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16th US National Congress of Theoretical and Applied Mechanics June 27 - July 2, 2010, State College, Pennsylvania, USA USNCTAM2010-822 MRI-BASED FINITE ELEMENT MODELING OF HEAD TRAUMA: SPHERICALLY FOCUSING SHEAR WAVES Ying Chen, Martin Ostoja-Starzewski Department of Mechanical Science and Engineering and Beckman Institute University of Illinois at Urbana-Champaign Urbana, IL 61801, USA martinos@illinois.edu large blood vessels in the subarachnoid space. While the skull and CSF are assumed to
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  16th US National Congress of Theoretical and Applied MechanicsJune 27 - July 2, 2010, State College, Pennsylvania, USA USNCTAM2010-822 MRI-BASED FINITE ELEMENT MODELING OF HEAD TRAUMA: SPHERICALLYFOCUSING SHEAR WAVES Ying Chen, Martin Ostoja-Starzewski Department of Mechanical Science and Engineering and Beckman InstituteUniversity of Illinois at Urbana-ChampaignUrbana, IL 61801, USAmartinos@illinois.edu ABSTRACT The mechanisms underlying blunt head trauma are notfully understood. We developed a computational model to studythe transient mechanics during head trauma events. Throughfrontal and side impact simulations, we discovered that the pressure input to the head gives rise not only to a fast pressurewave but also to a slow, and potentially more damaging, shear wave that converges spherically towards the brain center. A balance of wave amplification due to spherically convergentimplosion with wave damping due to viscoelastic brain isobserved, suggesting a stochastic competition of these twoopposite effects. INTRODUCTION Blunt head trauma (BHT) is a brain injury withoutdamage to skull. It occurs in traumatic events such astransportation accidents, falls, sports-related injuries, andexplosions. While several brain injury mechanisms have been proposed, the controversies persist [1, 2]. Since understandingwave dynamics in a human brain is key to understanding braindamage in BHT, we have developed a powerful finite element(FE) head model allowing studies of head impact processes. SUMMARY OF RESEARCH Our FE head model is based on T1- and T2-weightedstructural magnetic resonance imaging (MRI) dataset of aspecific subject. Image voxels (1 mm scale) are directlyconverted to eight-node hexahedral FEs. Individual FEs areassigned tissue types based on image segmentation results. Themodel includes four different tissue types – skull, cerebrospinalfluid (CSF), grey matter, and white matter – all assumedhomogeneous and isotropic. A mesh smoothing technique isthen implemented to obtain smooth mesh surface and interfaces between different tissues to improve numerical accuracy. TheCSF is modeled using solid FEs in order to take into accountthe shear resistance provided by the arachnoid trabeculae andlarge blood vessels in the subarachnoid space. While the skulland CSF are assumed to be linear elastic, the brain tissues aretaken as linear viscoelastic in shear but elastic in bulk behavior (Table 1). Continuity of traction and displacement is assumed atmaterial interfaces. In order to take into account the effect of neck on the head motion, we consider two extreme cases: freeand fixed boundary conditions (BCs). In the first case themodel is free to move without any displacement constraint onits base surface, while in the second case the displacement isfully constrained around the area of the foramen magnum.Since rotation about the occipital condyles is involved in actualhead motion, motivated by variational principles of mechanics,we argue that the responses predicted by these two extremecases provide bounds on the actual response.Our model is first validated on the intracranial pressuredata of a frontal cadaveric impact experiment [3]. The impactforce recorded in the experiment is directly applied to themodel as a pressure input. The experimental pressure data arefound to be well bounded by the responses computed from themodels with free and fixed BCs [4]. From the simulation themaximum pressure in the brain is on the order of 10-100 KPa  and the maximum shear stress is on the order of 1 KPa .Although the shear stress is 1-2 orders lower than the pressure,it is likely that it may cause damage because brain tissues havevery small resistance to shear compared with its resistance to pressure [5]. Due to brain tissues’ high bulk and low shear moduli, the pressure wave speed is three orders of magnitudelarger than that of shear waves. Therefore, the frontal impactgives rise not only to a fast pressure wave but also to a slow,and potentially more damaging, wave of distortion. Mostinterestingly, our simulation reveals a complex pattern of shear waves which converge spherically away from the skull towardsthe brain center. However, the shear waves do not increase inintensity as they converge inward. This can be explained fromthe standpoint of a competition of wave amplification due tospherically convergent implosion with wave damping due to1 2010 USNCTAM   brain tissue viscoelasticity. Given the fact that each and everyhuman brain is statistically variable, this competition has a paradigm in a model of wavefronts evolving (and possibly blowing up) in random, nonlinear elastic-dissipative media [6].The spherically convergent shear wave pattern is alsoobserved in a side impact (Fig. 1). The pressure and shear stressin this case are about one order of magnitude greater than thosein frontal impact, suggesting that side impact to the head maycause more damage to the brain than the frontal impact. CONCLUSIONS The unique architecture of the human head, consisting of the hard solid skull, the membranes and CSF, and theviscoelastic brain core, leads to a partial conversion of theenergy of pressure impact into a shear wave convergingtowards head’s center. This finding may also contribute to theongoing debate of the brain injury mechanism due to blastwaves [2]. ACKNOWLEDGMENTS Professors T. Paus (Nottingham University) and A. Ptito(Montreal Neurological Institute) suggested this researchdirection. It is also a pleasure to acknowledge Profs. B. Suttonand S. Broglio and Mr. M. Slavenas of the University of Illinoisin connection with MRI methods. Support by the Mary Jane Neer Research Fund for Research in Disability, University of Illinois, is gratefully acknowledged. REFERENCES [1] Hardy, W.N., Khalil, J. W., and King, A.T. Literaturereview of Head Injury Biomechanics.  International Journal of Impact Engineering , 15 :561-586, 1994.[2] Bhattacharjee, Y. Shell Shock Revisited: Solving thePuzzle of Blast Trauma, Science , 319 :556, 2008.[3] Nahum, A., Smith, R., and Ward, C. Intracranial PressureDynamics during Head Impact. Proceedings of 21st StappCar Crash Conference, 339-366, 1977.[4] Chen, Y., and Ostoja-Starzewski, M., MRI-based FiniteElement Modeling of Head Trauma: Spherically FocusingShear Waves.  Acta Mechanica , 2010, DOI 10.1007/s00707-009-0274-0.[5] Holbourn, A.H.S. Mechanics of Head Injury.  Lancet,   2 :438-441, 1943.[6] Ostoja-Starzewski, M.  Microstructural Randomness and Scaling in Mechanics of Materials. CRC Press, 2008. TABLE 1 . MECHANICAL PROPERTIES OFDIFFERENT TISSUES USED IN THE FE MODEL Tissue Density(kg/m 3 )Bulk modulusK (Pa)ShorttermShear modulusG 0 (Pa)Longtermshear modulusG ∞   (Pa)Decayfactor   β   (sec -1 )Skull 2070 3.61E+9 2.7E+9 N/ACSF 1004 2.19E+7 5.0E+4 N/AGreymatter 1040 2.19E+9 3.4E+4 6.4E+3 400Whitematter 1040 2.19E+9 4.1E+4 7.8E+3 400 AB   CD   FIG. 1.   vON MISES STRESS (UNIT: PA) IN THE BRAIN(AXIAL VIEW) AT (A) 5  ms , (B) 8  ms , (C) 11  ms , AND (D)13  ms DURING 15  ms SIDE IMPACT SIMULATION. 2 2010 USNCTAM

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