International Research Journal of Applied and Basic Sciences © 2013 Available online at www.irjabs.com ISSN 2251-838X / Vol, 6 (6): 875-881 Science Explorer Publications

Finite element modeling of the human Brain Under impact conditions Mh. Lashkari1, F. Frahmand2, K. Kangarlou3 * 1. Assistant Professor, Aja University of Medical Sciences, Dept. of Surgery, Tehran, Iran. 2. Professor, Sharif University of Technology, Dept. of Mechanical Engineering, Tehran, Iran. 3. Corresponding Author*: Ph.D. in structure engineering, Moscow State University of Civil Engineering and member of Young Researchers and Elite club, central Tehran Branch, *

Corresponding Author email: [email protected]

ABSTRACT: The head is the most vulnerable part of the body during crash situations and is often involved in life-threatening injuries. The main purpose of the present work is to build and validate a numerical model of human head in order to evaluate pressure and stress distributions in bones and brain tissues due to impact. Furthermore, the Head Injury Criterion (HIC) and the recently proposed Head Impact Power (HIP) criterion were evaluated with respect to the relative motion between the skull and the brain. It was found that the influence of impact direction had a substantial effect on the intracranial response. Geometrical characteristics for the finite element model have been extracted from CT and MRI scanner images, while material mechanical characteristics have been taken from literature. The analysis is performed using the program Ansys 3D to evaluate the risk of head injury in impact. The model is validated by comparing the numerical results and the experimental results obtained by Nahum in 1977. Keywords: Impact force, Traumatic Brain Injury (TBI), Finite element Analysis, Von Mises stress, Viscoelastic material, Ansys. INTRODUCTION Head injuries due to direct impact are major sources of death and disability as the result of transportation collisions, falls, assaults, military and sport accidents. In order to gain a better understanding of head injury mechanisms, it is useful to study the dynamic response of the head-brain complex as a mechanical system subject to impact loads. During many years scientists have been trying to explain pathologies due to cerebral trauma searching for injury mechanisms, psychophysic consequences and possible treatments. The development of a computer model that allows the study of such phenomena requires the knowledge of the anatomy of the human head, the mechanical properties of the tissues involved, the representation of various forces acting on the tissues and the boundary conditions reflecting a realistic head impact scenario. Subdural hematomas (SDH) and diffuse axonal injuries (DAI) are more lethal than most other brain lesions (Becker, 1972). This is of special interest in deriving injury criteria for SDH and DAI. Gennarelli (Chen and OstojaStarzewski, 2010) suggested that SDH was produced by short duration and high amplitude of angular accelerations, while DAI was produced by longer duration and low amplitude of coronal accelerations. A threshold for DAI has been proposed (DiMasi et al.,1995), which accounts for rotational impulses in the coronal plane. Generally, the head injury criterion (HIC) (Enouen, 1986) is used when evaluating the consequences of an impact to the head. HIC is based exclusively on the resultant, translational acceleration of the head. The basis underlying HIC was first introduced as a curve fit to the Wayne State Tolerance Curve (WSTC).The basic finding described by the WSTC was that high acceleration can be withstood for short durations, while lower accelerations can be tolerated for longer intervals. Moreover, studies by Ueno and Melvin (Gennarelli et al.1987) and DiMasi et al. (www.eurailsafe.net) found that the use of either translation or rotation alone may underestimate the severity of an injury. Recently, Zhang et al. (www.eurailsafe.net) concluded that both linear and angular accelerations are significant causes of mild traumatic brain injuries. The generalized acceleration model for brain injury threshold (GAMBIT) was an early effort to combine thresholds for translational and rotational kinematics (Kleiven and Holst, 2002). Because no dependency of the impulse duration is included, the GAMBIT can be seen as a peak-

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acceleration criterion for a combined rotational and translational impulse. Recently, a new global kinematic based head injury criterion, called the head impact power (HIP), was presented (Kleiven and Holst, 2002 10. Mohan et al., 1979). In that study, it was proposed that coefficients for the different directions could be chosen to normalize the HIP with respect to some selected failure levels for a specific direction. However, values of the coefficients were not presented and information regarding directional sensitivity was lacking. The HIC and HIP, were calculated according to the formulas below: ) ∫ ( )] ( ( ) ( ) In which a(t) denotes the translational head acceleration in g's as a function of time, and t 1 and t2 represent the initial and final times of an interval that maximizes this function. In 2000 revision, maximum critical time reduced 36 ms (HIC>1000→serious brain injury) to 15 ms (HIC>700→serious brain injury). Empirically determined relationships between HIC scores and the probability of head injury (NHTSA, 1997; 1 NHTSA, 1992) are widely used in the automotive industry to estimate the risk of injury. Some have compared AIS (abbreviated injury scale) scores for real life injuries to HIC scores or other indices of injury calculated from the reconstruction (Newman et al., 2000; O’Riordain K et al., 2003). HIC and tolerance levels have been explained (Walker et al., 1973; Zhang et al., 2003) and tabulated in Table 1. [

Table 1. Levels of consciousness in relation to head injury criteria (16). Head Injury Criteria 135 – 519 520 – 899 900 – 1254 1255 – 1574 1575 – 1859 > 1860

AIS Code 1 2 3 4 5 6

∫

Level Of Brain Concussion And Head Injury Headache or dizziness Unconscious less than 1 hour – linear fracture Unconscious 1 – 6 hours – depressed fracture Unconscious 6 – 24 hours – open fracture Unconscious greater than 25 hours – large haematoma Non survivable

∫

∫

∫

∫

∫

( )

The x-axis was defined along the Posterior-Anterior (PA) direction, the y-axis along the lateral-direction, and the z-axis in the Inferior-Superior (IS) direction (Fig.1). The following values were calculated for the model: m ~ 2 2 2 4.37 kg, Ixx ~ 0.0213 kgm , Iyy ~ 0.0275 kgm , Izz ~ 0.0204 kgm . These values are in the range of reported ones by Becker (16) and Walker et al. (17). ∫

∫ ∫

∫

∫

∫ ( )

Where ai, linear acceleration at the head’s center of gravity about anatomical coordinate axis i (i=x,y,z) 2 2 (m/s ) and i, rotation acceleration about axis i (rad/s ).

Figure 1. Load directions for translational and angular acceleration pulses.

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Finite-element human head model The human head consists of three main layers surrounding and protecting the brain, as illustrated in Figure 1 (20). The dura and arachnoid mater are separated by a space called subdural space, while the arachnoid and pia mater are separated by another space called the subarachnoid space. In this subarachnoid space, there is stringlike tissue called arachnoid trabeculae, which connects arachnoid to pia mater. Within the subarachnoid space, there is also water-like fluid called cerebrospinal fluid (CSF), which provides damping and cushions for the brain under impact situations.

Figure 2. The human head layers (20).

Various numbers of head components have been modeled by the deferent authors. The head is modeled with Lagrangian elements and directly from the design (CAD 3D) drawings (Figure3).

Figure 3. FE model of the human head.

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The material data used in this study are taken from the literature and listed in Table 2 and 3. Table 2. Elastic material properties of the skull and CSF layer Density ρ (kg/m3) 2070 1004

Tissue Skull CSF

Young’s modulus E (Pa) 6.5E+9 1.5E+5

Poisson’s ratio (υ) 0.20 0.49886

Table 3. Viscoelastic material properties of the brain Tissue

Density ρ (kg/m3)

Bulk modulus K (Pa)

Short-term shear modulus G0 (Pa)

Grey matter White matter

1040 1040

2.19E+9 2.19E+9

3.4E+4 4.1E+4

Long-term shear modulus G∞ (Pa) 6.4E+3 7.8E+3

decay constant β (s-1) 400 400

In this study, we use a material model which assumes linear viscoelastic, isotropic behavior for both grey and white matter. The standard linear solid model is applied to characterize the shear behavior, and the shear relaxation modulus is described by: β () ( ( ) ∞ ∞) where G0 is the short-term shear modulus, G∞ is the long-term shear modulus, and β is a decay constant. The material parameters used are the same as those in Zhang et al. (2001). The interface between all these tissue types are modeled as tied contact. The bottom of the neck is constrained in all six degrees of freedom to avoid rigid body motion. For verifying the finite element model, the numerical results were compared with those results of the cadaver experiment by Nahum (Nahum & Smith, 1977). The impact direction was along the specimen’s midsagittal plane, and the head was rotated forward such that the Frankfort anatomical plane was inclined 45° from the horizontal plane. The outline of the experiment is shown in Fig. 2(a). In the experiment, a 5 kg iron impactor was impacted to the head at 6 m/s.

Figure 4. Experiment by Nahum (Nahum & Smith, 1977). (a)The 5 kg iron impactor impacted the frontal region of the head at 6 m/s, and intracranial pressures were measured in the frontal (point A), parietal (point B) and occipital (point C) region of the head. (b) The input force curve obtained from the experiment.

RESULTS AND DISCUSSION Figure 5 illustrate the linearly distributed pressures in the skull at t=2.5, 5, 7.5 and 10 (ms) for the models with fixed boundary conditions. The linear pressure gradients along the impact direction may be considered as a result of a quasi-static event rather than a dynamic one. On the other hand, the maximum speed of shear wave propagation in the brain is around 6.3m/s, which is three orders of magnitude less than the speed of pressure waves, so that the minimum transit time of shear waves across the brain is approximately 22 ms. When the shear wave transit time is compared to the impact pulse lasting 9ms with a rise time of 2.5 ms, the wave effects become important. Figure 6 shows a sequence of the von Mises stress fields in the brain during the 15ms duration. From

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Figure 6, a marked difference in the shear stress can be observed between two boundary conditions. The model with fixed boundary at the head/neck junction predicts larger shear stress in the brain throughout the duration. This difference in shear stress magnitude is attributed to the fact that fixed boundary causes rotational motion of the head model while the free boundary leads to nearly translational motion.

Figure 5. Distributed pressures in the skull at t=2.5, 5, 7.5 and 10 for the models with fixed boundary conditions.

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Figure 6. The von Mises stress distribution in Pa in the brain (mid-sagittal view) during a 15ms frontal impact simulation (21).

CONCLUSION It is stressed that the scaling procedures and coefficients are proposed estimations using a parameterized and detailed FE model of the human head. Although the results give insight into directional sensitivity of impacts to the human head, further experimental validation of intracranial responses for the model in response to higher rotational loads needs to be performed before new head injury criteria can be suggested. Regarding the influence of inertial forces to all the degrees of freedom of the human head, this study shows the following:

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1. The results obtained by the FEM correlate with previous clinical and animal studies. 2. HIC is unable to predict consequences of a pure rotational impulse while HIP needs individual scaling coefficients for the different terms to account for difference in load direction. 3. Three additional components, implemented as Heaviside’s step functions, should be added to the original HIP in order to take into account the differences in response between opposite directions. 4. When using the proposed scaling procedure, a better prediction of SDH was obtained. 5. Further evaluation of synergic effects of combined terms of the PI is necessary to improve the injury prediction. REFERENCES Becker EB.1972. Measurement of mass distribution parameters of anatomical segments, in: 16th Stapp Car Crash Conference, SAE techn. paper no. 720964. pps. 160–185. Chen Y, Ostoja-Starzewski M. 2010.MRI-based finite element modeling of head trauma, Springer-Verlag DiMasi F, Eppinger RH, Bandak FA.1995. ‘Computational analysis of head impact response under car crash loadings’, Proc 39th stapp car crash conf, SAE Paper No. 952718, Society of Automotive Engineers, Warrendale, PA, pp. 425–438. Enouen SW. 1986. Development of experimental head impact procedures for simulating pedestrian head injury. In: Proc. 30th Stapp Car Crash Conf., pp. 199–218. Gennarelli TA, Thibault LE, Tomei G. et al.1987. Directional dependence of axonal brain injury due to centroidal and non-centroidal acceleration. in: 31st Stapp Car Crash Conf. SAE paper no. 872197. Society of Automotive Engineers. http://www.eurailsafe.net/subsites/operas/HTML/appendix/Table13.htm http://www.eurailsafe.net/subsites/operas/HTML/Section3/Page3.3.1.4.htm http://www.tandfonline.com/loi/gcmb20 Kleiven S, Von Holst H.2002b. Consequences of brain volume following impact in prediction of subdural hematoma evaluated with numerical techniques. Traffic Injury Prevention. 3, 303–310. Mohan D, Bowman BM, Snyder RG, Foust DR.1979. A biomechanical analysis of head impact injuries to children. J. Biomech. Eng. 101, 250– 260. National Highway Traffic Safety Administration (NHTSA), Department of Transportation, 1997.FMVSS201, Head Impact Protection, 49 CFR 571.201. National Highway Traffic Safety Administration, Department of Transportation (DOT), ‘Occupant crash protection – head injury criterion S6.2 of MVSS 571.208’, Docket 69-7, Notice 5, NHTSA, Washington, DC, 1972. Newman JA, Shewchenko N, Welbourne E. ‘A proposed new biomechanical head injury assessment function – the maximum power index’, Proc 44th stapp car crash conf, SAE Paper No. 2000-01-SC16, 2000. Newman JA.1986. ‘A generalized acceleration model for brain injury threshold’, Proc IRCOBI conf, pp. 121–131. O’Riordain K, Thomas PM, Phillips JP, Gilchrist MD. 2003.Reconstruction of real world head injury accidents resulting from falls using multibody dynamics. Clin Biomech 18:590–600. Prasad P, Mertz HJ. 1985. The position of the United States delegation to the ISO working group on the use of HIC in the automotive environment. SAE Paper 851246 Society of Automotive Engineers, Warrendale PA, USA. Ueno K, Melvin JW.1995. ‘Finite element model study of head impact based on hybrid III head acceleration: the effects of rotational and translational acceleration’, J Biomech Eng, 1995 117 (3) 319–328. Walker LB, Harris EH, Pontius UR. 1973. Mass, volume, center of mass, and mass moment of inertia of head and head and neck of human body, in: 17th Stapp Car Crash Conference. SAE technical paper no. 730985. pps. 525–537. Zhang L, Yang KH, King AI. ‘A proposed injury threshold for mild traumatic brain injury’, J Biomech Eng, 126 (1) 226–236. Zhang L, Yang KH, King AI.2001. Comparison of brain responses between frontal and lateral impacts by finite element modeling. J. Neurotrauma 18, 21–30. Zhang L, Yang KH, King AI.2004. ‘Comparison of brain responses between frontal and lateral impacts by finite element modeling’, J Neurotrauma, 2001 18 (1) 21–30.

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