title: Numerical Simulation of Focused Shock Shear Waves in Soft Solids and a Two-Dimensional Nonlinear Homogeneous Model of the Brain.
abstract: Shear waves that propagate in soft solids, such as the brain, are strongly nonlinear and can develop into shock waves in less than one wavelength. We hypothesize that these shear shock waves could be responsible for certain types of traumatic brain injuries (TBI) and that the spherical geometry of the skull bone could focus shear waves deep in the brain, generating diffuse axonal injuries. Theoretical models and numerical methods that describe nonlinear polarized shear waves in soft solids such as the brain are presented. They include the cubic nonlinearities that are characteristic of soft solids and the specific types of nonclassical attenuation and dispersion observed in soft tissues and the brain. The numerical methods are validated with analytical solutions, where possible, and with self-similar scaling laws where no known solutions exist. Initial conditions based on a human head X-ray microtomography (CT) were used to simulate focused shear shock waves in the brain. Three regimes are investigated with shock wave formation distances of 2.54 m, 0.018 m, and 0.0064 m. We demonstrate that under realistic loading scenarios, with nonlinear properties consistent with measurements in the brain, and when the shock wave propagation distance and focal distance coincide, nonlinear propagation can easily overcome attenuation to generate shear shocks deep inside the brain. Due to these effects, the accelerations in the focal are larger by a factor of 15 compared to acceleration at the skull surface. These results suggest that shock wave focusing could be responsible for diffuse axonal injuries.
authors.forename: B
authors.initials: B
authors.lastname: Giammarinaro
authors.forename: F
authors.initials: F
authors.lastname: Coulouvrat
authors.forename: G
authors.initials: G
authors.lastname: Pinton
mesh_terms: D001696:Biomechanical Phenomena; D001921:Brain / Q000000981:diagnostic imaging; D016489:Head Injuries, Closed; D006801:Humans; D016014:Linear Models; D008954:Models, Biological; D017711:Nonlinear Dynamics; D033081:Shear Strength; D055114:X-Ray Microtomography
references.citation: J Mech Behav Biomed Mater. 2011 Nov;4(8):1905-19
references.pmid: 22098889
references.citation: IEEE Trans Ultrason Ferroelectr Freq Control. 2014 Sep;61(9):1489-503
references.pmid: 25167149
references.citation: Conf Proc IEEE Eng Med Biol Soc. 2015 Aug;2015 :1568-71
references.pmid: 26736572
references.citation: Phys Rev Lett. 2003 Oct 31;91(18):184301
references.pmid: 14611285
references.citation: J Magn Reson Imaging. 2010 Sep;32(3):577-83
references.pmid: 20815054
references.citation: J Acoust Soc Am. 2004 Dec;116(6):3734-41
references.pmid: 15658723
references.citation: J Acoust Soc Am. 2011 Jul;130(1):20-32
references.pmid: 21786874
references.citation: J Acoust Soc Am. 2003 Oct;114(4 Pt 1):1758-71
references.pmid: 14587578
references.citation: J Acoust Soc Am. 2007 Oct;122(4):1917-26
references.pmid: 17902828
references.citation: Phys Rev Lett. 2003 Oct 17;91(16):164301
references.pmid: 14611406
references.citation: Front Neurol. 2012 May 08;3:70
references.pmid: 22586417
references.citation: IEEE Trans Ultrason Ferroelectr Freq Control. 2006 Jun;53(6):1103-17
references.pmid: 16846143
references.citation: J Acoust Soc Am. 1997 Nov;102(5 Pt 1):2539-48
references.pmid: 9373968
references.citation: Biomech Model Mechanobiol. 2015 Oct;14(5):1119-28
references.pmid: 25697960
references.citation: J Biomech Eng. 2006 Dec;128(6):925-33
references.pmid: 17154695
references.citation: J Neurotrauma. 2001 Jan;18(1):21-30
references.pmid: 11200247
references.citation: J Biomech. 2009 Nov 13;42(15):2479-85
references.pmid: 19674749
references.citation: Biorheology. 1997 Nov-Dec;34(6):377-85
references.pmid: 9640354
references.citation: J Acoust Soc Am. 2008 May;123(5):2488-95
references.pmid: 18529167
references.citation: J Acoust Soc Am. 2007 Dec;122(6):3211-9
references.pmid: 18247733
references.citation: J Acoust Soc Am. 2010 Dec;128(6):3334-43
references.pmid: 21218867
references.citation: IEEE Trans Ultrason Ferroelectr Freq Control. 2002 Apr;49(4):426-35
references.pmid: 11989698
references.citation: J Acoust Soc Am. 2010 Feb;127(2):683-91
references.pmid: 20136190
references.citation: J Acoust Soc Am. 2005 Jan;117(1):113-23
references.pmid: 15704404
references.citation: Stapp Car Crash J. 2000 Nov;44:205-13
references.pmid: 17458728
references.citation: Neurosurgery. 2008 Apr;62(4):789-98; discussion 798
references.pmid: 18496184
references.citation: J Biomech. 2004 Jan;37(1):127-34
references.pmid: 14672576
references.citation: J Biomech Eng. 2009 Jun;131(6):061007
references.pmid: 19449961
references.citation: Neuroimage. 2009 Aug;47 Suppl 2:T10-20
references.pmid: 19248833
references.citation: Biorheology. 2010;47(5-6):255-76
references.pmid: 21403381
references.citation: J Biomech Eng. 2004 Apr;126(2):226-36
references.pmid: 15179853
references.citation: Magn Reson Med. 2013 Aug;70(2):404-12
references.pmid: 23001771