Numerical Model of the Human Head under Side Impact

Transcription

1 J. Basic. Al. Sci. Res., 3(3)47-474, 3 3, TextRoad Publication ISSN Journal of Basic and Alied Scientific Research Nuerical Model of the Huan Head under Side Iact Behrooz Seehri (PHD), Shahaboddin Oidian Deartent of Mechanics, Mashhad Branch, Islaic Azad University, Mashhad, Iran ABSTRACT Head injury constitutes aroxiately 5 ercent of all injuries sustained in transition and it is a coon injury in sort and other huan activities. Matheatical odels rovide owerful tool in the analysis of the echanics of head iact. In articular the finite eleent ethod lends itself for the construction of a atheatical head odel because of its caability to describe colex geoetries. In this study huan head dynaic resonse to side iact is consider with finite eleent ethod. A two diensional odel of coronal section of huan head has been designed using the actual huan anatoy. The reference odel consisting of the three layer of skull (inner layer and outer layer are coact bone and id layer is songy bone), cerebral sinal fluid (CSF), brain ebranes (falx cerebri and tentoriu) and brain tissue. The odel is loaded by a sinusoidal ulse with a eak ressure of 4 kpa. Finite eleent analysis was conducted using Ansys software. Tie-ressure history in the cou ressure region was studied. The urose of this study was to deterine the effects of the ebrane and effects of viscoelastic aterial roerties for brain tissue on the dynaic resonse of the brain during side iact. In the reference odel as oosed the reality-no relative otion at all is ossible between brain and skull at their interface. Therefore the skull-brain interaction has been investigated in a araetric study using a contact algorith. KEYWORD: head injury, finite eleent, contact algorith, viscoelastic, transient resonse. -INTRODUCTION The huan head is one of the ost vulnerable arts of huan body, when subjected to an iact loading. Every year any unfortunate victis suffer brain traua. Head injury echaniss have been roosed for any years and in site of uch research devoted to their verification, there are still any unanswered question. In articular, the echanical factor causing brain dysfunction is still not cleared. It has been hyothesized that intracranial ressure during head iact roduce brain contusions and that relative dislaceent between the brain and skull roduce shear stresses in the brain causing cerebral bruising and heorrhage. [,] The study of huan head under iact conditions ay be slit in two tasks. Firstly: the calculation of the deforation atterns of the skull and its contents as a result of an iact loading and secondly the identification of ossible relationshis between a articular deforation in a tissue and an injury in this tissue. For the first task, nuerical odel rovide a owerful toll for the siulation of the deforations. They reduce the necessity of erforing large nuber of exerients. Moreover they enable the calculation of tissue loads and deforations that cannot ossibility be deterined in exerient. For the second tasks, exerients need to be erfored to deterine the level of resonse at which the biological tissues fail to recover. The focus in this study will be on the first task, the siulation of the deforation of the huan head using the nuerical odel. The objective of this study was to deterine the affects of ebranes on the brain rotection, the aterial roerty of the brain tissue, free contact between the brain and scull in the transient load. -MATERIALS AND METHOD --Nuerical odel Reference head odel have been obtained using MRI scan and actual huan head geoetry [3,4]. The above data have been digitalized for different surfaces of the head consisting of 3 layers of skull, 3 surfaces of brain tissue, cerebral sinal fluid (CSF) and falx, tentoriu ebrane aking u the boundary of the odel. Fig. [5]. Affect of brain-skull contact has been odeled using the actual structure fro the above data. In the reference odel the brain-skull contact is in couled for, while that of extended odel the free contact between the brain and skull has been taken into account, roviding a relative otion to the internal arts. (Figures., 3). *Corresonding Author: Behrooz Seehri, Deartent of Mechanics, Mashhad Branch, Islaic Azad University, Mashhad, Iran, E-ail: b_seehr@yahoo.co 47

2 Seehri and Oidian, 3 Fig..D odel of head coronal section Fig. Meshing odel of free contact Fig.3 contact eleent between brain and skull -- Constitutive equations The deforation of a continuu is governed by a set of two equations, describing conservation of ass and balance of oentu. [6, 7] d () d Where is the density of the continuu and V the volue occuied by the aterial. The equation of otion (balance of oentu) states that the tie rate of change of the total oentu of the continuu equals the vector su of all the external forces acting on the continuu:. b u () That denotes the stress tensor, b the body force vector er unit ass and u the dislaceent vector. The interactions between two or ore continua that are in states of contact are echanically accented for by alying a set of kineatics and dynaic conditions for each of the continua. These conditions are rescribed for those arts of the boundary that actually coe into contact. This art of the boundary of a continuu A is denoting by A e. For frictionless contact the contact conditions are:. No enetration ay occur during the eriod of tie the two continua are in state of contact. For two oints P and Q (with aterial coordinates and Q ), belonging two body A and B, resectively, the requireent of no enetration can be forulated as Q Q B Q (3) u, t] [ x u, t]). n, t ([ x A B Q Where X denote the initial osition of a oint and n, t n, t are be outward noral of the continua at the oints of contact.. The contact forces in the oint of contact are equal but oosite in sin for each of the bodies. A A B Q B Q, t. n, t, t. n, t (4) 3. Only coressive forces are transitted between the two continua in the oint of contact. A A (5), t. n, t 47

3 J. Basic. Al. Sci. Res., 3(3)47-474, 3 The contact conditions for contact without friction in Lagrange ultilier ethod are now restated as g (6) g The set of equations are obtained using finite eleent ethod, by taking the, g q equation into account with free resistance assution after substitution of contact forces ( f. n t oentu equation. M u c K u f c k k k, q(, g ) c f c, (8) (7) ) in the k For to the dislaceent degrees of freedo u, a Lagrange ultilier is added to the colun of unknown degrees of freedo for each node that coes into contact, where this extra unknown reresents the noral contact force. For every node that coes into contact an equation is added to the total syste of equations. The advantage of this ethod is that the contact conditions exactly et. -3-Material roerties The skull is reresented as a hoogenous isotroic structure with linear elastic aterial behavior [8-3]. The inner table, outer table of skull has coact bone characteristics, and diole with songy bone characteristics. In the reference odel the skull content with linier elastic characteristics was taken into account. Table. shows the aterial characteristics of head tissues. Head Tissue Outer Table Diloe Inner Table CSF Mebrane Brain Table. aterial characteristics of head tissues E(a) Kg ( ) 3.e e9 75.e9 3.48e e e Iact load and boundary conditions The boundary conditions and the load tye for both reference and free contact odels are the sae. Rotation of the head on the neck has been taken into account for the boundary conditions in the odel, where soe arts of the nods are taken as single hinge and soe others as double suort.fig.4. A side ressure with axiu alitude of 4 Ka in a sinusoidal ulse for was eloyed in the odel with s duration. Fig 5. Fig.4 Scheatic boundary conditions Fig.5 Sinusoidal ulse for was eloyed in the odel 47

4 Seehri and Oidian, 3 3-RESULT 3--Variation of linear viscoelastic brain roerties Siulation with the viscoelastic odel for two different values of the tie constant were coared with each other and with the elastic reference odel. The short ter behavior, governed by G, was derived fro the Young's odulus user for the reference odel. The values used for the araetric variation are suarized in table..the case with reresent a fast decays of the aterial stiffness whereas the 4 odel with lies between the forer value and the elastic aterial odel used in the reference odel. For the tie interval analyses ( s) it is exected that for the tie constant full relaxation of the aterial will have taken lace, before any significant ressure build u occurs. The ressure tie history for the side region in the brain are resented in figure 7. descrition Table. values used for the araetric studies G ( N ) G ( N ) 5.8e5.68e5 5.8e5.68e5 ( s ) e e 4 Kg ( 3.4e3.4e3 ) ( _ ) The decay in aterial stiffness becoes aarent after about s, and is best seen in the result for the ressure for the value. The trend seen was that the larger tie constant led to higher ressure levels than the saller tie constant. Fig.7 ressure tie history for various tie constant 3--relative otion between skull and brain A new odel was constructed by decouling the brain fro the skull in the reference odel. With this arrangeent nuber of eleents in reference odel was increased fro 4767 to 344 in the free contact odel, of who 433 are of contact eleents. Between the brain and the skull the corrected contact algorith, resented in above was alied. The result for the ressure in the cou is resent in fig 8. Fro the result it ay be directly concluded that the free skull-brain interface has a large influence on the result. The ressure tie histories for the cou region show uch lower alitude than the calculated ressures with the reference odel. Dou to the alication of contact algorith only coressive forces can be transferred across the interface. Fig. 8 cou ressure for the reference odel and free contact odel 3-3-Anatoical detail of the odel The falx cerebri and tentoriu have a iortant function in the huan head. The hyothesis regarding their echanical function is that when the head is iacted, they suort the cerebru. The odified odel 473

5 J. Basic. Al. Sci. Res., 3(3)47-474, 3 is consisting of all the reference odel arts excet for the falx and tentoriu ebranes, and connection between all structures are couled. Different arts of the odel are shown in figure 9. The intracranial contents were attached to the skull, and all additional substructures were also rigidly connected to each other. No relation otion was therefore ossible between brain and skull and skull and between searate structures. All the structure reresented as hoogeneous linear elastic aterial. Figure. deicted the calculated ressure in the cou region of the brain in coarison with the results calculated using the reference odel. The cou ressure for the new odel show a increase of axiu attained ressure level in coarison with the reference odel. Decrease in the ressure in the reference odel indicated the rotective nature for cerebru tissue. Fig. 8 Modified odel without ebrane 4-conclusion Fig. 9 Coarison of cou ressure in odels with and without ebrane The aterial roerties and ethod of odeling the skull-brain interface showed to significantly change the result for ressures for cou region in the brain. For brain tissue viscoelastic aterials the trend seen was that the larger tie constant led to higher ressure levels than the saller tie constant. In the contact odel the ressure-tie histories for the cou region show uch lower alitude than the calculated ressures with the reference odel. A geoetrically realistic D finite eleent odel of the huan head was develoed based on CT and MRI data. REFERENCES - Ward. C. C and Thoson. R. B." The Develoent of a Detailed Finite Eleent Brain Model,"roc.9 th sta car crash conf. SAE aer No.756, Nahu, A. M, Ward. C. C, Rasch, E., Adas, S., and Schneider, D., "Exeriental Studies of Side Iact," roc. 4 th sta car crash conf., SAE aer No. 83, Naval biodynaic laboratory arch (988).Anthrooetry and ass distribution for huan Analogues, New Orleans, and LA U.S. National library of Medicine (996). The Visible Huan roject. World Wide Web Page: htt:// huan. htl. 5-Fung, Y. C, (993), Bioechanics: Mechanical roerties of living tissues. Sringer- Verlag, Berlin. 6- Wriggers, P. (), Coutational contact echanics. John wily &Sons Inc, West Sussex PO9 8SQ, England 7-Wang, Y.C, V. Murti and S. Vallian (99). Assesent of the accuracy of the newark ethod in transient analyses of wave roagation robles. Earthquake Engineering and Structural Dynaics,, Ruan, J.S, T. Khalil and A.I. King (99).Huan head dynaic resonse to side iact by finite eleent odeling.journal of Bioechanical Engineering, 3, Arbogast. K. B. and D. F. Meaney (995). Bioechanical characterization of the constitutive relationshi for the brainste. In roceeding 39 th sta car crash conference, SAE aer 9576, ages Sringer- Verlag, Berlin. -Galford, J. E, and J. H, McElhaney (97).A viscoelastic study of scal, brain and dura. Journal of bioechanics, 3, -. -Oaya, A. K, L. Thibault, and F. A. Bandak(994). Mechaniss of head injury. International Journal of Iact Engineering, 5(4), Ruan, J.S, T. Khalil and A.I. King (994). Dynaic resonse of the huan head to iact by threediensional finite eleent analysis. Journal of Bioechanical Engineering, 6,