Development and validation of two subject-specific finite element models of human head against three cadaveric experiments

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERINGInt. J. Numer. Meth. Biomed. Engng. 2014; 30:397–415Published online 5 November 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cnm.2609

Development and validation of two subject-specific finite elementmodels of human head against three cadaveric experiments

Kwong Ming Tse 1,*,†, Long Bin Tan 1, Shu Jin Lee 2, Siak Piang Lim 1,3 andHeow Pueh Lee 1,3,*,†

1Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 1175762Division of Plastic, Reconstructive and Aesthetic Surger, National University Hospital, 5 Lower Kent Ridge Road,

Singapore 1190743National University of Singapore (Suzhou) Research Institute, 377 Lin Quan Street, Suzhou Industrial Park, Jiang Su,

People’s Republic of China, 215123

SUMMARY

Head injury, being one of the main causes of death or permanent disability, continues to remain a majorhealth problem with significant socioeconomic costs. Numerical simulations using the FEM offer a cost-effective method and alternative to experimental methods in the biomechanical studies of head injury.The present study aimed to develop two realistic subject-specific FEMs of the human head with detailedanatomical features from medical images (Model 1: without soft tissue and Model 2: with soft tissue anddifferentiation of white and gray matters) and to validate them against the intracranial pressure (ICP) andrelative intracranial motion data of the three cadaver experimental tests. In general, both the simulated resultswere in reasonably good agreement with the experimental measured ICP and relative displacements, despiteslight discrepancy in a few neutral density targets markers. Sensitivity analysis showed some variations in thebrain’s relative motion to the material properties or marker’s location. The addition of soft tissue in Model2 helped to damp out the oscillations of the model response. It was also found that, despite the fundamen-tal anatomical differences between the two models, there existed little evident differences in the predictedICP and relative displacements of the two models. This indicated that the advancements on the details ofthe extracranial features would not improve the model’s predicting capabilities of brain injury. Copyright ©2013 John Wiley & Sons, Ltd.

Received 27 March 2013; Revised 12 September 2013; Accepted 11 October 2013

KEY WORDS: finite element (FE); head injury; head model; computed tomography (CT); magneticresonance imaging (MRI); soft tissues; sensitivity

1. INTRODUCTION

In the past few decades, tremendous efforts had been made in the area of traumatic head impact,especially those regarding motor vehicle crashes. Experiments involving cadavers, animals, or phys-ical human simulacra (or dummies) have been performed extensively to investigate traumatic headinjury problems. There are, however, various issues regarding ethical and technical aspects. Forinstance, damaged dummy parts, after being used in experiments, require replacement which incurscosts. Moreover, some of the internal biomechanical responses of the brain cannot be measuredeasily by experimental techniques. With rapid advance in computational facilities, the FEM, whichhas been widely used in the biomedical field [1–5], offer a cost-effective alternative to experimen-tal methods in estimating the internal biomechanical responses of the human head or is at leastconsidered as a necessary alternative for experimental laboratory tests.

*Correspondence to: Kwong Ming Tse and Heow Pueh Lee, Department of Mechanical Engineering, National Universityof Singapore, 9 Engineering Drive 1, Singapore 117576.

†E-mail: [email protected] or [email protected] (Tse, K.M.); [email protected] (Lee, H.P.)

Copyright © 2013 John Wiley & Sons, Ltd.

398 K. M. TSE ET AL.

Since 1970s, there had been a number of attempts to construct finite element head models(FEHMs). The first attempt to model the behavior of the human head response by means of a finiteelement (FE) model was made by Hardy and Marcal [6] in their skull-only two-dimensional (2-D)FEHM. Their skull-only model was subsequently improved by Shugar [7] by adding an elastic fluid-filled brain which was assumed to be firmly attached to the skull. The early three-dimensional (3-D)FEHMs developed by Chan [8], as well as by Khalil and Hubbard [9] were generally simplified withregular geometry (spherical or ellipsoidal solid or shell). A 3-D homomorphic model representingthe basic anatomy of the head and neck was developed by Hosey and Liu [10] in 1981.These ear-lier FEHMs, which were developed mainly based on idealized geometry with simplifications in thefacial details and are generally considered unrealistic nowadays, did represent a first step in the theo-retical analysis of head injury biomechanic. It was only in the 1990s when the computing capabilityhad advanced to the point that the development of more realistic and comprehensive 3-D FE modelsof the human head, based on actual geometry of the human head, was possible.Among the existingFEHMs, the leading ones commonly reported in the literature are the Wayne State University BrainInjury Model (WSUBIM) developed by Ruan et al. [11] and later improved by Zhou et al. [12] andZhang et al. [13]; the University of Louis Pasteur FEHM by Kang and Willinger [14]; the KungligaTekniska Högskolan FEHM by Kleiven [15]; the Simulated Injury Monitor FEHM by Takhountsand Eppinger [16] in 200; and the University College Dublin Brain Trauma Model by Horgan andGilchrist [17].

The experimental validation of numerical model, before its applications, is necessary in deter-mining the degrees to which a model accurately predicts the physics of the real-world phenomenait is designed to replicate. Only when this is achieved, it does represent a powerful tool with whichto correlate the biomechanical parameters involved in the head injury with the clinical observations.Many of the FEHMs [11, 13, 15–20] had been validated against the intracranial pressure (ICP) dataof Nahum et al. [21]’s cadaver experiments, with some [13,15,19,22] having been validated againstadditional pressure historical data of Trosseille et al. [23]’s long duration impact. However, there iscontroversy about the appropriateness of validation using just pressure data [24] as diffuse axonalinjury is found to be dependent on strain rather than pressure [25]. To the authors’ knowledge,only WSUBIM [13], Tekniska Högskolan FEHM [15] and University College Dublin Brain TraumaModel [22] had been validated against experimental relative displacement data between the skulland the brain provided by Hardy et al. [26].

The objective of the research presented here is to build a more detailed, in regards to biomechan-ical aspects, a more appropriate and realistic model of subject-specific head using medical imagingdevices such as computed tomography (CT) or magnetic resonance imaging and to validate it againstboth ICP and strain data of the experimental cadaver tests under different impact conditions. Thepurpose is to better predict the mechanical responses of the human head during the time at whichhead injury occurs.

2. METHODS AND MATERIALS

2.1. Model description

In the present study, geometrical information of the human skull was obtained from 460 axial imagesof a middle-aged men with in-plane resolution of 512 by 512 pixels with a pixel size of 0.488 mmand slice thickness of 1.0 mm, collected from a set of enhanced CT scan data. Because of the lowvisibility of soft tissues in CT data, the magnetic resonance imaging data of the brain of anotherhealthy subject, with in-plane resolution of 1659 by 962 pixels with a pixel size of 0.500 mm andslice thickness of 4.0 mm, was employed for the segmentation of the model’s brain (Figure 1).These medical images were imported into Mimics v13.0–v14.0 (Materialise, Leuven, and Belgium)for segmentation and reconstruction of two assembled models of a human head and brain, namelya skull-brain model without soft tissue (Model 1) and the one with soft tissue (Model 2). It shall behighlighted that Model 2 had further differentiation of the cerebrum in gray matter, white matter,and ventricles (Figure 1).

A semi-automatic meshing technique was employed in HyperMesh v10.0 (Altair HyperWorks,Troy, MI, USA) to optimize between computational efficiency and element quality, with the average

Copyright © 2013 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Biomed. Engng. 2014; 30:397–415DOI: 10.1002/cnm

DEVELOPMENT & VALIDATION OF 2 SUBJECT-SPECIFIC FE MODELS OF HUMAN HEAD 399

Figure 1. (A) Various components of a subject-specific model of the human skull and brain (Model 1) seg-mented by Mimics, from computed tomography and magnetic resonance imaging data. The meshed modelon the right shows the mid-sagittal view of the skull and cerebral spinal fluid except the brain. (B) Variousintracranial components of Model 2, which includes soft tissues as well as more detailed segmentation ofthe brain components, are shown in this figure. The meshed model on the right shows the complexity of the

integration of the brain tissues into its segmented components.

element size of 1.35 mm and 1.57 mm, as well as aspect ratio of 1.75 and 1.61 for Model 1 andModel 2, respectively. It shall be noted that mesh convergence study was not performed due to thecomplexity of the models’ mesh. However, this was justifiable as the mesh sizes in the two modelswere comparable or relatively smaller than other existing head models.



Table I. Element number and element type in Model 1 and Model 2.

Model 1 Model 2

Components No. of Elements Element type No. of Elements Element type

Brainstem 3021 Linear hexahedral 6104 Linear tetrahedralCerebral Peduncle — — 1762 Linear tetrahedralCerebellum 16919 Linear hexahedral 21727 Linear tetrahedralCerebrum 151598 Linear hexahedral — —CSF 24486 Linear hexahedral 164864 Linear tetrahedralGray Matter — — 436917 Linear tetrahedralLateral Cartilage 1662 Linear hexahedral 2874 Linear tetrahedralSeptum Cartilage 1004 Linear hexahedral 3578 Linear tetrahedralSkull Bone 197720 Linear hexahedral 130482 Linear tetrahedralSoft Tissues — — 253894 Linear tetrahedralTooth 6766 Linear hexahedral — —Ventricles — — 36776 Linear tetrahedralWhite Matter — — 278925 Linear tetrahedral

All Components 403176 1337903

Model 1 consisted of a cranial skull with detailed facial bone features, teeth, cervical vertebrae,nasal septal cartilage, nasal lateral cartilages; brain components such as cerebrum, cerebellum andbrainstem, as well as the cerebrospinal fluid (CSF) separating the skull and the brain. The entireModel 1 weighted 4.82 kg and consisted of 483711 nodes and 403176 linear hexahedral elements(Figure 1 & Table I). As for Model 2, besides the additional soft tissue overlying the skull andnasal cartilages, the intracranial contents were further separated into white matter, gray matter,the cerebral peduncle (midbrain), and the entire ventricular system (i.e., bilateral lateral ventri-cles, third and fourth ventricle). The models also contained some of the interior details such asair-containing sinuses, namely frontal sinus, sphenoidal sinuses and maxillary sinuses. These infe-rior details have often been ignored in earlier models. The entire detailed FE model of human head(Model 2) weighted 4.73 kg and consisted of 327536 nodes and 1337903 linear tetrahedral elements(Figure 1 & Table I). Similar to many other studies [13,19,22,27], approximately two to three layersof solid elements were used to model the CSF between the skull and the brain tissue.

2.2. Material properties

From the biological perspectives, bone is microscopically considered to be a complex, multipha-sic, heterogeneous, and anisotropic structure [28]. In most previous FEHMs, however, it has beenconsidered to have homogeneous and isotropic behavior [6, 29, 30]. It is not possible to quan-tify the whole anisotropic structure of a bone organ with current techniques, although only onestudy with simple geometry [31] did include the anisotropic behavior of bone, but with a spatiallyconstant anisotropy ratio [28]. As for a complex structure, like the human skull, it is modeled aslinear elastic, isotropic materials similar to the other skeletal tissues such as cartilages, teeth, andcervical vertebrae.

Most of the recent established FEHMs have adopted a linear viscoelastic material behavior com-bined with the large-deformation theory, for the brain, to simulate the time-dependent relativeskull-brain motion [32–34]. This viscoelastic behavior of the brain has been characterized as inshear with a deviatoric stress rate dependent on the shear relaxation modulus, whereas the com-pressive behavior of the brain has been considered as elastic. The shear characteristics of this linearviscoelastic behavior of the brain have been given in the following expression:

G.t/DG1C .G0�G1/ e�ˇt (1)

where G1is the long-term shear modulus measured in MPa; G0is the short-term shear modulus inMPa; and ˇ is the decay factor in s�1.



Table II. Material properties of both the intracranial and extracranial components used in the models.

Material Properties

Young’s Modulus, E (MPa) Poisson’s Density,Components G.t/DG1C .G0 �G1/e

�ˇt ratio, � �.kg=mm3/ References

Brainstem G0 D 0.0225MPa,G1 D 0.0045MPa, 0.4996 1.06E-06 [22]ˇ D 80 s�1

Cerebral G0 D 0.0225MPa,G1 D 0.0045MPa, 0.4996 1.06E-06 [22]Peduncle ˇ D 80 s�1

Cerebrum G0 D 0.528MPa,G1 D 0.168MPa, 0.48 1.14E-06 [19, 34, 44–46]ˇ D 35 s�1

Cerebellum G0 D 0.528MPa,G1 D 0.168MPa, 0.48 1.14E-06 [7, 19, 34, 44, 46]ˇ D 35 s�1

CSF E D 1.314 0.4999 1.04E-06 Based on E D 3K.1� 2�/using KD 2190MPa [47, 48],� D 0.4999 [47]

Gray Matter G0 D 0.034MPa,G1 D 0.0064MPa, 0.4996 1.04E-06 [47, 48]ˇ D 700 s�1

Lateral Cartilage E D 30 0.45 1.50E-06 [49]Septum Cartilage E D 9 0.32 1.50E-06 [50]Bone E D 8000 0.22 4.74E-06 (Model 1); [48]

1.21E-06 (Model 2)Soft Tissues E D 16.7 0.46 1.04E-06 [38, 48]Tooth E D 2070 0.3 2.25E-06 [51, 52]Ventricles E D 1.314 0.4999 1.04E-6 Based onE D 3K.1� 2�/

usingK D 2190MPa [47, 48],� D 0.4999 [47]

White Matter G0 D 0.041MPa,G1 D 0.0078MPa, 0.4996 1.04E-06 [47]

All the material properties used in the research presented here, for the two FE models of thehuman head, are summarized in Table II. Both models involved different components, and the den-sities of these components were adjusted, respectively, in order to achieve the average human headand neck weight according to the recent review paper by Yoganandan et al. [35].

2.3. Interface conditions

The boundary conditions at the interfaces between various components of the head, especially theskull-brain interface, have been one of the most important aspects in FE modeling of the humanhead. The separation of the skull-brain structures by CSF allows relative motion between the skulland the brain during head impact. Following what most of the established FEHMs have implementedin their models [12, 34, 36, 37], the CSF layer has been modeled as linear elastic solid material withlow stiffness and low shear modulus. Additionally, contact conditions such as tangential slidingboundary condition, with the coefficient of friction of 0.2 [15, 38, 39], as well as normal hard con-tact pressure-overclosure boundary condition, have been applied on the interfaces between skulland CSF as well as CSF and brain tissues. All the interfaces between other intracranial contents andthose between skull, cartilages, and teeth have been implemented with tie constraints. The interac-tions between the head and the foreign impactors used in the three experiments have been defined bya contact algorithm, which has hard contact pressure-overclosure with default constrain enforcementmethod [40].

2.4. Experimental and simulated impacts

2.4.1. Nahum et al. [21]’s impact force, intracranial acceleration, and pressure data for short dura-tion impulse. The models were first validated against the ICP-time histories produced by Nahumet al. [21]’s cadaver experiment 37. In Nahum et al. [21]’s experiment 37, the seated cadaver sub-ject, with its upper torso restrained from motion, was impacted by a cylindrical mass of 5.59 kgwith constant velocity of 9.94 m�s�1, at the frontal bone region. The impact was along the speci-men’s mid-sagittal plane in an anterior-posterior manner, with the specimen’s head rotated forwardwith its Frankfort anatomical plane inclined 45ı from the horizontal. In each of the experiments of



Nahum et al. [21], the impactors surface was covered by unknown, yet unmentioned, padding mate-rials with various density and stiffness [21, 41], to alter the impact duration, as well as to minimizethe possibility of skull fracture. Pressure histories during impact were measured and recorded usingpressure transducers at the five locations of the brain tissue, namely the frontal region where theimpact was; the parietal region immediately posterior and superior to the coronal and squamosalsuture; the occipital region inferior to the bilateral lambdoid suture; and the occipital region at theposterior fossa.

In order to replicate the impact conditions, the Frankfort anatomical plane of the models, whichpasses through the superior edges of the two auditory meati and two intraorbital notches, is madeto be inclined at 45˚ with respect to the axis of the 5.59 kg cylindrical rigid impactor of diameterof 152.4 mm (or 6 inches) and 40 mm thickness (Figure 2A1 & Figure 2B1). In addition, variousmaterial models of foam paddings were employed and tested in order to reproduce the impact force-time history of Nahum et al. [21]’s experiment 37. It was found that the viscous foam model inAbaqus v6.10 (SIMULIA, RI, USA) [40] with appropriate material constants best replicate Nahum[21]’s experimental impulsive force-time graph (Table III). The thickness of the foam padding waschosen to be 44.45 mm (or 1.75 inches). A free boundary condition, which means there was no con-straint in the head’s 6 degrees of freedom, was used at the neck junction since Ruan et al. [42] and

Figure 2. Impact scenario in the cadaver experiments of (1) Nahum et al. [21]; (2) Trosseille et al. [23]; and(3) Hardy et al. [26] for (A) Model 1 and (B) Model 2.

Table III. Material Properties of the foam padding used for Nahum et al. [16]’s experiment 37.

Foam Padding Material Properties References

Density, �.kg/mm3/ 2.00E-08 [53, 54]Viscous Foam Material ConstantsInitial Young’s Modulus, E10(MPa) 0.017 Modified from Kleiven’s dataExponent in the power law for Young’s modulus, n1 4 Modified from Kleiven’s dataInitial value of the viscous coefficient, �20 0.0102 Modified from Kleiven’s dataYoung’s modulus, E20(MPa) 85 Modified from Kleiven’s dataExponent in the power law for the viscosity, n2 0.8 Modified from Kleiven’s dataPoisson’s ratio, � 0.05 Modified from Kleiven’s data



Willinger et al. [43] showed that the neck does not influence the kinematic responses of the head forshort duration impact (<15 ms) (in Nahum’s case, the impact duration was approximately 6 ms).

2.4.2. Trosseille et al. [23]’s intracranial pressure data for long duration impulse. As for longerduration impact (>15 ms), the experimental data chosen for validation were the experimental studyby Trosseille et al. [23] with six tests involving three cadavers. One of Trosseille’s experiments(experiment MS 428-2) was designed to replicate the head impact against the steering wheel of amotor car, and the seated cadaveric specimen was impacted at the face by a 23.4 kg impactor at avelocity of 7 m�s�1 in the anterior-posterior direction.

To simulate the Trosseille et al. [23]’s experiment, the FEHMs in the present study were impactedat the nasal region with the steering wheel, which was modeled as a rigid cylindrical of diameterof 250 mm and height of 40 mm, with inertial mass of 23.4 kg (Figure 2A2 & Figure 2B2). Ashypothesized by Willinger et al. [19], the effect of neck responses in the kinematics of the modelneed to be considered for long duration impact (�15 ms). The fixed boundary condition was,therefore, prescribed at the bottom surface nodes of the C6 vertebrae.

2.4.3. Hardy et al. [26]’s localized brain motion data. Besides the two experimental validationsagainst ICP mentioned previously, the models present in this study were also validated against therelative displacement data between the skull and the brain, provided by Hardy et al. [26]’s experi-ment C383-T1 frontal test. In Hardy et al. [26]’s experiment, high-speed biplane x-ray and neutraldensity targets (NDTs) were used to measure brain displacement and deformation of the cadavericspecimens when the specimens’ head was impacted at the frontal bone region at 45ı by a fixedangled acrylic block of 25 mm wide and 250 mm long [55], similar to Nahum et al. [21]’s study(Figure 2A3 & Figure 2B3). The cadaveric head was brought to a desired impact speed of 3 m s�1

by a pneumatic piston which slid along the piston rod attached to an adjustable fixture that interfacedwith the carriage and the brow of the head [55]. In the experiment C383-T1 frontal test, one anteriorcolumn (AC) of six NDTs of 10 mm spacing between the centers of the NDTs, was implanted inthe frontal lobe, whereas another posterior column was 80 mm posteriorly apart from the AC andplaced in the parietal lobe. Both columns were in the right hemisphere of the brain [55] (Figure 3).

In the simulation, the entire FEHMs were prescribed with the desired constant velocity towarda fixed angled block, which was modeled as a deformable body with acrylic material properties,with Young’s Modulus of 3200 MPa, Poisson’s ratio of 0.4, and density of 1185 kg�m�3. A fixityboundary condition was applied to the parallel side of the angled block in the impact direction.Thebottom surface of the neck was prescribed with displacement constraints in 5 degrees of freedom,except in the line of impact action, to simulate the motion of the head neck assembly attached on thepiston which slid along the piston rod. An additional step was created for the head motion before theimpact when the head and neck assembly was moving at the desired constant velocity as the exper-imental impact was prepared in such a way to minimize the flexure of the neck during accelerationand to maintain the initial conditions prior to the impact [55].

All the previously mentioned transient simulations were performed using the explicit codes inAbaqus v6.10 (SIMULIA, RI, USA). It should be noted that reduced integration scheme withenhanced hourglass control in Abaqus v6.10 (SIMULIA, RI, USA) [40] was used in the simula-tions to prevent instability of elements, particularly the brain elements, due to the unacceptably highhourglass energies when using reduced integration. Moreover, the gravitational effect was not simu-lated in this study because it was considered negligible as compared with high levels of accelerationthat would result in such high-speed impacts.

2.5. Evaluation of the results

To better correlate the results from experiments and simulations, Pearson correlation coefficient, r,whose formulation is given as in the succeeding text, had been used in the study [56].

CorrelationCoefficient, rDnPniD0 .XiYi/�

PniD0Xi

PniD0Yiq

nPniD0X

2i �.

PniD0Xi/

2qnPniD0Y

2i �.

PniD0Yi/

2(2)



Figure 3. Neutral density target column implantation configurations for (A) Model 1 and (B) Model 2 inHardy et al. [26]’s C383-T1 (Group A) test. It should be noted that the each of the neutral density targetmarkers consists of a cluster of several elements in which the elemental average values of the strain dataare collected. (C) The bar chart shows the percentage of material components in each of the neutral density

target marker clusters.

where X is one of the paired data set which is being compared with. In this case, it refers to theexperimental data;

Y is the other set of data. In this study, it refers to the simulation data sets for each individ-ual model;

n is the data size.



3. RESULTS AND DISCUSSIONS

3.1. Experimental validation against impact force, intracranial acceleration, and pressure data forshort duration impulse

Figure 4 shows the comparison between the experimental and simulated impact force and accelera-tion. It can be observed that the impulsive force-time graph of Model 2 has lower peak and longerimpulse duration. This behavior can be attributed to the additional ‘cushioning’ layer of soft tissue.As seen from Figure 4B, the calculated accelerations of the center of gravity of the FE models of thehuman head gave magnitudes and characteristics similar to the experimental results (with coefficientof correlation of 0.936 for Model 1 and 0.957 for Model 2) (Figure 5A).

Unlike the uniform distribution of ICP across the brain as reported by Willinger et al. [19], theICP in Model 2 was not completely uniform across the brain tissues (Figure 6). This was probablydue to the difference in the material properties of various intracranial contents, resulting in variationin stress wave speed in various intracranial contents.

Figure 7 shows the ICPs at various locations of the brain for the two models. General shape trends,magnitudes, and duration of the pressure pulses in the simulation agreed well with the experimentalpressure pulses, except for the bilateral occipital pressures and posterior fossa pressure of Model 1.In Model 1, the simulated pressures at the posterior part of the brain tended to have shorter troughduration, even though the trends and trough pressure magnitudes matched very well with that of theexperiment. As for Model 2, the trough duration in bilateral occipital and posterior fossa regionswas more comparable with that of the experimental results, but with overestimated troughs (13.9%and 17.6% for two bilateral occipital pressures; 11.7% for posterior fossa pressure). As seen fromFigure 7, there existed a rapid rise in pressure after the trough in Model 1, followed by several oscil-lations of significant amplitude, in the bilateral occipital regions, as well as in the posterior fossa.This discrepancy perhaps arose as a result of the difference of the intracranial material and dampingproperties between the model and the real human head. On the other hand, the general trend andduration of the occipital and posterior fossa pressure pulses matched reasonably well with experi-mental pressure (with correlation coefficient of 0.944, 0.829, and 0.924, respectively), except for theoverestimated peak magnitudes and the slight oscillations after peak pulses (Figure 5A). Unlike theexperimental results, there were relatively fewer variations in the general shape, duration, and maxi-mum value of the bilateral occipital pressure pulses, probably due to the lower degree of asymmetryin the subject-specific Model 1. With the differentiation of highly asymmetrical gray and white mat-ters in the brain, however, Model 2 experienced greater variations of the bilateral occipital pressures.Moreover, similar to the simulated occipital pressures, the simulated frontal and parietal pressuresseemed to oscillate after the impulses in both models, with lower magnitude of oscillations in

Figure 4. Comparison of impact force and head acceleration between simulations and the cadaver experi-ments by Nahum et al. [21] when the head was impacted at the frontal bone region by a padded cylindrical

impactor with a mass of 5.59 kg and impact velocity of 9.94 m�s�1.



Figure 5. Correlation coefficients of the predicted results of various models with the three cadaveric exper-iments, namely (A) Nahum et al. [21]’s experiment 37 on intracranial pressure data; (B) Trosseille et al.[23]’s experiment on intracranial pressure data; and (C) Hardy et al. [26]’s C383-T1 experiment on brain

motion data.

Model 2. This could be attributed to the addition of soft tissue overlying the skull in Model 2,which helped to damp out the oscillations.

In general, the frontal region first experienced compression while the occipital region experi-enced tension before the trend was reversed when the brain had rebounded. It was shown that both



Figure 6. The transient simulation of Nahum et al. [21] shows a non-uniformity in intracranial pressure forModel 2.

Figure 7. Comparison of intracranial pressure at various locations predicted by the head models in thisresearch and head models in other researches, with Nahum et al. [21]’s cadaver experiment. (A) Frontalpressure; (B) bilateral occipital pressure (right); (C) bilateral occipital pressure (left); (D) parietal pressure;

and (E) posterior fossa pressure.

models predicted a maximum coup pressure of 160 kPa at the impact site and a minimum pressureof -60 kPa in the contrecoup posterior fossa region. These predicted pressure values were effectivelylower than those proposed by Ward et al. [57] in which the tolerance thresholds of the brain pressurefor compression and tension were, respectively, 234 kPa and -186 kPa.



3.2. Experimental validation against intracranial pressure data for long duration impulse

Intracranial pressure histories in the frontal (coup) and occipital (contrecoup) regions, as predictedby both models for the frontal impact, are shown in Figure 8. The peak pressure (compression)occurred in the frontal lobe with a magnitude of 81.6 kPa for Model 1 and 88.2 kPa for Model 2,whereas the trough pressure (tension) at the occipital lobe was 37.8 kPa for Model 1 and 42.1 kPa forModel 2, respectively. It can be seen from Figure 8 that the predicted pressures at the frontal lobewere slightly underestimated (5.45%) for Model 1 and slightly overestimated (2.20%) for Model2, whereas the occipital pressures for both models were overestimated by a tremendous amountof approximately 267% for (Model 1) and 315% for (Model 2). This trend, which had not beenobserved in the earlier comparison with the shorter duration impact of Nahum et al. [21]’s, was alsonoted by other FEHMs except WSUBIM (Figure 8). Apart from the occipital region, the predicted

Figure 8. Comparison of intracranial pressure at various locations predicted by the head models in thisresearch and other head models with Trosseille et al. [23]’s cadaver experiment. (A) Frontal pressure; (B)

occipital pressure; and (C) temporal pressure.



pressure pulses at the frontal and temporal regions matched reasonably well with the Trosseilleet al. [23]’s cadaveric experiment, with correlation coefficients of 0.944 and 0.878 at the frontal andtemporal regions for Model 1, whereas 0.891 and 0.757, respectively, for Model 2 (Figure 5B). Asmentioned previously, there was an overestimation of the predicted occipital pressure, with arounda three-fold increase in the peak trough pressure value. The duration of the trough of the occipitalpressure predicted in both models was relatively close to that of experimental one, as compared withthat of other FEHMs (Figure 8).

Similar to the simulations of Nahum et al. [21]’s cadaveric impact test, all the predicted ICPs inthe simulations of Trosseille et al. [23’s cadaveric impact test were higher in Model 2 than in Model1. This observation agreed with the basic relationship in Newton’s second law that, an object expe-riences higher acceleration, when the same external impulsive force is applied to the object withlighter weight. Hence, the lighter Model 2 predicted higher acceleration and hence higher ICPs.

3.3. Experimental validation against localized brain motion data

The simulation results for the relative skull-brain displacement of the two arrays of six NDTs locatedin the frontal lobe and parietal lobe at the right side of the head during Hardy [26]’s C383-T1 frontalimpact are shown in Figures 9 and 10. Each plot in the figure represents the relative displacementof each NDT, which was calculated using the difference of the absolute displacements of each NDTand a fixed point on the skull. The relative x-displacement of the NDTs in AC is generally character-ized by a minima occurring between 20 and 45 ms and a maxima at around 70 to 95 ms, whereas theAC NDTs’ relative z-displacement reaches its minima in the range of 25 to 45 ms before reboundingto the maxima in the 70 to 90 ms range. Similar trends were observed for the NDTs in the posteriorcolumn with the minima and maxima in x-direction in the 30 to 45 ms range and the 70 to 100 msrange, respectively, whereas the maxima and minima in z-direction was in the 40 to 45 ms rangeand the 80 to 95 ms range, respectively.

There was an average deviation of 0.53 mm (21.46%) and 1.12 mm (62.83%) in the relative x-displacement amplitude, as well as 0.155 mm (8.76%) and 0.344 mm (36.76%) average differencein the z-relative displacement amplitude between the experiment and simulation for Model 1 andModel 2, respectively. The simulated x-relative displacement amplitude deviated the most at NDTp1marker of Model 1 with 3.46 mm deviation and percentage difference from experiment of 51.53%and at NDTp2 of Model 2 with 4.65 mm deviation (82.93%). It differed the least from the exper-iment in NDTa6 with 0.0554 mm deviation (4.20%) for Model 1 and in NDTa3 with 0.124 mmdeviation (4.55%) for Model 2. The largest deviation in z-direction was found in NDTa6 (2.23 mm;58.62%) and in NDTa5 (3.18 mm; 95.13%), whereas the smallest z-relative displacement amplitudewas located at NDTa1 (0.170 mm; 13.17%) and in NDTp3 (0.0475 mm; 3.41%), for Model 1 andModel 2, respectively.

When comparing the relative displacement characteristics of the simulation with the experiment,average correlation coefficients of x-relative displacement of 0.530 and 0.458 were found for bothModel 1 and Model 2, respectively, while that of the relative displacement in z-direction was 0.788and 0.516 for the two models, respectively (Figure 5C). The highest correlation coefficients of thex-displacement were noted in the NDTa2 marker for Model 1 (0.868) and in NDTa1 for Model 2,whereas the respective lowest x-displacement correlation coefficients for both models are 0.00966and 0.0964 at NDTa4 (Figure 5C). The simulated coefficient of correlation of the z-displacementranged, from the highest of 0.926 and 0.860 in the same NDTa4 marker of both models to the lowestof 0.428 in NDTa6 for Model 1 and 0.0183 in NDTp2 marker (Figure 5C).

3.3.1. Sensitivity test of localized brain motion data. In order to investigate the sensitivity of thesestrain measures to material properties and markers’ positions, additional elemental strain data weretapped and recorded around the original positions of the NDT markers with the lowest or inversecorrelation coefficient (i.e., NDTa4, NDTp2, and NDTp5) (Figure 11).

As shown in the relative displacement graphs of NDTa4 of Model 1, the predicted x-relativedisplacement and z-relative displacement seemed to be particularly sensitive to the z-position andx-position of the marker location, respectively (Figure 11A). Better correlation in both x-relative



Figure 9. Comparison of the relative skull-brain displacement of the anterior neutral density targets columnlocated in the frontal lobe between that predicted by simulations of the head models in this research and theKungliga Tekniska Högskolan head model and that obtained in Hardy et al. [26]’s C383-T1 frontal impact

experiment of a cadaver.

displacement and z-relative displacement between the experimental and simulated results wasseen in the elemental marker that was directly superior to the original location of NDTa4 marker(Figure 11A). This indicated the importance of correct positioning of the NDTa4 probe in affectingthe sensitivity of these strain measures.

The inverse behavior of the NDTp5’s x-relative displacement plots of Model 2 was most probablydue to the rippling effect in which a local compressed region can cause its surrounding regions tobulge in the opposite manner. Increasing magnitude of the correlation coefficient of the NDTp5’sx-relative displacement between Model 2 and the experiment was found in the elemental markers



Figure 10. Comparison of the relative skull-brain displacement of the posterior neutral density targets col-umn located in parietal lobe between that predicted by simulations of head models in this research and theKungliga Tekniska Högskolan head model and that obtained in Hardy et al. [26]’s C383-T1 frontal impact

experiment of a cadaver.

that are of gray matter material property (Figure 11B). However, on the other hand, its z-relativedisplacement did not change significantly with varying material properties or marker’s locations(Figure 11B).

As for NDTp2, its x-relative displacement history plot for Model 2 demonstrated that the resultsfrom those markers with material properties of gray matter or cerebellum agreed better with thecorresponding experimental result (Figure 11C). It might be inferred that the actual NDTp2’s loca-tion in the test might be located near the interface between the cerebellum and the cerebral graymatter. Another point to be noted was that the elements adjacent to the gray-white matters interface



Figure 11. Sensitivity study of the relative skull-brain displacement of the NDTa4, (B) NDTp5, and (C)NDTp2. Note: Additional six elemental markers (bottom, top, front, rear, left, and right) are located

approximately 2–3 mm away from each of the original neutral density target cluster.

at the NDTp2 marker generally went in the opposite direction, indicating that significant shearing inthe impact direction at the gray-white matters interface. On the other hand, the z-relative displace-ment of the NDTp2 was less sensitive to the material properties or marker’s location (Figure 11C).Despite the discrepancy in the NDTp2’s z-relative displacement history plots between experimentand simulation, the simulated result in terms of the general behavior and the peak amplitude wasstill considered to be reasonable as there are many complicated factors in both experiments andnumerical simulations contributing to this discrepancy.

Numerical factors affecting the accuracy of its prediction included the simplified modeling ofthe material properties for the anisotropic, non-homogeneous biological brain tissues, as well asthe complex interaction between brain tissues. This imperfect modeling of the interface conditionsbetween brain tissues might be the reason why there was better correlation in the simulated resultsof Model 1 with the experiment.



Experiments can also have their limitations as well. For example, the experimental data did notindicate whether there was any sliding between the brain tissues, whereas the simulation resultsfrom current study show that there was relative motion (in the direction of impact) between ele-ments at the gray–white matters interface. Moreover, experimental quality control, sources of error,and the degree of variability were typically unknown in this kind of indirect validation. In addition,the experimental strain data did not indicate the exact anatomical locations and materials of theNDT markers. However, it shall be noted that indirection validation was unavoidable as the requiredexperiments were cost prohibitive, difficult to perform and involve ethical issues.

Further investigation would be needed in the future and it would be beneficial to have multi-ple biomechanical parameters, such as axial strain and shear strain, measured in the future cadaverexperiment.

4. CONCLUSION

To date, there are a few FEHMs which have been validated against both ICP and strain data of thelimited number of cadaveric experiments. To the authors’ knowledge, there is no reported subject-specific FEHM, with such detailed features, including soft tissues, having been validated againstthese three cadaveric tests. In the present study, the two FEHMs, both with detailed anatomicalfeatures, had been developed and validated against the ICP and relative intracranial motion data ofthe three cadaver experimental tests. The comparisons of the simulated results were largely consis-tent and were in good agreement with the experimental measured ICP and relative displacements.Despite the fundamental differences in the numerical formulation in the two models due to variationsin components involved, material properties and element types, there existed few evident differencesin the predicted ICP and relative displacements when the two models were compared with the threeexperiments. This may indicate that the advancements on the details of the extracranial featureswould not improve the model’s predicting capabilities in brain injury as it seems that the predictionreplies more on the skull’s mass properties and kinematics rather than on its geometrical details. Asa corollary, a model with the attributes of simplified extracranial features may be sufficient for mod-eling traumatic brain injury. Nevertheless, these newly developed FEHMs, with detailed realisticanatomical features, can be used in the evaluation of either facial or brain injury and even for eval-uating concomitant facial and brain injuries. It shall be noted that these newly developed FEHMsmay only be applicable to blunt impacts with mass and impact velocities comparable with that ofthe validation tests.

ACKNOWLEDGEMENT

The authors would like to acknowledge the support by a grant from the Swiss-based CMF Clinical PriorityProgram of the AO Foundation under the project no. C-09-2L.

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Development and validation of two subject-specific finite element models of human head against three cadaveric experiments