A New Biomechanically-Based Criterion for Lateral Skull Fracture

Abstract

This work develops a skull fracture criterion for lateral impact-induced head injury using postmortem human subject tests, anatomical test device measurements, statistical analyses, and finite element modeling. It is shown that skull fracture correlates with the tensile strain in the compact tables of the cranial bone as calculated by the finite element model and that the Skull Fracture Correlate (SFC), the average acceleration over the HIC time interval, is the best predictor of skull fracture. For 15% or less probability of skull fracture the lateral skull fracture criterion is SFC < 120 g, which is the same as the frontal criterion derived earlier. The biomechanical basis of SFC is established by its correlation with strain.

In Europe, Japan, Australia, and the United States, the current standard for protection against generalized head injury in a frontal car crash is the Head Injury Criterion (HIC). Recently, biomechanically-based multicomponent criteria have been developed to separately protect against DAI, SDH, brain contusions [Takhounts, Eppinger, Campbell et al., 2003], and frontal skull fracture [Vander Vorst, Stuhmiller, Ho et al., 2003]. Current NCAP FMVSS 214 side impact crash tests use a side impact dummy (Part 572.F) coupled with a Hybrid III head-neck complex. There is no standard for head injury in FMVSS 214; however, the side-impact collision into a rigid pole in FMVSS 201 requires HIC to be less than 1000.

The objective of this study is to determine the best biomechanically consistent, statistically significant, and measurable criterion for lateral (i.e., side) impact-induced skull fracture for use in crash tests. This work amalgamates an anthropomorphic finite element model based on Computed Tomography (CT) imaging, Postmortem Human Subject (PMHS) test data, acceleration data from drop tests of a Hybrid III headform, and statistical analyses in order to determine the best skull fracture criterion. For injury data to be transformed into a biofidelic injury criterion, it must be analyzed using accepted and definitive statistical methods and the results must be tested against the underlying fundamental injury mechanism to produce a probabilistic risk curve with known confidence. No such statistically-based criterion exists to evaluate the risk of lateral skull fracture; however, such a criterion was previously developed for frontal skull fracture by Vander Vorst et al. (2003). They showed that an index called the Skull Fracture Correlate (SFC) is the best correlate to frontal, impact-induced, linear skull fracture. SFC, which is the average acceleration over the HIC time interval as measured by an Anthropomorphic Test Device (ATD), is biofidelic in the sense that it is an excellent correlate to tensile skull strain as calculated by a finite element model. It accounts for compliance of the impact target and is extensible to varying head weights. For a 15% or less probability of frontal skull fracture the criterion is SFC < 120 g, with a 95% confidence band of 88 < SFC < 135 g.

Some data on impact-induced lateral skull fracture exists in the open literature. Hodgson and Thomas (1971 and 1973) provide lateral fracture outcomes for varying impact speeds against flat and cylindrical rigid targets. In their tests, embalmed whole body specimens were placed on a hinged pallet pivoted at the feet, with the head extending over the edge. More PMHS data is needed, however, to extend the validity of injury criteria to a wider range of target compliance. Free drops of isolated head specimens would provide accurate specification of impact conditions and allow for higher impact speeds, as accomplished in the present work.

The search for the best risk factor must be guided by a biomechanical understanding of the underlying injury mechanism. In the case of the human skull, tensile strain in the compact tables is an indicator of fracture [Wood, 1971], but skull strain data at the location of fracture is difficult to measure in an impact test. Mechanical strain, however, can be calculated with a finite element model using the PMHS test conditions as input. Finite element models of varying complexity exist for the investigation of head injury; from highly refined whole-head models containing hundreds of thousands of elements [Zhang et al., 2001], to anthropomorphically correct models containing tens of thousands of elements concentrating on resolving the skull [Bandak, Vander Vorst, Stuhmiller et al., 1995], to simple spherical models containing thousands of elements [Khalil and Hubbard, 1977; Vander Vorst et al., 2003]. Since the purpose of the model in this study is to predict skull strain and ultimately to differentiate frontal and lateral impacts, a refinement of the anthropomorphic model of Bandak and Vander Vorst et al. was implemented.

METHODS

Drop tests were conducted using isolated PMHS head specimens. They are hereafter referred to as the MCW tests to distinguish these tests from previous tests available in the literature. Seventeen unembalmed specimens free from HIV and Hepatitis B and C were obtained. The intracranial contents were replaced with Sylgard Gel, except for four of the specimens which were left intact. The Institutional Review Board of the Medical College of Wisconsin approved the protocol. Pretest radiographs and CT images of the specimens were obtained. Lateral impact tests were conducted by dropping the specimens against either flat, 5-cm-thick 40-, or 90-Shore A durometer impact targets, at velocities ranging from 2 to 10 m/s. The inferior-superior axis of the specimen was situated at a 10 degree angle with respect to the target, and the anterior-posterior angle was parallel with the target. Twelve specimens were used with the durometer 40 target and five with the durometer 90 target. Each specimen was impacted at increasing heights with a single impact at each height, and radiographs were obtained between drops. Impact force histories were recorded using a six-axis load cell. Signals were recorded using a digital data acquisition system (DTS Technologies, Seal Beach, CA) at a sampling frequency of 12.5 kHz and filtered according to SAE Channel Class 1000 specifications [SAE, 1998]. Testing of a specimen was terminated when fracture was detected or the load cell limit was reached. The specimens underwent CT scanning after the final impact.

Additional lateral impact fracture data was extracted from the Hodgson and Thomas (1971 and 1973) data set: four specimens against flat rigid plates and 3 specimens against 5-cm-diameter rigid cylinders oriented along the anterior-posterior axis of the specimen.

To obtain kinematic and dynamic risk factors for injury correlation, drop tests using a 50^th percentile male Hybrid III headform were conducted corresponding to each PMHS test condition, Figure 1. Three repeated drops were made for each impact condition. Accelerations at the center-of-gravity of the headform were measured and filtered to meet SAE J211 Channel Class 1000 specifications for impact tests. Impact force was measured by a Kistler model 925M113 force gauge affixed to a 30-cm-deep concrete slab below the target mount. Data was recorded at a rate of 50 kHz using the National Instrument LabVIEW system and processed to give candidate kinematic and dynamic risk factors for skull fracture. Risk factors included HIC, the peak acceleration, A_max, the average acceleration over the entire contact time, A_av, and the average acceleration over the HIC time interval, SFC.

Figure 1.

Hybrid III Headform on Drop Assembly with Target

HIC was calculated as

$$\text{HIC}={\left[\frac{1}{({\text{t}}_2-{\text{t}}_1)}{\int }_{{\text{t}}_1}^{{\text{t}}_2}\text{adt}\right]}^{2.5}({\text{t}}_2-{\text{t}}_1)$$ (1)

where the resultant acceleration, a, is in units of g, and “t₁ and t₂ (in seconds) are any two points in time during the crash of the vehicle” [USCFR FMVSS 208, 2003]. The time interval, ΔT_HIC, that maximizes the integral in Equation 1 is

$$\mathrm{\Delta }{\text{T}}_{\text{HIC}}=({\text{t}}_2-{\text{t}}_1),$$ (2)

and the change in velocity, ΔV_HIC, over that interval is

$$\mathrm{\Delta }{\text{V}}_{\text{HIC}}={\int }_{{\text{t}}_1}^{{\text{t}}_2}\text{adt}.$$ (3)

HIC and SFC are then expressed as

$$\text{HIC}={(\mathrm{\Delta }{\text{V}}_{\text{HIC}})}^{2.5}/{(\mathrm{\Delta }{\text{T}}_{\text{HIC}})}^{1.5},\text{and}$$ (4)

$$\text{SFC}=\mathrm{\Delta }{\text{V}}_{\text{HIC}}/\mathrm{\Delta }{\text{T}}_{\text{HIC}}$$ (5)

Repeated tests were checked for consistency and computed risk factors were averaged over repeated tests for statistical analysis. Peak accelerations were verified against the ratio of force to headform weight.

In the modeling part of the study, maximum principal skull strain was calculated for each PMHS impact using a refinement of the anthropomorphic, medical imaging-based, finite element model of Bandak and Vander Vorst et al. (1995), Figure 2. The baseline model was composed of 24,000 elements and resolved the outer and inner tables, diploe, brain, scalp, and face. The mass of the baseline model was 4.54 kg. The skull components were modeled using fully integrated thick shells and the brain, scalp, and face were modeled with fully integrated bricks. Since this model was based on CT imaging of a PMHS, the skull shape and thickness are anatomically correct. The thickness of the compact skull tables was set to be 1 mm uniformly, since they were too thin to be resolved from the CT scan. The 1-mm value was based on measurements of photographic cross-sections from the Visible Man project [National Library of Medicine, 2000]. The properties of the biological materials were taken from the open literature, Table 1. The elastic properties of compact skull bone was from Wood (1971). Diploe was taken to be linear elastic [Khalil and Hubbard, 1977]. The linear viscoelastic properties of the brain were from Takhounts et al. (2003). Scalp was assumed to be viscoelastic with properties calibrated by Vander Vorst et al. (2003). For the gel-filled specimens, head weight was matched for each specimen by uniformly scaling the size of the model. For the other, i.e., nonfilled specimens, the head weight was set by adjusting the brain density. Material properties for the neoprene targets were linear viscoelastic and taken from Vander Vorst et al. (2003), Table 2. All finite element model simulations were performed using Version 9.70 of LS-Dyna3d software [Livermore Software Technology Corporation, 2003].

Figure 2.

Anthropomorphic CT-based Head Model Showing Face and Brain

Table 1.

Material Properties of Finite Element Model

Part – Material Property	Value
Brain – Viscoelastic
Specific gravity	1.0
Bulk modulus	0.55 GPa
Short term shear	10 kPa
Long term shear	5 kPa
Decay time	0.01 sec
Diploe – Linear elastic
Specific gravity	1.8
Young’s modulus	0.74 GPa
Poisson’s ratio	0.05
Scalp – Viscoelastic
Specific gravity	1.3
Bulk modulus	6.8 MPa
Short term shear	2.5 MPa
Long term shear	0.68 MPa
Decay time	0.17 ms
Tables – Elastic
Specific gravity	3.06
Young’s modulus	15.8 GPa
Poisson’s ratio	0.35

Table 2.

Neoprene Material Properties

Material	Long Term Shear Modulus (MPa)	Short Term Shear Modulus (MPa)	Decay Time (ms)
Durometer 90 neoprene	36	12	1.2
Durometer 40 neoprene	5.4	2.3	1.1

For each PMHS drop test, the risk factors calculated from the corresponding Hybrid III test and the strain calculated from the finite element model along with the fracture outcome of the test were placed in a database. To account for varying head weights the acceleration-based risk factors, SFC, A_max and A_av were normalized by the factor M_H/4.54 kg, where M_H is actual mass of the test specimen in kg [Vander Vorst et al., 2003]. The data was analyzed by logistic regression [Hosmer and Lemeshow, 1989] using the longitudinal, population-averaged model with presumed failure [Zeger and Lian, 1986; Chan, Ho, Kan et al., 2001]. The data was treated as longitudinal since each specimen proceeded through a test matrix from low to high exposure levels with repeated testing. Hence, the specimen responses were not independent between tests. When a specimen fractured at a given drop height, it was presumed to fail at all higher drop heights. The Hosmer-Lemeshow Goodness-of-Fit statistic, G, and the ROC statistic were calculated for each statistically significant regression. For comparison purposes, the frontal SFC regression from the previous study [Vander Vorst et al., 2003] was recalculated using the population-averaged model, since the previous analysis assumed that each impact was an independent event. All statistical computations were carried out using the STATA software [Stata, 1999].

RESULTS

Following the test protocol, seven of the fifteen MCW PMHS specimens were tested to fracture. The remainder were terminated because the range of the force gauge was exceeded. Skull fractures were primarily linear in nature, Figure 3.

Figure 3.

Three-Dimensional Reconstruction of Pretest and Posttest CT Scans

The peak maximum principal strain in the outer table, Figure 4, from the finite element model occurs in close proximity to the location of observed fracture, Figure 3. Figure 4 also shows the mesh cross-section at time of peak deformation as the head impacts the durometer 90 neoprene pad.

Figure 4.

FEM Results for Impact onto a Flat Durometer 90 Neoprene Pad Dropped from 0.92 Meters

All Hybrid III headfrom CG acceleration waveforms are unimodal, Figure 5. Impact durations vary between 3 and 9 ms with the shortest time duration for the rigid target and longest for the durometer 40 target.

Figure 5.

Hybrid III CG Acceleration by Target

Peak skull tensile strain, computed by the finite element model, was a statistically significant correlate with skull fracture,

$$ln[\text{P}/(1-\text{P})]=4.92*ln(\text{strain})+6.10$$ (6)

where P is the probability of fracture, Figure 6. The strain at 50% probability of fracture is 0.29%, the goodness-of-fit statistic, G, is 0.39, and ROC is 0.85.

Figure 6.

Logistic Regression of Calculated Strain to Skull Fracture

SFC was the best correlate to skull fracture followed closely by the peak acceleration (Table 3, Figure 7). The risk factors SFC, A_max, A_av and HIC were each statistically significant correlates, while SFC has the best G value. The confidence band of the SFC regression is well-behaved widening slightly at high probability of fracture, Figure 7. The ROC statistic is uniformly good (ROC > 0.80) for all the regressions except for the average acceleration, A_av. (Table 3)

Table 3.

Logistic Regressions to Skull Fracture (p < 0.000005 for All Regressions)

Correlations with ln[P/(1−P)]	Risk Factor	G	ROC
5.41*ln(SFC) − 27.62	SFC	0.74	0.86
5.36*ln(Amax) −28.9	Amax	0.67	0.85
4.60*ln(Aav) − 19.6	Aav	0.52	0.73
1.98*ln(HIC) − 15.0	HIC	0.33	0.86

Figure 7.

Logistic Regression of SFC to Lateral Impact Skull Fracture

The 50% probability of lateral impact skull fracture occurs at

$${\text{SFC}}_{50}=165\hspace{0.17em}\text{g},$$ (7)

as measured by the Hybrid III headform.

SFC at 15% probability of lateral skull fracture is

$${\text{SFC}}_{15}=120\hspace{0.17em}\text{g},$$ (8)

with 95% confidence band, Figure 7, of

$$73<{\text{SFC}}_{15}<149\hspace{0.17em}\text{g}.$$ (9)

The SFC regression to frontal impact skull fracture [Vander Vorst et al., 2003] was recalculated using the population-averaged logistic analysis, Figure 8. For frontal fracture, SFC₁₅ remained 120 g and SFC₅₀ decreased from 165 to 155 g. The frontal impact correlation is very similar to the lateral impact correlation; however, the confidence bands are tighter for the frontal correlation with

Figure 8.

Comparison of Lateral and Frontal Impact Regressions

$$96<{\text{SFC}}_{15-\text{front}}<133\hspace{0.17em}\text{g}.$$ (10)

The lateral impact regression falls within the 95% confidence bands of the frontal impact regression.

SFC is an excellent correlate to strain, demonstrating that SFC is biofidelic, Figure 9. From the regression of SFC to strain, the strain at SFC₅₀ is 0.26%, which is close to the independent result from the regression of strain to fracture of 0.29% at 50% probability of injury, Figures 6 and 8.

Figure 9.

SFC vs. Calculated Strain by Target Compliance

Conversely, HIC is a poor correlate to strain, Figure 10, requiring clearly separate HIC vs. strain regressions for the hard (rigid and durometer 90) targets and the softer durometer 40 target. HIC at strain of 0.29% is 700 for the hard targets and 3,000 for the softer durometer 40 target; i.e., HIC at fracture strongly depends on the compliance of the target.

Figure 10.

HIC vs. Calculated Strain by Target Compliance

DISCUSSION

SFC is the best biomechanically-based correlate to both lateral and frontal, impact-induced, linear skull fracture. Since SFC is ΔV_HIC/ΔT_HIC, the averaged acceleration over the HIC time interval, it is easily calculated from measurements and software algorithms currently in use. Moreover, since strain is a fundamental indicator of fracture, the excellent correlation of SFC with strain establishes the biomechanical basis for SFC as a skull fracture criterion. SFC at 15% probability of fracture is 120 g for both frontal and lateral impacts. This leads to a uniform criterion of SFC < 120 g for both lateral and frontal impact. HIC is not a good predictor of skull fracture. The HIC correlation with strain varies strongly with target compliance, giving multiple threshold values for different targets.

The major limitation of this work is that the results are for impact-induced, linear, skull fracture of postmortem human specimens. Other fracture types, such as focal fractures, were not considered.

Federal Motor Vehicle Safety Standards require that the HIC time interval, dtHIC, be limited to either 15 or 36 ms. Since dtHIC is less than 4 ms for the drop tests in this study, the results of this study apply to both FMVSS clipping intervals.

Since the LS-Dyna finite element analysis software does not support viscoelastic thick shells, the material properties of the skull bone were assumed to be linearly elastic. Young’s Modulus of compact skull tables is strain rate dependent [Wood, 1971],

$$\text{E}=(15.8+1.90log{\epsilon }^{\prime })\hspace{0.17em}\text{GPa},$$ (11)

over a strain rate from 0.05 to 200 sec⁻¹. However for the typical strain loading rates of 0.1 to 2 sec⁻¹ in this study, the elasticity varies by less than 10% from the mean, an amount presumably much less than the physical variability of individual specimens. Hence, the viscoelastic effect was accounted for in the model by using a linear elastic modulus approximating the mean viscoelastic modulus over the strain rates of interest.

Based on Wood’s (1971) study from mechanical testing of 118 specimens, the breaking strain of the compact layers of human skull bone was strain rate dependent with ultimate strain,

$${\epsilon }_{\text{ult}}=(0.63-0.04log{\epsilon }^{\prime })\hspace{0.17em}\%.$$ (12)

For the present data set, the average strain loading rate, ɛ′, varies between approximately 0.1 to 2 sec⁻¹. In this range the breaking strain, ɛ_ult, is nearly constant, varying between 0.62% and 0.67%, which is greater than the strain of 0.3% at 50% probability of fracture calculated by the finite element model. This discrepancy is not surprising and is probably due to the inherently stronger nature of the uniform thickness compact bone in the head model that does not account for stress concentrations due to thickness variations. However, the value of 0.3% from the anthropomorphic model is significantly greater than the value of 0.1% from the previous spherical model [Vander Vorst et al., 2003]. This increase is primarily due to the increased local curvature of the anthropomorphic model over that of the spherical model. In any case, the significant result is that SFC is an excellent correlate to calculated strain, Figure 9, establishing the biomechanical basis for SFC.

CONCLUSION

SFC, the average acceleration over the HIC time interval, is the best correlate to both frontal and lateral impact-induced, linear skull fracture for crashworthiness assessment. Its biomechanical basis is established by its correlation with skull strain. The criterion that the probability of skull fracture is less than 15% is

$$\text{SFC}<120\hspace{0.17em}\text{g},$$ (13)

for both lateral and frontal impact fracture.