1994) Fracture mechanical analysis of human skull. Period Polytech Civ Eng 38(4):367–374

  3. Chin PL (2011) Stress analysis, crack propagation and stress intensity factor computation of a Ti–6Al–4V aerospace bracket using ANSYS and FRANC3D. Sc Degree Rensselaer Polytechnic Institute Hartford Connecticut

  4. Coats B (2007) Mechanics of head impact in infants. PhD thesis, University of Pennsylvania

  5. Coats B, Margulies SS (2006) Material properties of human infant skull and suture at high rates. J Neurotrauma 23(8):1222–1232

  6. Coats B, Ji S, Margulies SS (2007) Parametric study of head impact in the infant. Technical report, SAE technical paper

  7. Corbani S, Castro J, Miranda A, Martha L, Carter B, Ingraffea A (2018) Crack shape evolution under bending-induced partial closure. Eng Fract Mech 188:493–508

  8. Cunningham C, Scheuer L, Black S (2016) Developmental juvenile osteology. Academic Press, Berlin

  9. Davis B, Wawrzynek P, Ingraffea A (2014) 3-D simulation of arbitrary crack growth using an energy-based formulation—part I: planar growth. Eng Fract Mech 115:204–220

  10. Erdogan F, Sih G (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85(4):519–525

  11. Farley R, Reece R, Robert M (2002) Recognizing when a child’s injury or illness is caused by abuse. US Department of Justice, Office of Juvenile Justice and Delinquency Prevention, NCJ 160938

  12. Fracture Analysis Consultants, Inc. (2018) FRANC3D reference manual, version 7.2 (online). Accessed 16 Feb 2019

  13. Grassberger M, Gehl A, Püschel K, Turk E (2011) 3D reconstruction of emergency cranial computed tomography scans as a tool in clinical forensic radiology after survived blunt head trauma—report of two cases. Forensic Sci Int 207(1–3):e19–e23

  14. Hajiaghamemar M, Lan IS, Christian CW, Coats B, Margulies SS (2018) Infant skull fracture risk for low height falls. Int J Leg Med 133:1–16

  15. Hazenberg JG, Taylor D, Lee TC (2006) Mechanisms of short crack growth at constant stress in bone. Biomaterials 27(9):2114–2122

  16. Hoenig A (1982) Near-tip behavior of a crack in a plane anisotropic elastic body. Eng Fract Mech 16(3):393–403

  17. Jacobsen C, Bech BH, Lynnerup N (2009) A comparative study of cranial, blunt trauma fractures as seen at medicolegal autopsy and by computed tomography. BMC Med Imaging 9(1):18

  18. Koester KJ, Ager Iii J, Ritchie R (2008) The true toughness of human cortical bone measured with realistically short cracks. Nat Mater 7(8):672

  19. Lee H, Choi J, Jung K, Im YT (2009) Application of element deletion method for numerical analyses of cracking. J Achiev Mater Manuf Eng 35(2):154–161

  20. Leventhal JM, Thomas SA, Rosenfield NS, Markowitz RI (1993) Fractures in young children: distinguishing child abuse from unintentional injuries. Am J Dis Child 147(1):87–92

  21. Li Z, Luo X, Zhang J (2013) Development/global validation of a 6-month-old pediatric head finite element model and application in investigation of drop-induced infant head injury. Comput Methods Programs Biomed 112(3):309–319

  22. Li Z, Liu W, Zhang J, Hu J (2015) Prediction of skull fracture risk for children 0–9 months old through validated parametric finite element model and cadaver test reconstruction. Int J Leg Med 129(5):1055–1066

  23. Li X, Sandler H, Kleiven S (2019) Infant skull fractures: Accident or abuse? Evidences from biomechanical analysis using finite element head models. Forensic Sci Int 294:173–182

  24. Loyd AM (2011) Studies of the human head from neonate to adult: an inertial, geometrical and structural analysis with comparisons to the ATD head. Duke University, Duke

  25. Lynn PP, Ingraffea AR (1978) Transition elements to be used with quarter-point crack-tip elements. Int J Numer Methods Eng 12(6):1031–1036

  26. Metcalf RM, Comstock JM, Coats B (2019) High-rate anisotropic and region-dependent properties in human infant cranial bone. Summer biomechanics, bioengineering, and biotransport conference. Seven Springs, PA June 2019

  27. Nalla R, Stölken J, Kinney J, Ritchie R (2005) Fracture in human cortical bone: local fracture criteria and toughening mechanisms. J Biomech 38(7):1517–1525

  28. Nguyen O, Repetto E, Ortiz M, Radovitzky R (2001) A cohesive model of fatigue crack growth. Int J Fract 110(4):351–369

  29. Peterson J, Dechow PC (2002) Material properties of the inner and outer cortical tables of the human parietal bone. Anat Rec 268(1):7–15

  30. Pettit RG (2000) Crack turning in integrally stiffened aircraft structures. PhD thesis, Cornell University

  31. Pettit R, Annigeri B, Owen W, Wawrzynek P (2013) Next generation 3D mixed mode fracture propagation theory including HCF–LCF interaction. Eng Fract Mech 102:1–14

  32. Raul JS, Baumgartner D, Willinger R, Ludes B (2006) Finite element modelling of human head injuries caused by a fall. Int J Leg Med 120(4):212–218

  33. Roth S, Raul JS, Willinger R (2008) Biofidelic child head FE model to simulate real world trauma. Comput Methods Programs Biomed 90(3):262–274

  34. Roth S, Raul JS, Willinger R (2010) Finite element modelling of paediatric head impact: global validation against experimental data. Comput Methods Programs Biomed 99(1):25–33

  35. Sahoo D, Deck C, Yoganandan N, Willinger R (2013) Anisotropic composite human skull model and skull fracture validation against temporo-parietal skull fracture. J Mech Behav Biomed Mater 28:340–353

  36. Shih C, Lorenzi Hd, German M (1976) Crack extension modeling with singular quadratic isoparametric elements. Int J Fract 12(4):647–651

  37. Song JH, Areias PM, Belytschko T (2006) A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Methods Eng 67(6):868–893

  38. Spear AD, Priest AR, Veilleux MG, Ingraffea AR, Hochhalter JD (2011) Surrogate modeling of high-fidelity fracture simulations for real-time residual strength predictions. AIAA J 49(12):2770–2782

  39. US Department of Health & Human Services, Administration for Children and Families, Administration on Children, Youth and Families, Children’s Bureau (2019) Child maltreatment 2017 (online). Accessed 8 Aug 2019

  40. Vannier MW, Marsh JL, Warren JO (1984) Three dimensional CT reconstruction images for craniofacial surgical planning and evaluation. Radiology 150(1):179–184

  41. Warzynek PA, Carter BJ, Banks-Sills L (2005) The M-integral for computing stress intensity factors in generally anisotropic materials. Technical report, NASA/CR–2005–214006

  42. Wawrzynek P, Carter B, Hwang CY, Ingraffea A (2010) Advances in simulation of arbitrary 3D crack growth using FRANC3DV5. J Comput Struct Eng Inst Korea 23(6):607–613

  43. Weber W (1984) Experimental studies of skull fractures in infants. Z Rechtsmed J Leg Med 92(2):87–94

  44. Weber W (1985) Biomechanical fragility of the infant skull. Z Rechtsmed J Leg Med 94(2):93–101

  45. Zhang L, Yang KH, Dwarampudi R, Omori K, Li T, Chang K, Hardy WN, Khalil TB, King AI (2001) Recent advances in brain injury research: a new human head model development and validation. Technical report, SAE technical paper

  46. Zimmermann EA, Launey ME, Ritchie RO (2010) The significance of crack-resistance curves to the mixed-mode fracture toughness of human cortical bone. Biomaterials 31(20):5297–5305

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This project was supported by Award No. 2016-DN-BX-0160, awarded by the National Institute of Justice, Office of Justice Programs, US Department of Justice. The opinions, findings, and conclusions or recommendations expressed in this publication, program, exhibition are those of the authors and do not necessarily reflect those of the Department of Justice. Initial development of the infant skull model was supported by the Centers for Disease Control and Prevention Grant NCIPC R49CE000411. The authors gratefully acknowledge Dr. Bruce Carter for his technical support on issues regarding the use of FRANC3D.

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Correspondence to Ashley D. Spear.

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He, J., Yan, J., Margulies, S. et al. An adaptive-remeshing framework to predict impact-induced skull fracture in infants. Biomech Model Mechanobiol (2020).

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  • Computational fracture mechanics
  • Infant skull fracture
  • Crack growth
  • Linear elastic fracture mechanics