The Effects of Skull Thickness Variations on Human Head Dynamic Impact Responses

Transcription

1 SAE TECHNICAL PAPER SERIES The Effects of Skull Thickness Variations on Human Head Dynamic Impact Responses Jesse Ruan and Priya Prasad Ford Motor Co. Reprinted From: Stapp Car Crash Journal, Vol. 45 (November 2001) (P 375) 45th Stapp Car Crash Conference San Antonio, Texas November 15-17, Commonwealth Drive, Warrendale, PA U.S.A. Tel: (724) Fax: (724)

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3 Stapp Car Crash Journal, Vol. 45 (November 2001), pp. Copyright 2001 The Stapp Association The Effects of Skull Thickness Variations on Human Head Dynamic Impact Responses Jesse Ruan and Priya Prasad Ford Motor Company ABSTRACT Variations in human skull thickness affecting human head dynamic impact responses were studied by finite element modeling techniques, experimental measurements, and histology examinations. The aims of the study were to better understand the influences of skull thickness variations on human head dynamic impact responses and the injury mechanisms of human head during direct impact. The thicknesses of the frontal bone of seven human cadaver skulls were measured using ultrasonic technology. These measurements were compared with previous experimental data. Histology of the skull was recorded and examined. The measured data were analyzed and then served as a reference to vary the skull thickness of a previously published threedimensional finite element human head model to create four models with different skull thickness. The skull thicknesses modeled are 4.6 mm, 5.98 mm, 7.68 mm, and 9.61 mm. These models were impacted by a cylinder with a mass of 5.23 kg and an initial velocity of 6.33 m/s. Model responses were compared between models in terms of intracranial pressures, head impact accelerations, brain shear stresses, and skull von Mises stresses. It has been shown that the thickness of the skull influenced the dynamic responses of the head during direct impact. As skull thickness increased, skull deformation decreased as the skull absorbed less impact energy. However, this relationship cannot be linearly interpolated to the other parameters such as head acceleration and intracranial pressure responses. Based on model responses to half-sine wave pulses, skull and brain iso-stress curves were constructed for the thicker and thinner skulls. Thresholds for skull fracture and reversible concussion were established for the population represented by these skulls. KEYWORDS Human Skull, Finite Element, Skull Thickness, Head Dynamic, Injury Mechanism, Direct Impact, Coup and Contrecoup Pressure, Skull Fracture Risk. INTRODUCTION The fracture tolerance of the frontal bone has been reported by various investigators to range between 2.3 kn to 9.9 kn (Nahum et al, 1968, Melvin et al, 1969, Hodgson et al, 1970, Schneider and Nahum, 1972). The variations of the fracture tolerance in these studies may be due to various factors the wide variations in skull thickness of the samples studied, the duration of impact and the maximum stress to failure of the cortical bone. Other factors like the bone condition factor and the anthropometrics of the human skull can also affect the fracture tolerance of the skull along with the external load distributions. The earliest study to evaluate the fracture tolerance of the frontal bone subjected to impact is well known and formed the basis for the Wayne State Tolerance Curve, which was further verified by Ono et al (1980). The Wayne State Tolerance Curve is the basis for the currently utilized Head Injury Criterion (HIC) in regulations worldwide. Prasad and Mertz (1985) have evaluated the efficacy of the HIC for predicting skull fracture in frontal impact. They developed the relationship between the population at risk for skull fracture for given HIC levels. A later study was conducted by Hertz (1993) utilizing the same data by Prasad and Mertz (1985). Further analysis of an expanded data set was conducted by Mertz et al (1996) and skull fracture risk curves based on HIC and peak acceleration were reported (Mertz et al, 1996). Finite element modeling studies of the relationship between skull/brain responses and HIC have been reported by Ruan et al (1993) and Ruan and Prasad (1994, 1998). The model results agreed with the Japan Automotive Research Institute (JARI) concussion and skull fracture curves reported by Ono et al (1980) for a skull/brain model representing a 50 th percentile head. The purpose of this paper is to report the results of a study where the skull thickness of the previous human head model was varied but the brain dimension was unchanged. The impact responses of the skull and brain with varying skull thickness are reported. Additionally, the time durations of the impact were also varied to determine the variations of

4 skull/brain responses with varying impact durations. The results of the modeling study were compared with those of Mertz et al (1996) and Hertz (1993). METHODS Frontal Bone Thickness Measurements The thicknesses of seven cadaver frontal bones were measured in this study. Ultrasonic technology was used to help identify the boundaries between the diploe, inner and outer tables to avoid human error in the process. Seven triangular frontal bone coupons were taken from seven unembalmded cadaver head after drop tests. The relative stiffness of the bony layers of these triangular coupons was mapped by acoustic microscopy. Each coupon was examined by scanning its three cross-sectional faces. A total of 21 slides were scanned. A 90 MHz ultrasonic transducer was used to achieve a spatial resolution of 30 microns. At this resolution, the trabecula-like architecture of the diploe layer was resolved, and the localized variations in stiffness within a trabecula were mapped. All specimens were fully hydrated when they were scanned. Greyscale mapping which indicates the relative stiffness of each 30-micron pixel were generated by digitizing the peak amplitude of the reflected ultrasonic wave. The thickness of the diploe, inner table, and outer table of three faces of each coupon was measured directly from the acoustic microscopy mapping by a software program. Finite Element Human Skull Models Development The finite element human head model developed by Ruan et al (1993) was used as a baseline model because it includes all the major anatomical components of the human head, while not being too large for parametric studies. Although this model has been validated against cadaveric test data previously, to further ensure model accuracy, head drop test simulations were performed in the current study to compare model responses with dummy and cadaver head drop test data. The geometry of the brain, cerebral spinal fluid, dura matter, and the falx are not changed. Four skull models were developed in this study to incorporate the smallest (4.6 mm) and largest (9.61 mm) skull thickness from experimental measurements. The thickness of the three-layered skull was varied fro m Model I to Model IV. In each model the thickness of the inner and outer tables is the same and the diploe is 80% thicker than the inner and outer tables. The total skull thicknesses in the four models are shown in Table 1. It should be noted that the total masses of the four heads varied between 3.44 to 4.28 kg. In all the four models, the thickness of the skull was uniform among the frontal, temporal, parietal, and occipital bones unlike the baseline model in which the thickness of the skull varied from the frontal to occipital bones. Skull thickness of the baseline model ranges from 5 mm to 8.7 mm in the frontal bone and 6.3 mm to 12.4 mm in the occipital bone. The mass of the baseline model is 3.66 kg. The material properties of the head tissues are the same as those used in the baseline model (Ruan et al, 1993). These four models were impacted by a rigid cylinder with a mass of 5.23 kg and an initial velocity of 6.33 m/s, the same impact condition reported in Ruan et al (1993). The models were further used to develop skull and brain iso-stress curves as a function of peak acceleration and impact duration using the method described by Ruan and Prasad (1995). RESULTS Frontal Bone Thickness Measurements A total of 21 greyscale relative stiffness mapping images were produced by acoustic microscopy scanning. Figs. 1-3 show the greyscale mapping images recorded from the sample skulls. The greyscale indicates the relative stiffness of each pixel location in the mapping with grey to white indicating low to high stiffness as shown on the right vertical margin of each mapping image. These relative stiffnesses are indications of density variations (Figs. 1-3). The boundaries between diploe and inner and outer tables of most mapping images are clearly Table 1 Dimensional Parameters for the Finite Element Head Models Skull Thickness (mm) Head Mass Skull Mass Model Inner Table Diploe Outer Table Total (kg) (kg) I II III IV

5 recognized (Fig.1), but in a few are hardly distinguishable (Fig.2). In one sample there is a void area (sinus) in the skull bone (Fig.3). These figures show the wide variation in the thickness of the outer and inner tables and the diploe layer that can be expected in the population. The thickness of the diploe, inner table, and outer table was measured directly from the acoustic microscopy mapping images. The results are shown in Table 2. The mean thickness of these seven skull bones is 6.51 mm with a standard deviation of 0.84 mm as indicated in Fig 4. The thickness ratios of diploe to inner and outer tables range from 1.48 to 6.90, showing a large variation. Fig. 4 shows the distribution of the total thickness of the frontal bone on a normal probability plot. These measurements were compared to those reported by Hodgson et al (1970) shown in Table 3. The mean thickness of Hodgson's data is 6.00 mm (6.5 mm from current study) with a standard deviation of 1.20 mm. The thickness ratios of diploe to inner and outer tables from Hodgson's data range from 1.1 to 2.5. The current skull thickness data were combined with those from Hodgson et al (1970), Ono et al (1980), and those from APR's test samples used by Prasad and Mertz (1985) for skull fracture risk assessment studies. A t-test shows that the means of these sets of data are statistically the same (with a p-value = 1.0 and confidence level of 95%). The distribution of the skull thickness for these four-set of data is shown in Fig. 5. It can be seen that skull thickness used in Model I (4.6 mm) corresponds to 5%, Model II (5.98 mm) to 40%, Model III (7.68 mm) to 80%, and Model IV (9.61 mm) to 98% of the skull thicknesses in the population represented by the data. Table 2 Human Cranial Bone Thickness Measurements (in mm) Sample Frontal Bone Thickness Cadaver # Side # Inner Table Diploe Outer Table Total Average # # # # # ??? # # ? Measurement is not possible because of indistinguishable boundaries

6 Author Name et al./stapp Car Crash Journal 45 (November 2001) Fig.1 Relative stiffness mapping of cranial bone, specimen #888/side 1 Fig.2 Relative stiffness mapping of cranial bone, specimen #735/side 2 Fig.3 Relative stiffness mapping of cranial bone, specimen #706/side 1

7 Normal Probability Plot of Skull Thickness ML Estimates - 95% CI Percent ML Estimates Mean StDev Goodness of Fit AD* Skull Thickness Fig. 4 Normal probability plot of seven frontal bone thickness Table 3 Thickness of Human Frontal Bone (in mm), Hodgson et al (1970) Cadaver # Inner Table Diploe Outer Tabel Total Average

8 Normal Probability Plot for Combined Data ML Estimates - 95% CI Percent ML Estimates Mean StDev Goodness of Fit AD* Skull Thickness Fig. 5 Normal probability plot of frontal bone thickness from combined data set Finite Element Analysis Results Head drop test simulations. Before doing the analysis of the effect of skull thickness variation, two head drop test simulations were carried out using the baseline model to simulate two drop heights, 7.4 and 14.8 inches. Table 4 lists the simulation results and the comparisons with dummy and cadaver head drop test results. The responses shown in Table 4 are Head Injury Criterion (HIC), peak resultant head accelerations and impact durations, and resultant impact forces, because only these results are experimentally available. The overall comparisons with known head drop data are favorable. Figs. 6 and 7 show head impact forces and head accelerations, respectively, from model simulations of head drop tests. In these figures, open circles represent responses from a 7.4-inch drop simulation and solid circles stand by a 14.8-inch drop. Table 4 Head Drop Tests and Simulation Results Drop Height Subject HIC Res. Accel. (G's) Duration (ms) Res. Force (N) Dummy In Model Dummy In Cadaver* Model * Cadaver responses are based on the average of seven cadaver head drop test results.

9 Fig. 6 Head impact forces from head drop simulations Fig. 7 Head accelerations from head drop simulations

10 Author Name et al./stapp Car Crash Journal 45 (November 2001) The effect of skull thickness variation. The rigid cylinder impact simulation results from four different skull thickness head models are summarized in Table 5. The responses were measured by energy absorbed by the heads, head impact forces, head accelerations and Delta V, coup and contrecoup pressures generated in the cerebral-spinal-fluid (CSF) and brain, brain shear stress, and skull von Mises stress. The time history of head impact forces and accelerations are shown in Figs. 8 and 9. It should be noted that there is no significant duration difference between models in figures 8 and 9; the phase shift shown is to differentiate between curves. The unusual curve shape of Model I shown in both Figs. 8 and 9 is associated with larger deformations and vibrations in the thinner skull. Fig. 10 shows the model responses in Table 5. As shown in Table 5 and Fig. 10, as skull thickness increases, less energy is absorbed by the skull. As a result, head impact forces increase with increase in thickness due to stiffening of the skulls. However, head accelerations decrease due to the lesser energy absorption from impact due to mass effects. As a result of larger skull deformation, coup pressures of the thinner skulls increase along with brain shear and skull von Mises stresses. Interestingly, brain contrecoup pressures increased (in magnitudes) as skull thickness increased. This is because a stiffer skull makes it easier to "snap back" due to the increasing overall skull stiffness. It should be noted that the change in velocity of the head is approximately 10% lower for the thickest skull when compared with that of the thinnest skull due to the increased mass of the head with the thickest skull. In spite of the difference in head masses of the Model I to Model IV, the contact forces increased by 10% between Model I and Model IV, and the peak head acceleration decreased by 17%. The peak von Mises stress decreased by 61 % showing a substantial protective effect as the skull thickness increases. The models also show a substantial reduction (40%) in brain shear stresses, and coup pressures in the CSF (36%) between the thickest and the thinnest skulls. The contrecoup pressures in the brain and the CSF were least sensitive to change in skull thickness. The spatial distributions of skull von Mises stress, intracranial pressures of the CSF and brain are shown in Figs. 11 to 13. The patterns of intracranial stresses and pressure distribution are not affected by variations in skull thickness. However, the magnitudes of the intracranial stresses and pressures are affected by variations in skull thickness. During head impact, skull von Mises stresses are generated at 3 ms when contact occurred. The maximum stress is developed at the center of impact at 5 ms (Fig. 11). At 8 ms, the skull stresses are negligible. Intrancranial pressures are also generated at 3 ms when contact begins. Tensile pressures were built up at impact point and the dorsal lateral part of brain stem in the cerebral-spinal-fluid (Fig. 12). Brain pressure distributions followed the coup-contrecoup pressure distribution theory and pattern discussed in the previous studies (Kopeck and Ripperger, 1969, Ruan et al, 1991, 1994) - positive pressure at impact site and negative pressure at site opposite to the impact (Fig. 13). Table 5 Summaries Results from Four Model Simulations Model Energy (J) Force (N) Accel. (G's) Delta V CSF Pressure (kpa) Brain Pressure (kpa) (m/s) Coup Contr. Coup Contr. Brain Shear (kpa) Skull von Mises I II III IV (Mpa)

11 9.61 mm 7.68 mm 5.98 mm 4.6 mm Fig. 8 Head impact forces of four different skull human head models 9.61 mm 7.68 mm 5.98 mm 4.6 mm Fig. 9 Head impact accelerations of four different skull human head models

12 Model III 7.68 mm Model I 4.6 mm Model II 5.98 mm Model IV 9.61 mm Fig. 10 Head impact responses of four different skull human head models Fig. 11 Peak skull von Mises stress contour (at 5 ms)

13 Fig. 12 Cerebral-spinal-fluid pressure contour (at 5 ms) Fig. 13 Peak brain pressure contour (at 5 ms)

14 Author Name et al./stapp Car Crash Journal 45 (November 2001) Model perturbations. Based on animal and human head impact tests, Ono et al (1980) have reported the development of the Japan Automotive Research Institute (JARI) Head Impact Tolerance Curves (JHTC). Two curves relating average head accelerations and impact durations to the threshold of skull fracture and reversible concussion of an average sized human head were reported. An earlier study of these tolerance curves by Ruan and Prasad (1995) utilizing the baseline model in the current study showed good correlation between the model and the skull fracture curve if it was assumed that the cortical bone fracture was associated with 100 Mpa peak von Mises stress in the cortical bone. Similarly, the threshold for reversible concussion curve followed a 22-kPa peak shear stress in the brain or approximately 5% strain in the brain. Utilizing the method reported by Ruan and Prasad (1995, 1998), iso-stress in the skull and the brain were developed as a function of peak acceleration and their durations for the four models in this study. Half-sine wave accelerations were used to perturb the four models. The results of the perturbation study are shown in Figs. 14 and 15. Fig. 14 shows the iso-stress (100 Mpa) curves for the skulls in Model I to IV as a function of peak accelerations and time durations. It can be seen that regardless of skull thickness, higher accelerations are required to generate 100 Mpa von Mises stress in the skull as the time duration of the impact is shortened. This trend has been identified by many studies in the past. It can also be seen in Fig. 14 that an asymptote is reached between 8 to 9 ms time duration. Beyond the 8-9 ms time duration, peak head acceleration alone will follow the isostress curve in the skull. This result is in good agreement with that reported by Ono et al (1980) utilizing experimental data. The iso-stress curves also show that the large variation in fracture tolerance of human skull reported in the literature can be explained by variations in skull thickness of the samples tested and time durations of impact mm 7.68 mm 5.98 mm 4.6 mm Increasing skull thickness Fig. 14 Skull iso-stress curves for 5 th, 40 th, 80 th and 98 th percentile skulls.

15 9.61 mm 7.68 mm 5.98 mm 4.6 mm Increasing skull thickness Fig. 15 Iso-stress curves for brains associated 5 th, 40 th, 80 th, and 98 th percentile skulls. Fig. 15 shows the brain iso-stress (22 kpa peak shear stress) curves for Model I to IV. The shapes of these curves are qualitatively similar to those of skull isostress curves. Examination of Fig. 15 reveals that as the skull thickness increases, the peak accelerations required to reach 22 kpa peak shear stress in the brain also increase at all time durations of impact. For a given skull thickness, as the pulse duration increases, the peak acceleration required to reach a brain shear stress of 22 kpa reaches an asymptote at about 10 ms. For a given pulse duration, the peak acceleration required to produce a brain shear stress of 22 kpa increases with increased skull thickness and reaches an asymptote at about the skull thickness of 9.61 mm of Model IV. For example, the increase in skull thickness between Models III and IV is 25%, but the increase in accelerations between Models III and IV are not significant. This effect is more clearly shown in Fig. 16 where iso-stress producing accelerations are shown as a function of skull thickness for 3 ms and 8 ms pulse durations. It can be seen that accelerations required to reach 22 kpa shear stress in the brain has an asymptotic behavior, whereas the skull fracture accelerations continue to increase substantially with increasing skull thickness. Further, a 67% increase in skull thickness from Model I to Model III increases the fracture acceleration from 150G's to 300 G's for 3 ms pulse, a 100% increase in strength. However, the concussion accelerations increase from 175 G's to 270 G's, a 54% increase. These results indicate that the protective effect associated with increased skull thickness is greater for skull fracture than for reversible concussion. This is more clearly seen in Fig. 16, a plot of skull and brain iso-stress at 3 and 8 ms impact duration, respectively, for four different thickness skulls. For a given skull thickness, peak accelerations for reversible concussion exhibit asymptotic behavior, however, this behavior is not observed for skull fracture.

16 Fig. 16 Iso -stresses of the skull and brain for 3 & 8 ms pulse durations as a function skull thickness If the results in Figs. 14 and 15 are compared, it can be seen that the brain iso-stress curves are lower than the skull iso-stress curves in Models II, III, and IV. This trend indicates that skull fracture tolerance is higher than that for reversible concussion. This also indicates that skull fractures can coexist with reversible concussion an observation made by Gurdjian et al (1966) who found the occurrence of concussion in 80% of their patient population who had linear skull fractures. The brain iso-stress curve is however higher than the skull iso-stress curve for Model I. This indicates that for a small population with thin skulls, skull fracture can occur without concussion. To compare model results with the results of Mertz et al (1996), skull fracture constant HIC curves for halfsine pulses used in the model to develop the iso-stress curves were generated, and are shown in Fig. 17. For the sake of completeness, reversible concussion constant HIC curves for the same pulses were also generated and are shown in Fig. 18, although the risk of reversible concussion as a function of HIC is currently unknown. For clarity, only the results of Model I, II, and III are shown in these two figures. It can be seen in Fig. 17 that the constant HIC curve of 1450 corresponds well with the iso-stress curve of Model II. However, the constant HIC curve does not show the asymptotic behavior of the iso-stress curve, indicating that the HIC may be conservative in impact durations between 9 to 15 ms. Note that the current HIC duration in FMVSS 208 is limited to a maximum of 15 ms. On the other hand, for shorter duration impacts, i.e., less than 3 ms, the HIC underestimates the risk for skull fracture. It can be further seen that the constant 450 HIC curve corresponds well with the results of Model I. Similarly, the 2000 HIC curve shows good

17 correlation with the results of Model III from 3 to 8 ms. Once again the HIC curve does not asymptote as the skull iso-stress curve. The asymptotic phenomena shown in Fig. 17 are also exhibited in Fig. 18, i.e., the constant HIC curves do not asymptote but brain iso-stress curves do. As seen in Fig. 18, a 1450 constant HIC curve is close to the results of Model III, a 900 HIC curve close to the results of Model II, and a 540 HIC curve close to the results of Model I. These three models represent three brains associated with a 5 th, 40 th, and 80 th percentile skulls. Note that the constant HIC for brain concussion are lower than those for skull fracture for Model II and III. However, for Model I, constant HIC for brain concussion is higher than that for skull fracture. A 700 constant HIC line is also shown and it lies between iso-stress curves of Model I and II mm 5.98 mm 4.6 mm Increasing skull thickness Fig. 17 Skull iso -stress curves for 5 th, 40 th, and 80 th percentile skulls. The constant HIC lines for HIC values of 450, 1450, and 2000 are shown by open triangles, open diamonds, and open circles, respectively. Skull iso-stress curves for Model I, II, and III are shown by solid triangles, solid diamonds, and solid circles, respectively. The 450 constant HIC line is close to Model I iso-stress curve, the 1450 close to Model II, and the 2000 close to Model III. Skull iso-stress curve for Model IV is above the 2000 HIC line it is not shown in the figure for sake of figure clarity. A 700 constant HIC line is also shown and it lies between iso-stress curves of Model I and II.

18 7.68 mm 5.98 mm 4.6 mm Increasing skull thickness Fig. 18 Brain iso-stress curves for brains associated with 5 th, 40 th, and 80 th percentile skulls. Brain iso-stress curves for Model I, II, and III are shown in the figure by solid triangle, solid diamonds, and solid circles, respectively. The constant HIC lines of 540, 900, and 1450 are shown by open triangles, open diamonds, and open circles, respectively. Notice that the constant HIC for brain concussion are lower than those for skull fracture for Model II and III. However, for Model I, constant HIC for brain concussion is higher than that for skull fracture. A 700 constant HIC line is also shown and it lies between iso-stress curves of Model I and II. DISCUSSION General Observations The measured skull thickness in the current study ranged from 5.05 to 8.13 mm. The data by Hodgson et al ranged from 4.3 to 9.4 mm. Other databases also show wide variability in skull thickness. For example, in Ono's et al data on 15 specimens show variation between 5 mm to 8.5 mm. Got's et al data containing 146 skulls, show a variation between 3.5 to 11.2 mm. The above data underscore the wide variability in skull thickness. The thickness ratios of diploe to inner and outer tables also varied substantially from skull to skull. Additionally the diploe is not always thicker than inner and outer tables. In some skull samples, the inner and outer tables are thicker than the diploe as they are shown in Tables 2 and 3 by bolded sizes. Histology of the skull also varies substantially from skull to skull (Figs. 1-3). These dimensional and histological differences may have an effect on the overall skull stiffness and hence the responses of the head subjected to impact. These factors may explain the wide range of skull fracture forces reported in the literature. The head drop test simulations have ensured model accuracy and further validated the head model against experimental data giving us the confidence to perform further analysis and parametric studies. The current study has shown the usefulness of finite element modeling studies that are not possible with

19 experimental models involving cadavers and other human surrogates. Comparisons of Model Results with Previous Studies Although fracture strength of the skull has been reported in the past in terms of forces, but the common practice now is to refer to peak fracture acceleration, and we have selected to do so in the paper. The dependence of fracture acceleration on time duration of impact is obvious from Figs. 14 and 15 and previous studies by the current authors. The dependency of peak and/or average acceleration versus impact durations is also noted experimentally by many, the most recent researchers being Ono et al (1980). The model results agree with Ono's et al test data for an average sized skull. The following section compares the current model results with other studies in the literature. A compilation and analysis of available skull fracture data were reported by Prasad and Mertz in At the time of the report, HIC's for fracture and nonfracture producing impacts were available for analysis. The lowest HIC value associated with a skull fracture was 450 and the highest value associated with non-skull fracture was It was noted that the highest non-fracture HIC was associated with the thickest skull (7.67 mm) in the sample. Also, a fracture at 516 HIC was associated with the thinnest skull (4.31 mm) in the sample. This data set was further expanded by including more cadaver head impact data in subsequent literature and reanalysis of the original data set was conducted to include pre-fracture impacts on some of the cadaver heads. The analysis results were reported by Mertz et al in 1996 and skull fracture risk curves as a function of HIC and peak acceleration were developed (Mertz et al, 1996). The analysis of the expanded data set showed that 1500 HIC corresponded to 50% risk of skull fracture of the samples tested. Depending on the statistical method used, the 50% risk could range between 1450 HIC to 1550 HIC approximately. Regardless of the statistical method, 1000 HIC corresponded to 16% risk of skull fracture, 450 HIC corresponded to approximately 3% risk of skull fracture. Model II, 40% 5.98 mm Model IV, 98% 9.61 mm Model I, 5% 4.6 mm Model III, 80% 7.68 mm Fig. 19 Comparisons of Skull Fracture Risk Curves of model prediction and from the literature

20 Author Name et al./stapp Car Crash Journal 45 (November 2001) The skull thickness of Model I corresponds to 5% of the skull in the samples considered in this study, Model II corresponds to 40% of the samples, and Model III to 80% of the samples. The skull iso-stress curves shown in Fig. 17, therefore, correspond to the threshold of fracture for 5%, 40%, and 80% of skull in the study. A comparison of the model results with various skull fracture risk curves is shown in Fig. 19. Considering that the experimental data contained cadaver samples with substantial variation in head size, weight and skull thickness, the current theoretical study results appear to support the Skull Fracture Risk Curve developed in Mertz's et al (1996) study. However, the results of the current study do not agree with the skull fracture risk curve developed by Hertz (1993) as shown in Fig. 19. A skull fracture risk curve as a function of peak head acceleration has also been developed by Mertz et al (1996). Although pulse durations in the experiments are not reported, HIC durations have been reported in the Prasad and Mertz's (1985) study. The average HIC durations are approximately 3 ms in the fracture producing impacts. The model results can be considered for the 3 ms duration for comparison with the skull fracture risk curve. Model I representing 5% skulls shows that the threshold of fracture is reached at 150 G's for 3 ms pulse duration. The risk curve shows 1-2% risk of skull fracture at this acceleration. Model II representing 40% of skulls shows that the threshold for fracture is reached at 262 G's, 40% risk of skull fracture is predicted by the risk curve to be between G's. Similarly, Model II representing 80% of skulls, shows the threshold for fracture is reached at 300 G's, 80% risk of skull fracture is predicted by the risk curve to be between G's. Once again, the theoretical analysis in this report appears to support the risk curve derived from experimental data. Reversible Concussion The risk of reversible concussion as a function of HIC or peak accelerations is currently unknown. However, for the sake of completeness, constant HIC curves are compared to the brain iso-stress curves for Model I, II, and III in Fig.18. It can be seen that there is qualitative and quantitative correlation between constant HIC curves 900 and 1450 with Model II and Model III results. Also shown in the figure, for reference, is a constant 700 HIC curve currently in the FMVSS 208 standards. It can be seen that only a small percentage of the population will be above the threshold for reversible concussion and the vast majority of the population will be below the threshold for reversible concussion. It can also be seen that even for a 5 th percentile skull thickness, high accelerations ranging between 125 G's (9 ms) and 175 G's can be tolerated without reaching the threshold of concussion. Limitations of the Current Study The current study investigated the effect of skull thickness variation on the response of the skull and brain for a cranial cavity of an average head. The scalp and brain dimensions were not varied, although both can be expected to affect skull and brain response to impact. The authors chose to investigate skull thickness variation effect due to the wide variability of skull thickness reported in the literature especially those by Got et al (1983). Their study showed that in a sample of 146 cadaveric specimens, skull thickness varied from 3.5 mm to 11.2 mm, nearly a 300% difference between the thinnest and thickest skulls. However, the anterior-posterior and transverse diameters of the head showed a variation of 25 to 30% between the shortest and the longest. Additionally, the effect of load distribution on the skull has not been investigated. This was chosen intentionally to maintain contact areas nearly the same to avoid confounding factors. This study has not investigated the effect of noncontact impacts in which angular accelerations are important factors affecting shear stresses in the brain. Therefore the results of this study are limited to contact impacts not involving high angular accelerations. Skull thickness of Model I is assumed to represent a 5 th percentile skull, but it might be anywhere between 1 and 9 percentile depending on various samples reported in the literature and in this study. CONCLUSIONS Based on ultrasonic measurement of seven skull samples and earlier data reported in the literature, four detailed head models were developed for finite element analysis. Several forehead impact simulations were conducted to evaluate the effect of skull thickness on skull and brain responses. Skull and brain iso-stress curves were constructed to study the threshold of skull fracture and reversible concussion. The results of the models were compared with existing skull fracture data. The following conclusions can be drawn from the study: 1. There is an increasing protective effect for the skull and brain with increasing skull thickness.

21 This increase in protection is more pronounced for skull fracture than for reversible concussion, which shows an asymptotic behavior (see Fig. 16). 2. Skull and brain iso-stress curves show an asymptotic behavior between 8 to 9 ms impact durations. Regardless of skull thickness, the threshold of skull fracture increases as impact durations decease. Similarly, the threshold for concussion increases with shorter duration impact. 3. Constant HIC curves represent the results of the model iso-stress curves well between 3 to 9 ms, but do not asymptote as the iso-stress curves. As a result, constant HIC curves are conservative in assessing the risk of skull fracture or reversible concussion in impact durations that are longer than 9 ms but less than 15 ms, the current limit on HIC duration in FMVSS The model results support the Skull Fracture Risk Curves generated by Prasad and Mertz (1985) and Mertz et al (1996). The skull fracture risk curve generated by Hertz is not supported by the model results. ACKNOWLEDGMENTS The experiments of cadaver skull thickness measurements were performed at Bioengineering Center of Wayne State University through a research contract with Ford Motor Company. REFERENCES Got, G., Guillon, F., Patel, A., Mack, P., Brun- Cassan, F., Fayon, A., Tarriere, C., and Hureau, J., (1983) Morphological and biomechanical study of 146 human skulls used in experimental impacts in relation with the observed injuries, Proc. 27 th Stapp Car Crash Conference, SAE Paper No Gurdjan, E.S., et al, (1966) Mechanisms of head injury, Clin. Neurosurg. Vol. 12, pp Hertz, E., (1993) A note on the Head Injury Criterion (HIC) as a predictor of the risk of skull fracture, 37 th Annual proceedings Association for the Advancement of Automotive Medicine, November 4-6, 1993, San Antonio, Texas. Hodgson, V.R., Brinn, J., Thomas, L.M., and Greenberg, S.W., (1970) Fracture behavior of the skull frontal bone against cylindrical surface, Proc. 14 th Stapp Car Crash Conference, SAE Paper No Kopecky, J.A., and Ripperger, E.A., (1969) Close brain injury: an engineering analysis, J. Biomechanics, (2), pp Mertz, H.J., Prasad, P., and Nusholtz, G., (1996) Head injury risk assessment for forehead impacts, SAE Paper No Ono, K., Kikuchi, A., Nakamura, M., Kobayashi, H., and Nakamura, N., (1980) Human head tolerance to sagittal impact reliable estimation deduced from experimental head injury using subhuman primates and human cadaver skull, Proc. 24 th Stapp Car Crash Conference, SAE Paper No Prasad, P., and Mertz, H.J., (1985) The position of the United States delegation to the ISO Working Group 6 on the use of HIC in automotive environment. SAE Paper No Ruan, J.S., Khalil, T.B., and King, A.I., (1991) Human head dynamic response to side impact by finite element modeling, ASME Journal of Biomechanical Engineering, (113), pp Ruan, J.S., Khalil, T.B., and King, A.I., (1993) Finite element modeling of direct head impact, Proc. 37th Stapp Car Crash Conf, SAE Paper No Ruan, J.S., Khalil, T.B., and King, A.I., (1994), Dynamic response of the human head to impact by three-dimensional finite element analysis, ASME Journal of Biomechanical Engineering, (116), pp Ruan, J. S., and Prasad, P., 1994, Head injury potential assessment in frontal impact by mathematical modeling, Proc. 38th Stapp Car Crash Conf, SAE Paper No Ruan, J. S., and Prasad, P., 1995, Coupling of a finite element head model with a lumped parameter Hybrid III dummy model - preliminary results, Journal of Neurotrauma, Vol. 12, No. 4, pp Ruan, J. S. and Prasad, P., 1998, Biomechanical study of head injury through finite element analysis,frontiers in Head and Neck Trauma - Clinical and Biomechanical, Editors, Yoganandan, N., and Pintar, F. A., Larson, S. J., and Sancers, A., ISO Press, 1998, pp